EnzymeTuning improves enzyme-constrained metabolic modeling and proteome abundance prediction through deep learning

Abstract

The accuracy of enzyme kinetic parameters, particularly enzyme turnover numbers (k_cat), is critical for the predictive performance of enzyme-constrained genome-scale metabolic models. However, currently available kinetic datasets remain sparse and often fail to capture in vivo enzyme behavior, thereby limiting model accuracy. To address these limitations, we develop EnzymeTuning, a generative adversarial network-based framework for global k_cat optimization. By further incorporating literature-derived protein degradation constants, we infer protein synthesis rates and systematically assess their impact on model performance. Here, we show that EnzymeTuning substantially improves prediction accuracy and expands proteome-level coverage across diverse organisms, including Saccharomyces cerevisiae, Kluyveromyces lactis, Kluyveromyces marxianus, Yarrowia lipolytica, and Escherichia coli. Furthermore, EnzymeTuning reveals context-dependent enzyme usage patterns and adaptive catalytic resource allocation under diverse carbon- and nitrogen-limited chemostat conditions, underscoring the substantial potential of this framework for integrative multi-omics analyses.

The accuracy of enzyme kinetic parameters is critical for the predictive performance of enzyme-constrained genome-scale metabolic models. Here the authors present EnzymeTuning, a generative adversarial network-based framework that refines enzyme parameters to improve metabolic models.

Introduction

Enzyme-constrained genome-scale metabolic models (ecGEMs) have emerged as powerful computational platforms for simulating cellular growth, metabolic reprogramming, and protein resource allocation. By integrating enzymatic capacity constraints, ecGEMs provide unprecedented insights into the regulation of metabolic networks and facilitate the optimization of microbial biosynthesis for high-value compounds such as pharmaceutical precursors^1,2. Owing to these advantages, ecGEMs have been widely applied in metabolic engineering to enhance the yield of target products³. Notably, the development of the GECKO 3.0 toolbox has simplified ecGEM construction across diverse species, enabling applications in both microbial systems (e.g., Saccharomyces cerevisiae) and mammalian cells (e.g., Chinese hamster ovary cells) for metabolic optimization⁴.

The predictive capacity of ecGEMs relies heavily on accurate enzyme kinetics, particularly the enzyme turnover number (k_cat)^1,5. In metabolic networks, k_cat values not only directly determine reaction fluxes but also modulate global metabolic flux distribution through protein resource allocation⁵. Nevertheless, the determination of physiologically relevant k_cat values remains a formidable challenge due to time-consuming in vitro methods that lack biological relevance^6,7. The low throughput of such assays has further resulted in sparse and error-prone kinetic datasets, thereby limiting the application of ecGEMs⁸.

To overcome these limitations, deep learning (DL)-based approaches have emerged as promising tools for large-scale kinetic parameter inference^9,10. Sequence-based tools, such as DLKcat and TurNup, leverage graph neural networks or Transformer architectures to predict k_cat values from protein sequences and substrate structures^11,12.

More recently, advanced frameworks like UniKP, CatPred, and DEKP have further integrated pre-trained protein language models and 3D structural information to enhance prediction robustness and coverage^9,13,14. While these “bottom-up” methods provided valuable initial estimates for uncharacterized enzymes, they inherently generated point estimates based on physicochemical properties, often neglecting the system-level physiological constraints (e.g., metabolic flux balance and proteome capacity) that govern in vivo enzyme behavior. Consequently, direct integration of these predicted enzyme kinetic parameter values into ecGEMs often led to suboptimal phenotype and protein abundance predictions.

To address the discrepancy between in vitro potentials and in vivo states, model-based refinement strategies (“top-down” methods) have been developed to calibrate k_cat values, thereby narrowing the gap between model predictions and experimentally measured values. Early approaches, such as the heuristic tuning in GECKO, manually adjusted the k_cat of growth-limiting enzymes to match experimental growth rates, but often failed to capture global proteome allocation patterns⁴. Statistical inference methods, such as Bayesian approaches and PRESTO, offered more rigorous corrections by integrating quantitative proteomics data to infer posterior parameter distributions^11,15. Additionally, hybrid frameworks like CAMEL coupled ecGEMs with machine learning (ML) regressors to improve abundance predictions¹⁶. However, these approaches were constrained by inherent methodological limitations. Bayesian frameworks were often computationally intensive and sensitive to prior distributions, whereas optimization-based methods (e.g., PRESTO) typically yielded deterministic point estimates that neglected biological variability. Furthermore, hybrid ML predictors often operated as “black boxes”, failing to provide the explicit, mechanistic parameters necessary for rational strain design.

Generative adversarial networks (GANs), a DL algorithm based on adversarial training between a generator and a discriminator, have been widely applied in biological engineering^17,18. For instance, GAN-based models have facilitated dimensionality reduction and feature extraction in single-cell RNA sequencing analysis, providing deeper insights into cellular heterogeneity¹⁹. Strikingly, GANs offer a data-efficient and distribution-oriented strategy for kinetic parameter inference. Recently, GANs have been applied to optimize kinetic parameters (e.g., Michaelis–Menten constant) in biologically relevant kinetic models, enabling the exploration of metabolic states with limited data²⁰. Nevertheless, the application of GANs to enzyme parameter inference in ecGEMs remains underexplored.

