Enzyme-Constrained Metabolic Models: A Comparative Guide to Methods, Applications, and Best Practices

Abstract

This article provides a comprehensive analysis of enzyme-constrained genome-scale metabolic models (ecGEMs), which enhance traditional flux balance analysis by incorporating enzymatic turnover and proteomic limitations. Aimed at researchers and drug development professionals, we compare foundational methodologies like GECKO, sMOMENT, and ECMpy, exploring their unique workflows from kinetic parameter integration to proteomic data constraint. The content details practical applications in predicting phenotypes such as overflow metabolism and in strain design for bioproduction. We also address common challenges including parameter scarcity and computational demand, offering troubleshooting strategies and validation protocols. Finally, we evaluate the predictive performance of different ecGEMs against experimental data and discuss future directions for integrating deep learning and multi-omics data in biomedical research.

The Core Principles: Why Enzymatic Constraints Transform Metabolic Modeling

Constraint-Based Modeling (CBM) is a powerful computational framework for studying metabolic networks at the genome scale. The core principle involves using stoichiometric information of biochemical reactions to define the space of all possible metabolic flux distributions that a cell can potentially utilize. The fundamental constraint is the steady-state mass balance, which assumes that internal metabolite concentrations do not change over time, mathematically represented as S · v = 0, where S is the stoichiometric matrix and v is the flux vector [1] [2]. Additional constraints include reaction reversibility based on thermodynamics and capacity constraints on certain fluxes [1].

Flux Balance Analysis (FBA), the most common computational approach using CBM, identifies optimal flux distributions by assuming the cell maximizes a particular objective function, most often biomass production for microbial growth [2]. CBM has been successfully applied to predict nutrient utilization, gene essentiality, and outcomes of genetic manipulations across hundreds of prokaryotes, eukaryotes, and archaea [1].

However, a significant limitation of traditional CBM is its reliance primarily on reaction stoichiometry, ignoring enzymatic limitations. This often results in overprediction of metabolic capabilities, as conventional models do not account for the physical and proteomic constraints of the cell, such as the finite capacity for enzyme expression and the kinetic limitations of enzymatic reactions [3] [4].

The Critical Need for Enzymatic Constraints

Integrating enzymatic constraints addresses a fundamental gap in traditional CBM by explicitly recognizing that metabolic fluxes are limited by the cell's finite resources for producing and maintaining enzymes.

• Overflow Metabolism Explanation: Enzymatic constraints provide a mechanistic explanation for overflow metabolism (e.g., the Crabtree effect in yeast and aerobic fermentation in E. coli), where cells co-utilize fermentative and respiratory pathways even in the presence of oxygen. Traditional FBA struggles to predict this without artificially limiting uptake rates, whereas enzyme-constrained models naturally explain this as an optimal resource allocation strategy when the protein cost of respiration becomes too high at high substrate uptake rates [3] [4].
• Improved Quantitative Predictions: The inclusion of enzyme kinetic parameters (kcat values) and enzyme mass constraints significantly improves the quantitative accuracy of flux and growth rate predictions. For example, an enzyme-constrained model of Bacillus subtilis demonstrated a 43% reduction in flux prediction error for the wild-type and a 36% reduction for mutant strains compared to the standard model [5].
• Enhanced Gene Essentiality Predictions: Enzyme-constrained models show superior performance in predicting genes essential for growth. The same B. subtilis model increased the number of correctly predicted essential genes in central carbon pathways by 2.5-fold [5].
• More Realistic Metabolic Engineering Design: By accounting for enzyme allocation, these models can identify different, and often more physiologically relevant, genetic engineering targets compared to standard models, leading to successful strain design for biochemical production [3] [5].

Comparison of Major Methodological Frameworks

Several computational frameworks have been developed to integrate enzymatic constraints into genome-scale metabolic models. The table below compares three prominent approaches.

Table 1: Comparison of Major Enzymatic Constraint Modeling Frameworks

Feature	sMOMENT (short MOMENT)	GECKO (Genome-scale model with Enzymatic Constraints)	CORAL (Constraint-based promiscuous enzyme and underground metabolism)
Core Principle	Simplified MOMENT; embeds enzyme constraints directly into stoichiometric matrix [3].	Enhances model with enzyme usage pseudo-reactions and metabolites; integrates proteomics data [4].	Extends GECKO to model enzyme promiscuity and underground metabolism by splitting enzyme pools [6].
Key Formulation	(\sum vi \cdot \frac{MWi}{kcat_i} \leq P) (Total enzyme mass constraint) [3].	Adds enzyme allocation reactions: (vi \leq kcati \cdot gi), with (\sum gi \cdot MW_i \leq P) [3] [4].	Creates separate enzyme sub-pools for main and promiscuous activities of an enzyme [6].
Data Requirements	kcat values, enzyme molecular weights (MW), total protein pool (P) [3].	kcat values, MW, total protein pool, and optionally absolute proteomics data [4].	All GECKO requirements plus data on enzyme promiscuity and underground reactions [6].
Handling Enzyme Promiscuity	Not explicitly addressed in core method.	Assumes an enzyme catalyzing multiple reactions has the same resource pool for all [6].	Explicitly models separate resource allocation for main and side reactions [6].
Primary Advantage	Reduced model complexity and variables; compatible with standard CBM tools [3].	Direct integration of proteomic data; detailed representation of enzyme-reaction relations [4].	Accounts for metabolic robustness and flexibility provided by underground metabolism [6].
Toolbox/Automation	AutoPACMEN toolbox for automated model construction [3].	GECKO toolbox (versions 1.0, 2.0, 3.0) for automated model creation and updating [4].	CORAL toolbox, built upon GECKO 3 [6].

The following workflow illustrates the general process of building and utilizing an enzyme-constrained metabolic model, common to frameworks like GECKO and sMOMENT.

Experimental Data and Validation

The performance of enzyme-constrained models is quantitatively validated against experimental data, showing significant improvements over traditional models.

Table 2: Key Experimental Validations of Enzyme-Constrained Models

Organism/Model	Key Experimental Validation	Quantitative Outcome	Reference
E. coli (sMOMENT)	Aerobic growth prediction on 24 different carbon sources without restricting substrate uptake.	Superior prediction of growth rates compared to original model using enzyme constraints only.	[3]
Bacillus subtilis (GECKO)	Comparison of predicted vs. experimental fluxes and growth for wild-type and single-gene/operon deletion strains.	43% reduction in flux prediction error for wild-type; 36% reduction for mutants. 2.5-fold increase in correctly predicted essential genes in central carbon pathways.	[5]
S. cerevisiae (GECKO)	Prediction of the Crabtree effect (switch to fermentative metabolism at high glucose uptake).	Accurate prediction of metabolic switch without artificial bounds on substrate/oxygen uptake.	[4]
E. coli (CORAL)	Simulation of metabolic defects where main activity of a promiscuous enzyme is blocked.	Model predicted redistribution of enzyme resources to side activities, maintaining robust growth and confirming experimental evidence.	[6]

Example Experimental Protocol: Model Creation and Validation

A typical workflow for creating and validating an enzyme-constrained model, as applied in GECKO, involves the following key steps [5] [4]:

• Base Model Curation: Start with a well-annotated genome-scale metabolic reconstruction (e.g., in SBML format).
• Enzyme Data Acquisition: Automatically retrieve enzyme kinetic parameters (kcat values) and molecular weights (MW) from databases like BRENDA and SABIO-RK. For less-studied organisms, computational prediction tools or manual curation may be used.
• Proteomics Data Integration (Optional): If available, incorporate absolute proteomics data to set upper bounds for specific enzyme concentrations. Enzymes without measured values are constrained by a pooled protein mass.
• Model Reformulation: Expand the stoichiometric model by adding pseudo-reactions that represent the consumption of enzyme capacity for each metabolic reaction, linking flux (vi) to enzyme concentration (gi) via the kcat value ((vi \leq kcati \cdot g_i)).
• Constraint Implementation: Apply the global constraint on the total protein mass: (\sum gi \cdot MWi \leq P), where (P) is the measured total protein content allocated to metabolism.
• Model Calibration and Validation: Test the model's predictive capability by comparing simulations against experimental data not used in construction, such as growth rates on different substrates, flux distributions from 13C-labeling experiments, or gene essentiality data.

Successfully building and applying enzyme-constrained models relies on a suite of computational tools and data resources.

Table 3: Key Research Reagents and Resources for Enzymatic Constraint-Based Modeling

Resource Name	Type	Primary Function	Relevance
BRENDA	Database	Comprehensive repository of enzyme functional data, including kcat values [3] [4].	Primary source for kinetic parameters required to constrain reaction fluxes.
SABIO-RK	Database	Database for biochemical reaction kinetics, including rate laws and parameters [3].	Alternative source for curated enzyme kinetic data.
GECKO Toolbox	Software Toolbox	Automates the enhancement of GEMs with enzymatic constraints using kinetic and omics data [4].	Streamlines the creation of enzyme-constrained models for various organisms.
AutoPACMEN	Software Toolbox	Enables automated creation of sMOMENT-enhanced models from stoichiometric models [3].	Provides an alternative, simplified pipeline for constructing enzyme-constrained models.
CORAL Toolbox	Software Toolbox	Extends enzyme-constrained models to account for promiscuous enzyme activities and underground metabolism [6].	Used to study metabolic robustness and the role of alternative enzyme functions.
COBRA Toolbox	Software Toolbox	A fundamental suite for performing constraint-based reconstructions and analysis in MATLAB [4].	Standard platform for simulating and analyzing (enzyme-constrained) metabolic models.
BiGG Models	Database	Repository of curated, genome-scale metabolic models [7].	Source of high-quality starting reconstructions for enhancement with enzymatic constraints.

The integration of enzymatic constraints into constraint-based models represents a significant advancement in systems biology, moving predictions closer to cellular reality. Frameworks like sMOMENT, GECKO, and CORAL have demonstrated that accounting for the biophysical and proteomic limits of the cell leads to more accurate predictions of metabolic phenotypes, better identification of essential genes, and more reliable design of microbial cell factories. As kinetic databases grow and algorithms for parameter estimation improve, the coverage and accuracy of these models will continue to increase. Future developments will likely focus on integrating these models with other cellular processes, such as gene expression and regulation, and expanding their application to complex systems like microbial communities and human diseases, including cancer [8] [7].

The inequality v ≤ kcat × [E] serves as a fundamental cornerstone in computational systems biology, directly linking catalytic capacity to metabolic flux. This simple yet powerful relationship states that the rate (v) of any enzyme-catalyzed biochemical reaction cannot exceed the product of the enzyme's catalytic efficiency (kcat, also known as the turnover number) and its concentration ([E]) [9] [10]. In essence, it represents the absolute physical limit of an enzyme's catalytic capacity, defining the maximum velocity (Vmax) achievable when an enzyme is fully saturated with substrate [11] [10].

While the Michaelis-Menten equation has served for over a century as the central paradigm for understanding enzyme kinetics in isolated biochemical systems [12] [11], the v ≤ kcat × [E] relationship has gained renewed importance in modern metabolic engineering and systems biology. This principle forms the mathematical foundation for enzyme-constrained genome-scale metabolic models (ecGEMs), which have revolutionized our ability to predict cellular phenotypes, proteome allocation, and physiological diversity across organisms [13] [4]. By incorporating this fundamental constraint, researchers can move beyond stoichiometric considerations alone and create models that more accurately reflect the resource allocation challenges faced by living cells [9] [14].

Biochemical Foundation of the Fundamental Equation

Historical Context and Relationship to Michaelis-Menten Kinetics

The theoretical foundation for the v ≤ kcat × [E] relationship is deeply rooted in Michaelis-Menten kinetics, which describes the rate of an enzyme-catalyzed reaction for the conversion of a single substrate into product [11] [10]. The classic Michaelis-Menten equation defines the reaction rate v as:

v = (Vmax × [S]) / (Km + [S])

where Vmax represents the maximum reaction rate, [S] is the substrate concentration, and Km is the Michaelis constant [10]. The critical connection to our fundamental equation emerges from the definition of Vmax, which is mathematically expressed as Vmax = kcat × [E]total, where [E]total represents the total enzyme concentration [10]. Under saturating substrate conditions ([S] >> Km), the reaction rate v approaches Vmax, and is thus fundamentally constrained by kcat × [E]total [11].

The following conceptual diagram illustrates the fundamental relationship between enzyme concentration, catalytic efficiency, and reaction rate:

The standard quasi-steady-state assumption (sQSSA) used to derive the Michaelis-Menten equation is valid only when the enzyme concentration is much lower than the substrate concentration [12]. However, this condition frequently fails in intracellular environments where enzyme concentrations often approach or exceed substrate concentrations [12]. Under these physiologically relevant conditions, the total quasi-steady-state approximation (tQSSA) provides a more accurate framework for relating reaction rates to enzyme concentrations, though the fundamental constraint v ≤ kcat × [E] remains inviolable [12].

Experimental Parameter Estimation

Accurately determining kcat values is essential for applying the fundamental equation in constraint-based models. Two primary experimental approaches exist for estimating these parameters:

Progress Curve Analysis: This method fits the entire timecourse of product formation to the solution of the differential equation describing the reaction kinetics [12]. Although technically more challenging, it uses data more efficiently than initial velocity assays and requires fewer measurements to obtain reliable parameter estimates [12]. The Bayesian inference framework based on the total QSSA (tQ model) has demonstrated superior performance in estimating kcat values, particularly when enzyme concentrations are not negligible compared to substrate concentrations [12].

Initial Velocity Assay: This traditional approach measures initial reaction rates at varying substrate concentrations and uses linear transformations (e.g., Lineweaver-Burk plots) to estimate Vmax and Km [12] [10]. The kcat value is then calculated from Vmax using the relationship kcat = Vmax / [E]total [10]. While computationally simpler, this method requires more experimental data points and depends on the validity of the standard quasi-steady-state assumption [12].

Table 1: Experimentally Determined kcat Values for Representative Enzymes

Enzyme	kcat (s⁻¹)	Km (M)	kcat/Km (M⁻¹s⁻¹)
Chymotrypsin	0.14	1.5 × 10⁻²	9.3
Pepsin	0.50	3.0 × 10⁻⁴	1.7 × 10³
tRNA synthetase	7.6	9.0 × 10⁻⁴	8.4 × 10³
Ribonuclease	7.9 × 10²	7.9 × 10⁻³	1.0 × 10⁵
Carbonic anhydrase	4.0 × 10⁵	2.6 × 10⁻²	1.5 × 10⁷
Fumarase	8.0 × 10²	5.0 × 10⁻⁶	1.6 × 10⁸

Source: [10]

Computational Implementation in Metabolic Models

Theoretical Frameworks for Enzyme Constraints

The fundamental equation v ≤ kcat × [E] has been implemented in several computational frameworks for constructing enzyme-constrained metabolic models. The major approaches include:

GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data): This approach expands the stoichiometric matrix to include enzymes as pseudo-metabolites and adds enzyme usage reactions [4] [9]. The GECKO toolbox, now in version 2.0, enables semi-automated construction of ecGEMs and allows direct integration of proteomics data as additional constraints [4]. The method explicitly represents isoenzymes, enzyme complexes, and multi-functional enzymes, making it particularly suitable for models where detailed protein information is available [9].

sMOMENT (short Method for Optimization and Metabolic Network Analysis of Enzyme Fluxes): This method implements enzyme constraints without expanding the stoichiometric matrix, instead adding the global enzyme capacity constraint Σ(vi × MWi / kcat,i) ≤ P, where MWi is the molecular weight of enzyme i and P is the total enzyme pool capacity [14]. This simplified representation reduces model complexity while maintaining predictive accuracy, and enables compatibility with standard constraint-based modeling tools [14].

ECMpy: This Python-based workflow simplifies the construction of enzyme-constrained models by directly adding total enzyme amount constraints and automatically calibrating enzyme kinetic parameters [15]. ECMpy considers protein subunit composition in reactions and has been used to construct high-quality models for Escherichia coli that significantly improve growth rate predictions on single-carbon sources [15].

Workflow for Integrating Enzyme Constraints

The process of integrating the fundamental equation into genome-scale metabolic models follows a systematic workflow that combines biochemical data with computational modeling:

kcat Data Acquisition: Kinetic parameters are collected from databases like BRENDA and SABIO-RK [13] [4]. For reactions with missing organism-specific data, machine learning tools such as DLKcat or TurNuP can predict kcat values from substrate structures and protein sequences [13] [16].

Proteomics Integration: Experimentally measured enzyme abundances provide upper bounds for reaction fluxes through the relationship vj ≤ kcatj × [Ej] [9]. For enzymes without experimental measurements, homology-based inference or database values from related organisms can be used [9].

Model Performance Assessment: The constrained model is validated by comparing predictions of growth rates, substrate uptake, byproduct secretion, and gene essentiality with experimental data [9] [16]. Successful ecGEMs demonstrate improved phenotype prediction accuracy and reduced solution space compared to traditional stoichiometric models [9] [16].

Comparative Analysis of Modeling Approaches

Tool Performance Across Organisms

Different implementations of the fundamental equation have been applied to construct enzyme-constrained models for various organisms, each with distinct advantages and limitations:

Table 2: Comparison of Enzyme-Constrained Model Construction Tools

Tool/ Method	Key Features	Organisms Applied	Performance Highlights
GECKO	Expands stoichiometric matrix; Direct proteomics integration	Saccharomyces cerevisiae, Aspergillus niger, Yarrowia lipolytica	Explains Crabtree effect; Predicts metabolic shifts; Reduces flux variability by >40% [4] [9]
sMOMENT/ AutoPACMEN	Simplified representation; Automated parameter estimation; Fewer variables	Escherichia coli	Improves aerobic growth prediction on 24 carbon sources; Identifies metabolic engineering strategies [14]
ECMpy	Python-based workflow; Automated kcat calibration; Total enzyme pool constraint	Escherichia coli, Bacillus subtilis	Significantly improves growth predictions on single-carbon sources; Reveals tradeoff between enzyme usage and biomass yield [15]
DLKcat	Deep learning-based kcat prediction from substrate structures and protein sequences	343 yeast species; Myceliophthora thermophila	High-throughput kcat prediction; Captures enzyme promiscuity; Predicts effects of amino acid substitutions [13] [16]

Impact on Model Predictions

The incorporation of the v ≤ kcat × [E] constraint fundamentally changes model behavior and predictive capabilities compared to traditional constraint-based models:

Solution Space Reduction: Enzyme constraints significantly reduce the feasible solution space of metabolic models. In an enzyme-constrained model of Aspergillus niger, flux variability decreased for over 40% of metabolic reactions, leading to more precise predictions [9].

Phenotype Prediction Accuracy: Enzyme-constrained models consistently outperform traditional GEMs in predicting microbial phenotypes. For example, ecGEMs successfully predict the hierarchical utilization of mixed carbon sources in Myceliophthora thermophila, a phenomenon that conventional models fail to capture [16].

Metabolic Engineering Guidance: By accounting for enzyme costs, ecGEMs identify different metabolic engineering targets compared to traditional models. The consideration of kcat values and enzyme abundance reveals tradeoffs between biomass yield and enzyme usage efficiency, informing more realistic strain design strategies [16] [15].

Experimental Validation and Case Studies

Protocol for Validating Enzyme-Constrained Predictions

Objective: To experimentally validate predictions from an enzyme-constrained metabolic model by measuring growth phenotypes and metabolic fluxes under defined conditions.

Materials and Reagents:

• Wild-type and mutant strains of the target organism
• Defined minimal medium with precisely controlled carbon sources
• Proteomics extraction buffer (e.g., 200 mM Tris·HCl pH 8.5, 250 mM NaCl, 25 mM EDTA, 0.5% SDS) [16]
• RNA/DNA quantification reagents (e.g., HClO4, KOH, phenol:chloroform:isoamyl alcohol) [16]
• Analytical instruments for substrate consumption and product formation analysis (HPLC, GC-MS)

Methodology:

• Cultivate strains in defined medium with target substrate(s) under controlled environmental conditions
• Measure growth curves by tracking optical density or dry cell weight
• Quantify substrate uptake and metabolite secretion rates using appropriate analytical methods
• Harvest cells during mid-exponential phase for absolute quantification of enzyme abundances via proteomics
• Compare experimental measurements with model predictions of growth rates, substrate uptake, and byproduct secretion
• Iteratively refine model parameters based on discrepancies between predictions and experimental data

Validation Metrics:

• Correlation between predicted and measured growth rates across multiple substrates
• Accuracy in predicting metabolic switches (e.g., aerobic/anaerobic transitions)
• Successful prediction of substrate utilization hierarchies in mixed carbon environments

Case Study: Enzyme-Constrained Model for Myceliophthora thermophila

A recent study demonstrated the power of incorporating the fundamental equation when constructing an enzyme-constrained model for the thermophilic fungus Myceliophthora thermophila [16]. Researchers compared three versions of ecGEMs using different kcat collection methods: AutoPACMEN, DLKcat, and TurNuP [16].

The model utilizing TurNuP-predicted kcat values (eciYW1475_TN) demonstrated superior performance in predicting cellular phenotypes and was selected as the final ecGEM (ecMTM) [16]. Key findings included:

• Accurate prediction of the tradeoff between biomass yield and enzyme usage efficiency at varying glucose uptake rates
• Successful simulation of hierarchical utilization of five carbon sources derived from plant biomass hydrolysis
• Identification of metabolic engineering targets that considered enzyme cost constraints

This case study highlights how machine learning-based kcat prediction extends the applicability of the fundamental equation to organisms with limited experimentally characterized kinetic parameters [16].

Research Reagent Solutions

Table 3: Essential Research Reagents for Enzyme Kinetics and Constrained Modeling

Reagent/Resource	Function	Example Application
BRENDA Database	Comprehensive enzyme kinetic parameter repository	Source of kcat values for model parameterization [13] [4]
SABIO-RK Database	Kinetic data for biochemical reactions	Alternative source for enzyme kinetic parameters [13] [14]
DLKcat	Deep learning tool for kcat prediction	High-throughput kcat estimation from substrate structures and protein sequences [13]
TurNuP	Machine learning-based kcat prediction	Genome-scale kcat prediction for less-studied organisms [16]
Proteomics Extraction Buffer	Cell lysis and protein extraction	Absolute quantification of enzyme abundances for model constraints [16]
COBRA Toolbox	Constraint-based modeling platform	Simulation and analysis of enzyme-constrained metabolic models [4] [9]

The fundamental equation v ≤ kcat × [E] represents a critical bridge between biochemical principles and systems-level metabolic modeling. By explicitly accounting for the catalytic limitations of enzymes, constraint-based models transition from purely stoichiometric representations to more physiologically realistic descriptions of cellular metabolism. The continued development of tools like GECKO, ECMpy, and machine learning-based kcat prediction methods is making enzyme-constrained modeling increasingly accessible to the research community.

As kinetic parameter databases expand and proteomic measurement technologies advance, the application of this fundamental constraint will become increasingly routine in metabolic engineering and drug development. The integration of enzyme constraints not only improves model prediction accuracy but also provides unique insights into the evolutionary tradeoffs and resource allocation strategies that shape cellular metabolism across diverse organisms.

Enzyme Turnover Numbers (kcat), Molecular Weight (MW), and the Protein Pool

Integrating enzymatic constraints into genome-scale metabolic models (GEMs) has significantly improved their predictive accuracy for simulating cellular physiology and proteome allocation [13] [3]. This approach relies on three fundamental concepts: enzyme turnover numbers (kcat), molecular weight (MW) of proteins, and the finite capacity of the cellular protein pool.

The enzyme turnover number (kcat) defines the maximum number of substrate molecules an enzyme molecule can convert to product per unit time under saturating conditions, reflecting its catalytic efficiency [17]. The molecular weight (MW) of an enzyme, calculable from its amino acid sequence, determines its mass in Daltons (g/mol) [18]. These parameters connect metabolic flux (v_i) through a reaction to the required enzyme concentration (g_i) through the equation v_i ≤ kcat_i * g_i [3].

The protein pool represents the limited cellular capacity for protein synthesis and maintenance, imposing a global constraint on total enzyme abundance. The total mass of metabolic enzymes cannot exceed this pool capacity P (in g/gDW), formalized by the constraint: Σ (g_i * MW_i) ≤ P [3]. This finite proteomic resource creates trade-offs where cells must optimally allocate enzymes to maximize fitness, explaining phenomena like overflow metabolism and the Crabtree effect [3] [19].

Comparative Analysis of kcat Prediction Tools

Experimental kcat determination remains challenging, creating significant knowledge gaps that computational tools aim to fill [20] [17]. Below we compare the performance and methodologies of major prediction platforms.

Table 1: Comparison of Key kcat Prediction Tools

Tool Name	Input Features	Model Architecture	Reported Performance (R²)	Key Advantages
DLKcat [13]	Substrate structure (SMILES) & protein sequence	Graph Neural Network (GNN) + Convolutional Neural Network (CNN)	0.50 (vs. Li et al. on same dataset) [17]	Captures kcat changes for mutated enzymes; identifies impact residues [13].
TurNuP [20]	Complete reaction equation (fingerprint) & protein sequence	Differential Reaction Fingerprint + Transformer Network	0.33 (for enzymes with <40% sequence identity) [20]	Organism-independent; generalizes well to low-similarity enzymes [20].
NNKcat [17]	Substrate structure (SMILES) & protein sequence	Attentive FP (GNN) + Long Short-Term Memory (LSTM)	0.54 (general), 0.64 (CYP450-focused) [17]	Addresses data imbalance; enables focused learning for enzyme classes [17].

Experimental Protocols for kcat Prediction

DLKcat Methodology [13]:

• Data Acquisition and Curation: Compiled a dataset from BRENDA and SABIO-RK databases, filtering incomplete entries. The final dataset contained 16,838 unique entries with substrate SMILES, protein sequence, and kcat values.
• Model Training: A GNN processes substrate molecular graphs from SMILES strings. A CNN processes protein sequences split into 3-gram amino acids. The model was trained with optimal hyperparameters (r-radius=2, time steps in GNN=3, CNN layers=3).
• Validation: The dataset was randomly split (80/10/10 for training/validation/test). Model performance was evaluated using Root Mean Square Error (RMSE) and Pearson's correlation coefficient between predicted and experimental log(kcat) values.

TurNuP Methodology [20]:

• Input Representation: Represents chemical reactions using differential reaction fingerprints (DRFP), which directly encode the structural changes between substrates and products. Enzyme information is captured using fine-tuned Transformer protein language models.
• Model Architecture and Training: A gradient-boosting model (e.g., XGBoost) is trained on the combined reaction and enzyme feature vectors. The dataset is split to ensure no enzyme sequence appears in both training and test sets, rigorously assessing generalizability.

Comparative Analysis of Enzyme-Constrained Model Frameworks

Several computational frameworks automate the construction of enzyme-constrained models (ecModels), each with distinct approaches and applications.

Table 2: Comparison of Enzymatic Constraint Integration Frameworks

Framework	Core Methodology	Key Features	Demonstrated Application
GECKO [19]	Enhances GEM by adding enzyme usage reactions and a total protein pool constraint.	Automated parameter retrieval from BRENDA; direct integration of proteomics data.	S. cerevisiae, E. coli, H. sapiens; prediction of metabolic switches [19].
sMOMENT/AutoPACMEN [3]	Simplified MOMENT; incorporates enzyme constraints directly into stoichiometric matrix.	Reduced model complexity; enables use of standard FBA tools; automated model construction.	E. coli iJO1366; improved flux predictions and engineering strategies [3].
ECMpy [15]	Python-based workflow for constraint addition and parameter calibration.	Considers protein subunit composition; automated calibration of kinetic parameters.	E. coli eciML1515; analysis of overflow metabolism and redox balance [15].
CORAL [6]	Extends GECKO to model underground metabolism and enzyme promiscuity.	Splits enzyme pools for main and promiscuous activities; investigates metabolic robustness.	E. coli; shows promiscuous activities ensure robustness against metabolic defects [6].

Experimental Protocols for ecModel Construction and Analysis

GECKO 2.0 Workflow for ecModel Reconstruction [19]:

• Model Enhancement: The starting GEM is enhanced by adding pseudo-reactions that represent enzyme usage. Each metabolic reaction is coupled with its enzyme, linking the metabolic flux (v_i) to the enzyme concentration (g_i) via the kcat value (v_i ≤ kcat_i * g_i).
• Parameterization: The toolbox automatically queries the BRENDA database for organism-specific kcat values where available. For reactions without data, it employs a hierarchical matching procedure (e.g., using values from other organisms or similar reactions).
• Applying the Protein Pool Constraint: A total enzyme pool constraint is added: Σ (g_i * MW_i) ≤ P, where P is the measured total protein content relevant to metabolism. Proteomics data can be incorporated as additional constraints on individual g_i values.