In this study, we develop a GAN-based framework named EnzymeTuning for global k_cat optimization within ecGEMs. Distinct from sequence-based methods (e.g., DLKcat, UniKP) that focused on single enzymes, EnzymeTuning functions as a “model refiner” that enforces global consistency between metabolic fluxes and proteome resources. Unlike sampling-based methods that are often limited by strong prior dependencies, EnzymeTuning enables a global and allocated inference of kinetic parameters. This formulation allows the model to learn biologically feasible distributions constrained by global proteomic resources, providing a robust alternative that reflects context-specific metabolic regulation. This approach has effectively improved the quantitative prediction of protein abundances in ecGEMs. Beyond k_cat inference, we extend EnzymeTuning to infer protein synthesis rates, thereby enabling a systematic evaluation of the predictive performance of ecGEMs upon incorporation of these rates as constraints. We validate the general applicability and superiority of EnzymeTuning by optimizing ecGEMs for Kluyveromyces lactis, Kluyveromyces marxianus, Yarrowia lipolytica, and Escherichia coli, achieving substantial improvements in protein abundance prediction. Furthermore, to investigate context-specific enzyme utilization, we analyze the shifting in vivo k_cat distributions from carbon-limited to nitrogen-limited chemostat conditions, revealing condition-dependent reprogramming of protein resource allocation. In addition, we demonstrate the practical utility of the ecGEM from EnzymeTuning by predicting key gene targets for enhanced product yields, highlighting the potential application of our toolbox in metabolic engineering. Collectively, our study introduces a robust, scalable, and generalizable computational framework for refining kinetic parameters in ecGEMs, paving the way for improved predictive modeling in systems and synthetic biology.

Results

Framework of EnzymeTuning

The EnzymeTuning framework employed a three-step optimization workflow initialized with Bayesian posterior distributions of k_cat values (Fig. 1)¹¹. In step 1, the initial parameter sets were first screened using empirical reference of Bayesian method for predicting growth phenotypes (the root mean squared error, RMSE < 2) and protein abundances (Pearson correlation coefficient, PCC > 0.4). Subsequently, high-performance sets were identified based on a comprehensive discriminator score, forming a labeled training dataset for a conditional generative adversarial network (cGAN)²⁰. In step 2, the cGAN architecture was iteratively trained to reproduce the distribution of high-performance k_cat sets. After each training generation, the top 100 parameter sets were evaluated with the ecGEM. In step 3, the generated parameter sets were systematically evaluated under various conditions, including carbon-limited and nitrogen-limited chemostat conditions, to assess both their rationality and the generalizability of the framework.

Fig. 1. Overview of the EnzymeTuning framework.

EnzymeTuning is a generative adversarial network (GAN)-based framework designed for the global, synergistic optimization of enzyme turnover numbers (k_cat). By leveraging a generator-discriminator mechanism constrained by multi-omics data, the framework captures the in vivo kinetic behavior of enzymes. Validation across species and industrial case studies demonstrates its potential in pinpointing metabolic bottlenecks for rational strain design.

In step 1, using the model organism S. cerevisiae as a representative case, its ecGEM was first updated using the k_cat parameter set derived from the Bayesian posterior distribution (Supplementary Fig. 1). The growth phenotype prediction was evaluated via RMSE under both batch and carbon-limited chemostat conditions. After 100 generations, the posterior-parameterized ecGEM achieved RMSEs below 1 with a k_cat distribution closely resembling those from DL-based methods (Supplementary Fig. 1a, b). The updated ecGEM also reproduced the Crabtree effect, improving the performance of phenotype prediction compared with the previous version (Supplementary Fig. 1c). For protein abundance prediction, the predicted abundances of metabolic enzymes in the updated ecGEM were compared with experimentally measured quantitative proteomics data under carbon-limited chemostat conditions (Supplementary Fig. 1d). The average PCC was 0.318 (P value < 0.05), indicating a modest predictive performance. Relative to the proteomics dataset, the updated ecGEM exhibited a high proportion of extreme enzyme abundance predictions, defined as predicted/measured abundance ratios greater than 100 or less than 0.01, which accounted for approximately one-fourth to one-third of all predictable enzymes. The combination of a modest PCC and a substantial fraction of extreme enzyme predictions further indicated the suboptimal accuracy of protein abundance prediction (Supplementary Fig. 1e, f).

Subsequently, we evaluated the EnzymeTuning framework for global k_cat tuning. Given that the Bayesian-based ecGEM achieved accurate growth phenotype predictions, our optimization primarily focused on k_cat parameters that were insensitive to growth phenotype prediction but poorly captured protein abundance. In this study, we conducted a global sensitivity analysis of k_cat parameters using the SALib method (Fig. 2a, b)²¹. Specifically, each k_cat value was individually perturbed by random sampling within seven ranges of the initial k_cat values: 1–3%, 10–30%, 50–70%, 90–110%, 110–130%, 150–170%, and 900–1100% (Fig. 2c). The first-order sensitivity coefficient (S1) and the total-order sensitivity coefficient (ST) from SALib were used to quantify parameter sensitivity. Since higher S1 and ST values indicated greater parameter influence on growth phenotype prediction, the top 25% of k_cat parameters with the highest S1 and ST values were classified as sensitive. Here, S1 quantified the effect of individual k_cat variations, whereas the ST value accounted for the combined influence of multiple k_cat parameters. By intersecting the set of k_cat parameters that were insensitive to growth phenotype prediction with those associated with extreme protein abundance predictions (Fig. 2d–f), a total of 237 k_cat parameters were identified for subsequent optimization using the EnzymeTuning framework.

Fig. 2. Sensitivity analysis of the k_cat optimization process and comparison of discriminator score effects.

a The workflow of the EnzymeTuning framework for k_cat prediction. b The workflow of the sensitivity analysis. c Cumulative distribution function (CDF) curves for the sensitivity analysis results. S1 first-order sensitivity index, ST total-order sensitivity index. d Venn diagram illustrating the intersection of k_cat values between ST and S1. e Venn diagram depicting the intersection of k_cat values between S1 and the set of extreme enzymes. f Venn diagram illustrating the intersection of k_cat values between ST and extreme enzymes. Comparison of the total number of predictable enzymes (g), the number of extreme enzymes (h), Pearson correlation coefficients of protein abundance predictions (i) with different discriminator scores. The annotations above the figure represented the two-sided t-test results comparing the GAN method with the discriminator score of Eq. 3 (GAN_corr) and the GAN method with the discriminator score of Eq. 4 (GAN_corr_rmse) groups, the GAN_corr and the GAN method with the discriminator score of Eq. 2 (GAN), and the GAN_corr_rmse and GAN groups, respectively. The data are derived from n = 9 independent experiments, each performed with biological triplicates. In each box plot, the central band represents the median, the box limits represent the upper and lower quartiles, and the whiskers extend to 1.5 times the interquartile range beyond the box range. Raw values are provided in the Source data.

Influence of key parameters on EnzymeTuning performance

To effectively improve the protein abundance prediction of ecGEMs, three performance aspects must be evaluated: (1) increasing the number of predictable enzymes, (2) reducing the number of extreme enzymes, and (3) improving prediction accuracy as quantified by the PCC. Here, we focused on reducing the extreme enzyme values (Eq. 1) by progressively optimizing enzyme subsets defined at five levels of fold changes between predicted and measured abundances: >100 or <0.01; >50 or <0.02; >10 or <0.1; >5 or <0.2; and >2 or <0.5. These groups comprised 198, 258, 369, 424, and 510 enzyme-reaction pairs, respectively. Across all groups, EnzymeTuning achieved robust and steadily converging predictive performance, indicating that the framework is not sensitive to the size of enzymes (Supplementary Fig. 2a–e). Importantly, the group with fold changes >50 or <0.02 yielded the best training outcome, achieving the highest number of predictable enzymes while maintaining a relatively low number of extreme enzymes (Supplementary Fig. 2f–h).

$$\mathrm{Fold}\mathrm{change}=\sqrt{\frac{1}{n}{\sum }_{i=0}^n\frac{\log {\mathrm{Predicted}\mathrm{abundance}}_i}{\log {\mathrm{Measured}\mathrm{abundance}}_i}}$$ 1

In addition, we investigated the impact of the discriminator score used during training on protein abundance prediction accuracy. Initially, we employed a discriminator score that simultaneously maximized the PCC and minimized the fold change between predicted and measured protein abundances (Eq. 2). As shown in Supplementary Fig. 3, this strategy led to a slight increase in the total number of predictable proteins from 289 to 298 (Supplementary Fig. 3a) and a modest decrease in the number of extreme enzymes from 84 to 70 (Supplementary Fig. 3b). By contrast, the PCC exhibited a statistically significant increase from 0.345 to 0.447 (Supplementary Fig. 3c, P < 0.05). These results suggested that while using PCC as an evaluation criterion for k_cat parameter sets enhanced prediction accuracy, directly optimizing fold change exerted a limited impact on reducing the number of extreme enzymes. This might be because averaging fold changes in protein abundance predictions diluted the influence of some extreme cases (e.g., fold change > 10,000). To address this, we replaced fold change with the number of extreme enzymes as the discriminator score (Eq. 3). Furthermore, to ensure generalizability where k_cat parameters were not pre-adjusted based on growth phenotype prediction, we extended the approach to Eq. 4 by incorporating growth phenotype prediction accuracy alongside protein abundance prediction for all k_cat parameters.

$$\min \mathrm{Normalized}\left(1-\mathrm{PCC}\right)+\mathrm{Noramlized}\left(\mathrm{fold}\mathrm{change}\right)$$ 2

$$\min \mathrm{Normalized}\left(1-\mathrm{PCC}\right)+\mathrm{Noramlized}\left(\mathrm{extreme}\_\mathrm{number}\right)$$ 3

$$\min \mathrm{Normalized}\left(1-\mathrm{PCC}\right)+\mathrm{Noramlized}\left(\mathrm{extreme}\_\mathrm{number}\right)+\mathrm{Normalized}\left(\mathrm{RMSE}\right)$$ 4

Here, fold change was the log₁₀-transformed ratio of predicted to measured protein abundances, and extreme_number represented the number of extreme enzymes.

Based on these three discriminator scores, we adjusted the EnzymeTuning framework and compared the resulting protein abundance prediction (Fig. 2g–i). The ecGEMs parameterized with k_cat sets optimized using Eqs. 3 and 4 did not exhibit significant changes in the number of predictable proteins; however, both approaches consistently outperformed the Eq. 2-based optimization (Fig. 2g). Across all three methods, simultaneously considering the number of extreme enzymes and growth phenotype prediction (RMSE) led to a significant reduction in the number of extreme enzymes and a marked increase in PCC for protein abundance prediction (Fig. 2h, i). These results highlighted that incorporating growth phenotype prediction accuracy was crucial for constructing realistic k_cat distributions. Growth phenotype directly reflected the global balance of intracellular metabolic fluxes. Thus, ensuring accurate phenotype predictions indirectly constrained the feasible flux space of the metabolic models, thereby narrowing the solution space for the k_cat values and guiding them toward biologically realistic enzyme catalytic capabilities. Consequently, Eqs. 3 and 4 were established as the final discriminator scores. Equation 3 was employed for k_cat tuning within the specific parameter subset after sensitivity analysis, whereas Eq. 4 was applied to global k_cat optimization. Both metrics were utilized in the subsequent modeling analyses.