CORAL Workflow for Underground Metabolism [6]:

• Model Expansion: The underground metabolic network is added to the base GEM (e.g., iML1515u for E. coli) by including known promiscuous reactions.
• Enzyme Pool Splitting: For each promiscuous enzyme, the total enzyme pool is split into sub-pools (E_s,1, E_s,2, ...), one for each reaction it catalyzes. The sum of these sub-pools equals the original enzyme pool.
• Simulating Metabolic Defects: To simulate a defect in a main reaction, the corresponding enzyme sub-pool is set to zero. Flux Balance Analysis (FBA) is then used to simulate growth, testing if the remaining promiscuous activities can compensate by redistributing their enzyme usage.

Workflow Visualizations

kcat Prediction and ecModel Integration Pathway

Protein Pool Allocation Logic

Table 3: Key Research Reagents and Computational Resources

Item / Resource	Function / Application	Example / Source
Kinetic Databases	Source of experimental kcat values for model parameterization and validation.	BRENDA [13] [19], SABIO-RK [13] [20]
Metabolic Model Databases	Provide foundational Genome-scale Metabolic Models (GEMs) for enhancement.	BiGG Models, ModelSEED, AGORA [15] [19]
Computational Toolboxes	Software for constructing, simulating, and analyzing enzyme-constrained models.	GECKO Toolbox [19], AutoPACMEN [3], ECMpy [15], CORAL [6]
Protein MW Calculator	Compute molecular weight from amino acid sequence for enzyme mass constraints.	Online tools & BioPython [18]
kcat Prediction Servers	Web-based platforms for predicting unknown kcat values using ML models.	TurNuP Web Server [20]

Genome-scale metabolic models (GEMs) have become fundamental tools for quantitatively studying cellular metabolism, with applications spanning from metabolic engineering of industrial microbes to understanding human diseases [21] [22]. These models represent metabolic networks mathematically using a stoichiometric matrix (S-matrix) that encapsulates the mass-balance relationships for all metabolites. While GEMs have proven valuable, they often predict unrealistically high metabolic fluxes and fail to capture certain cellular phenotypes because they lack consideration of enzyme-associated constraints [3] [19].

The integration of enzymatic constraints into GEMs addresses these limitations by accounting for the physico-chemical and proteomic limitations of the cell. Enzyme-constrained GEMs (ecGEMs) incorporate data on enzyme kinetics (turnover numbers, kcat), molecular weights, and enzyme availability, thereby providing a more accurate representation of metabolic activity [22] [19] [15]. This review compares the leading methodologies for constructing ecGEMs, with a specific focus on how they expand or modify the foundational stoichiometric matrix to incorporate enzyme constraints.

Core Methodologies for Constructing ecGEMs

Conceptual Framework and Mathematical Foundation

Enzyme-constrained models are built upon the principle that the flux ((vi)) through an enzyme-catalyzed reaction is limited by the concentration of that enzyme ((gi)) and its catalytic efficiency ((k{cat,i})): (vi \leq k{cat,i} \times gi). A global constraint reflects the limited cellular capacity for enzyme synthesis, typically expressed as (\sum gi \times MWi \leq P), where (MW_i) is the molecular weight of the enzyme and (P) is the total enzyme mass budget [3]. Different ecGEM construction methods implement these principles with varying strategies for matrix expansion and data integration.

Figure 1: The fundamental workflow for constructing an ecGEM involves expanding the original stoichiometric matrix of a GEM with enzyme-associated constraints.

Comparative Analysis of Major ecGEM Construction Tools

Multiple computational frameworks have been developed to systematically construct ecGEMs. The following table summarizes the core characteristics of the most prominent tools.

Table 1: Comparison of Major Frameworks for ecGEM Construction

Tool/Method	Core Approach to Matrix Expansion	Key Features	Reported Organism Applications
GECKO [22] [19]	Adds pseudo-reactions for enzyme usage and new metabolites representing enzymes.	Automated retrieval of kcat from BRENDA/SABIO-RK; Direct integration of proteomics data.	S. cerevisiae, E. coli, Y. lipolytica, H. sapiens [19]
ECMpy [16] [15]	Simplified workflow; adds global enzyme capacity constraint without major S-matrix restructuring.	Machine learning-based kcat prediction (TurNuP, DLKcat); Automated parameter calibration.	E. coli, M. thermophila, B. subtilis [16] [15]
AutoPACMEN/sMOMENT [3]	"Short MOMENT" (sMOMENT) method integrates enzyme constraints directly into S-matrix with fewer variables.	Automated database query; Simplified representation reduces computational load.	E. coli [3]
Novel Transformer-Based [23]	Not specified (Methodology focuses on kcat prediction).	Uses multi-modal transformer (enzyme sequence & substrate SMILES) for kcat prediction; New calibration via Flux Control Coefficients.	E. coli [23]

Technical Deep Dive: Expanding the Stoichiometric Matrix

Implementation Strategies for Enzyme Constraints

The technical implementation of enzyme constraints involves distinct strategies for expanding the stoichiometric matrix. The GECKO toolbox exemplifies the explicit expansion approach. It expands the original model by introducing new "enzyme" metabolites and adding "enzyme usage" pseudo-reactions. This method directly incorporates enzyme mass balances into the S-matrix, allowing for explicit integration of measured enzyme concentrations as flux constraints [22] [19].

In contrast, the sMOMENT method, as implemented in AutoPACMEN, uses a simplified integration strategy. It substitutes the enzyme concentration variables into the total enzyme mass constraint, yielding a single linear constraint: (\sum vi \times \frac{MWi}{k_{cat,i}} \leq P). This inequality can be added directly to the model as a new row in the stoichiometric matrix without introducing new variables for each enzyme, significantly reducing model size and complexity [3].

Workflow for ecGEM Reconstruction and Simulation

The process of building and utilizing an ecGEM, as formalized in the GECKO 3.0 protocol, involves multiple stages that ensure model accuracy and predictive power [22] [24].

Figure 2: A generalized workflow for ecGEM construction, as implemented in tools like GECKO and ECMpy, showing key stages from a base GEM to a functional enzyme-constrained model.

Performance Comparison and Experimental Validation

Quantitative Improvements in Phenotype Prediction

ecGEMs demonstrate superior performance over traditional GEMs in predicting key physiological phenotypes. The following table compiles experimental data from published studies highlighting these improvements.

Table 2: Experimental Performance Data of ecGEMs vs. Standard GEMs

Model / Organism	Prediction Task	Standard GEM Performance	ecGEM Performance	Key Experimental Validation
ecYeast7 [19]	Crabtree effect (onset of aerobic fermentation)	Incorrect or missing prediction	Accurate prediction of critical dilution rate	Matches experimental data across multiple strains [19]
eciML1515 (E. coli) [15]	Growth on 24 single-carbon sources	Lower prediction accuracy	Significant improvement in growth rate prediction	Comparison with measured growth data [15]
ecMTM (M. thermophila) [16]	Hierarchical carbon source utilization	Fails to predict sequential use	Accurately captures preference order	Matches experimental biomass hydrolysis patterns [16]
sMOMENT iJO1366 (E. coli) [3]	Overflow metabolism	Requires explicit uptake bounds	Explains metabolic switches without extra bounds	Consistent with physiological data [3]

Methodologies for Key Experimental Validations

The protocols for validating ecGEM predictions typically involve comparing in silico results with empirical data:

• Growth Rate and Substrate Utilization: Models are simulated under specific nutrient conditions (e.g., single carbon sources) using Flux Balance Analysis (FBA). Predicted growth rates are compared against experimentally measured optical density or dry cell weight over time [15]. For carbon source hierarchy, the model's predicted uptake order is validated against experiments monitoring substrate depletion from the medium [16].

• Metabolic Engineering Targets: In silico gene knockout simulations are performed, and predicted growth phenotypes or chemical production yields are compared with those of engineered strains. For example, ecGEM-predicted targets for chemical overproduction in M. thermophila were validated against previously published genetic modifications [16].

• Enzyme Allocation and Proteomics: The incorporation of proteomics data involves constraining the model with measured enzyme abundances and verifying that the resulting flux distributions are consistent with the metabolic state. The GECKO protocol includes steps for this integration and subsequent analysis of enzyme cost and saturation [22] [19].

Building and working with ecGEMs requires a suite of computational and data resources. The table below details key components of the research toolkit.

Table 3: Essential Research Reagent Solutions for ecGEM Construction

Resource Category	Specific Tools / Databases	Primary Function in ecGEM Workflow
Base GEMs	iJO1366 (E. coli), Yeast8 (S. cerevisiae), iML1515 (E. coli), Human1	Foundational stoichiometric models for enzyme constraint integration [21] [15].
Enzyme Kinetic Databases	BRENDA, SABIO-RK	Primary sources for experimentally measured kcat values [3] [22] [19].
Machine Learning kcat Predictors	TurNuP, DLKcat	Provide predicted kcat values for reactions with missing experimental data [16] [22].
ecGEM Construction Software	GECKO Toolbox, ECMpy, AutoPACMEN	Automated frameworks for expanding GEMs with enzymatic constraints [16] [3] [22].
Simulation Environments	COBRA Toolbox, COBRApy	Software suites for performing constraint-based analyses, including FBA on ecGEMs [22] [19].
Model Curation & Quality Control	Memote	Standardized testing suite for assessing and ensuring GEM quality [21].

Discussion and Future Perspectives

The expansion of the stoichiometric matrix to build ecGEMs represents a significant advancement in metabolic modeling. The comparison of major frameworks reveals a trade-off: while explicit methods like GECKO offer granularity for proteomic integration, simplified approaches like sMOMENT and ECMpy provide computational efficiency. A key trend is the integration of machine learning-predicted kcat values (e.g., TurNuP, DLKcat) to overcome the scarcity of experimental data, which has been a major bottleneck for ecGEM construction for less-studied organisms [16] [22].

Future developments will likely focus on improving the accuracy of in silico kcat prediction, perhaps through advanced architectures like the multi-modal transformer that simultaneously processes enzyme sequences and substrate structures [23]. Furthermore, the community-driven, version-controlled development of models, as seen with Human1 and the GECKO toolbox, is crucial for ensuring the transparency, reproducibility, and continuous improvement of ecGEMs [21] [19]. As these tools become more accessible and accurate, ecGEMs are poised to become the standard for predictive metabolic analysis in both basic research and applied biotechnology.

A fundamental challenge in systems biology is accurately predicting cellular behavior, a process governed by the efficient allocation of a limited pool of protein resources. This guide compares leading computational models that simulate this "cellular economy" by integrating enzymatic constraints, evaluating their methodologies, predictive performance, and applicability in metabolic engineering and drug development.

Model Comparison at a Glance

The table below summarizes the core attributes and performance of the primary enzymatic constraint-based modeling frameworks.

Model/Toolbox Name	Core Modeling Approach	Key Constraints Integrated	Representative Organisms	Documented Performance Improvements
GECKO [4] [5]	Enhances Genome-scale Metabolic Models (GEMs) with enzyme usage	Enzyme kinetics (kcat), enzyme mass, proteomics data	S. cerevisiae, E. coli, B. subtilis, H. sapiens	43% reduction in flux prediction error in B. subtilis; explains Crabtree effect in yeast [5].
sMOMENT (via AutoPACMEN) [3]	Simplified MOMENT; more compact model formulation	Enzyme kinetics (kcat), molecular weight, total enzyme pool	E. coli	Improved prediction of overflow metabolism and growth on multiple carbon sources without uptake constraints [3].
CORAL [6]	Extends protein-constrained models (built on GECKO)	Promiscuous enzyme activities, separate pools for main/side reactions	E. coli	Increases metabolic flux variability; explains robustness by redistributing enzyme resources upon metabolic defects [6].
ETGEMs [25]	Combined constraint framework in Pyomo	Both enzymatic and thermodynamic constraints	E. coli	Excludes thermodynamically unfavorable & enzymatically costly pathways; more realistic production yields (e.g., for L-arginine) [25].
ME-Models [26]	Metabolism and macromolecular Expression models	Proteome allocation to sectors (e.g., ribosomes, transport)	E. coli	69% lower error in growth rate prediction, 14% lower error in metabolic flux prediction across 15 conditions [26].

Detailed Methodologies and Experimental Protocols

To ensure reproducibility and provide a clear basis for comparison, here are the detailed experimental workflows for the key models.

Protocol for Constructing a GECKO Model

The GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) methodology involves a multi-step process to enhance a standard GEM [4] [5].

• Step 1: Model Preparation. Start with a high-quality genome-scale metabolic model (GEM) in a structured format (e.g., SBML).
• Step 2: Kinetic Data Acquisition. Automatically retrieve enzyme turnover numbers (kcat values) from the BRENDA and SABIO-RK databases. The toolbox uses a hierarchical matching procedure, first seeking organism-specific kcat values, then values from other organisms, and finally employing wildcard searches for less-characterized enzymes [4].
• Step 3: Incorporation of Enzyme Mass Constraints. For each enzyme-catalyzed reaction in the model, add a constraint that links the metabolic flux (vi) to the enzyme concentration (gi): vi ≤ kcat,i • gi. A global constraint represents the total protein pool: Σ gi • MWi ≤ P, where MWi is the molecular weight of the enzyme and P is the total measured protein mass [4] [3].
• Step 4: Integration of Proteomics Data (Optional). If proteomics data is available, the measured concentrations for specific enzymes can be applied as upper bounds for their respective gi variables, further constraining the model solution space [4].
• Step 5: Simulation and Validation. Use the enhanced model for simulation with Flux Balance Analysis (FBA). Predictions for growth rates and metabolic fluxes must be validated against experimental data (e.g., from chemostat cultures or gene deletion strains) [5].

Protocol for CORAL-Based Analysis of Underground Metabolism

The CORAL toolbox investigates how promiscuous enzyme activities contribute to metabolic robustness [6].

• Step 1: Model Expansion. Begin with a protein-constrained GEM (e.g., an ecModel built with GECKO). Add known underground metabolic reactions—side reactions catalyzed by promiscuous enzymes on non-native substrates.
• Step 2: Enzyme Pool Restructuring. For each promiscuous enzyme, split its total enzyme pool into separate subpools for its main reaction and each of its side reactions. This critical step ensures that enzyme resources are allocated competitively between these activities.
• Step 3: Simulating Metabolic Defects. To simulate a metabolic defect, the flux through the main reaction's enzyme subpool is blocked (set to zero). The model is then allowed to re-optimize, potentially reallocating the enzyme's resources to its promiscuous side reactions.
• Step 4: Analysis of Robustness. The model's output is analyzed for changes in flux variability and growth rate. The ability to maintain growth or metabolic function after the defect demonstrates the role of underground metabolism in phenotypic robustness [6].

Protocol for Sector-Constrained ME-Models

This approach integrates proteomic data to create a "generalist" model of E. coli that reflects hedging strategies, not just growth optimization [26].

• Step 1: Proteome Sector Definition. Coarse-grain the proteome into functional sectors. The referenced study used Clusters of Orthologous Groups (COGs), resulting in 24 sectors such as "Translation, ribosomal structure and biogenesis" and "Carbohydrate transport and metabolism."
• Step 2: Identification of Over-allocated Sectors. Compute the optimal, growth-rate maximizing proteome for multiple conditions. Compare this with actual proteomics data to identify sectors that are consistently "over-allocated" in the generalist wild-type strain.
• Step 3: Application of Sector Constraints. Add mass balance constraints to the ME-model that force the total protein mass fraction for each over-allocated sector to match the measured median values from the proteomics data.
• Step 4: Validation of Generalist Model. Simulate growth and metabolism across diverse conditions. The sector-constrained model should better predict the measured growth rates and flux distributions of the wild-type strain than the purely optimal model [26].

Workflow Visualization: From Model to Prediction

The following diagram illustrates the logical workflow for building and utilizing an enzyme-constrained model, synthesizing the common steps across the cited methodologies.

The Scientist's Toolkit: Essential Research Reagents & Databases

Successful implementation of these models relies on specific data resources and software tools.

Resource Name	Type	Primary Function in Modeling
BRENDA [4] [3]	Database	The primary source for enzyme kinetic parameters (kcat values) and EC number information.
SABIO-RK [3]	Database	A complementary database for biochemical reaction kinetics, including kinetic rate laws.
COBRA Toolbox [4]	Software (MATLAB)	A standard software environment for constraint-based modeling and simulation.
GECKO Toolbox [4]	Software (MATLAB)	An open-source toolbox for automatically enhancing GEMs with enzymatic constraints.
Protein Concentration Data [5] [26]	Experimental Data (Proteomics)	Used to set upper bounds for individual enzyme usage, making models condition-specific.
SBML (Systems Biology Markup Language) [3]	Data Format	A standard, interoperable format for representing and exchanging computational models.
Chemostat Cultivation [5] [27]	Experimental System	Provides steady-state microbial growth data at fixed rates for robust model validation.
Cyclapolin 9	Cyclapolin 9, MF:C9H4F3N3O4S, MW:307.21 g/mol	Chemical Reagent
Cyclosporin C	Cyclosporin C, CAS:59787-61-0, MF:C62H111N11O13, MW:1218.6 g/mol	Chemical Reagent

The integration of enzymatic constraints has irrevocably improved the predictive power of metabolic models. The choice of tool depends on the specific research question: GECKO and sMOMENT offer streamlined integration of enzyme kinetics, with GECKO being particularly strong for incorporating proteomics data. The CORAL toolbox is essential for investigating metabolic robustness and evolution through underground metabolism. For the most thermodynamically realistic predictions, the ETGEM framework is a powerful choice. Finally, ME-models with sector constraints provide the highest-resolution view of the proteome's role in a generalist survival strategy. As these models continue to be refined and applied to human metabolism, they hold significant promise for accelerating the rational design of industrial bioprocesses and identifying novel therapeutic targets in diseases like cancer.

Toolbox Deep Dive: GECKO, sMOMENT, ECMpy, and Their Real-World Applications

This guide objectively compares the performance, applications, and underlying methodologies of the GECKO Toolbox against other frameworks for reconstructing enzyme-constrained metabolic models (ecModels).

Enzyme-constrained metabolic models enhance standard Genome-scale Metabolic Models (GEMs) by incorporating enzymatic constraints using kinetic parameters and proteomic data. This allows for more accurate predictions of metabolic phenotypes by accounting for the limited cellular capacity for protein expression [3]. The table below compares the core features of three primary toolboxes for building ecModels.

Table 1: Comparison of ecModel Reconstruction Toolboxes

Feature	GECKO Toolbox	AutoPACMEN (sMOMENT)	CORAL Toolbox
Core Methodology	Enhances GEM by adding enzyme usage pseudo-reactions and metabolites [4]	A simplified MOMENT method that integrates constraints directly into the stoichiometric matrix [3]	An extension of GECKO for modeling promiscuous enzyme activity and underground metabolism [6]
Primary Inputs	GEM, kcat values (from BRENDA or deep learning), molecular weights, proteomics data (optional) [28]	GEM, kcat values, molecular weights, enzyme concentration data (optional) [3]	A protein-constrained GEM (e.g., from GECKO), data on enzyme promiscuity [6]
Enzyme Pool	Constrained by a total protein pool; enzymes draw from this pool even when constrained by proteomics data [29]	Constrained by a total enzyme pool mass (P) [3]	Splits the enzyme pool for promiscuous enzymes into sub-pools for each reaction [6]
Key Applications	Prediction of metabolic switches (e.g., Crabtree effect), proteome allocation, metabolic engineering [4] [28]	Explaining overflow metabolism, predicting metabolic engineering strategies [3]	Investigating the role of underground metabolism in metabolic flexibility and robustness [6]
Representative Output	Enzyme-constrained model (ecModel) with expanded reaction and metabolite list (e.g., from 2712 to 8331 reactions in E. coli) [6]	sMOMENT-enhanced model with fewer variables than original MOMENT [3]	Model with further expanded network (e.g., from 8331 to 16,605 reactions in E. coli) [6]

Experimental Protocols for ecModel Reconstruction and Validation

A direct comparison of toolboxes requires a standard workflow. The following protocol, based on GECKO 3.0, outlines the general steps for ecModel reconstruction, against which the performance of other tools can be measured.

Stage 1: Expansion from a starting metabolic model to an ecModel structure. The base GEM is expanded to include pseudo-reactions that represent enzyme usage. These reactions draw from a pool representing the total protein content available for metabolic functions [28] [22].

Stage 2: Integration of enzyme turnover numbers into the ecModel structure. The turnover numbers (kcat) for each enzyme are integrated into the model. GECKO 3.0 automates the retrieval of kcat values from the BRENDA database and incorporates deep learning-predicted enzyme kinetics to fill gaps where experimental data is missing [28] [22].

Stage 3: Model tuning. The enzyme protein pool is calibrated so that the model's maximum growth rate prediction matches experimentally determined values. This step ensures the model is correctly parameterized for the specific organism and condition [28].

Stage 4: Integration of proteomics data into the ecModel. If available, absolute proteomics data can be incorporated as upper bounds for the respective enzyme usage pseudo-reactions, further constraining the model with real, measured protein concentrations [28].

Stage 5: Simulation and analysis of ecModels. The completed ecModel can be used for various simulations, such as Flux Balance Analysis (FBA) and Flux Variability Analysis (FVA), to predict metabolic phenotypes, identify engineering targets, and study proteome allocation [28] [22].

Performance Benchmarking: Predictive Power and Applications

Different tools have been validated through specific case studies that highlight their predictive capabilities. The following table summarizes key performance outcomes from experimental applications.

Table 2: Experimental Performance and Validation Data

Toolbox / Model	Experimental Validation / Predictive Outcome	Quantitative Result / Application Impact
GECKO (ecYeast)	Accurately predicted the Crabtree effect (switch to fermentative metabolism) in S. cerevisiae without needing to constrain substrate uptake rates [4].	Explained long-term yeast adaptation to stress; predicted upregulation of amino acid metabolism enzymes [4].
AutoPACMEN (sMOMENT for E. coli)	Improved prediction of overflow metabolism (e.g., acetate secretion) and markedly changed the predicted spectrum of metabolic engineering strategies for different target products compared to the base model [3].	Successfully predicted aerobic growth rates on 24 different carbon sources using only enzyme mass constraints [3].
CORAL (eciML1515u)	Demonstrated that underground metabolism increases flexibility. Blocking an enzyme's main activity showed redistribution of enzyme resources to side activities, maintaining robust growth [6].	Increased flux variability in 79.85% of reactions and enzyme usage variability in 82.13% of subpools, confirming enhanced flexibility [6].

Building and simulating ecModels requires a suite of software tools and data resources. The following table details key components of the research toolkit.

Table 3: Essential Reagents and Resources for ecModel Reconstruction

Item	Function in ecModel Reconstruction	Example Sources / Software
Base Genome-Scale Model (GEM)	The foundational metabolic reconstruction that will be enhanced with enzymatic constraints.	Model repositories like BioModels, GEM repositories for specific organisms.
Kinetic Parameter Database	Provides the enzyme turnover numbers (kcat) required to constrain reaction fluxes.	BRENDA [4], SABIO-RK [3].
Deep Learning kcat Predictor	Fills gaps in experimental kinetic data by providing predicted kcat values for a wide range of enzymes and organisms.	Integrated in GECKO 3.0 via DLKcat [28] [22].
Proteomics Data	Used to set upper bounds for enzyme concentrations, adding organism- and condition-specific constraints.	Mass spectrometry-based absolute proteomics measurements.
Simulation Software	The computational environment for building the models and performing constraint-based analyses.	COBRA Toolbox (MATLAB) [4], COBRApy (Python) [4].

The choice of toolbox depends on the research question. GECKO provides a comprehensive and user-friendly protocol for general-purpose ecModel reconstruction. In contrast, CORAL is a specialized extension for investigating underground metabolism, while AutoPACMEN offers a simplified model structure. Understanding these differences allows researchers to select the most appropriate tool for modeling enzymatic constraints.

Constraint-based metabolic models (CBM) have become a powerful framework for describing, analyzing, and redesign cellular metabolism across diverse organisms [14] [3]. Traditional stoichiometric models incorporate mass balance constraints and reaction reversibility to define a space of feasible metabolic flux distributions. While valuable, these models often lack biological constraints that limit their predictive accuracy [14] [30]. Enzyme-constrained approaches address this limitation by incorporating enzymatic parameters and enzyme mass constraints, recognizing that cells possess limited resources for protein synthesis [14] [3]. These enhanced models better explain observed metabolic behaviors, such as overflow metabolism and the Crabtree effect, where microorganisms preferentially utilize fermentative pathways even under aerobic conditions [14] [30]. The integration of enzyme constraints has emerged as a crucial advancement for improving phenotype predictions in metabolic modeling research.

Several methodological frameworks have been developed to incorporate enzymatic constraints, including MOMENT (Metabolic Modeling with Enzyme Kinetics) and GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) [14] [3]. While these approaches have proven valuable, they often substantially increase model size and complexity, creating barriers to widespread adoption [14] [30]. The sMOMENT (short MOMENT) method and AutoPACMEN (Automatic integration of Protein Allocation Constraints in MEtabolic Networks) toolbox were developed specifically to address these challenges, providing simplified, automated workflows for constructing enzyme-constrained models [14] [3]. This comparison guide objectively evaluates these approaches against alternatives, examining their methodologies, performance, and applications within the broader context of enzymatic constraint modeling.

Comparative Analysis of Enzyme-Constraining Frameworks

Methodological Approaches and Key Innovations

The table below compares the core methodological characteristics of major frameworks for constructing enzyme-constrained metabolic models:

Table 1: Methodological Comparison of Enzyme-Constrained Modeling Frameworks

Framework	Core Approach	Key Innovation	Model Size Impact	Automation Level
sMOMENT	Simplified protein allocation constraints	Direct constraint integration without additional variables [14]	Minimal increase [14]	Medium (with AutoPACMEN) [14]
AutoPACMEN	Automated model creation pipeline	Toolbox for sMOMENT model generation & parameter calibration [14] [3]	Depends on base method	High (automated data retrieval & model reconfiguration) [14]
GECKO	Enzyme usage pseudo-reactions	Explicit enzyme representation with pseudo-reactions [30]	Significant increase [30]	Medium (GECKO 2.0 offers improved automation) [4]
ECMpy	Direct enzyme constraint addition	Python-based workflow without reaction modification [30] [31]	Minimal increase [30]	High (automated parameter calibration) [30]
Original MOMENT	Enzyme concentration variables	Incorporation of kcat parameters & enzyme mass constraints [14]	Significant increase (additional variables) [14]	Low (manual parameterization) [14]

The sMOMENT method represents a significant simplification over its predecessor MOMENT, achieving equivalent predictions with substantially fewer variables [14]. While MOMENT introduces separate enzyme concentration variables for each reaction, sMOMENT incorporates the enzymatic constraints directly into the stoichiometric matrix through a pooled enzyme capacity constraint [14]. This mathematical reformulation enables the direct application of standard constraint-based modeling tools to enzyme-constrained models, overcoming a significant limitation of the original MOMENT approach [14].

AutoPACMEN builds upon the sMOMENT methodology by providing an automated pipeline for model construction [14] [3]. This toolbox automatically retrieves and processes relevant enzymatic data from databases such as SABIO-RK and BRENDA, then reconfigures the stoichiometric model to embed the enzymatic constraints according to sMOMENT [14] [3]. Additionally, it includes tools for parameter adjustment based on experimental flux data, facilitating model calibration and refinement [14].

Performance and Predictive Accuracy

Experimental validations demonstrate that enzyme-constrained models generally outperform traditional constraint-based models in predicting microbial phenotypes. The following table summarizes key performance metrics reported across studies:

Table 2: Performance Comparison of Enzyme-Constrained Models in Experimental Validation

Model/Organism	Growth Rate Prediction	Overflow Metabolism Prediction	Key Experimental Validation
sMOMENT E. coli (iJO1366-based)	Improved prediction across 24 carbon sources [14]	Accurate explanation of aerobic acetate production [14]	Metabolic switches & engineering strategies [14]
GECKO S. cerevisiae (ecYeast7)	Superior growth prediction without uptake constraints [4]	Crabtree effect prediction without explicit bounds [4]	Proteomic data integration & mutant strains [4]
ECMpy E. coli (eciML1515)	Significant improvement on 24 carbon sources [30]	Redox balance identification in overflow metabolism [30]	13C flux consistency & enzyme usage analysis [30]
MOMENT E. coli	Superior aerobic growth predictions [14]	Explanation of overflow metabolism [14]	Growth on diverse carbon sources without uptake limits [14]

When applied to the E. coli genome-scale model iJO1366, the sMOMENT approach demonstrated significant improvements in flux predictions, successfully explaining overflow metabolism and other metabolic switches [14]. Notably, the enzyme constraints were shown to markedly change the spectrum of predicted metabolic engineering strategies for different target products, highlighting the practical implications of these methodological refinements [14].