EnzymeTuning improves the quantitative proteomics prediction

In step 2, we applied the EnzymeTuning framework to optimize the 237 k_cat parameter sets identified through sensitivity analysis. The model was trained for 50 generations, generating a new k_cat parameter distribution every 10 epochs. Quantitative proteomics datasets under both carbon-limited and nitrogen-limited chemostat conditions, obtained from the literature, were used to validate the generalizability and robustness of the predicted outcomes²².

As shown in Fig. 3a, b, the PCC for protein abundance predictions steadily increased, whereas the prediction error consistently decreased across training generations. These trends indicated that the generator within the EnzymeTuning framework successfully learned to produce k_cat distributions yielding progressively more accurate protein abundance predictions. Moreover, the training process exhibited convergence (Fig. 3c), confirming the reliability and stability of the EnzymeTuning framework. Subsequently, we parameterized the ecGEM with the k_cat values optimized by EnzymeTuning and compared its predictive performance with the Bayesian-based ecGEM (Fig. 3d–g). The results revealed an increase in PCC for protein abundance predictions (Fig. 3d) and a reduction in the number of extreme enzymes (Fig. 3e), while maintaining the total number of predicted proteins (Fig. 3f). While the PCC remained largely stable in later generations, analysis of the generated k_cat distributions showed that the mean values gradually converged and the associated standard deviations decreased as training proceeded (Supplementary Fig. 4a, b). Moreover, the PCA trajectory demonstrated that iteration-wise k_cat mean vectors collapsed into a compact region in parameter space during later generations (Supplementary Fig. 4c). These results indicated that EnzymeTuning generated robust and stable k_cat distributions, and thus effectively improved the accuracy of protein abundance predictions. Importantly, similar improvements were also observed under three alternative nitrogen source conditions (glutamate, isoleucine, and phenylalanine) (Supplementary Fig. 5), further validating the generalizability of the framework.

Fig. 3. Performance of the GAN approach for protein abundance prediction.

a Changes in the criteria values calculated via Eq. 1 during GAN training. b Changes in Pearson correlation coefficients for protein abundance predictions in the training process. Data are presented as median ± SD based on generated k_cat parameter sets (n = 100) per generation. c Discriminator loss (green), generator loss (orange), and discriminator accuracy (blue) over training epochs. d Comparison of Pearson correlation coefficients of protein abundance predictions between the GAN method and the Bayesian approach. e Comparison of the number of extreme enzymes using the GAN method and the Bayesian approach. f Comparison of the total number of predictable enzymes using the GAN method versus the Bayesian approach. g Pearson correlation coefficients and corresponding P values for protein abundance predictions across GAN training. P value was calculated using a two-sided t-test. *P value < 0.05, **P value < 0.01, ***P value < 0.005. The data are derived from n = 9 independent experiments, each performed with biological triplicates. In each box plot, the central band represents the median, the box limits represent the upper and lower quartiles, and the whiskers extend to 1.5 times the interquartile range beyond the box range. Raw values are provided in the Source data.

To rigorously evaluate the performance of EnzymeTuning, we conducted a comprehensive benchmark analysis against three representative state-of-the-art k_cat inference approaches (Bayesian-based ecGEM, PRESTO, and CAMEL) in S. cerevisiae under carbon-limited chemostat conditions on a standard workstation (Intel i7-12700H, RTX 3050 Ti). The comparison focused on phenotype prediction fidelity, proteome abundance accuracy, and computational utility (Table 1).

Table 1.

Comparison of EnzymeTuning with representative k_cat inference approaches in S. cerevisiae under carbon-limited chemostat cultivation

Methods		Bayesian11	PRESTO15	CAMEL16	EnzymeTuning
Phenotype accuracy	RMSE	0.732	1.170	1.495	0.789
Proteome accuracy	PCC	0.301	0.371	0.356	0.426
	Predictable number	262	260	259	265
	Extreme enzyme	53	76	59	46
Efficiency	Runtime	~24 h	~7 h	~6 h	~24 h

All computational tasks were performed on a standardized workstation equipped with an Intel Core i7-12700H CPU and an NVIDIA GeForce RTX 3050 Ti GPU, operating on Windows 11.

In terms of phenotype prediction, EnzymeTuning achieved an RMSE of 0.789, which was lower than that of CAMEL (1.495) and PRESTO (1.170), indicating that the GAN-based ecGEM accurately captured the growth phenotypes (Supplementary Fig. 6). Beyond the overall RMSE comparison, the Bayesian and GAN-based methods were superior in simulating the trends of specific exchange rates, such as glucose and oxygen uptake rates under carbon-limited chemostat conditions. Beyond growth predictions, EnzymeTuning demonstrated superior performance in predicting intracellular protein levels with a higher PCC between predicted and measured protein abundances (Table 1). In addition, pathway-level analysis using EnzymeTuning further demonstrated that high prediction accuracy was achieved for central carbon metabolic pathways, including glycolysis/gluconeogenesis (PCC = 0.54, P value < 0.05), pyruvate metabolism (PCC = 0.52, P value < 0.05), and the pentose phosphate pathway (PCC = 0.68, P value < 0.05) (Supplementary Fig. 7). These results suggested that EnzymeTuning not only enhanced the overall protein abundance prediction but also effectively captured the protein allocation patterns in the central carbon metabolic pathways. Furthermore, EnzymeTuning achieved a proteome coverage comparable to that of the Bayesian method, enabling the prediction of 265 enzymes versus 262 for the Bayesian-based ecGEM. Notably, the number of extreme enzymes was reduced to 46, suggesting that EnzymeTuning generated k_cat distributions that were more consistent with in vivo proteomic constraints.