The ECMpy workflow, when used to construct the eciML1515 model for E. coli, demonstrated particularly strong performance in growth rate predictions on 24 single-carbon sources, showing significant improvement compared to other enzyme-constrained models of E. coli [30]. This framework also revealed the tradeoff between enzyme usage efficiency and biomass yield when exploring metabolic behaviors under different substrate consumption rates [30].

Experimental Protocols and Methodologies

Workflow for Enzyme-Constrained Model Construction

The following diagram illustrates the core workflow for constructing enzyme-constrained models using the AutoPACMEN toolbox with sMOMENT methodology:

The construction of enzyme-constrained models follows a systematic workflow beginning with a stoichiometric model in SBML format [14] [3]. The AutoPACMEN toolbox automatically retrieves relevant enzymatic data, including turnover numbers (kcat) and molecular weights (MW), from kinetic databases such as BRENDA and SABIO-RK [14] [3]. These parameters undergo processing before being incorporated into the model via the sMOMENT reformulation, which applies the enzyme mass constraint: ∑(vᵢ × MWᵢ / kcatᵢ) ≤ P, where vᵢ represents flux through reaction i, and P is the total enzyme capacity [14]. The final step involves model calibration using experimental flux data to refine parameters and improve predictive accuracy [14] [30].

Mathematical Formulation of Enzyme Constraints

The core mathematical formulation differentiating these approaches is visualized below:

The sMOMENT method mathematically reformulates the enzyme constraints to eliminate the need for additional variables [14]. Where MOMENT introduces separate enzyme concentration variables (gᵢ) for each reaction with constraints vᵢ ≤ kcatᵢ · gᵢ and ∑gᵢ · MWᵢ ≤ P, sMOMENT directly substitutes these into a single pooled constraint: ∑(vᵢ · MWᵢ / kcatᵢ) ≤ P [14]. This reformulation can be incorporated into the standard stoichiometric matrix as an additional reaction: -∑vᵢ · (MWᵢ/kcatᵢ) + vPool = 0, with vPool ≤ P, where v_Pool represents the total enzyme mass required [14]. This elegant mathematical simplification enables more efficient computation while maintaining the biological fidelity of the original MOMENT approach.

Parameter Calibration Protocols

The calibration of enzyme kinetic parameters follows systematic protocols across these frameworks:

Table 3: Parameter Calibration Methods Across Modeling Frameworks

Framework	kcat Sourcing	Calibration Principles	Proteomics Integration
AutoPACMEN	BRENDA, SABIO-RK, custom databases [14]	Adjustment based on experimental flux data [14]	Supported (similar to GECKO) [14]
GECKO	BRENDA (automated retrieval) [4]	Manual curation for key enzymes [4]	Direct integration as enzyme constraints [4]
ECMpy	BRENDA, SABIO-RK (maximum values) [30]	Enzyme usage (<1% total) & 13C flux consistency [30]	Calculated enzyme mass fraction from proteomics [30]

The ECMpy workflow employs two specific principles for parameter calibration: (1) reactions with enzyme usage exceeding 1% of total enzyme content require correction, and (2) reactions where the kcat multiplied by 10% of total enzyme amount is less than the flux determined by 13C experiments need adjustment [30]. This systematic approach to parameter refinement contributes to the improved predictive accuracy observed with enzyme-constrained models.

Essential Research Reagents and Computational Tools

Successful implementation of enzyme-constrained modeling frameworks requires specific computational tools and data resources:

Table 4: Essential Research Reagents and Computational Tools

Resource	Type	Function/Purpose	Availability
BRENDA Database	Kinetic database	Comprehensive source of enzyme kinetic parameters (kcat) [14] [4]	Publicly available
SABIO-RK	Kinetic database	Source of enzyme kinetic parameters and rate laws [14]	Publicly available
COBRA Toolbox	Modeling software	Constraint-based reconstruction and analysis [32]	MATLAB, open-source
COBRApy	Modeling software	Python implementation of COBRA methods [32]	Python, open-source
SBML	Model format	Systems Biology Markup Language for model exchange [32]	Standard format
BiGG Models	Model database	Curated genome-scale metabolic models [32]	Public repository

These resources form the foundation for constructing, simulating, and analyzing enzyme-constrained metabolic models across the different frameworks discussed. The standardized SBML format enables interoperability between tools, while the kinetic databases provide the essential enzymatic parameters required for implementing the constraints [14] [32].

The development of sMOMENT and AutoPACMEN represents significant advancements in the field of enzyme-constrained metabolic modeling, offering simplified yet powerful alternatives to earlier approaches. The methodological refinement of sMOMENT reduces computational complexity while maintaining predictive accuracy, and the automation provided by AutoPACMEN makes enzyme-constrained modeling more accessible to researchers [14] [3]. When evaluated against alternative frameworks such as GECKO and ECMpy, these tools demonstrate complementary strengths in model construction efficiency, predictive performance, and integration with existing computational workflows.

Experimental validations consistently show that enzyme constraints improve flux predictions and enable more accurate representation of metabolic behaviors, including overflow metabolism and substrate utilization patterns [14] [30]. The demonstrated impact on predicted metabolic engineering strategies underscores the practical significance of these methodological advances [14]. As the field progresses, the availability of multiple streamlined workflows for constructing enzyme-constrained models promises to enhance our understanding of cellular metabolism and support more effective metabolic engineering designs across diverse biotechnology and biomedical applications.

Constraint-based metabolic modeling has become a cornerstone of systems biology, enabling researchers to predict metabolic phenotypes from genomic information. Genome-scale metabolic models (GEMs) provide a mathematical representation of an organism's metabolism, detailing the biochemical reactions and gene-protein relationships that define metabolic capabilities [32]. The most common simulation technique, flux balance analysis (FBA), assumes cells operate their metabolism according to optimality principles under stoichiometric constraints [4]. However, classical GEMs often fail to accurately predict suboptimal metabolic behaviors, such as overflow metabolism, where organisms incompletely oxidize substrates even in the presence of oxygen [30].

To address these limitations, researchers have developed methods that incorporate enzymatic constraints into metabolic models. These approaches recognize that cellular metabolism is constrained not only by stoichiometry but also by biophysical and biochemical limitations, particularly the finite capacity of cells to produce and maintain enzymes [4] [3]. By integrating enzyme kinetic parameters (kcat values) and incorporating the limited total protein budget of cells, enzyme-constrained models (ecModels) significantly improve phenotype predictions across various organisms and conditions [4] [30].

This review comprehensively compares ECMpy against other prominent enzymatic constraint modeling frameworks, with a particular focus on applications to Escherichia coli—a gram-negative bacterium that serves as a fundamental model organism in biological research due to its rapid growth, genetic simplicity, and well-characterized biology [33].

Fundamental Principles of Enzyme Constraints

Enzyme-constrained metabolic models extend traditional GEMs by incorporating two fundamental biological constraints: enzyme kinetics and protein allocation. The core mathematical formulation introduces a relationship between metabolic fluxes (vi), enzyme concentrations (gi), and turnover numbers (kcat_i):

[ vi \leq k{cat,i} \cdot g_i ]

This equation indicates that the flux through any metabolic reaction cannot exceed the product of the enzyme concentration catalyzing that reaction and its catalytic efficiency. A second critical constraint accounts for the limited protein resources within a cell:

[ \sum gi \cdot MWi \leq P ]

where MW_i represents the molecular weight of each enzyme and P denotes the total protein mass available for metabolic functions [3]. These combined constraints effectively limit the metabolic solution space to biologically realistic flux distributions, explaining phenomena like the Crabtree effect in yeast and overflow metabolism in E. coli that traditional FBA cannot predict without arbitrary flux bounds [4] [30].

Comparative Framework for Enzymatic Constraint Methods

Several computational frameworks have been developed to implement enzymatic constraints in metabolic models, each with distinct methodological approaches:

GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) extends classical FBA by incorporating a detailed description of enzyme demands for all metabolic reactions in a network. The method introduces additional reactions and metabolites to reflect enzyme usage, allowing direct integration of proteomics data as constraints for individual protein demands [4]. GECKO employs a hierarchical procedure for retrieving kinetic parameters from the BRENDA database, providing high coverage of kinetic constraints [4].

sMOMENT (short MOMENT) presents a simplified version of the earlier MOMENT approach, yielding equivalent predictions with significantly fewer variables. This method incorporates enzyme constraints directly into the standard constraint-based model representation without expanding the model size substantially, enhancing computational efficiency [3]. The core sMOMENT formulation combines the enzyme kinetic and allocation constraints into a single inequality:

[ \sum vi \cdot \frac{MWi}{k_{cat,i}} \leq P ]

This compact representation facilitates the application of standard constraint-based modeling tools to enzyme-constrained models [3].

AutoPACMEN (Automatic integration of Protein Allocation Constraints in MEtabolic Networks) provides an automated toolbox for creating sMOMENT-enhanced stoichiometric models, featuring automatic retrieval of enzymatic data from SABIO-RK and BRENDA databases [3].

ECMpy Workflow and Implementation

Architecture and Core Algorithm

ECMpy implements a simplified Python-based workflow for constructing enzymatic constrained metabolic network models. The framework enhances existing GEMs by directly incorporating total enzyme amount constraints while considering protein subunit composition in reactions and automating the calibration of enzyme kinetic parameters [30]. A key advantage of ECMpy is its simplified implementation that avoids modifying existing metabolic reactions or adding numerous new reactions, unlike earlier approaches like GECKO that significantly increase model complexity and size [30].

The core enzymatic constraint in ECMpy follows this formulation:

[ \sum{i=1}^{n} \frac{vi \cdot MWi}{\sigmai \cdot k{cat,i}} \leq p{tot} \cdot f ]

where ( \sigmai ) represents the saturation coefficient of the i-th enzyme, ( p{tot} ) is the total protein fraction, and ( f ) denotes the mass fraction of enzymes calculated based on proteomic abundance data [30]. For reactions catalyzed by enzyme complexes, ECMpy uses the minimum value of the kcat/MW ratio among all subunits in the complex, ensuring thermodynamic feasibility.

Workflow Diagram

ECMpy workflow for constructing enzyme-constrained models.

Key Features and Innovations

ECMpy introduces several innovative features that distinguish it from earlier approaches:

• Automated kcat Calibration: ECMpy implements principles for automated adjustment of original kcat values to improve agreement with experimental data. Reactions with enzyme usage exceeding 1% of total enzyme content require parameter correction, as do reactions where the kcat multiplied by 10% of the total enzyme amount is less than the flux determined by 13C experiments [30].

• Simplified Model Representation: Unlike GECKO, which adds numerous pseudo-reactions and metabolites for enzyme usage, ECMpy incorporates enzyme constraints without modifying the core metabolic network structure, resulting in more compact models [30].

• Python-Based Implementation: Built on open-source Python packages including COBRApy, ECMpy benefits from extensive ecosystem integration and accessibility for researchers without proprietary software licenses [30] [32].

• Comprehensive Database Integration: The workflow automatically retrieves kinetic parameters from multiple sources, primarily the BRaunschweig ENzyme DAta base (BRENDA) and System for the Analysis of Biochemical Pathways - Reaction Kinetics databases (SABIO-RK) [30].

Comparative Analysis of Model Performance

Experimental Framework and Evaluation Metrics

To objectively evaluate ECMpy against alternative enzymatic constraint methods, we established a consistent experimental framework centered on E. coli metabolism. The evaluation utilized the latest E. coli GEM (iML1515) as the base model, with performance assessed across multiple carbon sources and genetic backgrounds [30]. Model predictions were compared against experimental growth rates and flux measurements from 13C labeling experiments.

Key evaluation metrics included:

• Growth Rate Prediction Accuracy: Estimation error calculated as ( \frac{|v{growth,sim} - v{growth,exp}|}{v_{growth,exp}} ) [30]
• Phenotypic Prediction: Ability to simulate overflow metabolism without arbitrary flux constraints
• Computational Efficiency: Model size and simulation time requirements
• Parameter Coverage: Proportion of reactions with organism-specific kinetic parameters

Quantitative Performance Comparison

Table 1: Comparative performance of enzymatic constraint methods for E. coli

Method	Base Model	Average Growth Rate Error	Overflow Metabolism Prediction	Reactions with kcat Values	Model Size Increase
ECMpy	iML1515	Significantly reduced [30]	Accurate [30]	High coverage [30]	Minimal [30]
GECKO	Yeast7	Improved [4]	Accurate (Crabtree effect) [4]	48.35% from other organisms [4]	Substantial [30]
sMOMENT/AutoPACMEN	iJO1366	Improved [3]	Accurate [3]	Database-dependent [3]	Moderate [3]
Traditional FBA	iML1515	Higher [30]	Requires arbitrary constraints [30]	Not applicable	None

Case Study: Overflow Metabolism in E. coli

A critical test for enzymatic constraint methods is their ability to predict overflow metabolism in E. coli—the phenomenon where cells partially oxidize glucose to acetate rather than completely through the respiratory pathway, even under aerobic conditions [30]. ECMpy successfully simulated this metabolic switch by revealing that redox balance is a key factor differentiating E. coli and Saccharomyces cerevisiae overflow metabolism [30].

When analyzing the trade-off between enzyme usage efficiency and biomass yield, ECMpy implemented a parsimonious FBA-inspired approach to minimize total enzyme amount while maintaining maximum growth rate:

[ \text{minimize} \sum{i=1}^{n} \frac{vi \cdot MWi}{\sigmai \cdot k_{cat,i}} ]

subject to:

[ S \cdot v = 0, \quad v{lb} \leq v \leq v{ub}, \quad \sum{i=1}^{n} \frac{vi \cdot MWi}{\sigmai \cdot k{cat,i}} \leq p{tot} \cdot f, \quad v_{biomass} = \max(\text{growth rate}) ]

This analysis revealed how E. coli strategically balances enzyme investment against metabolic yield under different substrate conditions [30].

Research Applications and Implementation Toolkit

Essential Research Reagents and Computational Tools

Table 2: Essential research toolkit for enzymatic constraint modeling

Resource	Type	Function	Availability
BRENDA Database	Kinetic database	Provides enzyme turnover numbers (kcat)	Public [4] [30]
SABIO-RK	Kinetic database	Curated enzyme kinetic parameters	Public [3]
COBRApy	Python package	Constraint-based reconstruction and analysis	Open-source [32]
BiGG Models	Model repository	Curated genome-scale metabolic models	Public [32]
E. coli K-12 MG1655	Reference strain	Well-annotated model organism for validation	Strain collections [34]
MEMOTE	Test suite	Quality assessment of metabolic models	Open-source [32]
CPI-905	CPI-905, CAS:931078-17-0, MF:C18H20N2O5, MW:344.4 g/mol	Chemical Reagent	Bench Chemicals
Crilvastatin	Crilvastatin, CAS:120551-59-9, MF:C14H23NO3, MW:253.34 g/mol	Chemical Reagent	Bench Chemicals

Implementation Protocol for ECMpy

Implementing ECMpy for constructing enzyme-constrained models involves these critical steps:

• Model Preparation: Start with a high-quality genome-scale metabolic model in SBML format. The E. coli iML1515 model serves as an ideal starting point with its comprehensive coverage of metabolic genes [30].

• Kinetic Parameter Integration: Retrieve kcat values from BRENDA and SABIO-RK databases, prioritizing organism-specific measurements when available. For reactions without specific data, implement hierarchical matching criteria based on enzyme commission numbers and phylogenetic proximity [4] [30].

• Enzyme Mass Fraction Calculation: Determine the mass fraction of enzymes (f) using proteomics data according to the formula:

[ f = \frac{\sum{i=1}^{p_num} Ai MWi}{\sum{j=1}^{g_num} Aj MWj} ]

where A represents protein abundances in mole ratios [30].

• Parameter Calibration: Adjust kcat values using the two-principle approach: (1) correct parameters for reactions with enzyme usage >1% of total enzyme content, and (2) ensure kcat values support fluxes consistent with 13C experimental data [30].

• Model Simulation and Validation: Utilize COBRApy functions for flux balance analysis and compare predictions against experimental growth rates across multiple conditions [30] [32].

Comparative Framework Diagram

Comparison framework of enzymatic constraint methods versus traditional FBA.

Discussion and Research Implications

Advantages of ECMpy for Metabolic Engineering

ECMpy represents a significant advancement in enzymatic constraint modeling by providing a balanced approach that maintains predictive accuracy while minimizing model complexity. The simplified workflow demonstrates particular strength in metabolic engineering applications, where it enables more reliable prediction of metabolic phenotypes under various genetic perturbations [30]. By accurately simulating the trade-offs between enzyme investment and metabolic yield, ECMpy provides valuable guidance for optimizing microbial cell factories.

For E. coli-based biotechnology, ECMpy offers enhanced prediction of growth rates on 24 single-carbon sources, significantly improving upon traditional FBA and other enzyme-constrained models [30]. This capability is particularly valuable for designing growth strategies on non-traditional substrates, a common requirement in industrial bioprocesses.

Limitations and Future Directions

Despite its advantages, ECMpy shares common challenges with other enzymatic constraint methods. The limited coverage of organism-specific kinetic parameters remains a significant constraint, particularly for non-model organisms [4]. Database analysis reveals extreme bias in kinetic characterization, with human, E. coli, rat, and S. cerevisiae accounting for 24.02% of all BRENDA entries, while most organisms have a median of just 2 entries [4].

Future development should focus on machine learning approaches to predict unknown kinetic parameters and multi-scale modeling that integrates transcriptional and translational constraints. Additionally, expanding applications to understudied microorganisms beyond traditional model organisms like E. coli will be essential for broader biological insights [35].

ECMpy establishes itself as a valuable addition to the enzymatic constraint modeling toolbox, particularly for researchers working with E. coli and related organisms. Its Python-based implementation, simplified workflow, and minimal model expansion provide accessibility without sacrificing predictive power. While GECKO offers more detailed representation of enzyme-reaction relationships and sMOMENT provides computational efficiency, ECMpy strikes an effective balance for practical metabolic engineering applications.

The continued development of enzymatic constraint methods represents a crucial frontier in constraint-based modeling, moving beyond stoichiometric considerations to capture the fundamental proteomic constraints that shape metabolic evolution and function. As kinetic databases expand and computational methods advance, enzyme-constrained models will play an increasingly vital role in both basic microbial physiology and applied biotechnology.

The construction of highly accurate, predictive metabolic models is fundamentally constrained by the scarcity of reliable enzyme kinetic data. Enzyme turnover numbers (kcat) are essential parameters for understanding cellular metabolism, proteome allocation, and physiological diversity, as they define the maximum catalytic rate of enzymes [36]. Despite their critical importance, experimentally measured kcat values remain sparse and noisy in databases such as BRENDA and SABIO-RK [37] [36]. This data scarcity presents a significant bottleneck for the development of enzyme-constrained genome-scale metabolic models (ecGEMs), which rely on kcat values to incorporate enzymatic limitations into flux predictions [3] [4].

Traditionally, researchers have depended on manual curation from biochemical databases to parameterize these models. However, the emergence of deep learning approaches now offers a complementary pathway to overcome kinetic data limitations. This article provides a comparative analysis of these distinct strategies—database integration and prediction-driven approaches—evaluating their performance, methodological frameworks, and practical applications in metabolic modeling research.

Comparative Analysis of Kinetic Data Sourcing Strategies

The following table summarizes the core characteristics of the primary methods for sourcing kcat values in metabolic modeling.

Table 1: Comparison of Kinetic Data Sourcing Methods for Metabolic Models

Method	Core Approach	Data Sources	Coverage	Key Advantages	Inherent Limitations
Database-Driven (BRENDA/SABIO-RK)	Manual curation & automated querying of experimental data	BRENDA, SABIO-RK [3] [14]	Limited by experimental characterization; uneven across organisms [4]	Direct experimental basis; established in traditional workflows	Sparse data for less-studied organisms; measurement variability due to different assay conditions [36]
Prediction-Driven (DLKcat)	Deep learning prediction from substrate structures & protein sequences	Uses BRENDA/SABIO-RK for training, then generates predictions [36]	High; can be applied to any enzyme with known sequence and substrate [36]	High-throughput capability; applicable to novel enzymes and organisms	Predictive uncertainty; model dependency; requires computational expertise
Hybrid (GECKO)	Hierarchical matching combining databases & algorithmic gap-filling	BRENDA as primary source, with wildcard and organism-specific matching [4]	Moderate to high, depending on curation intensity	Balances experimental data with systematic gap-filling	Can propagate incorrect annotations; complex parameterization

Performance and Experimental Validation

Quantitative Performance Metrics

Rigorous benchmarking studies provide quantitative insights into the predictive performance of deep learning approaches compared to traditional methods.

Table 2: Performance Metrics of DLKcat and Related Deep Learning Models

Model	Test Dataset RMSE	R-squared (R²)	Pearson's r	Key Innovations
DLKcat	1.06 (log10 scale) [36]	N/R	0.71 (test dataset), 0.88 (whole dataset) [36]	Graph neural network for substrates; CNN for proteins; handles enzyme promiscuity [36]
DLTKcat	0.88 (log10 scale) [37]	0.66 [37]	N/R	Incorporates temperature features; bidirectional attention mechanism [37]
Traditional Database Queries	N/A	N/A	N/A	Limited to experimentally characterized enzymes only [4]

The performance metrics demonstrate that deep learning models can predict kcat values within approximately one order of magnitude of experimental values, with DLKcat achieving a Pearson correlation of 0.71 on its test dataset [36]. The more recent DLTKcat model shows improved RMSE and R² values, potentially due to its incorporation of temperature dependence [37].

Functional Validation in Metabolic Modeling

Beyond statistical metrics, the true validation of these approaches lies in their performance when integrated into enzyme-constrained metabolic models.

• Phenotype Prediction: ecGEMs parameterized with DLKcat-predicted kcat values outperformed database-driven ecGEMs in predicting microbial growth phenotypes and proteome allocations [36]. The DLKcat-enhanced models successfully explained phenotypic differences across yeast species, demonstrating the biological relevance of the predictions [36].

• Metabolic Engineering Design: Enzyme constraints significantly alter predicted optimal metabolic engineering strategies. sMOMENT models applied to E. coli revealed that enzyme limitations can redirect theoretical flux distributions, suggesting more realistic genetic modification targets [3] [14].

• Temperature Response Modeling: DLTKcat enabled the first incorporation of temperature-dependent kcat values into metabolic models, potentially allowing simulation of microbial behavior under different environmental conditions [37].

Methodological Frameworks and Experimental Protocols

Database-Driven Workflow (AutoPACMEN/sMOMENT)

The automated construction of enzyme-constrained models from database resources follows a systematic protocol.

Database-Driven ecGEM Construction

The sMOMENT method simplifies the integration of enzyme constraints by converting the enzyme allocation problem into a single linear constraint [3] [14]:

[ \sum vi \cdot \frac{MWi}{kcat_i} \leq P ]

Where (vi) is the flux through reaction i, (MWi) is the enzyme molecular weight, (kcat_i) is the turnover number, and P is the total enzyme pool capacity.

Deep Learning Prediction Pipeline (DLKcat)

The DLKcat framework employs a multi-modal deep learning approach to predict kcat values from fundamental biochemical information.

DLKcat Prediction Workflow

The model training protocol involves:

• Data Collection: Curating 16,838 unique enzyme-substrate pairs from BRENDA and SABIO-RK with substrate SMILES, protein sequences, and kcat values [36]
• Preprocessing: Removing redundant entries, splitting sequences into 3-mer subsequences, converting SMILES to molecular graphs [37] [36]
• Model Architecture: Implementing separate pathways for substrate (Graph Neural Network) and protein (Convolutional Neural Network) feature extraction [36]
• Training: Using mean squared error loss with Adam optimizer, 80/10/10 train/validation/test split [36]

Advanced Integration: Temperature Dependence (DLTKcat)

The DLTKcat model extends the prediction framework to incorporate temperature effects, crucial for modeling microbial behavior in varying environments.

DLTKcat Architecture with Temperature

The temperature integration is inspired by the Arrhenius equation, with the model incorporating both temperature (T) and inverse temperature (1/T) features to capture the nonlinear relationship between temperature and enzyme activity [37].

Table 3: Key Research Tools and Resources for Kinetic Data Integration

Tool/Resource	Type	Primary Function	Application Context
BRENDA	Database	Comprehensive enzyme kinetic data repository	Manual curation; reference data for validation [36] [4]
SABIO-RK	Database	Biochemical reaction kinetics with rate equations	Detailed kinetic parameter extraction [38]
DLKcat	Software Tool	Deep learning-based kcat prediction from sequences	High-throughput kcat estimation for ecGEMs [36] [39]
GECKO 2.0	Modeling Toolbox	Automated ecGEM construction with enzyme constraints	Genome-scale modeling with proteomic constraints [4]
AutoPACMEN	Modeling Toolbox	Automated sMOMENT model generation	Simplified enzyme-constrained model construction [3] [14]
RDKit	Cheminformatics	SMILES processing and molecular graph conversion	Preprocessing substrate structures for deep learning [37]

The integration of kinetic data from traditional databases and deep learning predictions represents a paradigm shift in metabolic modeling. While database-driven approaches provide experimentally grounded parameters, their limited coverage constrains model completeness. Prediction-driven methods offer unprecedented coverage but introduce computational dependencies. The most promising path forward involves hybrid frameworks that leverage the strengths of both approaches—using experimental data where available and high-quality predictions where necessary.

Future developments will likely focus on improving prediction accuracy through larger training datasets, incorporating additional environmental factors beyond temperature, and creating more seamless integration pipelines. As these tools mature, they will progressively overcome the kinetic data scarcity problem, enabling more accurate predictions of cellular behavior, more rational metabolic engineering designs, and ultimately, accelerating biotechnology and pharmaceutical development.

Overflow metabolism, a phenomenon where cells preferentially use inefficient fermentative pathways over efficient respiration even in the presence of oxygen, represents a fundamental puzzle in cellular metabolism. Known as the Crabtree effect in yeast and the Warburg effect in mammalian cells, this metabolic strategy occurs across diverse organisms from bacteria to human cancer cells [40] [41] [42]. While respiration generates approximately 10 times more ATP per glucose molecule than fermentation, the fermentative strategy allows cells to achieve higher growth rates under nutrient-rich conditions [40]. This apparent paradox has driven the development of sophisticated computational models that can explain and predict when and why cells switch between respiratory and fermentative metabolic states.

Traditional genome-scale metabolic models (GEMs) based solely on stoichiometric constraints have limited ability to predict overflow metabolism, as they lack mechanistic connections between enzyme levels and metabolic fluxes [3] [43]. The integration of enzyme constraints has emerged as a critical advancement, enabling models to account for the proteomic costs of metabolic pathways and the kinetic limitations of enzymes [4] [43]. This review compares the leading enzymatic constraint-based modeling frameworks, evaluates their performance in predicting Crabtree effects, and provides experimental guidance for researchers studying eukaryotic metabolism.

Computational Frameworks for Enzyme-Constrained Metabolic Modeling

Several computational frameworks have been developed to integrate enzyme constraints into metabolic models, each with distinct methodologies and applications. The table below compares the key features of major enzyme-constrained modeling frameworks.

Table 1: Comparison of Major Enzyme-Constrained Metabolic Modeling Frameworks

Framework	Key Features	Data Requirements	Organisms Applied	Predictive Capabilities
GECKO [4] [43]	Adds enzyme usage pseudo-reactions; Direct proteomics integration; Handles isoenzymes & complexes	kcat values, Molecular weights, Optional proteomics data	S. cerevisiae, E. coli, H. sapiens, Y. lipolytica, K. marxianus	Crabtree effect, Growth on multiple carbon sources, Gene knockout phenotypes
sMOMENT [3]	Simplified MOMENT approach; Fewer variables; Standard model representation	kcat values, Enzyme molecular weights, Total enzyme pool estimate	E. coli	Overflow metabolism, Metabolic engineering strategies
ME-models [43]	Integrated metabolism & gene expression; Detailed protein synthesis	Transcription/translation rates, Protein maturation data	E. coli, T. maritima, L. lactis	Growth rate prediction, Resource allocation
FBAwMC [43]	Molecular crowding constraints; Total enzyme volume limits	Enzyme sizes, Cellular volume constraints	E. coli, S. cerevisiae, Human cells	Overflow metabolism, Enzyme saturation

Technical Implementation and Workflow

The GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) methodology extends traditional GEMs by incorporating enzymes as explicit constraints on metabolic fluxes [43]. The core principle implements the biochemical reality that any metabolic flux (vi) cannot exceed the product of the corresponding enzyme concentration (ei) and its turnover number (kcati): vi ≤ kcati × ei. The framework adds rows representing enzymes and columns representing enzyme usage reactions to the stoichiometric matrix, with kcat values serving as conversion factors between metabolic fluxes and enzyme usage [43].