We also compared the computational costs of these methods (Table 1). The total runtime for EnzymeTuning was approximately 24 h, which was comparable to that of the Bayesian-based method, yet higher than the CAMEL (~6 h) and PRESTO (~7 h). The computational gap can be greatly mitigated by leveraging high-performance computing (HPC) clusters. Given the parallelizable nature of the algorithm, the increased computational demand was a trade-off for its superior accuracy in capturing in vivo proteomic constraints and minimizing prediction errors.

Estimation of protein synthesis rates (v_syn) for “dark proteins” inferred by EnzymeTuning

Despite optimization with EnzymeTuning, the ecGEM did not show a significant increase in the number of predictable proteins. In the S. cerevisiae ecGEM, 1151 metabolic enzymes are represented, while only 200–300 enzymes had their abundances predicted, leaving many enzymes unaccounted for. This limitation might arise because most metabolic reactions in the genome-scale network lack constraints, rendering them inactive (flux = 0). This discrepancy highlights a substantial fraction of experimentally abundant yet computationally “silent” enzymes (flux = 0), which we collectively term “dark proteins” due to their functional invisibility in the ecGEM. To address this, we sought to broaden the predictive scope by constraining enzyme abundances using predicted v_syn, which were derived from literature-reported protein degradation constants (k_deg) (Fig. 4a)^23,24.

Fig. 4. Performance of the GAN approach for protein synthesis rate prediction.

a The workflow of the GAN approach for protein synthesis rate prediction. b Discriminator loss (green), generator loss (orange), and discriminator accuracy (blue) over training epochs. c Comparison of the total number of predictable enzymes using the GAN method versus the GAN method for protein synthesis rate (GAN + v_syn). d Comparison of the number of extreme enzymes using the GAN method and the GAN method for protein synthesis rate (GAN + v_syn). e Comparison of Pearson correlation coefficients of protein abundance predictions between the GAN method and GAN method for protein synthesis rate (GAN + v_syn). P value was calculated using a two-sided t-test. The data are derived from n = 9 independent experiments, each performed with biological triplicates. In each box plot, the central band represents the median, the box limits represent the upper and lower quartiles, and the whiskers extend to 1.5 times the interquartile range beyond the box range. f Correlation between GAN-predicted v_syn values and v_syn values calculated via Eq. 5. P value for the Pearson correlation coefficient was calculated using a two-sided t-test. g Venn diagram representing the overlap predicted proteins between the GAN method and the GAN method with protein synthesis rate (GAN + v_syn). The GO enrichment results of proteins uniquely predicted by the GAN method (h) and the GAN + v_syn method (i). Raw values are provided in the Source data.

Using protein mass conservation relationships and k_deg values, we converted degradation rates into corresponding protein synthesis rates (v_syn) (Eqs. 6–9). Initially, we constrained the ecGEM with all available v_syn values; however, this over-constraining markedly reduced predictive performance. Consequently, we sought an optimal range of v_syn constraints that maximized improvements in protein abundance prediction. To this end, we ranked the experimentally measured protein abundances of dark proteins in descending order, and selected the top 10, 25, 50, 60, 70, 80, 90, 100, 110, 120, 130, 150, 170, 200, 300, and 400 proteins as candidate datasets for v_syn optimization. The comparative analyses (Supplementary Fig. 8) revealed that constraining the top 100 v_syn values provided the best trade-off between protein abundance prediction and phenotype prediction accuracy. These optimized v_syn values were subsequently used to define the upper and lower bounds of enzyme exchange reactions.

As shown in Fig. 4b, the EnzymeTuning framework exhibited stable convergence during v_syn optimization, confirming the stability of the learned k_cat distributions. To evaluate the effect of introducing additional constraints, we compared two ecGEM variants under batch cultivation: (1) parameterized solely with GAN-optimized k_cat values, and (2) further constrained with v_syn-derived protein synthesis bounds. The v_syn-constrained ecGEM demonstrated superior predictive performance with the number of predictable enzymes increasing to ~400 and a marked reduction in the number of extreme enzyme (Fig. 4c–e). Collectively, these improvements highlighted the potential of v_syn constraints to substantially expand the predictive scope and accuracy of ecGEMs.

Comparison of protein synthesis rates (v_syn) estimated by ecGEM and those derived from protein degradation constants (k_deg) revealed that the ecGEM-predicted v_syn values were generally higher (Fig. 4f). This discrepancy reflected that ecGEM simulations focused primarily on protein synthesis without fully accounting for protein degradation. V_syn represented the total rather than net synthesis rates, thus potentially leading to overestimation. Nevertheless, the two approaches were strongly correlated (r = 0.91), indicating that ecGEM reliably captured the relative variations in synthesis rates despite absolute offsets. This was consistent with previous findings that protein synthesis rates were major determinants of protein abundance^25,26. We further evaluated the performance of protein synthesis rate prediction in Supplementary Fig. 9. The density distribution of log₁₀-transformed v_syn values for predicted and measured data (Supplementary Fig. 9a) demonstrated substantial overlap, indicating that the model accurately reproduced the global distribution of v_syn. Residual analysis (Supplementary Fig. 9b) revealed small and unbiased errors across most of the range, with slightly increased variance at high synthesis rates. Consistently, the comparison of predicted and measured v_syn values showed a strong linear relationship, with an R² of 0.90 (Supplementary Fig. 9c), confirming that the model provided quantitatively accurate estimates of protein synthesis rates.

To identify which proteins benefited from the incorporation of v_syn constraints, we compared the predicted protein abundances between the v_syn-constrained GAN-based ecGEM and the original GAN-based ecGEM. Gene Ontology (GO) enrichment analysis was then performed for proteins uniquely predictable by each model (Fig. 4g–i). Proteins predicted exclusively by the GAN-based ecGEM were primarily enriched in GO terms associated with core metabolism and cellular maintenance functions, including cofactor metabolic process and cellular amino acid metabolic process (Fig. 4h). Interestingly, several GO categories related to peripheral or conditional-specific processes, such as conjugation, meiotic cell cycle, and regulation of cell cycle, were also enriched. The enrichment of these GO terms suggested that the GAN-based ecGEM was capable of accommodating proteins whose expression was weakly constrained by core metabolic objectives. These proteins might vary in a context-dependent manner, rather than being limited to enzymes with strong growth coupling.

By contrast, proteins that became predictable only after introducing v_syn constraints were enriched in cellular ion homeostasis (Fig. 4i), a category typically characterized by low expression, high variability, and strong post-transcriptional regulation²⁷. This category typically comprised transporters, such as H⁺/Na⁺ pumps and metal ion transporters, whose abundances were sensitive to environmental fluctuations and translational regulation²⁸. Such proteins often exhibited weak correlations between metabolic flux demands and steady-state abundance, making them challenging to predict through ecGEMs. The incorporation of v_syn constraints improved the ability of ecGEM to capture these functionally peripheral proteins. Collectively, these findings further supported that incorporating the v_syn constraints effectively expanded the predictive capacity of ecGEMs for proteins governed by complex regulatory and environmental control.

Automatic reconstruction of high-quality ecGEMs for diverse species using EnzymeTuning

The EnzymeTuning framework successfully optimized the k_cat parameter set in Crabtree-positive S. cerevisiae. We next assessed its applicability for enzyme kinetic parameter tuning in three Crabtree-negative yeasts (Y. lipolytica, K. marxianus, and K. lactis) to evaluate its generalizability across species with distinct metabolic strategies. These species were selected to highlight the broad utility of EnzymeTuning. The genome-scale metabolic models for each microorganism have been constructed, providing the foundation for ecGEM modeling. Parameter optimization was then conducted following the EnzymeTuning workflow, using published experimental data for growth phenotypes and quantitative proteomics²⁹. As shown in Fig. 5a–c, EnzymeTuning consistently improved predictive performance across all three species. In K. lactis, the number of predictable proteins significantly increased, with the median rising from 240 to 247 (P value < 0.05; Fig. 5a). Figure 5b demonstrated a clear reduction in the number of extreme enzymes in all three yeasts. For example, in Y. lipolytica, the number of extreme enzymes dropped from ~65 to ~40 (P value < 0.05), indicating that EnzymeTuning alleviated reliance on outlier enzyme parameters. Correspondingly, prediction accuracy improved in all three yeasts, with PCC values increasing from ~0.33 to ~0.37 in K. marxianus (P value < 0.05), from ~0.21 to ~0.29 in K. lactis (P value < 0.05), reflecting enhanced proteome-level performance (Fig. 5c). Collectively, these results further validated the robustness of EnzymeTuning in improving the predictive capability and demonstrated its applicability to non-model organisms, supporting metabolic optimization of industrial strains. Nevertheless, the improvements observed in other yeast species were less pronounced than those in S. cerevisiae. These results suggested that the efficacy of k_cat optimization was critical modulated by the quality of the GEMs and the availability of experimental constraints for each species, which remained relatively limited for less-studied organisms.

Fig. 5. Performance of the GAN approach in K. marxianus, Y. lipolytica, K. lactis, and E. coli, and comparison of k_cat distributions between Crabtree-positive and Crabtree-negative yeasts.

Comparison of the total number of predictable enzymes (a), the number of extreme enzymes (b), and Pearson correlation coefficients of protein abundance predictions (c) using the GAN method versus the Bayesian approach in K. marxianus, Y. lipolytica, and K. lactis. Data are derived from the k_cat parameter sets (n = 100). Density scatter plots comparing predicted k_cat values between the GAN and Bayesian approaches for the three Crabtree-negative yeasts: K. marxianus (d), K. lactis (e), and Y. lipolytica (f). g Venn diagram showing the overlap of genes used in the models across the four yeasts (S. cerevisiae, K. marxianus, K. lactis, and Y. lipolytica). h Hierarchical clustering analysis of k_cat values for the 742 conserved enzymes shared across the four yeast species. The heatmap displayed the log₁₀-transformed k_cat values (s^–1), where rows represented individual enzymes and columns represented species. The color scale ranges from blue (low) to red (high). The hierarchical clustering of species (top) and enzymes (left) based on kinetic similarity, highlighting the divergence between Crabtree-positive (S. cerevisiae) and Crabtree-negative yeasts. i The GO enrichment of genes with significantly different k_cat values between Crabtree-negative and Crabtree-positive species, showing the top 10 enriched GO-slim terms. Comparison of the total number of predictable enzymes (j), the number of extreme enzymes (k), and Pearson correlation coefficients of protein abundance predictions (l) using the GAN method versus the Bayesian approach in E. coli. The data are derived from n = 10 independent experiments, each performed with biological triplicates. In each box plot, the central band represents the median, the box limits represent the upper and lower quartiles, and the whiskers extend to 1.5 times the interquartile range beyond the box range. P value was calculated using a two-sided t-test. Raw values are provided in the Source data.