The GECKO toolbox automates model construction by querying kinetic parameters from databases like BRENDA and SABIO-RK, handling isoenzymes, enzyme complexes, and promiscuous enzymes through specialized formalisms [4] [43]. The resulting enzyme-constrained models (ecModels) can incorporate absolute proteomics data as upper bounds for enzyme usage reactions, significantly reducing flux variability and improving prediction accuracy [43]. For reactions without experimental enzyme abundance data, constraints can be implemented via a total enzyme pool mass constraint similar to FBAwMC [43].

Figure 1: Workflow for Constructing Enzyme-Constrained Genome-Scale Models (ecGEMs). The process enhances stoichiometric models with enzymatic constraints using kinetic parameters from databases and optional proteomic data.

Experimental Validation and Performance Comparison

Physiological Basis of Crabtree Effects in Yeast

Experimental studies comparing Crabtree-positive yeasts (S. cerevisiae, S. pombe) and Crabtree-negative yeasts (K. marxianus, S. stipitis, P. kluyveri) reveal distinct physiological and proteomic differences underlying their metabolic strategies [40] [44]. Under glucose excess conditions, Crabtree-positive yeasts exhibit approximately 2-3 times higher glucose uptake rates, secrete significant ethanol (42-47% of consumed glucose), and achieve biomass yields around 0.1 g DW/g glucose [40]. In contrast, Crabtree-negative species fully oxidize glucose through respiration, with minimal byproduct formation and significantly higher biomass yields (0.44-0.58 g DW/g glucose) [40].

Absolute proteome quantification demonstrates that these physiological differences emerge from distinct proteomic allocation strategies. Crabtree-positive yeasts allocate their proteome to maximize glucose utilization rate, accepting lower energy efficiency to minimize proteome cost per metabolic flux [40]. Conversely, Crabtree-negative yeasts employ a strategy maximizing ATP yield through efficient respiration, supported by higher abundance of respiratory chain components including Complex I in S. stipitis [40] [44]. The presence of Complex I, which increases the phosphate-to-oxygen (P/O) ratio and ATP yield per mitochondrial NADH oxidized, partially explains the higher biomass yield in S. stipitis compared to other Crabtree-negative yeasts [40].

Table 2: Physiological Parameters of Crabtree-Positive and Crabtree-Negative Yeasts Under Glucose Excess Conditions [40]

Parameter	S. cerevisiae (Crabtree+)	S. pombe (Crabtree+)	K. marxianus (Crabtree-)	S. stipitis (Crabtree-)
Growth rate (h⁻¹)	0.42	0.22	0.44	0.47
Glucose uptake rate (mmol/gDW/h)	13.5	7.8	4.1	3.5
Ethanol secretion (% glucose carbon)	47%	42%	<3% (as acetate)	Minimal
Biomass yield (g DW/g glucose)	~0.1	~0.1	0.44	0.58
Respiratory Quotient (RQ)	~9	~9	1.09	1.15
Oxygen uptake rate (mmol/gDW/h)	4.5	2.2	7.5	3.8

Model Performance in Predicting Metabolic Phenotypes

Enzyme-constrained models significantly outperform traditional GEMs in predicting key metabolic phenotypes, particularly overflow metabolism. The ecYeast7 model (GECKO-enhanced Yeast7) successfully predicts the Crabtree effect in S. cerevisiae, including the critical dilution rate at which respiro-fermentative metabolism begins, without requiring artificial constraints on substrate uptake or oxygen availability [43]. The model accurately describes yeast physiology across diverse conditions including growth on different carbon sources, stress responses, and pathway overexpression [43].

Similar performance improvements have been demonstrated in ecModels for other organisms. The enzyme-constrained E. coli model (ec_iJO1366) based on sMOMENT correctly predicts aerobic acetate secretion at high growth rates and provides superior growth rate predictions across 24 different carbon sources compared to the base model [3]. Notably, enzyme-constrained models can explain overflow metabolism as an optimal proteomic allocation strategy rather than an unexplained metabolic inefficiency [40] [41].

Recent advancements incorporate deep learning approaches for kcat prediction, such as multi-modal transformer networks that use enzyme amino acid sequences and reaction substrate structures (SMILES) to predict kinetic parameters [23]. These methods address the limited availability of experimentally measured kcat values, particularly for less-studied organisms, and have demonstrated state-of-the-art performance in ecGEM construction for E. coli [23].

Experimental Protocols for Model Validation

Physiological Characterization of Microbial Strains

To validate enzyme-constrained model predictions or generate training data, researchers can employ well-established bioreactor cultivation protocols with continuous monitoring of physiological parameters [40]:

• Chemostat Cultivation: Maintain microbial cultures in steady-state growth under glucose limitation at various dilution rates below and above the critical dilution rate where overflow metabolism begins. For S. cerevisiae, the critical dilution rate typically falls between 0.2-0.3 h⁻¹ [42].

• Batch Cultivation: Grow cultures in glucose-excess conditions (e.g., 20 g/L initial glucose) with dissolved oxygen maintained above 60% to ensure aerobic conditions [40]. Monitor biomass growth (OD600 or dry weight), substrate consumption, and metabolite production throughout growth phases.

• Pulse Experiments: Subject glucose-limited, respiring cultures to glucose pulses (short-term Crabtree effect) and monitor rapid metabolic responses including immediate ethanol production in Crabtree-positive strains [42] [45].

• Parameter Measurement: Quantify key physiological parameters including:

  • Biomass concentration and growth rate
  • Glucose uptake rate (GUR)
  • Oxygen uptake rate (OUR)
  • Carbon dioxide evolution rate (CER)
  • Respiratory quotient (RQ = CER/OUR)
  • Extracellular metabolite concentrations (ethanol, acetate, etc.)

Figure 2: Metabolic Switching in Crabtree Effect. Under high glucose, Crabtree-positive yeasts favor fermentative pathway despite lower ATP yield, enabling faster glucose utilization and growth through optimized proteome allocation.

Proteomic Quantification for Model Input and Validation

Absolute proteome quantification provides critical data for constructing and validating enzyme-constrained models. The following mass spectrometry-based protocol has been successfully applied to yeast systems [40]:

• Sample Preparation: Harvest cells from mid-exponential phase, disrupt cells using mechanical lysis, and digest proteins with trypsin following standard proteomics protocols.

• Protein Quantification:

  • Use intensity-based absolute quantification (iBAQ) with Proteomics Dynamic Range Standard (UPS2) as internal standard [40]
  • Employ tandem mass tag (TMT)-based mass spectrometry using pooled reference samples as internal references
  • Quantify 3,500-4,100 proteins per sample for comprehensive coverage

• Data Integration: Incorporate absolute enzyme concentrations into ecGEMs as upper bounds for enzyme usage reactions. For unmeasured enzymes, use the total enzyme pool constraint.

• Flux Validation: Compare predicted metabolic fluxes from ecGEMs with experimental ({}^{13}C) flux measurements to validate model accuracy.

Research Reagent Solutions for Metabolic Studies

Table 3: Essential Research Reagents for Studying Overflow Metabolism

Reagent/Category	Specific Examples	Research Application	Technical Function
Model Organisms	S. cerevisiae (CEN.PK, S288C), K. marxianus, S. stipitis, P. kluyveri	Comparative physiology	Crabtree-positive vs. negative metabolic strategies
Cultivation Systems	Bioreactors with DO control, Chemostat systems, Microplate readers	Physiological characterization	Maintain controlled growth conditions, monitor growth parameters
Analytical Instruments	HPLC/UPLC, GC-MS, LC-MS/MS, NMR	Metabolite quantification, Flux analysis	Measure extracellular metabolites, ¹³C labeling patterns
Proteomics Platforms	Q-Exactive Orbitrap, TripleTOF, TimsTOF	Absolute protein quantification	Determine enzyme abundances for model constraints
Kinetic Databases	BRENDA, SABIO-RK, UniProt	kcat parameterization	Source enzyme kinetic parameters for model construction
Software Tools	GECKO toolbox, AutoPACMEN, COBRA, MultiMetEval	Model construction & simulation	Build, simulate, and analyze enzyme-constrained models

Enzyme-constrained metabolic models represent a significant advancement in predicting overflow metabolism and Crabtree effects, moving beyond phenomenological descriptions to mechanistic explanations based on proteomic allocation principles. The GECKO framework has demonstrated particular success in eukaryotic systems, correctly predicting metabolic switches without requiring artificial constraints [4] [43].

Future methodology developments will likely focus on improved kcat prediction through deep learning approaches [23], enhanced integration of multi-omics data, and expansion to less-studied organisms. As these models become more accessible through automated tools like GECKO 2.0 and AutoPACMEN [3] [4], their application will expand across metabolic engineering, biotechnology, and biomedical research, enabling model-driven strain design and therapeutic targeting of metabolic dysregulation in human diseases.

For researchers investigating eukaryotic metabolism, enzyme-constrained models provide a powerful framework for predicting metabolic phenotypes, designing engineering strategies, and understanding the fundamental principles of cellular resource allocation.

Use Cases in Metabolic Engineering and Therapeutic Development

Genome-scale metabolic models (GEMs) have become established tools for systematic analysis of metabolism across diverse organisms, enabling prediction of cellular phenotypes from genotype information [4]. However, traditional constraint-based approaches considering only stoichiometric constraints often predict metabolic fluxes that deviate from experimentally observed phenotypes, as they fail to account for critical biological limitations like enzyme capacity and cellular protein allocation [46] [47]. This limitation has driven the development of enzyme-constrained genome-scale models (ecGEMs), which incorporate enzymatic constraints using kinetic parameters (kcat values) and molecular weights to better represent cellular realities [46] [4].

The integration of enzyme constraints has proven particularly valuable in metabolic engineering and therapeutic development, where accurate phenotype prediction is essential for strain design and enzyme engineering. By accounting for the metabolic costs of enzyme production and the limitations imposed by enzyme kinetics, ecGEMs provide more reliable predictions of metabolic behavior under various genetic and environmental perturbations [46] [16]. Several computational frameworks have been developed to construct ecGEMs, including GECKO, AutoPACMEN, and ECMpy, each offering different approaches for incorporating enzymatic constraints into metabolic models [4] [3] [30].

This review compares the major enzymatic constraint modeling approaches, their applications in metabolic engineering and therapeutic development, and provides experimental protocols for their implementation. We examine how these methods enhance prediction accuracy for industrial strain optimization and drug development, supported by quantitative performance comparisons across multiple organisms and case studies.

Methodological Approaches for Enzyme-Constrained Modeling

Major Computational Frameworks

Table 1: Comparison of Major Enzyme-Constrained Modeling Approaches

Method	Key Features	Required Parameters	Implementation	Notable Applications
GECKO [4]	Adds enzyme usage reactions and pseudo-metabolites; Direct proteomics data integration	kcat values, Enzyme molecular weights, Protein mass fraction	MATLAB-based toolbox with automated model construction	S. cerevisiae, E. coli, H. sapiens [4]
AutoPACMEN [3]	Simplified MOMENT (sMOMENT) approach; Minimal model expansion; Automated parameter retrieval	kcat values, Enzyme molecular weights, Total enzyme pool size	Python-based toolbox with BRENDA/SABIO-RK integration	E. coli, C. ljungdahlii [46] [3]
ECMpy [30]	Direct enzyme constraint without model modification; Machine learning kcat prediction	kcat values, Enzyme molecular weights, Protein mass fraction	Python-based workflow with TurNuP integration	E. coli, M. thermophila, C. glutamicum [16] [47]
GECKO 2.0 [4]	Enhanced parameterization; Automated model updating; Improved kinetic parameter coverage	kcat values, Enzyme molecular weights, Proteomics data	MATLAB toolbox with continuous model updating	S. cerevisiae, Y. lipolytica, K. marxianus [4]

The GECKO (Genome-scale model to account for Enzyme Constraints using Kinetic and Omics data) framework extends traditional GEMs by incorporating detailed enzyme demands for metabolic reactions through additional pseudo-reactions and metabolites representing enzyme utilization [4]. This approach allows direct integration of proteomics data as upper bounds for individual enzyme capacities. The recently upgraded GECKO 2.0 provides an automated pipeline for continuous, version-controlled updates of enzyme-constrained models and improved kinetic parameter coverage, even for less-studied organisms [4].

AutoPACMEN (Automatic integration of Protein Allocation Constraints in MEtabolic Networks) utilizes a simplified MOMENT (sMOMENT) approach that requires significantly fewer variables than original implementations [3] [48]. This method incorporates enzyme constraints directly into the standard constraint-based model representation without extensive model expansion, maintaining compatibility with standard simulation tools while automatically retrieving enzymatic parameters from databases like BRENDA and SABIO-RK [3].

ECMpy offers a simplified workflow that directly adds total enzyme amount constraints without modifying the stoichiometric matrix structure [30]. This approach has incorporated machine learning-based kcat prediction tools like TurNuP to address limited availability of measured enzyme kinetic parameters, particularly for non-model organisms [16].

Core Conceptual Framework

The fundamental principle shared across enzyme-constrained modeling approaches is that flux through each enzyme-catalyzed reaction (vi) is limited by the product of the enzyme concentration (gi) and its turnover number (kcat_i):

[vi \leq kcati \times g_i]

Additionally, the total cellular resources allocated to metabolic enzymes are constrained by an upper limit (P), representing the total enzyme mass per gram dry cell weight:

[\sum gi \times MWi \leq P]

These core constraints can be combined into a single inequality that doesn't require explicit enzyme concentration variables:

[\sum \frac{vi \times MWi}{kcat_i} \leq P]

This formulation accounts for the enzyme cost of each reaction, effectively constraining the solution space of possible metabolic fluxes [3] [30].

Figure 1: General workflow for constructing enzyme-constrained metabolic models, integrating stoichiometric models with enzyme kinetic and omics data through specialized computational frameworks.

Metabolic Engineering Applications

Industrial Strain Optimization

Enzyme-constrained models have demonstrated significant value in metabolic engineering for identifying optimal genetic modifications to enhance production of valuable chemicals. Several case studies across different industrially relevant microorganisms highlight the practical benefits of ecGEMs over traditional stoichiometric models.

Table 2: Metabolic Engineering Applications of Enzyme-Constrained Models

Organism	Model	Target Product	Engineering Strategy	Key Results
Clostridium ljungdahlii [46]	ec_iHN637	Acetate, Ethanol	OptKnock knockouts under syngas/mixotrophic conditions	Identified non-redundant knockouts for different products; Improved CO2 fixation
Myceliophthora thermophila [16]	ecMTM	Fumarate, Succinate, Malate	Enzyme cost-based target prediction	New engineering targets identified; Substrate hierarchy utilization explained
Corynebacterium glutamicum [47]	ecCGL1	L-lysine	Gene modification targets based on enzyme limitations	Identified known and new targets for L-lysine overproduction
Escherichia coli [3] [30]	eciML1515	Succinate, Ethanol	Knockout strategies considering enzyme costs	Changed spectrum of engineering strategies vs. standard GEM

In Clostridium ljungdahlii, an acetogenic bacterium capable of converting synthesis gas (CO/CO2/H2) to valuable chemicals, the enzyme-constrained model ec_iHN637 showed improved prediction accuracy for growth rates and product profiles compared to the original metabolic model iHN637 [46]. The model was used with the OptKnock computational framework to identify gene knockouts that enhance production of acetate and ethanol under both syngas fermentation and mixotrophic conditions [46]. Notably, the model predicted different engineering strategies for different feeding conditions and suggested that mixotrophic growth could couple improved cell growth and productivity with net CO2 fixation [46].

For Myceliophthora thermophila, a thermophilic fungus with applications in biomass conversion, construction of ecMTM using machine learning-predicted kcat values demonstrated superior performance in predicting metabolic engineering targets compared to the non-constrained model [16]. The enzyme-constrained model accurately captured the hierarchical utilization of five carbon sources derived from plant biomass hydrolysis and identified new potential targets for chemical production based on enzyme cost considerations [16].

The enzyme-constrained model for Corynebacterium glutamicum (ecCGL1), constructed using the ECMpy workflow, improved predictions of metabolic phenotypes and identified gene modification targets for L-lysine production [47]. Most predicted targets aligned with previously reported genes, validating the approach, while also suggesting new potential modifications [47].

Protocol: Building an Enzyme-Constrained Model with ECMpy

Objective: Construct an enzyme-constrained metabolic model for a target organism using ECMpy workflow.

Materials:

• Genome-scale metabolic model in SBML format
• Python environment with ECMpy installed
• BRENDA and SABIO-RK database access
• Organism-specific proteomics data (optional)

Procedure:

• Model Preparation:

  • Convert reversible reactions to irreversible representations to accommodate direction-specific kcat values
  • Verify gene-protein-reaction (GPR) rules and correct subunit composition information
  • Annotate model enzymes with UniProt identifiers for kinetic data mapping

• Kinetic Data Collection:

  • Retrieve kcat values from BRENDA and SABIO-RK databases using automated queries
  • Apply machine learning-based kcat prediction (TurNuP) for missing values
  • Manually curate kcat values for central metabolic reactions based on literature

• Molecular Weight Determination:

  • Obtain protein molecular weights from UniProt
  • Correct for multimeric enzyme complexes using subunit composition data
  • Account for stoichiometry of subunits in heteromeric complexes

• Model Constraint Integration:

  • Calculate enzyme mass fraction from proteomics data or literature values
  • Add enzyme capacity constraint using the ECMpy get_enzyme_constraint_model function
  • Store constraint information in JSON format with metabolic network

• Parameter Calibration:

  • Identify reactions with enzyme usage exceeding 1% of total enzyme content
  • Flag reactions where kcat × 10% of total enzyme amount is less than fluxes from 13C data
  • Adjust kcat values iteratively to improve agreement with experimental growth data

• Model Validation:

  • Compare predicted versus experimental growth rates on multiple carbon sources
  • Verify prediction of overflow metabolism phenomena
  • Test substrate co-utilization patterns against experimental observations

This protocol successfully constructed eciML1515 for E. coli, which demonstrated improved growth rate predictions on 24 single-carbon sources compared to the base model and correctly simulated overflow metabolism [30].

Figure 2: ECMpy workflow for constructing enzyme-constrained metabolic models, showing key steps from initial model preparation to final validated model.

Therapeutic Development Applications

Enzyme Engineering for Therapeutic Applications

Enzyme-constrained approaches have also proven valuable in therapeutic development, particularly in engineering improved enzymes for treating metabolic disorders. A notable application involves ornithine transcarbamylase (OTC) deficiency, a rare but serious metabolic disease caused by loss of OTC catalytic activity [49].

Traditional enzyme engineering approaches like rational design and directed evolution have limitations in exploring the vast sequence space of possible functional variants. Researchers applied deep learning-based generative modeling to engineer improved OTC enzymes with enhanced thermal stability and catalytic activity [49]. By training a variational autoencoder (VAE) on a large multi-sequence alignment of OTC homologs, the team generated novel OTC variants that maintained evolutionary correlations present in functional enzymes [49].

The majority of these AI-generated variants exhibited improved stability, specific activity, or both compared to wild-type human OTC [49]. Importantly, the deep learning-derived library outperformed a consensus library that didn't incorporate residue-residue correlations, demonstrating the value of capturing higher-order sequence relationships for enzyme engineering [49]. This approach has significant implications for mRNA therapeutics, where improved enzyme potency could enable lower and less frequent dosing regimens.

Protocol: Deep Learning-Enabled Therapeutic Enzyme Engineering

Objective: Engineer therapeutic enzyme variants with improved stability and catalytic activity using generative neural networks.

Materials:

• Multiple sequence alignment of target enzyme homologs
• Python with deep learning frameworks (TensorFlow/PyTorch)
• Protein expression and purification system
• Enzyme activity and stability assays

Procedure:

• Sequence Dataset Curation:

  • Perform BLAST search to identify homologs of the target therapeutic enzyme
  • Filter sequences to remove fragments and those causing excessive gaps in alignment
  • Create weighted training dataset favoring human-like sequences to reduce immunogenicity concerns

• Generative Model Training:

  • Implement variational autoencoder (VAE) architecture with encoder, stochastic sampling, and decoder components
  • Train model to reproduce input sequences from encoded latent representations
  • Validate model capture of site-wise conservation statistics and pairwise mutual information

• Sequence Generation and Selection:

  • Encode human wildtype enzyme and sample from its encoded distribution
  • Scale variance of distribution to control mutation load relative to human sequence
  • Select variants with 95-98% identity to human wildtype for experimental testing

• Experimental Validation:

  • Express and purify selected enzyme variants
  • Measure thermal stability using thermal shift assays or differential scanning calorimetry
  • Determine catalytic efficiency (kcat/Km) using enzyme-specific activity assays
  • Compare performance against wildtype enzyme and consensus-designed variants

This protocol generated 87 unique near-human OTC variants with an average of >98% identity to human wildtype, most showing improvements in stability, specific activity, or both [49].

Performance Comparison and Discussion

Quantitative Assessment of Prediction Accuracy

Enzyme-constrained models consistently demonstrate improved prediction accuracy compared to traditional stoichiometric models across multiple organisms and growth conditions.

Table 3: Performance Comparison of Enzyme-Constrained Models

Model	Organism	Validation	Performance Improvement	Reference
ec_iHN637 [46]	C. ljungdahlii	Growth rate & product profile	Improved prediction accuracy vs. iHN637	[46]
ecMTM [16]	M. thermophila	Substrate utilization hierarchy	Accurate capture of carbon source preference	[16]
eciML1515 [30]	E. coli	Growth on 24 carbon sources	Reduced estimation error vs. iML1515	[30]
ecYeast7 [4]	S. cerevisiae	Crabtree effect prediction	Correct prediction of metabolic switch	[4]
ecCGL1 [47]	C. glutamicum	Overflow metabolism	Phenomena prediction without uptake constraints	[47]

For Escherichia coli, the enzyme-constrained model eciML1515 showed significantly improved growth rate predictions on 24 single-carbon sources compared to the base model iML1515 [30]. The model successfully simulated overflow metabolism and revealed that redox balance was the key factor differentiating E. coli and Saccharomyces cerevisiae overflow metabolism patterns [30].

The ecCGL1 model for Corynebacterium glutamicum improved prediction of cellular phenotypes and simulated overflow metabolism, which cannot be properly explained by models considering only reaction stoichiometries [47]. The model also recapitulated the trade-off between biomass yield and enzyme usage efficiency, a fundamental constraint in cellular metabolism [47].

Research Reagent Solutions

Table 4: Essential Research Reagents and Tools for Enzyme-Constrained Modeling

Reagent/Tool	Function	Application Context
BRENDA Database [3]	Comprehensive enzyme kinetic data repository	kcat value retrieval for model parameterization
SABIO-RK [3]	Biochemical reaction kinetic database	Kinetic parameter collection for metabolic reactions
UniProt [47]	Protein sequence and functional information	Molecular weight data and subunit composition
TurNuP [16]	Machine learning kcat prediction	å¡«è¡¥Missing kinetic parameters for non-model organisms
COBRA Toolbox [50]	Constraint-based modeling and analysis	Metabolic network simulation and flux prediction
GECKO Toolbox [4]	ecGEM construction and simulation	Automated enzyme-constrained model development
ECMpy [30]	Python workflow for ecGEM construction	Simplified enzyme-constrained model building

Enzyme-constrained metabolic models represent a significant advancement over traditional stoichiometric models, providing more accurate predictions of cellular phenotypes by accounting for the fundamental limitations of enzyme kinetics and cellular protein allocation. The compared methodologies—GECKO, AutoPACMEN, and ECMpy—offer complementary approaches with different strengths in model complexity, parameter requirements, and implementation frameworks.

In metabolic engineering, ecGEMs have demonstrated value in identifying optimal strain engineering strategies for chemical production in industrially relevant microorganisms like C. ljungdahlii, M. thermophila, and C. glutamicum. In therapeutic development, the principles underlying enzyme-constrained approaches have enabled engineering of improved enzyme therapeutics for metabolic disorders through deep learning-driven sequence design.

As kinetic parameter databases expand and machine learning approaches for kcat prediction improve, enzyme-constrained models will become increasingly accurate and accessible for non-model organisms. These advancements will further enhance their utility in both metabolic engineering and therapeutic development, enabling more reliable prediction of metabolic behavior and more efficient design of microbial cell factories and enzyme therapeutics.

Solving Practical Challenges: Parameterization, Calibration, and Model Performance

In the field of constraint-based metabolic modeling, enzyme-constrained genome-scale metabolic models (ecGEMs) have emerged as a powerful framework for predicting cellular phenotypes, proteome allocation, and metabolic fluxes more accurately than traditional models. These models integrate enzyme turnover numbers (kcat values) to represent the catalytic capacity of enzymes, imposing biophysically realistic constraints on metabolic networks. However, a significant challenge in constructing ecGEMs is the limited coverage of experimentally measured kcat values in databases like BRENDA and SABIO-RK. This kcat coverage gap affects model completeness and predictive accuracy, necessitating methods to fill these data gaps. Two primary approaches have been developed: wildcard matching, as implemented in the GECKO toolbox, and deep learning prediction, exemplified by the DLKcat tool. This guide provides a detailed comparison of these methodologies, their experimental protocols, performance metrics, and implications for metabolic modeling research.

Understanding the kcat Coverage Problem

The reconstruction of high-quality enzyme-constrained metabolic models is fundamentally limited by the scarcity of reliable enzyme kinetic parameters. Experimental kcat data are sparse, noisy, and unevenly distributed across organisms and enzyme classes. In fact, for well-studied organisms like Saccharomyces cerevisiae, only about 5% of enzymatic reactions in a genome-scale model have fully matched kcat values in the BRENDA database [51]. This coverage problem is exacerbated for less-studied non-model organisms, where experimentally characterized enzymes are even rarer.

The biological implications of incomplete kcat data are substantial. ecGEMs rely on these parameters to accurately simulate metabolic behaviors, including overflow metabolism (e.g., the Crabtree effect in yeast or acetate secretion in E. coli), proteome allocation, and growth rates across different nutrient conditions. Without complete kcat coverage, models must rely on approximations that can compromise prediction accuracy and limit applications in metabolic engineering and synthetic biology. The kcat coverage gap thus represents a critical bottleneck in systems biology that both wildcard matching and deep learning approaches aim to address.

Wildcard Matching Methodology

Core Principles and Workflow

The wildcard matching approach, implemented in the GECKO toolbox, employs a hierarchical method to assign kcat values to reactions lacking organism-specific or enzyme-specific data. This methodology uses Enzyme Commission (EC) numbers as primary identifiers to query kinetic databases, with progressively relaxed matching criteria when exact matches are unavailable [4].

The GECKO workflow follows these hierarchical steps:

• Exact EC number matching from the target organism
• Exact EC number matching from any organism
• Wildcard EC number matching (e.g., using EC.1.1.1.- for an unknown specific enzyme in class 1.1.1)
• Similar substrate or reaction type matching when EC numbers are unavailable

This approach leverages the observation that kcat values for enzymes with similar functions or from related organisms often fall within comparable ranges, providing reasonable estimates for missing data points.

Implementation in GECKO

The GECKO toolbox automates this wildcard matching process through several key steps. First, it expands a conventional Genome-Scale Metabolic Model (GEM) to include enzyme usage reactions. Next, it queries the BRENDA database using the hierarchical matching criteria, with the flexibility to incorporate manual curation for critical enzymes [43]. The resulting enzyme-constrained model (ecModel) includes additional constraints that ensure metabolic fluxes do not exceed the maximum catalytic capacity determined by enzyme abundance and kcat values.

A key feature of GECKO is its ability to integrate experimental proteomics data when available, using measured enzyme concentrations to further constrain flux predictions. For enzymes without experimental data, GECKO can apply a total enzyme pool constraint, similar to earlier methods like FBA with Molecular Crowding (FBAwMC) [3] [43].

Deep Learning Prediction Methodology

Core Principles and Workflow

The deep learning approach represents a paradigm shift in kcat prediction, moving away from database matching toward computational prediction based on molecular features. DLKcat, a recently developed tool, predicts kcat values using only substrate structures and protein sequences as inputs, requiring no prior experimental measurements for the specific enzyme [51].

The DLKcat framework combines two neural network architectures:

• A Graph Neural Network (GNN) processes substrate structures represented as molecular graphs converted from SMILES strings
• A Convolutional Neural Network (CNN) processes protein sequences split into overlapping n-gram amino acids

These networks learn the complex relationships between enzyme sequences, substrate structures, and catalytic efficiency from the available training data, enabling prediction of kcat values for any enzyme-substrate pair.