Subsequently, we compared the k_cat distribution optimized by GAN and Bayesian methods across the three yeast species (Fig. 5d–f). Density plots revealed overall positive correlations between the two approaches. However, k_cat values predicted by the GAN method tended to be lower in specific regions. This discrepancy arose because the GAN method was trained to capture the full distribution, including the tails of real distributions (e.g., lower-value regions). In contrast, the Bayesian inference typically yielded smoother estimates that might overestimate k_cat values in sparse regions.

To further investigate the enzymatic catalytic capacities, we analyzed 742 proteins shared among the three Crabtree-negative yeasts and the Crabtree-positive S. cerevisiae (Fig. 5g). Their corresponding k_cat values were shown in a heatmap (Fig. 5h). Correlation analysis revealed strong consistency among the three Crabtree-negative species (r > 0.9), indicating high conservation of enzymatic efficiency within this group, consistent with their predominant reliance on respiratory metabolism. This observation aligned well with previous reports showing that Crabtree-negative yeasts exhibited elevated mitochondrial respiratory capacity and oxidative phosphorylation³⁰.

In contrast, pronounced differences were observed when comparing the Crabtree-negative species with S. cerevisiae. The GO enrichment analysis of proteins with differential k_cat values (Fig. 5i) revealed enrichment in the functional categories, including lipid metabolism, cellular amino acid metabolism, nucleobase-containing small molecule metabolism, ion transport, and cofactor metabolism. A comparative analysis of k_cat distributions among proteins co-expressed by three Crabtree-negative yeasts (K. lactis, K. marxianus, and Y. lipolytica) and the Crabtree-positive yeast S. cerevisiae was investigated (Fig. 5h, i). On average, Crabtree-negative yeasts exhibited higher catalytic efficiencies for enzymes involved in amino acid metabolism but lower efficiencies for lipid metabolism enzymes compared with S. cerevisiae. These trends likely reflected fundamental differences in metabolic strategies, resource allocation, and physiological adaptations. In Crabtree-negative yeasts, the k_cat values observed for amino acid metabolic enzymes might support their strong reliance on aerobic respiration, enabling higher growth rates and enhanced protein synthesis³¹. Enhanced mitochondrial function and nitrogen utilization capacity in these yeasts necessitated efficient amino acid biosynthesis to satisfy the cellular demand for nitrogen-containing intermediates. Conversely, during fermentative metabolism, S. cerevisiae constantly remodeled its membrane systems (e.g., plasma membrane, endoplasmic reticulum) to counter fluctuations in intracellular pH and osmotic pressure³². This dependence on lipid remodeling might impose higher catalytic efficiency requirements on lipid metabolic enzymes. Overall, these findings suggested that Crabtree-negative yeasts prioritized catalytic efficiency toward amino acid metabolism, reflecting a strategic trade-off in enzyme resource allocation to optimize energy and nutrient utilization under distinct metabolic regimes.

To further assess the general applicability of EnzymeTuning beyond yeast species, we extended our framework to a prokaryotic system and applied it to Escherichia coli. Specifically, we constructed an ecGEM for E. coli based on the genome-scale metabolic model iML1515 and optimized the k_cat parameters under 17 distinct nutrient conditions. These conditions spanned a diverse set of carbon sources, enabling a systematic evaluation of model behavior in a bacterial system.

As shown in Fig. 5j–l, EnzymeTuning consistently outperformed the Bayesian approach. As shown in Fig. 5j, the two methods exhibited comparable performance, with negligible differences observed in the total number of predictable enzymes. The number of extreme enzymes decreased from a median of approximately 41 to 20 (Fig. 5k, P value < 0.05), suggesting a more rational k_cat distribution. Consistently, the accuracy of protein abundance prediction was improved with the PCC increasing from 0.37 to 0.47 (Fig. 5l, P value < 0.05). These results indicated that EnzymeTuning enabled more effective calibration of k_cat parameters, thus improving the proteome-level prediction performance of bacterial ecGEMs.

Estimation of k_cat under nitrogen-limited and anaerobic conditions using EnzymeTuning

To investigate the regulatory mechanisms of enzyme catalytic capacity under diverse carbon-to-nitrogen (C/N) conditions, we trained condition-specific GAN-based ecGEMs under four distinct C/N ratios (3, 30, 50, and 115)²⁹. Among these, C/N = 3 was defined as carbon-limited conditions, whereas C/N = 30, 50 and 115 were categorized as nitrogen-limited conditions. For subsequent analyses, C/N = 3 and C/N = 115 were selected as representative states. We evaluated whether the overall k_cat distributions differed significantly across nutrient conditions using the Kolmogorov–Smirnov (KS) test⁶. No significant global differences were detected, indicating that nutrient-dependent regulation was not reflected at the level of overall k_cat distributions, as confirmed by the KS tests between carbon-limited and nitrogen-limited states (KS-stat = 0.076, P value > 0.05). To capture condition-specific enzyme utilization more sensitively, we introduced a relative enzyme usage metric, defined as the ratio of condition-specific predicted k_cat of each protein to the maximum k_cat value ($k_{cat}^{\max }$)³³.

Partial least squares discriminant analysis based on the relative enzyme usage revealed a clear separation between carbon-limited and nitrogen-limited chemostat conditions (Fig. 6a)³⁴. The functional enrichment analysis of the proteins with high variable importance in projection scores indicated that metabolic adaptation was driven by a coordinated reprogramming of central carbon metabolism, amino acid metabolism, lipid metabolism, and cell wall biogenesis (Fig. 6b, c).