Model Training and Validation

DLKcat was trained on a comprehensive dataset of 16,838 unique enzyme-substrate pairs from BRENDA and SABIO-RK databases, encompassing 7,822 unique protein sequences from 851 organisms and 2,672 unique substrates [51]. The model demonstrated strong predictive performance with a root mean square error (RMSE) of 1.06 for kcat values (on a log scale), meaning predicted values typically fall within one order of magnitude of experimental measurements. The correlation between predicted and experimental values was high (Pearson's r = 0.88 for the full dataset) [51].

Notably, DLKcat can capture subtle aspects of enzyme function, including enzyme promiscuity (differentiating between preferred and alternative substrates) and the effects of amino acid substitutions on catalytic efficiency. The model also incorporates an attention mechanism that identifies amino acid residues with strong impacts on kcat values, providing interpretable insights into sequence-function relationships [51].

Performance Comparison

Table 1: Comparison of Key Performance Metrics Between Wildcard Matching and Deep Learning Approaches

Performance Metric	Wildcard Matching (GECKO)	Deep Learning (DLKcat)
kcat Coverage	~5-50% (organism-dependent) [51]	Potentially 100% (any enzyme with sequence data)
Prediction Accuracy	Varies by matching level; manual curation often needed for key enzymes	RMSE = 1.06; Pearson's r = 0.88 [51]
Organism Scope	Limited to enzymes with EC numbers in databases	Broad applicability to any organism with sequence data
Handling Enzyme Variants	Limited to existing natural variants in databases	Can predict effects of mutations and engineered enzymes
Experimental Validation	Successful prediction of metabolic switches in yeast/E. coli [43]	Improved phenotype and proteome predictions across 343 yeast species [51]
Automation Level	Semi-automated with manual curation	Fully automated pipeline

Table 2: Practical Implementation Considerations for Research Applications

Consideration	Wildcard Matching	Deep Learning
Data Requirements	Existing GEM with gene associations	GEM plus protein sequences and substrate structures
Computational Resources	Moderate	Significant for training; moderate for prediction
Integration with ecGEM Tools	Directly in GECKO toolbox	Available in GECKO 3.0 and standalone
Handling of Atypical Enzymes	Limited to characterized enzyme classes	Potentially broader applicability
Interpretability	Clear provenance from database matches	"Black box" with some attention mechanism insights
Update Frequency	Dependent on database releases	Improves as training data expands

Experimental Protocols

Protocol for Wildcard Matching with GECKO

The standard protocol for implementing wildcard matching in GECKO involves these key steps [52] [24]:

• Model Preparation: Start with a high-quality genome-scale metabolic model in SBML format with gene-protein-reaction associations.

• Model Expansion: Use GECKO to expand the metabolic model to include enzyme usage reactions, creating the ecModel structure.

• kcat Assignment:

  • Query BRENDA database using hierarchical matching
  • Apply exact EC number matching first
  • Progress to wildcard matching for unresolved reactions
  • Incorporate manual curation for critical enzymes

• Parameter Tuning: Adjust total enzyme pool constraint to match experimental growth rates.

• Proteomics Integration (Optional): Incorporate experimental proteomics data as additional constraints.

• Model Simulation: Use flux balance analysis or related methods to simulate phenotypes.

This protocol typically requires approximately 5 hours for yeast models [52], though this varies by organism and model complexity.

Protocol for Deep Learning Prediction with DLKcat

The protocol for implementing deep learning-based kcat prediction includes [51]:

• Data Preparation:

  • Collect protein sequences for all enzymes in the metabolic model
  • Identify substrate structures for each metabolic reaction
  • Convert substrates to SMILES representations

• kcat Prediction:

  • Input protein sequences and substrate structures into DLKcat
  • Generate kcat predictions for all enzyme-substrate pairs
  • Resolve multiple isozyme or complex scenarios

• ecGEM Reconstruction:

  • Integrate predicted kcat values into enzyme constraints
  • Apply Bayesian pipeline for parameterization
  • Validate model with experimental growth data

• Model Analysis:

  • Simulate metabolic phenotypes
  • Compare predictions with experimental data
  • Identify key flux-limiting enzymes

This approach has been successfully applied to generate ecGEMs for 343 yeast species, demonstrating its scalability [51].

Research Toolkit

Table 3: Essential Research Tools and Resources for Implementing kcat Assignment Methods

Tool/Resource	Function	Availability
GECKO Toolbox	ecModel reconstruction with wildcard matching	MATLAB-based, open-source [4]
DLKcat	Deep learning prediction of kcat values	Python-based, available on GitHub [51]
BRENDA Database	Repository of experimental enzyme kinetics	Public database with web API [4]
SABIO-RK	Kinetic parameter database	Public database [3]
AutoPACMEN	Automated construction of enzyme-constrained models	Toolbox for sMOMENT models [3]
ECMpy	Simplified workflow for ecGEM construction	Python-based package [15]
COBRA Toolbox	Constraint-based modeling and analysis	MATLAB-based, open-source [43]
Cythioate	Cythioate	Cythioate analytical standard for research. An organophosphate used in veterinary flea control studies. For Research Use Only. Not for human or veterinary use.
DA-E 5090	DA-E 5090, CAS:131420-84-3, MF:C17H18O4, MW:286.32 g/mol	Chemical Reagent

Workflow Visualization

Wildcard Matching Workflow

Wildcard Matching Methodology for kcat Assignment

Deep Learning Prediction Workflow

Deep Learning Approach for kcat Prediction

The comparison between wildcard matching and deep learning approaches for addressing the kcat coverage gap reveals complementary strengths and limitations. Wildcard matching, as implemented in GECKO, provides a practical, database-driven approach that benefits from existing experimental data and allows manual curation, but suffers from limited coverage and organism-specific biases. Deep learning prediction with DLKcat offers dramatically expanded coverage and the ability to predict kcat values for any enzyme with sequence data, including engineered variants, though with potential "black box" limitations and computational resource requirements.

The field is increasingly moving toward hybrid approaches, as evidenced by the integration of DLKcat predictions into GECKO 3.0 [52]. This combined methodology leverages the strengths of both approaches: the experimental grounding of database mining and the comprehensive coverage of deep learning. For researchers, the choice between methods depends on specific application requirements, with wildcard matching suitable for well-characterized model organisms and deep learning preferred for non-model organisms or studies requiring complete kcat coverage.

As ecGEMs continue to advance applications in metabolic engineering, biotechnology, and biomedical research, resolving the kcat coverage gap remains essential. Both wildcard matching and deep learning approaches represent valuable tools in the systems biology toolkit, contributing to more accurate, predictive models of cellular metabolism.

The accurate parameterization of enzymatic constraint models is pivotal for enhancing the predictive power of genome-scale metabolic simulations. This guide compares state-of-the-art calibration methodologies, with a specific focus on the emerging use of Flux Control Coefficients (FCCs) for systematic parameter tuning. We objectively evaluate the performance of this technique against established alternatives, such as the GECKO toolbox, by examining key metrics including calibration efficiency, prediction accuracy for experimental growth rates, and quantitative agreement with carbon-13 flux data and enzyme abundance measurements. Supporting experimental data are summarized to provide researchers and drug development professionals with a clear comparison for selecting appropriate calibration frameworks for their specific applications.

The integration of enzymatic constraints into genome-scale metabolic models (GEMs) has marked a significant evolution in constraint-based modeling, enabling more accurate predictions of metabolic phenotypes by accounting for limited enzyme capacity and catalytic efficiency. Methods such as the GECKO toolbox facilitate this enhancement by incorporating enzyme turnover numbers ((k{cat})) and imposing constraints on total enzyme pool capacity [4]. However, a major bottleneck persists: the in-vivo (k{cat}) data required for parameterization are notoriously scarce and costly to obtain, leading to initial models that often rely on incomplete or approximate parameters [23] [4]. This parameter uncertainty fundamentally limits model accuracy, making subsequent calibration—the process of tuning model parameters to align with experimental data—a critical step.

Traditional calibration methods often involve laborious, large-scale optimization that requires adjusting dozens or even hundreds of parameters simultaneously, a process that is computationally intensive and can lack a clear biological rationale [23]. Within this context, Flux Control Coefficients (FCCs) have emerged as a powerful, theoretically grounded tool for guiding efficient parameter tuning. FCCs, a core concept in Metabolic Control Analysis (MCA), quantitatively describe the sensitivity of a system's flux to small changes in the activity of an enzyme or a group of enzymes [53]. Formally, the flux control coefficient of enzyme (i) over flux (J) is defined as: [ C^J{Ei} = \frac{dJ}{dEi} \frac{Ei}{J} ] This metric identifies which enzymatic parameters exert the most significant influence on network fluxes, thereby providing a systematic means to prioritize parameters for calibration.

Comparative Analysis of Calibration Techniques

This section objectively compares the performance of the novel FCC-based calibration method against existing state-of-the-art alternatives. The evaluation is based on key metrics critical for model reliability in both academic research and industrial applications, such as drug target identification and metabolic engineering.

Table 1: Comparison of Key Calibration Performance Metrics

Calibration Method	Number of Parameters Requiring Calibration	Prediction of Experimental Growth Rates	Agreement with C-13 Flux Data	Prediction of Enzyme Abundances
FCC-Guided Calibration [23]	8 key (k_{cat}) values	Matches or outperforms state-of-the-art	Matches or outperforms state-of-the-art	Matches or outperforms state-of-the-art
State-of-the-art (Prior to FCC)	Not specified (Significantly higher)	Baseline performance	Baseline performance	Baseline performance
GECKO 2.0 Framework [4]	Not explicitly specified	Improved predictions across organisms	N/A	Enabled integration of proteomics data

The experimental data supporting this comparison is derived from the construction of enzyme-constrained models for Escherichia coli using a multi-modal transformer to predict (k_{cat}) values. Prior to any calibration, models built with this approach matched the performance of existing methods. The pivotal test involved a subsequent calibration step using FCCs [23].

The key differentiator for the FCC-based method is its calibration efficiency. By calculating FCCs—which were shown to be identical to the enzyme cost at the FBA optimum—researchers could identify just 8 key (k_{cat}) values whose recalibration was necessary to achieve superior performance. This represents an 81% reduction in the number of parameters requiring adjustment compared to the previous state-of-the-art method used as a benchmark [23]. This drastic reduction in parameter space streamlines the calibration process and enhances its biological interpretability by focusing on the enzymes that truly control systemic flux.

Experimental Protocols and Methodologies

A clear understanding of the experimental and computational workflows is essential for the practical application of these techniques. Below, we detail the core protocols for the featured FCC-based calibration and the alternative GECKO approach.

Detailed Protocol: FCC-Guided (k_{cat}) Calibration

This protocol outlines the specific steps for calibrating an enzyme-constrained model using Flux Control Coefficients, as pioneered by Schooneveld et al. [23].

• Initial Model Construction: Begin by building an enzyme-constrained genome-scale metabolic model (ecGEM). Utilize a computational method, such as a protein-chemical transformer, to predict (k_{cat}) values for all enzymatic reactions based on enzyme amino acid sequences and reaction substrate SMILES annotations. This provides the initial parameter set [23].
• Flux Control Coefficient Calculation: At the optimal solution of the flux balance analysis (FBA) problem, calculate the Flux Control Coefficients for each enzyme (k{cat}). The FCC is defined as the derivative of the log flux with respect to the log (k{cat}) ((C = d \log J / d \log k_{cat})). The study establishes that this coefficient is mathematically identical to the enzyme cost at the FBA optimum, providing a direct link between control theory and resource allocation [23].
• Identification of Key Parameters: Rank the enzymes based on the magnitude of their calculated FCCs. Select the top enzymes with the highest FCCs, as these represent the "flux checkpoints" whose catalytic efficiency most significantly controls the overall network function. In the benchmark study, this step identified 8 key enzymes [23].
• Targeted Recalibration: Recalibrate only the (k_{cat}) values of the identified key enzymes using available experimental data (e.g., measured growth rates, flux data). This involves adjusting these select parameters within biologically plausible ranges to improve the model's fit to the experimental observations.
• Model Validation: Validate the final, calibrated model by testing its predictions against a separate set of experimental data not used in the calibration, such as experimental growth rates, Carbon-13 fluxes, and enzyme abundances [23].

The following workflow diagram illustrates this process:

Established Protocol: GECKO 2.0 Model Enhancement

For comparison, the GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) toolbox provides an automated, widely adopted framework for building enzyme-constrained models [4].

• Database Query and kcat Assignment: Automatically retrieve kinetic parameters from databases like BRENDA. The toolbox employs a hierarchical matching strategy to assign (k_{cat}) values, prioritizing organism-specific data, then data from other organisms, and finally using non-specific wildcards to fill gaps [4].
• Model Expansion: Enhance the base stoichiometric model by adding pseudo-reactions and pseudo-metabolites that represent enzyme usage. This explicitly links each metabolic reaction to its catalyzing enzyme [4].
• Proteomic Constraints: Impose a global constraint on the total protein pool available for metabolic enzymes. Optionally, integrate quantitative proteomics data to apply upper bounds to the concentrations of individual, measured enzymes [4].
• Simulation and Analysis: Use the resulting enzyme-constrained model for simulation with standard constraint-based methods. The model can predict growth rates, flux distributions, and protein allocation patterns [4].

The Scientist's Toolkit: Essential Research Reagents and Solutions

Success in constructing and calibrating enzymatic constraint models relies on a suite of computational tools and data resources. The following table details key components of the modern researcher's toolkit in this field.

Table 2: Key Research Reagents and Computational Tools

Item Name	Type	Primary Function in Research
BRENDA Database [4]	Kinetic Database	Primary source for manually curated enzyme kinetic data, including (k_{cat}) values.
GECKO Toolbox [4]	Software Toolbox	Automated reconstruction of enzyme-constrained GEMs from standard GEMs; integrates kinetic and proteomic data.
CORAL Toolbox [6]	Software Toolbox	Extends protein-constrained models to account for enzyme promiscuity and underground metabolism by splitting enzyme pools.
Flux Control Coefficient (FCC) [23] [53]	Theoretical & Analytical Metric	Identifies and ranks enzymes with the greatest control over network flux for targeted parameter calibration.
Protein-Chemical Transformer [23]	Machine Learning Model	Predicts missing (k_{cat}) values using enzyme amino acid sequences and substrate information.
DifferentiableMetabolism.jl [54]	Software Library	Enables fast, implicit differentiation and sensitivity analysis of optimal solutions in constraint-based models.

Discussion and Comparative Outlook

The integration of enzymatic constraints is not a monolithic approach, but rather a spectrum of methodologies. The following diagram situates the discussed FCC calibration method within the broader ecosystem of advanced constraint-based modeling techniques.

As illustrated, FCC-guided calibration serves as a powerful refinement layer on top of existing enzyme-constrained models. Its primary advantage lies in addressing the parameter uncertainty problem with high efficiency and biological insight. While frameworks like GECKO 2.0 excel at the automated, large-scale integration of enzymatic constraints [4], and tools like CORAL push the resolution further by accounting for enzyme promiscuity [6], the FCC method answers the critical subsequent question: "Which parameters should I tune first to improve my model?"

The experimental evidence indicates that for researchers seeking the most efficient path to a highly accurate model with minimal manual parameter adjustment, the FCC-based approach currently offers a superior strategy. It transforms calibration from a "black-box" optimization of dozens of parameters into a principled process focused on biologically significant control points. Future developments are likely to tightly couple automated model construction with integrated sensitivity analysis, making advanced, calibrated models accessible to a broader range of scientists in basic research, metabolic engineering, and drug development.

Enzyme-constrained metabolic models (ecModels) represent a significant advancement in constraint-based metabolic modeling by explicitly incorporating enzymatic constraints using kinetic parameters and proteomic limitations. These models extend traditional genome-scale metabolic models (GEMs) by adding constraints that account for the limited cellular capacity for enzyme expression and the catalytic efficiency of enzymes [4] [3]. The core principle involves quantifying the enzyme mass required to support a specific metabolic flux, based on the relationship between enzyme concentration (g/gDW), molecular weight (g/mmol), and turnover number (kcat, 1/h) [3]. This approach effectively links metabolic fluxes to proteomic allocation, enabling more accurate predictions of cellular phenotypes under various genetic and environmental conditions [4] [6].

The fundamental transformation from a standard GEM to an ecModel involves adding constraints that represent enzyme usage demands, typically implemented through the addition of pseudo-reactions and metabolites that track enzyme utilization [4] [3]. This implementation can follow different mathematical frameworks, including the GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) approach [4] or the sMOMENT (short MOMENT) method [3], with the latter offering a more compact representation by directly incorporating enzyme constraints into the stoichiometric matrix without significantly expanding model size.

Table 1: Core Components of Enzyme-Constrained Models

Component	Description	Role in ecModels
Stoichiometric Matrix (S)	Matrix representation of metabolic reaction networks	Forms the foundation of both GEMs and ecModels [32]
Turnover Numbers (kcat)	Enzyme catalytic constants	Determine flux capacity per enzyme molecule [4] [3]
Enzyme Pool Constraints	Limits on total enzyme mass	Represent cellular proteomic limitations [4] [3]
Molecular Weights (MW)	Mass of enzyme proteins	Convert between molar and mass constraints [3]
Gene-Protein-Reaction (GPR)	Relationships linking genes to enzymes to reactions	Connect genomic information to enzymatic capabilities [16]

Defining Full and Light ecModels

Full-Scale ecModels

Full-scale ecModels represent comprehensive implementations that incorporate enzyme constraints across entire genome-scale metabolic networks. These models typically expand significantly upon their parent GEMs by adding numerous new metabolites and reactions to explicitly represent enzyme usage [4] [6]. For example, the ecYeast model constructed using GECKO methodology added substantial complexity to the original Yeast7 model to account for enzymatic limitations [4]. Similarly, when constructing an ecModel for E. coli iML1515 that included underground metabolism, the resulting model contained 8,331 reactions and 3,774 metabolites – a substantial expansion from the original GEM's 2,712 reactions and 1,877 metabolites [6]. This expansion directly translates to increased computational demands during simulation and analysis.

The key characteristic of full ecModels is their comprehensive coverage of enzymatic constraints across the entire metabolic network, making them particularly valuable for discovering non-obvious engineering targets or understanding system-level metabolic adaptations [4] [6]. However, this comprehensiveness comes at the cost of computational complexity, with simulations requiring more memory and processing time, and some advanced analyses becoming computationally prohibitive for large-scale models [55].

Light ecModels

Light ecModels represent streamlined approaches that focus enzymatic constraints on central metabolic pathways or utilize simplified mathematical formulations to reduce computational burden. These models maintain the core benefits of enzyme constraints while improving computational tractability [3] [55]. The iCH360 model of E. coli core and biosynthetic metabolism exemplifies this approach – it is a manually curated "Goldilocks-sized" model containing 323 metabolic reactions mapped to 360 genes, derived from the comprehensive iML1515 reconstruction which contains 2,712 reactions and 1,515 genes [55].

Another approach to creating light ecModels involves mathematical simplification rather than network reduction. The sMOMENT method achieves this by reformulating enzyme constraints to be directly incorporated into the stoichiometric matrix without adding numerous new variables [3]. This method yields equivalent predictions to the original MOMENT approach but requires significantly fewer variables and enables the use of standard constraint-based modeling tools [3]. Light ecModels sacrifice some network comprehensiveness for improved computational performance, making them suitable for applications requiring rapid iteration or complex analyses like metabolic engineering design or extensive sampling procedures [55].

Comparative Analysis: Performance and Applications

Computational Demand Comparison

The computational differences between light and full ecModels span multiple dimensions, including memory usage, simulation time, and analytical feasibility. Full ecModels, with their expanded reaction and metabolite sets, require significantly more memory to store and manipulate the stoichiometric matrices [6]. For instance, the CORAL toolbox application to E. coli iML1515 demonstrated how incorporating enzyme promiscuity and underground metabolism dramatically increased model size from 3,774 metabolites and 8,331 reactions in the standard ecModel to 12,048 metabolites and 16,605 reactions in the restructured version [6]. This expansion directly impacts computational performance, particularly for memory-intensive analyses.

Table 2: Computational Performance Comparison

Analysis Type	Full ecModel Performance	Light ecModel Performance	Key Factors
Flux Balance Analysis	Moderate speed, high memory use [6]	Fast execution, lower memory use [55]	Model size, solver efficiency
Flux Variability Analysis	Computationally intensive [6]	More feasible [55]	Number of reactions/variables
Pathway Analysis	Challenging for full network [55]	More tractable [55]	Network complexity
Sampling Methods	High-dimensional space [32]	Reduced dimensions [55]	Solution space size
Strain Design Algorithms	May identify non-physiological bypasses [55]	More reliable predictions [55]	Network comprehensiveness

Simulation time represents another critical differentiator. Methods that require iterative solving or multiple optimizations, such as flux variability analysis or sampling of flux distributions, become progressively more time-consuming as model size increases [32] [55]. For the iCH360 light model, such analyses remain computationally feasible, whereas they can become prohibitive for genome-scale ecModels [55]. This difference enables more rapid prototyping and testing of hypotheses when using light ecModels.

Predictive Performance

While computational efficiency favors light ecModels, predictive accuracy must be evaluated across different biological contexts. Both approaches demonstrate improved prediction of physiological behaviors compared to standard GEMs, particularly for overflow metabolism and substrate utilization patterns [4] [3] [16]. For example, enzyme-constrained models successfully predict the Crabtree effect in yeast and aerobic acetate secretion in E. coli – phenomena that standard GEMs often fail to capture without arbitrary flux constraints [4] [3].

The key difference emerges in the scope and context of predictions. Full ecModels potentially offer more comprehensive predictions, particularly for non-central metabolism or when non-obvious bypasses become relevant [6]. However, light ecModels based on well-curated central metabolism can provide excellent predictions for core physiological behaviors with greater computational efficiency [55]. For instance, the compact iCH360 model maintained accurate predictions for central carbon metabolism while offering advantages in interpretability and analysis feasibility [55].

Application-Specific Considerations

The choice between light and full ecModels should be guided by the specific research question and analytical requirements. Full ecModels are particularly valuable when studying system-wide metabolic adaptations, investigating non-intuitive network bypasses, or when comprehensive proteomic allocation is the focus [4] [6]. For example, studying how underground metabolism provides robustness through promiscuous enzyme activities requires the comprehensive network coverage of full ecModels [6].

Light ecModels excel in scenarios requiring rapid iteration, extensive sampling, or complex analyses that become computationally prohibitive at genome-scale [3] [55]. Metabolic engineering applications often benefit from light ecModels, as they enable efficient testing of multiple strain designs and cultivation conditions [16] [55]. Educational uses and method development also favor light ecModels due to their manageability and interpretability [55].

Experimental Protocols and Methodologies

Protocol for Full ecModel Construction (GECKO Framework)

The GECKO framework provides a systematic protocol for constructing comprehensive enzyme-constrained models [4]. The process begins with model expansion, where a starting metabolic model is enhanced to include an ecModel structure through the addition of enzyme usage reactions and metabolites [4]. This expanded framework explicitly represents the protein demand for each enzymatic reaction, creating the foundation for enzymatic constraints.

The second critical step involves kcat integration, where enzyme turnover numbers are incorporated into the ecModel structure [4]. These kinetic parameters can be sourced from various databases including BRENDA and SABIO-RK, or predicted using machine learning approaches like DLKcat or TurNuP when experimental data is limited [4] [16]. The parameterization process often employs hierarchical matching criteria to maximize coverage across the metabolic network [4].

Model tuning follows parameter integration, adjusting the total enzyme pool constraint to match physiological observations [4]. This calibration typically uses reference growth data to ensure the model produces biologically realistic predictions. Finally, the framework allows for proteomics data integration, where experimentally measured enzyme abundances can be incorporated as additional constraints to further refine predictions [4]. This comprehensive protocol produces detailed ecModels capable of predicting proteome-limited phenotypes.

Protocol for Light ecModel Construction

Light ecModel construction follows alternative pathways, either through network reduction or mathematical simplification. The network reduction approach, exemplified by the iCH360 model, begins with selecting core metabolic pathways essential for energy production and biosynthesis of main biomass building blocks [55]. This curated subnetwork maintains key functionalities while eliminating peripheral pathways, creating a metabolically functional but computationally manageable model [55].

The mathematical simplification approach, as implemented in sMOMENT, takes a different path by reformulating how enzyme constraints are represented [3]. Rather than adding numerous new variables, sMOMENT incorporates enzyme mass constraints directly into the stoichiometric matrix through inequality constraints that limit the total enzyme mass expenditure [3]. This method significantly reduces variable count while maintaining equivalent predictions for enzyme-limited fluxes [3].

Both light ecModel approaches incorporate enzyme constraints using kinetic parameters, though typically with more focused parameterization on central metabolism [55]. The resulting models are compatible with standard constraint-based modeling tools and can simulate enzyme allocation strategies under various growth conditions [3] [55].

The Researcher's Toolkit

Essential Software and Databases

Table 3: Essential Research Tools for ecModel Construction and Analysis

Tool Name	Function	Applicability
GECKO Toolbox [4]	ecModel reconstruction and simulation	Full ecModels, multiple organisms
COBRA Toolbox [32]	Constraint-based modeling framework	Both model types, MATLAB environment
COBRApy [32]	Python package for constraint-based modeling	Both model types, open-source platform
AutoPACMEN [3]	Automated enzyme constraint integration	Both model types, high automation
ECMpy [16]	Automated ecModel construction	Both model types, Python environment
BRENDA Database [4] [3]	Enzyme kinetic parameters	kcat sourcing for both model types
SABIO-RK [3]	Enzyme kinetic parameters	kcat sourcing for both model types
TurNuP [16]	Machine learning kcat prediction	kcat prediction when data is limited
Escher [55]	Metabolic pathway visualization	Model visualization and interpretation

Selection Guidelines for Research Applications

Choosing between light and full ecModels requires careful consideration of research objectives, computational resources, and desired outcomes. Researchers should consider these key decision factors:

• Research Question Scope: For system-wide investigations of metabolic adaptation or comprehensive proteome allocation, full ecModels are preferable [4] [6]. For focused studies on central metabolism or specific pathways, light ecModels provide sufficient coverage with better performance [55].

• Computational Resources: Projects with limited computational capacity or requiring high-throughput analyses benefit from light ecModels [3] [55]. When resources permit and model comprehensiveness is prioritized, full ecModels are appropriate [4].

• Analytical Complexity: Studies employing methods like flux sampling, extensive parameter scanning, or complex strain design algorithms may require light ecModels for computational feasibility [32] [55]. Standard FBA and FVA can typically be performed with full ecModels [6].

• Data Availability: The construction of high-quality full ecModels typically requires extensive kinetic parameter data, which may be limited for non-model organisms [4] [16]. Light ecModels can be parameterized more readily with limited data [55].

• Validation Requirements: Well-curated light ecModels often produce more interpretable results that are easier to validate experimentally [55]. Full ecModels may capture more complex behaviors but can be challenging to validate comprehensively [6].

The field continues to evolve with emerging methods like machine learning-based kcat prediction [16] and tools for handling enzyme promiscuity [6] further enhancing both approaches. Researchers may also consider hybrid strategies, beginning with light ecModels for initial screening and progressing to full ecModels for promising candidates.

The integration of experimental proteomics data is revolutionizing constraint-based metabolic modeling. By incorporating protein abundance and enzyme kinetic data, researchers can transform traditional Genome-scale Metabolic Models (GEMs) into enhanced enzyme-constrained models (ecModels) that significantly improve predictive accuracy for a wide range of organisms, from microbes to human cells [4]. This integration addresses a fundamental limitation of classical flux balance analysis (FBA), which assumes optimal metabolic operation without accounting for the physical limitations imposed by enzyme capacity, protein availability, and cellular space [4]. Enzymatic constraints, derived from experimental proteomics, provide crucial boundaries on metabolic reaction rates, enabling more biologically realistic simulations of cellular metabolism under various genetic and environmental conditions [4] [56].

The value of this integration spans multiple domains of biotechnology and medicine. In metabolic engineering, ecModels facilitate the identification of optimal enzyme modulation strategies for enhanced biochemical production [4]. In drug discovery, integrated proteomic profiles help identify novel drug targets and understand disease mechanisms at the molecular level [57] [58]. Furthermore, the combination of spatial proteomics and transcriptomics on the same tissue sections enables unprecedented analysis of the tumor-immune microenvironment, advancing our understanding of disease heterogeneity and therapeutic response [59].

Enzymatic Constraint Modeling Frameworks

Core Frameworks and Tools

Table 1: Comparison of Major Enzymatic Constraint Modeling Frameworks

Framework/Tool	Primary Function	Key Features	Supported Organisms	Input Requirements
GECKO 2.0 [4]	Enhancement of GEMs with enzymatic constraints	Automated parameter retrieval from BRENDA, proteomics integration, version-controlled model updates	S. cerevisiae, E. coli, H. sapiens, and others	GEM reconstruction, kcat values, proteomics data (optional)
NIDLE [56]	Estimation of apparent in vivo catalytic rates (kappmax)	Minimization of non-idle enzymes, handles isoenzyme decomposition, does not assume growth optimization	C. reinhardtii (applicable to others)	Quantitative proteomics, metabolic model, growth rates
Weave [59]	Multi-omics spatial integration	Co-registration of ST/SP/H&E data from same section, interactive visualization, cross-modal correlation	Human tissue samples (demonstrated on lung cancer)	Spatial transcriptomics, spatial proteomics, H&E images

Technical Implementation and Workflow

The process of integrating proteomics data into metabolic models follows a structured workflow with distinct computational and experimental phases. The GECKO 2.0 framework implements a systematic approach to enhance existing GEMs through the addition of enzyme constraints [4]. This begins with the formulation of enzyme usage pseudo-reactions that represent the consumption of enzyme capacity for each metabolic reaction. The framework then incorporates kinetic parameters, primarily enzyme turnover numbers (kcat), which can be obtained from databases like BRENDA or estimated from experimental proteomics data [4]. The resulting ecModels explicitly account for enzyme limitations, enabling more accurate predictions of metabolic behavior under resource-limited conditions.

For organisms with sparse kinetic characterization, the NIDLE approach provides an alternative method for estimating in vivo catalytic rates [56]. This method minimizes the number of "idle enzymes" - those with measured abundance but minimal metabolic flux - across multiple growth conditions. By analyzing the relationship between enzyme abundance and reaction flux, NIDLE calculates apparent in vivo turnover rates (kappmax) that reflect the maximal observed catalytic efficiency for each enzyme under the studied conditions [56]. This approach has demonstrated particular value for non-model organisms like Chlamydomonas reinhardtii, where traditional kinetic parameters are largely unavailable.

Figure 1: Workflow for integrating proteomics data into metabolic models

Experimental Protocols for Proteomics Data Generation

Mass Spectrometry-Based Proteomics

Mass spectrometry (MS) has emerged as the cornerstone technology for generating quantitative proteomics data suitable for integration with metabolic models [58]. The typical workflow begins with protein extraction from biological samples under defined growth conditions, followed by enzymatic digestion (usually with trypsin) to generate peptides. These peptides are then separated using liquid chromatography (LC) and introduced into the mass spectrometer for analysis [56] [58]. For absolute quantification required by enzymatic constraint models, the QConCAT method employs isotopically labeled artificial proteins containing concatenated peptides of multiple endogenous proteins as external standards, enabling precise measurement of protein abundance across different conditions [56].

Critical considerations for MS-based proteomics include achieving sufficient coverage of the metabolic proteome and ensuring quantitative accuracy. In a recent study on Chlamydomonas reinhardtii, researchers quantified 936 of the 1,460 enzymes (64%) included in the iCre1355 metabolic model, with a median of 3,376 proteins quantified across 27 sample conditions [56]. This comprehensive coverage enabled the calculation of apparent catalytic rates for 568 enzymatic reactions, representing a 10-fold increase over previously available in vitro data for this organism [56].

Spatial Proteomics Technologies

For tissue-level metabolic modeling, spatial proteomics technologies provide crucial context by preserving the spatial distribution of protein expression. The COMET platform (Lunaphore Technologies) enables hyperplex immunohistochemistry (hIHC) for spatial profiling of up to 40 protein markers simultaneously on the same tissue section [59]. This technology employs cyclical staining, imaging, and elution to generate a stacked fluorescence image with multiple channels. When combined with spatial transcriptomics on the same section, this approach enables direct correlation of RNA and protein expression at cellular resolution, revealing insights into post-transcriptional regulation and microenvironment-specific metabolism [59].

Table 2: Experimental Methods for Proteomics Data Generation

Method	Principle	Quantification Type	Throughput	Spatial Context	Key Applications
LC-MS/MS with QConCAT [56]	Mass spectrometry with isotopically labeled standards	Absolute quantification	Medium to High	No	Genome-scale kappmax estimation for ecModels
COMET hIHC [59]	Sequential immunofluorescence cycling	Relative protein abundance	Medium	Yes (cellular/subcellular)	Tissue microenvironment studies, tumor heterogeneity
Protein Microarrays [58]	Array-based protein binding	Relative abundance	High	No	High-throughput screening, biomarker discovery
2D Gel Electrophoresis [58]	Separation by size and charge	Relative abundance	Low	No	Basic protein profiling, post-translational modifications

Multi-Omics Integration Strategies

Computational Integration Approaches

The integration of proteomics with other omics data types requires sophisticated computational methods to address challenges of data heterogeneity, normalization, and biological interpretation [60] [61]. Similarity Network Fusion represents one approach that constructs networks for each data type separately then combines them to identify consensus patterns [62]. Multiple-Omics Factor Analysis implements a statistical framework for unsupervised integration that disentangles shared and specific sources of variation across omics layers [62]. For supervised integration, sparse canonical correlation analysis and regularized multivariate regression identify relationships between different omics datasets while handling high-dimensionality [62].

In spatially resolved omics, tools like Weave employ automated non-rigid registration algorithms to align spatial transcriptomics, proteomics, and histology data from the same tissue section [59]. This co-registration enables direct cell-to-cell comparison of RNA and protein expression, revealing systematic differences between transcript and protein levels that reflect post-transcriptional regulation [59]. Such integrated analysis has demonstrated particular value for characterizing the tumor-immune microenvironment in human lung cancer samples with distinct immunotherapy outcomes [59].

Figure 2: Multi-omics data integration workflow

Data Processing and Quality Control

Effective integration of proteomics data requires rigorous quality control and preprocessing steps. For mass spectrometry-based proteomics, this includes background subtraction, normalization to internal standards, and imputation of missing values using appropriate statistical methods [56] [60]. Platforms like Polly offer automated quality checks with approximately 50 QA/QC checks to ensure data completeness and reliability before integration [60]. For spatial proteomics, image processing pipelines perform background subtraction and cell segmentation using nuclear (DAPI) and membrane markers (PanCK) to define cellular boundaries for protein quantification [59].

A critical challenge in proteomics integration is the frequent low correlation observed between mRNA and protein levels, which complicates direct translation of transcriptomic data to protein abundance [59] [61]. Studies performing integrated spatial transcriptomics and proteomics on the same tissue sections have systematically observed these discrepancies, highlighting the importance of direct protein measurement rather than inference from RNA data [59]. This underscores the essential role of experimental proteomics in generating accurate constraints for metabolic models.

Research Reagent Solutions

Table 3: Essential Research Reagents and Platforms for Proteomics Integration

Reagent/Platform	Vendor/Developer	Primary Function	Key Specifications	Application in Proteomics Integration
Xenium In Situ [59]	10x Genomics	Spatial transcriptomics	289-gene panel, single-cell resolution	Co-analysis with spatial proteomics on same section
COMET [59]	Lunaphore Technologies	Spatial proteomics	40 protein markers, sequential immunofluorescence	Tumor microenvironment characterization, cell typing
QConCAT Standards [56]	Custom synthesis	Absolute protein quantification	Isotopically labeled concatenated peptides	Calibration for mass spectrometry-based proteomics
GECKO Toolbox [4]	SysBioChalmers	Enzyme constraint modeling	MATLAB-based, BRENDA database integration	ecModel construction from proteomics data
Weave [59]	Aspect Analytics	Multi-omics spatial integration	Web-based visualization, non-rigid registration	Interactive exploration of integrated ST/SP data
Polly [60]	Elucidata	Data harmonization	30+ metadata fields, quality checks	Preprocessing and normalization of omics data

Applications and Case Studies

Microbial Metabolic Engineering

The integration of proteomics data has demonstrated significant value in metabolic engineering of microbial cell factories. In Saccharomyces cerevisiae, the ecYeast model enhanced with enzymatic constraints successfully predicted the Crabtree effect and cellular growth across diverse environments [4]. Similarly, enzyme-constrained models of Yarrowia lipolytica and Kluyveromyces marxianus provided insights into long-term adaptation to stress factors, revealing that upregulation and high saturation of enzymes in amino acid metabolism represent a common adaptive strategy across organisms [4]. These findings suggest that metabolic robustness, rather than optimal protein utilization, may be the dominant cellular objective under nutrient-limited conditions.

Biomedical and Clinical Applications

In biomedical research, integrated proteomics has enabled significant advances in understanding disease mechanisms and identifying therapeutic targets. Spatial multi-omics analysis of human lung carcinoma samples with distinct immunotherapy outcomes (progressive disease versus partial response) revealed how combined transcriptomic and proteomic signatures can identify key differences in the tumor-immune microenvironment [59]. In Alzheimer's disease research, proteomic profiling of brain tissue identified proteins associated with amyloid plaque formation, contributing to diagnostic test development and novel therapeutic approaches [58].

For drug development, proteomics integration helps identify ideal drug target properties, including mechanistic involvement in disease, selective distribution in diseased tissues, and accessibility for drug molecules [63]. Comprehensive proteome analysis enables researchers to measure tissue distribution of potential protein targets, determine intracellular localization, and identify drug-protein interactions that might cause off-target effects [63]. These applications demonstrate how proteomics integration directly addresses the high failure rates in drug development by providing deeper insight into target biology before significant resources are invested.

Comparative Performance Analysis

Predictive Accuracy Across Modeling Frameworks

Table 4: Performance Comparison of Proteomics Integration Approaches

Framework	Predictive Accuracy	Coverage of Proteome	Handling of Isoenzymes	Ease of Implementation	Computational Demand
GECKO 2.0 [4]	High for model organisms	Database-dependent (BRENDA)	Comprehensive treatment	Moderate (requires MATLAB)	Medium
NIDLE [56]	High for organisms with proteomics data	Experimental data-dependent	Linear/quadratic decomposition	Challenging (MILP formulation)	High
pFBA-based kapp [56]	Moderate	Experimental data-dependent	Limited handling	Moderate	Medium
Spatial Integration (Weave) [59]	Context-dependent on spatial resolution	Targeted panels (40-300 markers)	Not specifically addressed	User-friendly interface	High (image processing)

Limitations and Technical Challenges

Despite significant advances, several challenges remain in effectively integrating experimental proteomics into metabolic models. Technical limitations include the complexity of protein mixtures, low abundance of critical metabolic enzymes, and the dynamic range of protein expression that exceeds the detection limits of current mass spectrometry platforms [56] [58]. For spatial proteomics, the limited multiplexing capacity (typically 40-50 markers) restricts comprehensive pathway analysis compared to mass spectrometry-based approaches that can quantify thousands of proteins [59].

Data processing challenges include the need for sophisticated normalization across experimental batches, imputation of missing values, and integration of heterogeneous data types with different noise characteristics and dynamic ranges [60]. Biological complexities such as post-translational modifications, protein-protein interactions, and subcellular localization further complicate the direct translation of protein abundance to enzyme capacity [61]. These limitations highlight the need for continued development of both experimental technologies and computational methods to fully realize the potential of proteomics integration in metabolic modeling.

In the realm of constraint-based metabolic modeling, the accurate representation of enzyme kinetics is paramount for predicting cellular physiology and metabolic fluxes. A significant challenge in this field lies in handling enzyme complexes and multimers—assemblies of multiple protein subunits that catalyze metabolic reactions. The process of kcat aggregation refers to the computational strategies used to derive a single, effective turnover number (kcat) for these multi-enzyme structures from the kinetic parameters of their individual components. Enzyme-constrained metabolic models (ecModels) enhance standard genome-scale metabolic models by integrating enzymatic constraints, primarily using kcat values to represent the catalytic capacity of enzymes [3] [19]. This integration allows for more accurate predictions of metabolic behaviors, such as overflow metabolism and proteome allocation, under various genetic and environmental conditions [3] [19]. However, the presence of enzyme complexes and multimers complicates this process, as a single kcat value must represent the collective activity of multiple subunits. This guide provides a comprehensive comparison of the predominant computational frameworks designed to address this challenge, evaluating their methodologies, performance, and applicability for researchers in metabolic engineering and drug development.

Comparative Analysis of kcat Aggregation Frameworks

The table below summarizes the core characteristics of four major frameworks that handle enzyme complexes and enzymatic constraints.

Table 1: Key Characteristics of Enzymatic Constraint Modeling Frameworks

Framework Name	Core Methodology	Primary Use-Case	Handling of Enzyme Complexes	Key Input Parameters
GECKO 2.0 [19]	Enhances GEMs with enzymatic constraints using kinetic and omics data.	General-purpose ecModel construction for any organism with a GEM.	Accounts for isoenzymes, promiscuous enzymes, and enzymatic complexes in enzyme demands.	kcat values, Enzyme Molecular Weights, Proteomics data (optional)
sMOMENT [3]	Simplified MOMENT method; incorporates enzyme mass constraints directly into stoichiometric matrix.	Creating enzyme-constrained models with reduced computational complexity.	Assumes a unique enzyme catalyzes each reaction; aggregation needed for complexes.	kcat values, Enzyme Molecular Weights, Total enzyme pool mass (P)
RealKcat [64]	Machine learning (gradient-boosted trees) trained on curated kinetic data.	Prediction of mutant enzyme kinetics and catalytic residue impact.	Framed as a classification problem; implicitly learns complex kinetic relationships.	Enzyme sequence (ESM-2 embeddings), Substrate structures (ChemBERTa embeddings)
TurNuP [20]	Machine learning combining protein Transformer Networks and differential reaction fingerprints.	Organism-independent prediction of turnover numbers for wild-type enzymes.	Represents the complete enzyme-reaction pair; generalizes to enzymes with low similarity to training data.	Enzyme sequence, Complete reaction equation (DRFPs)

Performance and Experimental Validation

The performance of these frameworks is validated through their ability to accurately predict metabolic phenotypes and kinetic parameters.

Table 2: Performance Metrics and Experimental Validation of Modeling Frameworks

Framework Name	Reported Accuracy / Performance	Experimental Validation Method	Key Strengths	Limitations / Challenges
GECKO 2.0 [19]	Successfully predicts Crabtree effect in yeast; improves growth predictions across environments.	Validation against experimental growth rates and proteomic allocation in S. cerevisiae.	High-quality, manual curation of kcat for key enzymes; direct integration of proteomics data.	Kinetic parameter availability varies by organism; manual curation can be intensive.
sMOMENT [3]	Explains overflow metabolism without bounding substrate uptake; changes predicted metabolic engineering strategies.	Application to E. coli model iJO1366; comparison of predictions with and without enzyme constraints.	Simplified representation reduces computational load; compatible with standard constraint-based modeling tools.	Requires a single, aggregated kcat per reaction, necessitating pre-processing for complexes.
RealKcat [64]	>85% test accuracy for kcat prediction; 96% accuracy within one order of magnitude on PafA mutant dataset.	Validation on a curated dataset of 27,176 entries and 1,016 single-site mutants of alkaline phosphatase (PafA).	High sensitivity to mutations; demonstrates complete loss of activity upon catalytic residue deletion.	Preprint (not yet peer-reviewed); performance depends on diversity of training data.
TurNuP [20]	Outperforms previous models (DLKcat); generalizes well to enzymes with <40% sequence identity to training set.	Parameterization of yeast metabolic models leading to improved proteome allocation predictions.	Organism-independent; considers the complete chemical reaction, not just a single substrate.	Trained on wild-type enzymes; performance on mutated enzymes or non-natural reactions may be limited.

Methodologies for kcat Aggregation and Experimental Workflows

Conceptual Workflow for Integrating Enzyme Complexes

The following diagram illustrates the general logical workflow for handling enzyme complexes in metabolic models, synthesizing the approaches of the featured frameworks.

Diagram 1: Workflow for kcat aggregation in enzyme complexes.

Detailed Experimental Protocols

Protocol for GECKO 2.0 ecModel Construction and kcat Integration

This protocol outlines the steps for building an enzyme-constrained model using GECKO 2.0, which includes handling enzyme complexes [19].

• Model and Data Acquisition:

  • Obtain a high-quality Genome-Scale Metabolic Model (GEM) for your target organism in SBML format.
  • Acquire kinetic parameters (kcat values) from specialized databases like BRENDA and SABIO-RK. GECKO 2.0 includes an automated procedure for this retrieval.
  • Gather proteomics data (if available) for measured enzyme concentrations and molecular weights of the enzymes.

• kcat Assignment and Complex Handling:

  • The toolbox uses a hierarchical matching criteria to assign kcat values to reactions, prioritizing organism- and substrate-specific values.
  • For enzyme complexes, the model accounts for the stoichiometry of the complex. The enzyme demand for a reaction catalyzed by a complex is calculated based on the subunit composition, and the kcat value is interpreted as the turnover per complex, not per subunit.

• Model Enhancement:

  • Run the GECKO functions to add enzyme pseudo-reactions and constraints to the base GEM.
  • The total enzyme pool constraint is applied, representing the limited cellular capacity for protein expression.

• Model Simulation and Validation:

  • Use Flux Balance Analysis (FBA) on the resulting ecModel to predict growth rates or metabolic fluxes under different conditions.
  • Validate predictions against experimental data, such as observed growth rates or substrate consumption rates. Manually curate kcat values for key enzymes if predictions deviate significantly from experimental observations.

Protocol for Kinetic Parameterization Using Machine Learning (RealKcat/TurNuP)

This protocol describes the use of machine learning models to predict kcat values for enzymes, including those within complexes, based on sequence and reaction information [64] [20].

• Input Preparation:

  • For RealKcat: Encode the enzyme amino acid sequence using ESM-2 embeddings to capture evolutionary context. Encode substrate structures using ChemBERTa embeddings.
  • For TurNuP: Encode the enzyme using a fine-tuned Transformer Network (like ESM-1b). Represent the complete chemical reaction using Differential Reaction Fingerprints (DRFPs), which consider all substrates and products.

• Model Application and Prediction:

  • Input the prepared feature vectors into the pre-trained model (RealKcat or TurNuP).
  • The model outputs a predicted kcat value. RealKcat frames this as a classification problem, predicting the order of magnitude of the kcat, which is often more functionally relevant for metabolic modeling than an exact value.

• Integration into Metabolic Models:

  • Incorporate the ML-predicted kcat values into an enzyme-constrained modeling framework like sMOMENT or GECKO.
  • For an sMOMENT model, the central constraint takes the form: Σ (v_i * MW_i / kcat_i) ≤ P, where v_i is the flux, MW_i is the molecular weight, kcat_i is the turnover number, and P is the total enzyme pool mass [3]. The predicted kcat is used directly in this constraint.

• Validation of Predictions:

  • Validate the overall model performance by its ability to recapitulate known metabolic phenomena (e.g., overflow metabolism) or match experimental flux data.
  • For specific enzyme complexes, compare the ML-predicted kcat with experimentally measured values from the literature, if available.

Diagram 2: kcat aggregation strategy pathways.

Table 3: Key Research Reagent Solutions for kcat Aggregation Studies

Item Name	Function / Application	Relevance to kcat Aggregation
BRENDA Database [3] [19]	Comprehensive enzyme information database, including kinetic parameters like kcat and KM.	Primary source for experimentally determined kcat values used in rule-based frameworks like GECKO and sMOMENT.
SABIO-RK Database [3]	Database for biochemical reaction kinetics, providing curated kinetic data.	Secondary source for kinetic parameters, helping to expand the coverage of kcat values for less-studied enzymes.
ErrASE / CorrectASE Kit [65]	Enzymatic error correction method for synthetic DNA.	Critical for ensuring sequence fidelity in gene synthesis, which is foundational for experimentally validating predicted kcat values in engineered enzymes.
T7 Endonuclease I [65]	Mismatch-cleaving enzyme used for error correction in synthetic gene assemblies.	Used in conjunction with error correction protocols to produce high-quality DNA constructs for expressing enzyme complexes.
MutS Protein [65]	Mismatch-binding protein used to enrich for perfect DNA sequences during gene synthesis.	Improves the quality of synthetic genes, reducing errors that could confound experimental measurements of kcat for complexes.
Group Contribution Method (GCM) [66]	Computational method to estimate thermodynamic properties of metabolites.	Used in thermodynamic curation of metabolic models (e.g., estimating Gibbs free energy), which provides context for kinetic parameterization and model consistency checking.

Benchmarking Success: Validating Predictive Power and Cross-Model Comparison

The integration of enzymatic constraints into genome-scale metabolic models (GEMs) represents a paradigm shift in systems biology, enabling more accurate predictions of cellular behavior under various genetic and environmental conditions. These advanced models, including GECKO (Genome-scale model enhancement with Enzymatic Constraints using Kinetic and Omics data) and sMOMENT (short MOMENT), fundamentally enhance traditional constraint-based approaches by incorporating enzyme kinetics and abundance data [4] [3]. However, the predictive power and reliability of these models depend critically on rigorous validation against experimental benchmarks. Three key classes of quantitative measurements have emerged as essential for this validation: microbial growth rates, 13C metabolic flux analysis (13C-MFA), and enzyme abundance profiles [67] [68] [69]. This guide provides a comprehensive framework for comparing enzymatic constraint models against these critical benchmarks, offering detailed protocols and quantitative reference data to empower researchers in metabolic engineering, biotechnology, and drug development.

Table 1: Key Enzymatic Constraint Modeling Approaches and Their Characteristics

Modeling Approach	Core Methodology	Data Requirements	Key Applications	References
GECKO	Enhances GEMs with enzyme usage pseudo-reactions	kcat values, MW, proteomics data	Predicting proteome-limited growth, metabolic switches	[4]
sMOMENT	Simplified protein allocation constraints via flux balance	kcat values, enzyme molecular weights	Overflow metabolism, metabolic engineering design	[3]
Enhanced FPA (eFPA)	Pathway-level integration of enzyme expression data	Proteomic/transcriptomic data, flux measurements	Predicting relative flux levels across conditions	[68]

Model Comparison: Quantitative Performance Benchmarks

Growth Rate Predictions

Growth rate serves as a fundamental benchmark for validating enzymatic constraint models, as it represents the integrated output of cellular metabolism. The performance of various models can be quantitatively assessed by their ability to predict growth rates under different nutrient conditions and genetic backgrounds.

Table 2: Experimental Growth Rate Data for Model Validation

Organism	Strain/Condition	Growth Rate (h⁻¹)	Key Metabolic Feature	Reference
Escherichia coli	Wild-type (MG1655) in chemostat	Variable with dilution rate	Balanced catabolism/anabolism	[67]
E. coli	Glycolysis knockout (Δpgi)	Reduced vs. wild-type	Redirected flux through OPPP	[67]
E. coli	OPPP knockout (Δzwf)	Reduced vs. wild-type	Enhanced glycolytic flux	[67]
Saccharomyces cerevisiae	Wild-type in glucose-limited chemostat	Variable with dilution rate	Crabtree effect at high uptake	[4]

Enzyme-constrained models have demonstrated remarkable success in predicting growth rates without requiring explicit bounds on substrate uptake. For instance, the ec_iJO1366 model of E. coli (an sMOMENT-enhanced model) accurately predicted aerobic growth rates on 24 different carbon sources using only enzyme mass constraints [3]. Similarly, GECKO-enhanced yeast models successfully simulated the Crabtree effect—the switch to fermentative metabolism at high glucose uptake rates—without artificially constraining oxygen or substrate uptake rates [4] [3].

13C Metabolic Flux Analysis Validation

13C-MFA provides a gold standard for quantifying intracellular metabolic fluxes, offering critical validation data for enzyme-constrained models. Comparative studies have revealed that models incorporating enzymatic constraints show significantly improved agreement with 13C-MFA flux measurements compared to traditional FBA.

Key findings from flux validation studies include:

• Central Carbon Metabolism Accuracy: Genome-scale models with enzymatic constraints accurately predict net fluxes in glycolysis and the TCA cycle, though predictions for the oxidative pentose phosphate pathway can show greater variability [70].
• Stress Condition Predictions: Enzyme-constrained models successfully predict both the direction and magnitude of flux changes under stress conditions, such as increased TCA cycle flux at higher temperatures and general flux decreases under hyperosmotic stress [70].
• Pathway-Level Correlations: The enhanced Flux Potential Analysis (eFPA) algorithm demonstrates that flux changes correlate more strongly with enzyme expression changes at the pathway level rather than individual reactions or the entire network [68].

Enzyme Abundance Integration

The integration of proteomics data provides a critical third benchmark for validating enzymatic constraint models. The GECKO framework, for instance, enables direct integration of measured enzyme concentrations as upper limits for flux capacities [4] [3].

Table 3: Enzyme Abundance and Kinetic Parameters for Model Constraints

Enzyme	Organism	kcat (s⁻¹)	Molecular Weight (kDa)	Typical Abundance (mg/gDW)	Pathway
G6PD (Zwf)	E. coli	Varies by organism and enzyme	Varies by organism and enzyme	Not specified in results	OPPP
Pgi	E. coli	Varies by organism and enzyme	Varies by organism and enzyme	Not specified in results	Glycolysis
Various	S. cerevisiae	Retrieved from BRENDA	Retrieved from databases	Proteomics data	Central metabolism

Systematic analyses have revealed that the upregulation and high saturation of enzymes in amino acid metabolism represent a common adaptation across organisms and conditions, suggesting the importance of "metabolic robustness" as a cellular objective rather than strictly optimal protein utilization [4]. Furthermore, enzyme-constrained models have demonstrated that approximately 48% of kinetic parameters in the BRENDA database require integration of values from other organisms or the use of wildcard matches to E.C. numbers to achieve sufficient coverage for comprehensive modeling [4].

Experimental Protocols for Benchmark Data Generation

High-Resolution 13C Metabolic Flux Analysis

The following protocol, adapted from Antoniewicz (2019), provides a robust methodology for generating high-precision flux data suitable for model validation [69]:

Step 1: Experimental Design and Tracer Selection

• Perform parallel labeling experiments using at least two complementary 13C-labeled glucose tracers (e.g., [1-13C]glucose and [U-13C]glucose)
• Ensure optimal tracer combinations using precision and synergy scoring systems
• Cultivate cells in controlled bioreactors with defined medium composition

Step 2: Cultivation and Sampling

• Grow microbial cultures in chemostat or batch mode with precise environmental control
• Monitor growth parameters (OD600, dry cell weight, substrate consumption)
• Harvest cells during mid-exponential phase (OD600 ≈ 0.6-1.2) for metabolic steady state
• Collect samples for GC-MS analysis: culture volume equivalent to OD600 = 3

Step 3: Sample Processing and Derivatization

• Centrifuge culture samples and hydrolyze pellets with 6N HCl at 100°C for 16 hours
• Derivatize amino acids using MTBSTFA + 1% TBDMCS at 60°C for 30 minutes
• Analyze proteinogenic amino acids via GC-MS (30m HP-5MS column, 5°C/min to 280°C)

Step 4: Flux Calculation and Statistical Analysis

• Calculate fluxes using specialized software (e.g., Metran)
• Perform comprehensive statistical analysis to determine goodness of fit
• Calculate confidence intervals for all flux estimates
• Validate flux estimates with additional measurements (e.g., glycogen and RNA labeling)

This protocol quantifies metabolic fluxes with a standard deviation of ≤2%, representing a substantial improvement over previous implementations [69].

Proteomics Integration for Enzyme-Constrained Models

The GECKO 2.0 toolbox provides a systematic framework for integrating enzyme abundance data into metabolic models [4]:

Automated Model Enhancement

• Input: Standard SBML metabolic model
• Retrieve kcat values from BRENDA database with hierarchical matching
• Incorporate enzyme molecular weights and structural data
• Add enzyme constraints as pseudo-reactions

Proteomics Data Integration

• Map mass spectrometry-based proteomics data to model enzymes
• Constrain measured enzymes with experimental abundances
• Constrain unmeasured enzymes with pooled protein mass budget
• Adjust total enzyme pool based on physiological measurements

Model Simulation and Validation

• Implement enzyme-constrained flux balance analysis
• Compare predictions with experimental growth and flux data
• Iteratively refine kcat values and enzyme constraints
• Perform sensitivity analysis on key parameters

Deep Labeling for Comprehensive Metabolic Activity Profiling

The "deep labeling" approach provides a hypothesis-free method for discovering endogenous metabolites and pathway activities [71]:

Medium Design

• Create custom medium with 13C-labeled fundamental precursors (glucose, amino acids)
• Maintain 12C-labeled vitamins, cofactors, and serum components
• Ensure coverage of all major metabolic pathways

Cell Culture and Sampling

• Culture cells for ≥6 population doublings to achieve >98% 13C incorporation
• Extract polar metabolites for LC-HRMS analysis
• Annotate metabolites using accurate mass and retention time

Data Analysis and Interpretation

• Identify endogenous metabolites by 13C incorporation patterns
• Distinguish synthesized metabolites from scavenged compounds
• Map active pathways based on labeling patterns
• Discover novel metabolites through unique mass isotopomers

Figure 1: Integrated workflow for developing and validating enzymatic constraint models against experimental benchmarks.

Table 4: Key Research Reagent Solutions for Metabolic Flux Studies

Reagent/Resource	Function/Purpose	Example Applications	Key References
13C-labeled substrates	Metabolic tracer for flux analysis	[1-13C]glucose, [U-13C]glucose, [1,2-13C]glycerol	[72] [69]
Stable isotope-labeled amino acids	Tracing amino acid metabolism and protein synthesis	[13C6]-Phe for lignin flux in plants	[73]
GC-MS systems	Measurement of isotopic labeling in metabolites	Analysis of proteinogenic amino acid labeling	[72] [69]
LC-HRMS systems	Comprehensive detection of labeled metabolites	Untargeted analysis of polar metabolites	[71]
Enzyme kinetics databases	Source of kcat values for model constraints	BRENDA, SABIO-RK	[4] [3]
Modeling software tools	Simulation and analysis of enzyme-constrained models	GECKO 2.0, AutoPACMEN, COBRA Toolbox	[4] [3]
Chemostat cultivation systems	Maintain steady-state growth for precise flux measurements	Controlled growth rate studies	[67]

The integration of growth rates, 13C metabolic fluxes, and enzyme abundances provides a robust, three-dimensional benchmark for validating enzymatic constraint models. The continuing development of databases like BRENDA, automated toolboxes such as GECKO 2.0 and AutoPACMEN, and sophisticated experimental protocols is steadily enhancing the predictive power of these models [4] [3]. As these frameworks become more sophisticated and widely adopted, they promise to accelerate metabolic engineering efforts and deepen our understanding of cellular physiology across diverse organisms from E. coli and S. cerevisiae to human cell lines [4]. The benchmarks and methodologies outlined in this guide provide a foundation for researchers to critically evaluate and implement these powerful modeling approaches in their own work.

Genome-scale metabolic models (GEMs) are fundamental computational tools for predicting cellular behavior in systems biology and metabolic engineering. However, traditional constraint-based models, which rely primarily on reaction stoichiometry, often predict optimal metabolic states that diverge from experimentally observed phenotypes. To address this limitation, enzyme-constrained metabolic models (ecModels) have been developed, incorporating proteomic limitations to enhance biological realism. Three major methodologies—GECKO, sMOMENT, and ECMpy—have emerged as leading frameworks for constructing these advanced models. This guide provides a comparative analysis of their predictive accuracy, underpinned by experimental data and structured protocols, offering researchers a foundation for selecting appropriate tools in drug development and basic research.

Methodological Frameworks and Implementation

Core Principles and Mathematical Formulations

Each methodology incorporates enzyme constraints differently, impacting model complexity and application.

• GECKO (Genome-scale model with Enzymatic Constraints using Kinetic and Omics): Enhances a base GEM by adding pseudo-reactions and metabolites that represent enzyme usage. It expands the model to include enzyme dilution constraints and allows for the direct integration of proteomics data to set upper limits for individual enzyme concentrations. The total enzyme pool is constrained by: ∑(vi / kcat_i) * MW_i ≤ P_total, where vi is the flux, kcat_i is the turnover number, MW_i is the molecular weight, and P_total is the total enzyme mass budget [19] [74].

• sMOMENT (short MOMENT): A simplified version of the MOMENT approach that avoids introducing new variables for enzyme concentrations. It directly adds a single global constraint on the total enzyme usage: ∑ vi * (MW_i / kcat_i) ≤ P. This results in a more compact model that can be handled with standard constraint-based modeling software, though incorporating specific enzyme concentration data is less direct than in GECKO [3].

• ECMpy (Enzymatic Constrained Metabolic model in Python): Introduces enzyme constraints without modifying existing metabolic reactions or adding new ones. Its workflow emphasizes automated calibration of enzyme kinetic parameters and considers the protein subunit composition in enzymatic reactions. The constraint takes the form: ∑(vi * MW_i) / (σ_i * kcat_i) ≤ p_tot * f, where σ_i is an enzyme saturation coefficient and f is the mass fraction of enzymes in the total protein pool [30] [15].

Implementation and Workflow

The tools differ significantly in their software implementation and user workflow, which affects their accessibility and integration with existing data.

• GECKO: Implemented primarily in MATLAB, it features a comprehensive workflow from model expansion and kcat integration to model tuning and proteomics data incorporation. The GECKO 3.0 protocol is highly detailed, and the toolbox is designed for community development and version-controlled updates [19] [74].

• sMOMENT: Available through the AutoPACMEN toolbox, which automates the creation of ecModels from a standard SBML file. It automatically retrieves enzymatic data from databases like BRENDA and SABIO-RK [48] [3].

• ECMpy: A Python-based workflow that leverages the COBRApy toolbox. It is designed for simplicity and outputs models in JSON format. Its automated parameter calibration is a key feature for improving agreement with experimental data [30] [15].

The following diagram summarizes the core conceptual workflow shared by these methodologies for building an enzyme-constrained model.

Comparative Performance Analysis

Direct, side-by-side comparisons of all three tools on identical datasets are limited in the literature. However, experimental applications on model organisms like E. coli and S. cerevisiae demonstrate their relative strengths. The table below summarizes key performance metrics as reported in foundational studies.

Table 1: Comparative Performance of ecModel Tools in Key Studies

Tool	Base Model (Organism)	Key Performance Achievement	Reported Metric
GECKO	Yeast 7 (S. cerevisiae)	Accurate prediction of the Crabtree effect (overflow metabolism) without bounding substrate uptake rates [19].	Qualitative and quantitative agreement with experimental flux data [19].
sMOMENT/AutoPACMEN	iJO1366 (E. coli)	Improved prediction of overflow metabolism and other metabolic switches; altered spectrum of metabolic engineering strategies [3].	Demonstrated superior flux predictions compared to standard FBA [3].
ECMpy	iML1515 (E. coli)	Significantly improved growth rate predictions on 24 single-carbon sources compared to other E. coli ecModels [30].	Lower estimation error and normalized flux error versus experimental data [30].
ECMpy	iML1515 (E. coli)	Revealed redox balance as a key difference in overflow metabolism between E. coli and S. cerevisiae [30].	Analysis of reaction enzyme cost and oxidative phosphorylation ratio [30].

Experimental Protocols for Model Validation

The validation of an enzyme-constrained model typically involves simulating growth phenotypes under defined conditions and comparing the predictions to empirical data. The following protocol, commonly used in studies like those for ECMpy and GECKO, outlines this process [30] [74].

Table 2: Key Reagents and Computational Tools for ecModel Construction

Research Reagent / Tool	Function in ecModel Construction	Source
BRENDA Database	Primary source for enzyme kinetic parameters (kcat values).	https://www.brenda-enzymes.org/
SABIO-RK Database	Alternative source for enzyme kinetics and reaction data.	https://sabio.h-its.org/
COBRApy	Python toolbox for constraint-based modeling and simulation.	https://opencobra.github.io/cobrapy/
SBML Model (e.g., iML1515)	The starting genome-scale metabolic model for enhancement.	BioModels Database / BiGG Models

Protocol: Validating Growth Predictions on Single Carbon Sources

• Model Preparation: Start with a tuned ecModel (e.g., eciML1515 for E. coli constructed with ECMpy, or an ecYeast model from GECKO).
• Condition Setup: For each of the 24 single-carbon sources (e.g., acetate, fructose, fumarate), set the respective carbon uptake reaction as the sole carbon source. Set its upper bound to a defined value (e.g., 10 mmol/gDW/h). Set all other carbon source uptake rates to zero.
• Simulation: Perform a Flux Balance Analysis (FBA) with the objective function set to maximize the biomass reaction.
• Data Collection: Record the predicted maximal growth rate for each carbon source.
• Comparison with Experiments: Calculate the estimation error for the growth rate on each carbon source using the formula: |v_growth_sim - v_growth_exp| / v_growth_exp, where v_growth_exp is the experimentally determined growth rate [30].
• Overall Assessment: Compute the normalized flux error across all carbon sources to evaluate the overall improvement of the ecModel over the original GEM: √[∑(v_growth_sim_i - v_growth_exp_i)²] / √[∑(v_growth_exp_i)²] [30].

This workflow for performance validation is illustrated below.

Trade-offs and Selection Guidelines

The choice between GECKO, sMOMENT, and ECMpy involves trade-offs between model complexity, ease of use, and specific predictive tasks.

• GECKO offers a highly detailed and customizable framework, making it suitable for deep mechanistic studies, especially when proteomics data is available for integration. Its connection to a curated model repository and large community are significant advantages, though its primary implementation in MATLAB may present a barrier for some Python-centric research groups [19] [74].
• sMOMENT provides a computationally efficient and simplified alternative. Its integration with AutoPACMEN facilitates automated construction, and its compact formulation is advantageous for complex analyses like calculating Minimal Cut Sets. It strikes a balance between predictive improvement and operational simplicity [3].
• ECMpy stands out for its Python-based simplicity and automated calibration workflow. Published results showing superior quantitative accuracy in predicting E. coli growth on diverse carbon sources are a strong point in its favor [30]. It is an excellent choice for researchers seeking a streamlined path to generating accurate ecModels within a Python environment.

Future Directions and Integration

The field is moving towards multi-constraint integration. For instance, models like EcoETM combine enzymatic and thermodynamic constraints to resolve conflicts and further improve prediction accuracy [75]. Furthermore, tools like GECKO 3.0 are beginning to incorporate deep learning-predicted kcat values, which promise to expand the coverage and quality of kinetic parameters for less-studied organisms, thereby enhancing the predictive power and general applicability of ecModels [74].

In conclusion, while GECKO, sMOMENT, and ECMpy all successfully incorporate enzyme constraints to improve the predictive accuracy of metabolic models beyond standard GEMs, they cater to different user needs and computational preferences. GECKO is feature-rich and detailed, sMOMENT is streamlined and efficient, and ECMpy demonstrates high accuracy with an automated, user-friendly Python workflow. Researchers should select the tool that best aligns with their organism of interest, available data, and computational infrastructure.

Genome-scale metabolic models (GEMs) are powerful computational tools that simulate cellular metabolism by representing biochemical reactions, metabolites, and gene-protein-reaction relationships. However, traditional GEMs lack enzymatic constraints, often leading to predictions of unrealistically high metabolic fluxes and growth rates. Enzyme-constrained GEMs (ecGEMs) address this limitation by incorporating enzyme kinetic parameters (kcat values) and molecular weights to account for the cell's limited protein biosynthesis capacity. This case study provides a comprehensive comparison of ecGEM performance in two well-studied model organisms: Escherichia coli and Saccharomyces cerevisiae [19].

The fundamental principle underlying ecGEMs is that the flux through each metabolic reaction is limited by the concentration and catalytic efficiency of its corresponding enzyme. This is mathematically represented by the constraint vi ≤ kcat,i × [Ei], where vi is the metabolic flux through reaction i, kcat,i is the enzyme's turnover number, and [Ei] is the enzyme concentration. Additionally, the total enzyme mass is constrained by the cellular protein budget, ensuring that the sum of all enzyme masses does not exceed the cell's total protein synthesis capacity [3] [30]. This approach significantly improves the prediction of various metabolic phenotypes, including overflow metabolism, substrate utilization patterns, and growth rates under different conditions.

Methodological Approaches for ecGEM Construction

Reconstruction Workflows and Tools

Several computational workflows have been developed to construct ecGEMs, each with distinct approaches to integrating enzymatic constraints. The table below summarizes the primary tools used for ecGEM reconstruction in E. coli and S. cerevisiae.

Table 1: Comparison of ecGEM Reconstruction Workflows

Tool	Underlying Method	Key Features	Application in E. coli	Application in S. cerevisiae
GECKO [19]	Enzyme usage pseudo-reactions	Adds enzyme metabolites to stoichiometric matrix; direct proteomics integration	ec_iML1515 reconstruction	ecYeast7/ecYeast8 development [76]
AutoPACMEN [3]	Simplified MOMENT	Automated kcat retrieval from BRENDA/SABIO-RK; minimal model expansion	sMOMENT-enhanced iJO1366	Compatible with yeast models
ECMpy [30]	Direct enzymatic constraint	No matrix modification; constraint-based kcat calibration	eciML1515 construction [47]	Supports yeast model development
DLKcat [13]	Deep learning prediction	Predicts kcat values from substrate structures & protein sequences	Enables kcat prediction for less-studied organisms	Genome-scale kcat prediction for 300+ yeast species

Core Enzymatic Constraint Principles

The following diagram illustrates the fundamental mathematical and biochemical principles shared by ecGEM reconstruction methods:

Diagram Title: Core Principles of Enzyme-Constrained Modeling

All ecGEM methods incorporate three fundamental constraint types: (1) Stoichiometric constraints ensuring mass-balance for all metabolites (S·v = 0), (2) Enzyme capacity constraints limiting reaction fluxes by catalytic efficiency (vi ≤ kcat,i·gi), and (3) Proteome allocation constraints restricting total enzyme mass based on cellular protein synthesis capacity (Σgi·MWi ≤ P) [3] [1]. The GECKO approach explicitly represents enzyme usage through additional pseudo-reactions and metabolites in the stoichiometric matrix, while ECMpy implements enzyme constraints directly without modifying the original model structure [30] [19].

kcat Parameter Acquisition and Calibration

A critical challenge in ecGEM construction is obtaining reliable kcat values. The following workflow illustrates the multi-source kcat parameterization process:

Diagram Title: kcat Parameter Acquisition Workflow

Experimental kcat values are primarily sourced from the BRENDA and SABIO-RK databases, though coverage is incomplete [13]. Machine learning approaches like DLKcat have emerged to predict kcat values from substrate structures and protein sequences, achieving predictions within one order of magnitude of experimental values (Pearson's r = 0.88) [13] [16]. For missing values, kcat numbers from enzymes with similar substrates or from other organisms are used, followed by calibration steps to ensure consistency with experimental flux data [30] [19].

Performance Evaluation in E. coli Models

Model Construction and Experimental Validation

The enzyme-constrained model for E. coli (eciML1515) was constructed using the ECMpy workflow based on the iML1515 GEM. This implementation added constraints for total enzyme amount while considering protein subunit composition and incorporating automated calibration of enzyme kinetic parameters [30]. The reconstruction process systematically addressed challenges such as quantitative subunit composition of enzyme complexes, which significantly impacts molecular weight calculations and enzyme usage costs [47].

For experimental validation, the accuracy of ecGEM predictions was quantified using published mutant fitness data across thousands of genes and 25 different carbon sources. The area under a precision-recall curve (AUC) was identified as a robust metric for evaluating model accuracy, particularly due to its effectiveness in handling imbalanced datasets where correct prediction of gene essentiality is more biologically meaningful than prediction of non-essentiality [77].

Quantitative Performance Metrics

Table 2: E. coli ecGEM Performance Assessment

Performance Metric	Standard GEM (iML1515)	Enzyme-Constrained GEM (eciML1515)	Experimental Validation
Growth prediction on 24 carbon sources [30]	Large errors in growth rates	Normalized flux error significantly reduced	Consistent with experimental growth rates
Overflow metabolism prediction	Requires arbitrary uptake constraints	Predicts acetate secretion without constraints	Matches experimental observations
Gene essentiality prediction [77]	Declining accuracy in newer models (AUC trend)	Improved after vitamin/cofactor availability correction	RB-TnSeq mutant fitness data
Flux prediction accuracy	Less consistent with 13C data	Improved correlation with 13C flux measurements	13C metabolic flux analysis

The enzyme-constrained model eciML1515 demonstrated significantly improved prediction of growth rates across 24 single-carbon sources compared to the traditional iML1515 model. Without enzyme constraints, models typically predict unrealistic metabolic fluxes at high substrate uptake rates, but eciML1515 successfully simulated overflow metabolism (acetate secretion) without needing to artificially constrain substrate uptake rates [30]. This improvement stems from the model's inherent representation of proteomic limitations, which naturally redirect flux toward less protein-efficient pathways when substrates are abundant.

Error analysis revealed that vitamin and cofactor availability significantly impacted essentiality prediction accuracy. Specifically, 21 genes involved in biotin, R-pantothenate, thiamin, tetrahydrofolate, and NAD+ biosynthesis were falsely predicted as essential because the corresponding vitamins/cofactors were not included in the simulated growth medium [77]. This highlights the importance of accurately representing the experimental culture conditions in model simulations.

Performance Evaluation in S. cerevisiae Models

Model Construction and Implementation

The enzyme-constrained model for S. cerevisiae (ecYeast8) was developed using the GECKO method, which expands the stoichiometric matrix to include enzyme usage pseudo-reactions. This framework enables direct integration of proteomics data as additional constraints on enzyme allocation [76] [19]. The ecYeast8 model incorporates kcat values from multiple sources, including experimental measurements, database mining, and computational predictions, followed by parameter calibration to improve consistency with physiological data.

A distinctive feature of yeast ecGEMs is their explicit representation of the protein pool constraint, which limits the total amount of enzyme protein available for metabolic functions. This constraint successfully captures the metabolic trade-offs that yeast cells face under different growth conditions, particularly the shift between respiratory and fermentative metabolism [76].

Quantitative Performance Assessment

Table 3: S. cerevisiae ecGEM Performance Assessment

Performance Metric	Standard GEM (Yeast8)	Enzyme-Constrained GEM (ecYeast8)	Experimental Validation
Crabtree effect prediction [76]	Cannot predict critical dilution rate	Predicts Dₐᵣᵢₜ of 0.27 h⁻¹	Matches experimental range (0.21-0.38 h⁻¹)
Substrate hierarchy utilization	Incorrect order of consumption	Correctly predicts glucose>xylose>arabinose	Matches experimental observations
Byproduct secretion patterns	Limited prediction capability	Accurate ethanol, acetaldehyde, acetate prediction	Chromatography measurements
Dynamic flux predictions [76]	Poor correlation with experimental data	Improved intracellular flux predictions	13C metabolic flux analysis
Enzyme usage efficiency	No proteome allocation trade-offs	Captures yield-enzyme efficiency trade-off	Consistent with resource allocation theories

The ecYeast8 model demonstrated remarkable accuracy in predicting the Crabtree effect - the transition from respiratory to fermentative metabolism at high growth rates. The model predicted a critical dilution rate (Dₐᵣᵢₜ) of 0.27 h⁻¹, which falls within the experimentally observed range of 0.21-0.38 h⁻¹ for different S. cerevisiae strains [76]. This capability stems from the enzyme constraints, which make fermentative pathways more economical than respiratory pathways at high glucose uptake rates due to lower protein costs.

Additionally, ecYeast8 successfully predicted the hierarchical utilization of mixed carbon sources, correctly simulating the preferential consumption of glucose before xylose and arabinose [76]. The model also accurately simulated batch and fed-batch fermentation dynamics, including substrate uptake rates, growth phases, and byproduct secretion patterns, outperforming traditional GEMs in both qualitative and quantitative predictions [76] [16].

Comparative Analysis and Applications

Cross-Species Performance Patterns

Both E. coli and S. cerevisiae ecGEMs demonstrate significant improvements over traditional GEMs, but with organism-specific characteristics:

• Overflow metabolism explanation: In E. coli, enzyme constraints revealed that redox balance was the key determinant of acetate secretion, while in S. cerevisiae, protein costs of respiratory versus fermentative pathways explained ethanol production [76] [30].

• Growth rate predictions: ecGEMs for both organisms showed improved correlation with experimental growth rates across multiple carbon sources, with E. coli ecGEMs achieving particularly notable improvement on 24 single-carbon sources [30].

• Metabolic engineering: Enzyme constraints alter predicted optimal engineering strategies by accounting for enzyme costs. In S. cerevisiae, this improved prediction of targets for chemical production; in E. coli, it changed optimal gene knockout strategies for biochemical production [3] [16].

Practical Implementation Toolkit

Table 4: Essential Research Reagents and Computational Tools for ecGEM Construction

Tool/Resource	Type	Function in ecGEM Development	Example Applications
BRENDA Database [3]	Kinetic database	Primary source of experimental kcat values	Manual curation of enzyme parameters
SABIO-RK [3]	Kinetic database	Additional source of enzyme kinetic parameters	Cross-verification of kcat values
DLKcat [13]	Deep learning tool	Predicts kcat from substrate structures & protein sequences	Filling gaps in kcat coverage
GECKO Toolbox [19]	Model reconstruction	Automated ecGEM construction from GEMs	ecYeast8 development
ECMpy [30]	Model reconstruction	Simplified workflow with direct constraint implementation	eciML1515 construction
COBRA Toolbox [19]	Simulation platform	Flux balance analysis and constraint-based modeling	ecGEM simulation & validation
UniProt Database [47]	Protein database	Molecular weight and subunit composition data	Enzyme mass calculations

This case study demonstrates that enzyme-constrained genome-scale metabolic models significantly outperform traditional GEMs for both E. coli and S. cerevisiae in predicting key metabolic phenotypes. The incorporation of enzyme kinetic parameters and proteomic constraints enables more accurate simulation of overflow metabolism, substrate utilization hierarchies, growth rates, and byproduct secretion patterns.

While implementation approaches vary between the GECKO and ECMpy workflows, the fundamental improvement stems from accounting for the cellular protein budget, which creates natural trade-offs between metabolic efficiency and enzyme costs. The continued development of machine learning tools for kcat prediction and automated model construction workflows will further enhance the accessibility and accuracy of ecGEMs for fundamental research and metabolic engineering applications.

Future directions in ecGEM development include improved integration with multi-omics data, expansion to microbial communities, and incorporation of additional cellular constraints beyond metabolism. As these models continue to mature, they will provide increasingly powerful tools for predicting cellular behavior and designing optimized microbial cell factories.

Genome-scale metabolic models (GEMs) serve as powerful computational frameworks for predicting cellular phenotypes from genomic information by representing the entire metabolic network of an organism as a stoichiometric matrix of biochemical reactions [78]. While standard GEMs have proven valuable for metabolic engineering and biological discovery, they often predict physiologically impossible metabolic states because they lack constraints representing fundamental biological limitations. Enzyme-constrained models (ecModels) address this critical limitation by incorporating enzymatic constraints using kinetic parameters (kcat values) and proteomic data, effectively bridging the gap between an organism's genotype and its phenotypic expression under various conditions [4] [3].

The integration of enzyme constraints has demonstrated remarkable success in improving phenotypic predictions. For Saccharomyces cerevisiae, enzyme-constrained models successfully simulated the Crabtree effect—the switch to fermentative metabolism at high glucose uptake rates—without explicitly bounding substrate or oxygen uptake rates [3]. Similarly, for Bacillus subtilis, incorporating enzymatic constraints reduced flux prediction errors by 43% in wild-type strains and 36% in mutant strains compared to standard GEMs [79]. These improvements highlight how enzymatic constraints render models more biologically realistic by accounting for the limited protein resources available in the cell.

However, incorporating enzymatic constraints introduces significant trade-offs between model size, computational cost, and prediction accuracy that researchers must carefully balance. This comparison guide objectively evaluates the performance characteristics of major enzymatic constraint modeling approaches to inform selection decisions for specific research applications.

Comparative Analysis of Modeling Approaches

Table 1: Key Frameworks for Constructing Enzyme-Constrained Metabolic Models

Framework	Core Methodology	Key Features	Supported Organisms	Implementation
GECKO [4]	Enhances GEMs with enzymatic constraints using kinetic and proteomic data	Detailed enzyme demands for all reaction types; automated parameter retrieval; direct proteomics integration	S. cerevisiae, E. coli, H. sapiens, Y. lipolytica, K. marxianus	MATLAB
GECKO 2.0 [4]	Upgraded toolbox with expanded functionality	Automated, version-controlled updates of ecModels; improved parameter coverage; community development platform	Any organism with compatible GEM	MATLAB, Python module for BRENDA query
sMOMENT [3]	Simplified version of MOMENT approach	Reduced variables; direct constraint integration; compatible with standard COBRA tools	E. coli (iJO1366), general applicability	Through AutoPACMEN toolbox
AutoPACMEN [3]	Automated creation of sMOMENT models	Automatic enzymatic data retrieval from SABIO-RK and BRENDA; parameter calibration based on flux data	Any organism (SBML input)	Not specified
ECMpy [15]	Simplified Python workflow	Total enzyme amount constraints; subunit composition consideration; automated parameter calibration	E. coli (iML1515)	Python
ETGEMs [75]	Integration of enzymatic and thermodynamic constraints	Combined enzyme kinetics and thermodynamics; avoids conflicts between constraint types	E. coli	Python (Cobrapy, Pyomo)

Quantitative Performance Comparison

Table 2: Performance Metrics Across Different Enzyme-Constrained Modeling Approaches

Framework	Model Size Increase	Computational Demand	Growth Prediction Accuracy	Flux Prediction Improvement	Reference Case Study
GECKO	Significant expansion with additional reactions/metabolites [3]	High due to complex formulation [3]	Superior across multiple carbon sources [4]	43% error reduction in B. subtilis [79]	B. subtilis γ-PGA production [79]
sMOMENT	Minimal increase (compact representation) [3]	Reduced vs. original MOMENT [3]	Comparable to MOMENT with fewer variables [3]	Improved overflow metabolism prediction [3]	E. coli iJO1366 [3]
ECMpy	Moderate (direct GEM enhancement) [15]	Moderate (Python implementation) [15]	Significant improvement on 24 carbon sources [15]	Accurate overflow metabolism prediction [15]	E. coli eciML1515 [15]
ETGEMs	High (multiple constraint types) [75]	High (non-linear constraints) [75]	Identifies thermodynamically feasible routes [75]	Resolves pathway bottlenecks [75]	E. coli serine synthesis [75]

Experimental Data and Validation Protocols

Experimental Objective: Integrate enzymatic constraints to improve prediction accuracy of central carbon metabolic fluxes and secretion rates in B. subtilis, then validate through γ-PGA production strain design.

Methodology:

• Kinetic Data Curation: Manual collection of kcat values from BRENDA and SABIO-RK databases for 29 enzymes in central carbon metabolism, with molecular weights
• Specific Activity Conversion: When kcat values were unavailable, specific activity (SA) values were converted using: kcat [s⁻¹] = (SA [μmol/mg/min] × MW [mg/μmol]) / 60 [s/min]
• Proteomic Integration: Absolute protein quantification data (molecules/cell) from LC/MSE analysis converted to mmol/gDW using cellular dry weight assumptions
• Model Enhancement: iYO844 GEM constrained with enzyme kinetics and abundance data following GECKO principles
• Validation: Comparison of predicted versus experimental fluxes in wild-type and mutant strains
• Application: Identification of gene deletion targets for enhanced γ-PGA production

Key Results:

• Flux prediction error reduction: 43% for wild-type, 36% for mutants
• 2.5-fold increase in correctly predicted essential genes in central carbon pathways
• Significant flux variability reduction in >80% of reactions
• Twofold higher γ-PGA concentration and production rate in engineered strains

Experimental Objective: Develop a novel multi-modal transformer approach to predict kcat values for E. coli using amino acid sequences and reaction substrates, addressing limited in-vivo data.

Methodology:

• Architecture: Multi-modal transformer with cross-attention mechanisms
• Input Features: Enzyme amino acid sequences and SMILES annotations of reaction substrates
• Heteromeric Enzyme Handling: Evaluation of multiple subunit kcat aggregation strategies
• Calibration Innovation: Flux control coefficient-based calibration (derivatives of log flux with respect to log kcat)
• Validation: Benchmarking against state-of-the-art models using experimental growth rates, Carbon-13 fluxes, and enzyme abundances

Key Results:

• Pre-calibration performance matching or outperforming existing methods
• Identification of 8 key kcat values for calibration using flux control coefficients
• Superior post-calibration performance with 81% fewer calibrations
• Flux control coefficients shown identical to enzyme cost at FBA optimum

Technical Implementation and Workflows

Model Construction Pipelines

Diagram 1: Enzyme constraint model workflow comparison

Key Trade-off Relationships

Diagram 2: Trade-off relationships in enzymatic constraint models

Research Reagent Solutions

Table 3: Essential Research Reagents and Tools for Enzyme-Constrained Modeling

Category	Specific Tool/Database	Function	Access	Key Features
Kinetic Databases	BRENDA [4] [3]	Comprehensive enzyme kinetic data	Public	38,280 entries for 4,130 unique EC numbers [4]
	SABIO-RK [3] [79]	Kinetic data with reaction conditions	Public	Biochemical reaction parameters
Modeling Software	COBRA Toolbox [4]	Constraint-based modeling in MATLAB	Open-source	Comprehensive FBA methods
	COBRApy [4] [32]	Python implementation of COBRA	Open-source	Object-oriented model representation
	GECKO Toolbox [4]	ecModel construction and simulation	Open-source	Automated parameter retrieval
Model Construction	AutoPACMEN [3]	Automated sMOMENT model creation	Not specified	Database integration, parameter calibration
	ECMpy [15]	Simplified Python workflow for ecModels	Open-source	Total enzyme amount constraints
	gapseq [80]	Automated metabolic pathway prediction	Open-source	Curated reaction database, gap-filling
Model Testing	MEMOTE [32]	Metabolic model test suite	Open-source	Quality control, version tracking
Visualization	Pathway Tools [78]	Pathway visualization and analysis	License required	Metabolic network visualization

Strategic Implementation Guidelines

Framework Selection Criteria

For Maximum Prediction Accuracy: GECKO 2.0 provides the most comprehensive framework for integrating diverse enzymatic constraints, with demonstrated 43% improvement in flux prediction accuracy for B. subtilis [79]. The automated parameter retrieval and community development model ensure continuous improvement, though this comes at the cost of increased computational requirements.

For Large-Scale Studies: sMOMENT implemented through AutoPACMEN offers the most computationally efficient approach for high-throughput applications, providing comparable predictions to full MOMENT with significantly reduced variables [3]. This approach is particularly valuable for multi-organism community modeling or extensive condition screening.

For Integrated Constraint Analysis: ETGEMs represents the most sophisticated framework for analyzing interactions between different constraint types, successfully resolving conflicts between stoichiometric, enzymatic, and thermodynamic constraints [75]. This approach is essential when studying pathways where thermodynamic feasibility significantly impacts flux distributions.

Optimization Recommendations

Parameter Coverage Enhancement: Leverage transformer-based kcat prediction approaches to address the critical limitation of kinetic parameter scarcity [23]. The multi-modal transformer with cross-attention mechanisms has demonstrated superior performance with 81% fewer calibrations required, significantly reducing experimental burden.

Context-Specific Implementation: For metabolic engineering applications where product yield optimization is paramount, GECKO models provide the most reliable predictions, as demonstrated by the successful twofold improvement in γ-PGA production in B. subtilis [79]. For basic research investigating metabolic pathway structures, ETGEMs offers unique insights into thermodynamic and enzymatic constraints.

Tool Integration Strategy: Combine gapseq for initial pathway prediction and model reconstruction [80] with GECKO 2.0 for enzymatic constraint integration [4]. This pipeline leverages the superior enzyme activity prediction of gapseq (6% false negative rate versus 28-32% for alternatives) with the sophisticated constraint implementation of GECKO 2.0.

The field of enzymatic constraint modeling continues to evolve rapidly, with emerging approaches like transformer-based kcat prediction [23] addressing fundamental data limitation challenges. As these methods mature and integrate with established frameworks, the trade-offs between model size, computational cost, and prediction accuracy will likely become less pronounced, enabling more researchers to leverage these powerful approaches for metabolic engineering and biological discovery.

Genome-scale metabolic models (GEMs) are computational representations of cellular metabolism that enable mathematical exploration of metabolic behaviors within cellular and environmental constraints [81]. However, conventional GEMs have limitations in accurately predicting certain phenotypes, as they primarily consider stoichiometric constraints without accounting for enzyme kinetics and proteome allocation [3]. Enzyme-constrained GEMs (ecGEMs) represent a significant advancement in this field by incorporating enzymatic constraints using kinetic and omics data, thereby improving the predictive power of metabolic models [81]. The fundamental principle behind ecGEMs is the recognition that cellular metabolism is limited by the finite amount of protein resources available, requiring optimal allocation of enzymes to different metabolic processes [3]. These models integrate enzyme turnover numbers (kcat values), which define the maximum catalytic rate of enzymes, and molecular weights to constrain flux distributions based on enzyme capacity limitations [13] [3]. This approach more accurately reflects biological reality, where metabolic fluxes are constrained not only by reaction stoichiometry but also by enzyme catalytic efficiency and abundance.

Methodological Approaches for Constructing ecGEMs

Key Computational Frameworks

Several computational frameworks have been developed for the systematic construction of ecGEMs. The GECKO (Genome-scale model enhancement with Enzymatic Constraints accounting for Kinetic and Omics data) toolbox is one of the most widely adopted approaches [6] [81]. GECKO enhances GEMs by adding explicit constraints on enzyme usage, incorporating both enzyme kinetic parameters (kcat values) and proteomic data [81]. The latest version, GECKO 3.0, provides a comprehensive protocol for reconstructing, simulating, and analyzing ecGEMs, including the integration of deep learning-predicted enzyme kinetics to expand model coverage [81]. The methodology involves five key stages: (1) expansion from a starting metabolic model to an ecModel structure, (2) integration of enzyme turnover numbers, (3) model tuning, (4) integration of proteomics data, and (5) simulation and analysis of ecModels [81].

Alternative approaches include the MOMENT (Metabolic Optimization with Enzyme Kinetics and Thermodynamics) method and its simplified derivative sMOMENT, which incorporate enzyme mass constraints with fewer variables while maintaining predictive accuracy [3]. The ECMpy workflow offers another automated pipeline for ecGEM construction, enabling the integration of machine learning-predicted kcat values from tools like TurNuP [82]. More recently, transformer-based approaches have emerged, utilizing protein language models and cross-attention mechanisms between enzyme sequences and substrate structures to predict kcat values with enhanced accuracy [23]. These frameworks share the common objective of constraining the solution space of metabolic models using enzyme kinetic parameters, thereby generating more biologically realistic predictions.

Addressing Enzyme Promiscuity and Underground Metabolism

A significant challenge in ecGEM construction involves accounting for enzyme promiscuity - the ability of enzymes to catalyze multiple reactions with different substrates. The CORAL (Constraint-based promiscuous enzyme and underground metabolism modeling) toolbox addresses this challenge by explicitly modeling resource allocation between main and side activities of promiscuous enzymes [6]. CORAL restructures enzyme usage in ecGEMs by splitting the enzyme pool for each promiscuous enzyme into multiple subpools corresponding to different catalytic activities [6]. This approach recognizes that enzymes are predominantly occupied by their primary substrates, with reduced availability for secondary reactions. Implementation of CORAL in Escherichia coli models demonstrated that underground metabolism increases flexibility in both metabolic fluxes and enzyme usage, with promiscuous enzymes playing a vital role in maintaining robust metabolic function and growth, particularly when primary metabolic pathways are disrupted [6].

Performance Validation Against Experimental Data

Quantitative Assessment of ecGEM Predictive Accuracy

The predictive performance of ecGEMs has been rigorously validated against experimental data across multiple organisms, with consistently superior results compared to traditional GEMs. The table below summarizes key validation metrics from representative studies:

Table 1: Experimental Validation of ecGEM Predictive Performance

Organism	ecGEM Framework	Validation Metrics	Performance Improvement vs. Traditional GEM	Citation
Saccharomyces cerevisiae (Yeast)	GECKO	Prediction of growth rates, metabolic fluxes, and enzyme abundances	Explains Crabtree effect without bounding substrate uptake rates; improved proteome allocation predictions	[3] [81]
Escherichia coli	sMOMENT/AutoPACMEN	Aerobic growth rate prediction on 24 carbon sources	Superior prediction without restricting carbon source uptake rates	[3]
Escherichia coli	Transformer-based approach	Growth rates, C-13 fluxes, enzyme abundances	Matches or outperforms state-of-the-art with 81% fewer calibrations	[23]
343 Yeast/Fungi species	DLKcat	Phenotype simulation and proteome prediction	Outperformed original ecGEMs in predicting phenotypes and proteomes	[13]
Myceliophthora thermophila	ECMpy with TurNuP	Substrate hierarchy utilization	Accurately captured hierarchical utilization of five carbon sources from plant biomass	[82]
Escherichia coli	CORAL	Metabolic flexibility and robustness	Explained compensation mechanisms for metabolic defects via underground metabolism	[6]

Case Study: ecGEMs in Microbial Physiology

The application of ecGEMs has yielded fundamental insights into microbial physiology, particularly in understanding metabolic switches and resource allocation strategies. For Saccharomyces cerevisiae, ecGEMs successfully explain the Crabtree effect - the switch to fermentative metabolism at high glucose uptake rates even under aerobic conditions - based solely on enzyme capacity constraints, without requiring artificial bounds on oxygen uptake [3]. This represents a significant advancement over traditional GEMs, which typically fail to predict this fundamental physiological response without additional constraints. Similarly, in Escherichia coli, ecGEMs accurately predict overflow metabolism (the simultaneous production of acetate and biomass during aerobic growth on glucose) as a consequence of optimal proteome allocation under kinetic constraints [3].

A particularly compelling demonstration comes from the reconstruction of 343 ecGEMs for diverse yeast species using DLKcat, a deep learning approach for kcat prediction from substrate structures and protein sequences [13]. These models significantly outperformed previous ecGEM pipelines in predicting cellular phenotypes and proteome allocation, enabling researchers to explain phenotypic differences across species based on underlying enzyme kinetic parameters [13]. This large-scale validation across multiple organisms highlights the generalizability and robustness of the ecGEM approach.

Case Study: ecGEMs in Metabolic Engineering

ecGEMs have proven particularly valuable in metabolic engineering applications, where they enable more accurate prediction of engineering targets and physiological responses. For the thermophilic fungus Myceliophthora thermophila, the construction of ecMTM (an ecGEM based on machine learning-predicted kcat values) significantly improved predictions of carbon source utilization hierarchy compared to the traditional GEM [82]. The model accurately simulated the experimentally observed preferential utilization of glucose over xylose and other plant biomass-derived sugars, providing insights into the enzyme-centric constraints underlying this hierarchy [82]. Furthermore, ecMTM successfully predicted established metabolic engineering targets and identified new potential targets for chemical production, demonstrating the practical utility of ecGEMs in guiding strain design.

Table 2: ecGEM Applications in Metabolic Engineering and Biotechnology

Application Domain	Specific Use Case	ecGEM Contribution	Citation
Biomass Conversion	Myceliophthora thermophila	Explained carbon source hierarchy and predicted engineering targets for chemical production	[82]
Human Health	Colorectal cancer metabolism	Identified hexokinase as crucial therapeutic target in cancer-associated fibroblast crosstalk	[8]
Microbial Communities	Gut microbiome	Predicted pairwise metabolic interactions between 773 gut microbes under different dietary conditions	[1]
Enzyme Engineering	Human purine nucleoside phosphorylase	Identified amino acid residues with strong impact on kcat values using neural attention mechanisms	[13]
Underground Metabolism	Escherichia coli	Revealed role of promiscuous enzymes in maintaining metabolic robustness after genetic perturbations	[6]

Experimental Protocols for ecGEM Validation

Standard Workflow for ecGEM Development and Testing

The validation of ecGEMs typically follows a systematic workflow that integrates computational modeling with experimental verification. The standard protocol, as implemented in GECKO 3.0, involves five key stages with specific validation checkpoints [81]:

• Model Expansion: Conversion of a baseline GEM to an ecModel structure through the addition of enzyme-related constraints and pseudoreactions.
• kcat Integration: Incorporation of enzyme turnover numbers from experimental databases or machine learning predictions, followed by parameter sensitivity analysis.
• Model Tuning: Adjustment of the total enzyme pool constraint to match physiological growth rates, ensuring the model operates within biologically realistic parameters.
• Proteomics Integration: Incorporation of experimental enzyme abundance data where available, enabling validation of predicted enzyme usage patterns.
• Simulation and Analysis: Comprehensive testing of model predictions against experimental data, including growth rates, substrate uptake patterns, and product secretion.

This workflow emphasizes iterative validation at each stage, with discrepancies between predictions and experimental data used to refine model parameters and structure.

Diagram 1: ecGEM Development and Validation Workflow

Specialized Validation Methodologies

Different research applications require specialized validation approaches tailored to specific biological questions:

For metabolic engineering applications, validation typically involves comparing predicted versus actual production yields, growth rates, and substrate consumption patterns for both wild-type and engineered strains [82]. This includes testing the model's ability to predict the outcomes of gene knockouts, overexpression strategies, and pathway modifications. Important validation metrics include the correlation between predicted and measured fluxes (using 13C metabolic flux analysis), accuracy in predicting essential genes, and identification of high-impact metabolic engineering targets that successfully improve product yields when implemented experimentally [82] [1].

For biomedical applications, such as cancer metabolism, validation focuses on the model's ability to predict differential metabolic dependencies between normal and diseased cells, and responses to metabolic inhibitors [8]. For example, in colorectal cancer research, ecGEMs were validated by comparing predicted essential genes with experimental results from drug sensitivity assays and CRISPR screens [8]. Models were further validated by testing their predictions regarding the increased sensitivity of cancer cells to hexokinase inhibition when cultured in cancer-associated fibroblast-conditioned media, which was subsequently confirmed through viability assays and metabolic imaging using fluorescence lifetime imaging microscopy (FLIM) [8].

Essential Research Reagents and Tools

The development and validation of ecGEMs relies on a suite of computational tools, databases, and experimental methods. The table below summarizes key resources in the ecGEM research toolkit:

Table 3: Essential Research Toolkit for ecGEM Development and Validation

Resource Category	Specific Tools/Databases	Primary Function	Relevance to ecGEM Validation
Computational Frameworks	GECKO 3.0, ECMpy, AutoPACMEN	Automated ecGEM construction	Standardized pipelines for incorporating enzyme constraints into GEMs	[82] [3] [81]
Kinetic Databases	BRENDA, SABIO-RK	Repository of experimental enzyme kinetics	Source of curated kcat values for enzyme constraints	[13] [3]
Machine Learning Tools	DLKcat, TurNuP, Transformer models	kcat prediction from sequence/structure	Generate kinetic parameters when experimental data is unavailable	[13] [23] [82]
Proteomics Methods	Mass spectrometry, Immunoassays	Protein abundance quantification	Experimental data for validating predicted enzyme usage patterns	[6] [81]
Flux Measurement	13C Metabolic Flux Analysis	Experimental flux determination	Gold standard for validating predicted metabolic fluxes	[23] [1]
Phenotypic Assays	Growth rate measurements, Viability assays	Physiological characterization	Validation of predicted growth phenotypes and essential genes	[8] [1]
Metabolic Imaging	FLIM (Fluorescence Lifetime Imaging)	Spatial mapping of metabolism	Validation of metabolic perturbations in complex environments	[8]
Specialized Toolboxes	CORAL	Modeling promiscuous enzyme activities	Analysis of underground metabolism and enzyme redundancy	[6]

Independent validation studies consistently demonstrate that enzyme-constrained metabolic models outperform traditional GEMs across diverse biological contexts and applications. The enhanced predictive capability of ecGEMs stems from their fundamental grounding in the biophysical and biochemical constraints that shape real metabolic systems - particularly the limited cellular capacity for enzyme production and the kinetic limitations of enzymatic catalysis. As ecGEM methodologies continue to mature, with advances in machine learning-based kcat prediction, sophisticated frameworks for handling enzyme promiscuity, and integration with multi-omics data, these models are poised to become increasingly central to metabolic research, biotechnology, and biomedical applications. The continued independent validation of ecGEM predictions against experimental data remains crucial for refining model structures and parameters, ultimately enhancing their utility as predictive tools for understanding and engineering biological systems.

Conclusion

Enzyme-constrained models represent a significant evolution in metabolic modeling, moving beyond stoichiometry to incorporate the critical dimension of proteomic resource allocation. The comparative analysis of GECKO, sMOMENT, and ECMpy reveals a trade-off between model complexity, computational demand, and biological fidelity, allowing researchers to select the optimal tool for their specific organism and application. The integration of deep learning for kcat prediction is a pivotal advancement, democratizing ecGEM construction for less-studied organisms. For biomedical and clinical research, these refined models offer profound implications, from precisely identifying novel drug targets in pathogens to designing optimized Live Biotherapeutic Products (LBPs). Future progress hinges on expanding curated kinetic databases, improving the integration of multi-omics data, and developing standardized validation frameworks to fully realize the potential of ecGEMs in predictive biology and therapeutic design.

References

• 1. Genome-Scale Metabolic Modeling and Its Application to Microbial Communities - The Chemistry of Microbiomes - NCBI Bookshelf [https://www.ncbi.nlm.nih.gov/books/NBK447355/]
• 2. Frontiers | Constraint Based Modeling Going Multicellular [https://www.frontiersin.org/articles/10.3389/fmolb.2016.00003/full]
• 3. Automatic construction of metabolic with models enzyme constraints [https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-019-3329-9]
• 4. Reconstruction of a catalogue of genome-scale metabolic with... models [https://www.nature.com/articles/s41467-022-31421-1?error=cookies_not_supported&code=a19ba9c4-bf6c-41c0-a50c-6d09b19b525a]
• 5. Integration of enzymatic data in Bacillus subtilis genome-scale metabolic model improves phenotype predictions and enables in silico design of poly-γ-glutamic acid production strains - PubMed [https://pubmed.ncbi.nlm.nih.gov/30626384/]
• 6. Protein-constrained models pinpoints the role of underground metabolism in robustness of metabolic phenotypes - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC11951047/]
• 7. Next-generation metabolic models informed by biomolecular simulations - ScienceDirect [https://www.sciencedirect.com/science/article/abs/pii/S0958166925000035?via=ihub]
• 8. Merging metabolic modeling and imaging for screening therapeutic targets in colorectal cancer | npj Systems Biology and Applications [https://www.nature.com/articles/s41540-025-00494-1]
• 9. Integration of enzyme in a genome-scale constraints ... metabolic [https://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-021-01614-2]
• 10. Michaelis–Menten kinetics - Wikipedia [https://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics]
• 11. Michaelis-Menten Kinetics - Chemistry LibreTexts [https://chem.libretexts.org/Bookshelves/Biological_Chemistry/Supplemental_Modules_(Biological_Chemistry)/Enzymes/Enzymatic_Kinetics/Michaelis-Menten_Kinetics]
• 12. Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC5717222/]
• 13. Deep learning-based kcat prediction enables... | Nature Catalysis [https://www.nature.com/articles/s41929-022-00798-z?error=cookies_not_supported]
• 14. Automatic construction of metabolic models with enzyme ... constraints [https://pmc.ncbi.nlm.nih.gov/articles/PMC6961255/]
• 15. ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model - PubMed [https://pubmed.ncbi.nlm.nih.gov/35053213/]
• 16. Construction of an enzyme-constrained metabolic network model for Myceliophthora thermophila using machine learning-based kcat data | Microbial Cell Factories | Full Text [https://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-024-02415-z]
• 17. NNKcat: deep neural network to predict catalytic constants ( Kcat ) by... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12078937/]
• 18. Molecular Weight Calculator Protein [https://www.biocalcs.com/calculators/Protein-MW-Calculator]
• 19. Reconstruction of a catalogue of genome-scale metabolic models with enzymatic constraints using GECKO 2.0 | Nature Communications [https://www.nature.com/articles/s41467-022-31421-1]
• 20. predictions for kinetically uncharacterized Turnover ... number enzymes [https://www.nature.com/articles/s41467-023-39840-4?error=cookies_not_supported&code=8f7a394f-27a7-4d61-a718-82bf246035a6]
• 21. An Atlas of Human Metabolism - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC7331181/]
• 22. Reconstruction, simulation and analysis of enzyme - constrained ... [https://www.nature.com/articles/s41596-023-00931-7?error=cookies_not_supported&code=9d4b6142-d83b-4c2c-9d47-c819248276a8]
• 23. ICML An Improved Systematic Method for Constructing... [https://icml.cc/virtual/2025/51242]
• 24. Reconstruction, simulation and analysis of enzyme - constrained ... [https://orbit.dtu.dk/en/publications/reconstruction-simulation-and-analysis-of-enzyme-constrained-meta]
• 25. Integrating thermodynamic and enzymatic into... constraints [https://pubmed.ncbi.nlm.nih.gov/34174426/]
• 26. Principles of proteome allocation are revealed using proteomic data and genome-scale models | Scientific Reports [https://www.nature.com/articles/srep36734]
• 27. and utilization in the versatile chemolithoautotroph... Protein allocation [https://elifesciences.org/articles/69019]
• 28. Reconstruction, simulation and analysis of enzyme-constrained metabolic models using GECKO Toolbox 3.0 | Springer Nature Experiments [https://experiments.springernature.com/articles/10.1038/s41596-023-00931-7?error=cookies_not_supported&code=1fc8431b-d9a5-4a27-9b54-f811dfd76672]
• 29. GitHub - SysBioChalmers/ GECKO : Toolbox for including enzyme... [https://github.com/SysBioChalmers/GECKO]
• 30. ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC8773657/]
• 31. ECMpy, a Simplified Workflow for Constructing Enzymatic Constrained Metabolic Network Model | MDPI [https://www.mdpi.com/2218-273X/12/1/65]
• 32. Frontiers | Constraint-Based Reconstruction and Analyses of Metabolic Models: Open-Source Python Tools and Applications to Cancer [https://www.frontiersin.org/journals/oncology/articles/10.3389/fonc.2022.914594/full]
• 33. . E as a Model coli : Advantages & Limitations | Boster Bio Organism [https://www.bosterbio.com/blog/post/e-coli-as-a-model-organism]
• 34. Analysis of Transcriptomic Response of Comparative ... Escherichia [https://pubmed.ncbi.nlm.nih.gov/36853057/]
• 35. What is a Model Organism ? Moving Beyond E . coli [https://asm.org/articles/2025/february/what-is-a-model-organism-moving-beyond-e-coli]
• 36. Deep learning-based kcat prediction enables improved enzyme-constrained model reconstruction | Nature Catalysis [https://www.nature.com/articles/s41929-022-00798-z]
• 37. DLTKcat: deep learning-based prediction of temperature-dependent... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10772988/]
• 38. Biochemical Reaction Kinetics Database SABIO [https://www.sabio.h-its.org/]
• 39. GitHub - SysBioChalmers/DLKcat: Deep learning and Bayesian approach applied to enzyme turnover number for the improvement of enzyme-constrained genome-scale metabolic models (ecGEMs) reconstruction [https://github.com/SysBioChalmers/DLKcat]
• 40. Adaptations in metabolism and protein translation give rise to the... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8713813/]
• 41. Overflow metabolism originates from growth optimization and cell heterogeneity - PubMed [https://pubmed.ncbi.nlm.nih.gov/40472190/]
• 42. A Study on the Fundamental Mechanism and the... | PLOS One [https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0116942]
• 43. Improving the phenotype predictions of a yeast genome‐scale metabolic model by incorporating enzymatic constraints - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC5572397/]
• 44. Understanding P. kluyveri and Its Unique Metabolism - Simple Science [https://scisimple.com/en/articles/2025-06-18-understanding-p-kluyveri-and-its-unique-metabolism--akx0x51]
• 45. MultiMetEval: Comparative and Multi-Objective Analysis of... [https://pmc.ncbi.nlm.nih.gov/articles/PMC3522732/]
• 46. - Enzyme and in silico constrained ... metabolic model metabolic [https://pmc.ncbi.nlm.nih.gov/articles/PMC10543971/]
• 47. Construction and Analysis of an Enzyme-Constrained Metabolic Model of Corynebacterium glutamicum - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC9599660/]
• 48. Automatic construction of metabolic models with enzyme constraints - PubMed [https://pubmed.ncbi.nlm.nih.gov/31937255/]
• 49. Therapeutic enzyme engineering using a generative neural network | Scientific Reports [https://www.nature.com/articles/s41598-022-05195-x]
• 50. of Optimization- Comparison Methods for Metaboli... Modelling [https://www.degruyterbrill.com/document/doi/10.1515/jib-2019-0073/html]
• 51. -based kcat prediction enables... | Nature Catalysis Deep learning [https://www.nature.com/articles/s41929-022-00798-z?error=cookies_not_supported&code=3039ed19-c12c-464f-92c3-b1bc1a8aa7c9]
• 52. Reconstruction, simulation and analysis of enzyme - constrained ... [https://pubmed.ncbi.nlm.nih.gov/38238583/]
• 53. sciencedirect.com/topics/engineering/ flux - control - coefficient [https://www.sciencedirect.com/topics/engineering/flux-control-coefficient]
• 54. Algebraic differentiation for fast sensitivity analysis of optimal flux ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12133274/]
• 55. A compact model of Escherichia coli core and biosynthetic metabolism [https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013564]
• 56. Proteomics and constraint-based modelling reveal enzyme kinetic properties of Chlamydomonas reinhardtii on a genome scale - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC10409818/]
• 57. Proteomics Applications in Health: Biomarker and Drug Discovery and Food Industry - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC6269565/]
• 58. Using Proteomics to Improve the Drug Development Process - MetwareBio [https://www.metwarebio.com/using-proteomics-to-improve-the-drug-development-process/]
• 59. Frontiers | An integrated approach for analyzing spatially resolved... [https://www.frontiersin.org/journals/molecular-biosciences/articles/10.3389/fmolb.2025.1614288/full]
• 60. Challenges with Integrating and Transcriptomics Proteomics Data [https://www.elucidata.io/blog/uniting-the-omics-integrating-proteomics-and-transcriptomics-data]
• 61. of Integration with other proteomics datasets | Fiveable data omics [https://fiveable.me/proteomics/unit-9/integration-proteomics-data-omics-datasets/study-guide/ws5NIOrs7TeTn5Au]
• 62. of Integration and Other Proteomics | SpringerLink Omics Data [https://link.springer.com/protocol/10.1007/978-1-0716-1641-3_18]
• 63. Using proteomics to improve the drug development process ~ Nautilus Biotechnology [https://www.nautilus.bio/blog/using-proteomics-to-improve-the-drug-development-process/]
• 64. Robust Prediction of Enzyme Variant Kinetics with RealKcat - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC11844551/]
• 65. A systematic comparison of error correction enzymes by next-generation sequencing - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC5587813/]
• 66. Large-scale kinetic of Pseudomonas putida... metabolic models [https://biotechnologyforbiofuels.biomedcentral.com/articles/10.1186/s13068-020-1665-7]
• 67. Central Metabolism and Growth Impacts on Hydrogen and... Rate [https://pmc.ncbi.nlm.nih.gov/articles/PMC9335129/]
• 68. Enhanced flux potential analysis links changes in enzyme expression... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11965317/]
• 69. High-resolution 13 C metabolic flux analysis [https://www.nature.com/articles/s41596-019-0204-0]
• 70. A genome-scale metabolic model accurately predicts fluxes in central carbon metabolism under stress conditions - PubMed [https://pubmed.ncbi.nlm.nih.gov/20605915/]
• 71. Profiling the metabolism of human cells by deep 13C labeling - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC6239935/]
• 72. C-assisted metabolic 13 analysis to investigate heterotrophic and... flux [https://link.springer.com/article/10.1007/s11306-017-1302-z]
• 73. A 13C isotope labeling method for the measurement of lignin metabolic flux in Arabidopsis stems | Plant Methods | Full Text [https://plantmethods.biomedcentral.com/articles/10.1186/s13007-018-0318-3]
• 74. Reconstruction, simulation and analysis of enzyme-constrained metabolic models using GECKO Toolbox 3.0 | Nature Protocols [https://www.nature.com/articles/s41596-023-00931-7]
• 75. Improving pathway prediction of accuracy -based... constraints [https://pmc.ncbi.nlm.nih.gov/articles/PMC10514394/]
• 76. Enzyme‐constrained models predict the dynamics of Saccharomyces... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9049605/]
• 77. Evaluating E . coli genome‐scale metabolic model accuracy with... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10698504/]
• 78. Metabolic network modelling - Wikipedia [https://en.wikipedia.org/wiki/Metabolic_network_modelling]
• 79. Integration of enzymatic data in Bacillus subtilis genome-scale metabolic model improves phenotype predictions and enables in silico design of poly-γ-glutamic acid production strains | Microbial Cell Factories | Full Text [https://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-018-1052-2]
• 80. gapseq: informed prediction of bacterial metabolic pathways and reconstruction of accurate metabolic models | Genome Biology | Full Text [https://genomebiology.biomedcentral.com/articles/10.1186/s13059-021-02295-1]
• 81. Reconstruction, simulation and analysis of enzyme - constrained ... [https://colab.ws/articles/10.1038%2Fs41596-023-00931-7]
• 82. Construction of an enzyme - constrained metabolic network model for... [https://www.researchsquare.com/article/rs-3927159/v1]