Fig. 6. Condition-specific metabolic adaptations and dynamic flux predictions.

a Partial least squares discriminant analysis (PLS-DA) of k_cat values under carbon-limited and nitrogen-limited conditions. Each point represents a sample, colored by the corresponding nutrient condition (carbon-limited: green; nitrogen-limited: orange). b Variable importance in projection (VIP) scores of k_cat parameters derived from the PLS-DA model. The top 20 enzymes with the highest contribution to group discrimination were shown. c KEGG pathway enrichment analysis of differential proteins. P values were calculated using a two-sided hypergeometric test with Benjamini–Hochberg adjustment for multiple comparisons. Metabolic fluxes of key enzymes (ADH1 (d), HXK2 (e), and PDC1 (f)) across specific growth rates under anaerobic conditions. Green dashed line: GAN-based ecGEM; red dashed line: Bayesian-based ecGEM.

To decipher the specific regulatory mechanism, we analyzed the density distributions of relative enzyme usage for key functional modules (Supplementary Fig. 10a). Crucially, the predicted patterns showed high consistency with established physiological responses reported in the literature, substantiating the biological relevance of our model. The model predicted a significant reduction in the relative usage of enzymes involved in energetically costly lipid pathways (e.g., glycerophospholipid and sterol biosynthesis) under nitrogen-limited chemostat conditions. This prediction aligned with the “proteome economy” principle observed in quantitative proteomic studies, which reported that yeast cells actively downregulated non-critical biosynthetic machinery to preserve proteome resources under nitrogen scarcity^29,35. Conversely, enzymes facilitating nitrogen recycling and redox balance, such as ornithine acetyltransferase (ARG8) and aldehyde dehydrogenase (ALD2), displayed increased utilization under nitrogen-limited chemostat conditions. This upregulation mirrored experimental findings, where nitrogen limitation triggers the induction of scavenging pathways (e.g., the Arg/Orn cycle) to mobilize intracellular nitrogen reservoirs^36,37. Additionally, the increased usage of glycolysis and glycerol metabolism enzymes (e.g., GPD2) under nitrogen-limited chemostat conditions suggested a shift towards maintaining redox homeostasis and precursor supply, a strategy consistent with previously described metabolic remodeling mechanisms under nutrient stress^38,39.

To demonstrate that the robustness of EnzymeTuning extended beyond aerobic environments, we further applied the framework to simulate metabolic phenotypes and protein abundances under anaerobic carbon-limited chemostat conditions across five specific growth rates (0.05, 0.10, 0.15, 0.20, and 0.25 h^–1). As shown in Supplementary Fig. 10b–d, no significant differences were observed between the Bayesian-based and GAN-based ecGEMs in terms of the total number of predictable enzymes or the number of extreme enzymes across growth rates (Supplementary Fig. 10b, c). In contrast, EnzymeTuning achieved a clear improvement in protein abundance prediction accuracy. The PCC between predicted and measured protein abundances increased from 0.19 to 0.28 across all growth rates (P value < 0.05; Supplementary Fig. 10d). These results indicated that the ecGEMs incorporating k_cat values optimized by EnzymeTuning also achieved improved predictive performance in protein abundance under anaerobic conditions.

Furthermore, we analyzed metabolic flux distributions to assess the physiological consistency of the model predictions. As illustrated in Fig. 6d–f, the Bayesian-based ecGEM exhibited unrealistic “flux shifting” artifacts in key enzymes, including alcohol dehydrogenase (ADH1), hexokinase (HXK2), and pyruvate decarboxylase (PDC1). Under anaerobic carbon-limited chemostat conditions, the flux of HXK2 increased linearly with the specific growth rate to match the glucose uptake rate, while the fluxes of PDC1 and ADH1 concomitantly rose to regenerate cytosolic NAD⁺ and generate ATP^40,41. The Bayesian-based ecGEM violated this principle, showing abrupt oscillations or zero-flux artifacts at intermediate growth rates (e.g., 0.15 h^–1), whereas EnzymeTuning generated smooth, continuous trajectories. The subsystem-level analysis also revealed that EnzymeTuning correctly captured the global flux redistribution, which was consistent with the quantitative metabolic flux analysis (MFA) studies⁴². Specifically, EnzymeTuning correctly captured the global flux redistribution characteristic of anaerobic metabolism. The carbon flux was predominantly redirected towards glycolysis/gluconeogenesis to support growth, while the tricarboxylic acid (TCA) cycle operated as a minimized, branched pathway for biosynthesis rather than energy generation⁴². In contrast, the Bayesian-based ecGEM incorrectly predicted high respiratory activity (oxidative phosphorylation) and unstable fluxes of the TCA cycle.

Implications of EnzymeTuning for rational design of cell factories

The potential applications of EnzymeTuning for metabolic engineering have been verified by a recent study from our group⁴³. In that study, GAN-based parameters were crucial for enabling the ecGEMs to accurately predict production targets for various high-value chemicals, validating the reliability of our toolbox in broader application. To further evaluate the utility of EnzymeTuning in identifying gene targets, we conducted an additional case study on threonine production. We applied the FSEOF algorithm using both Bayesian-based and GAN-based ecGEMs⁴⁴. Comparison of the two models revealed that EnzymeTuning identified a broader landscape of potential targets (28 vs. 20 proteins in Bayesian-based ecGEM), showing high consistency with the state-of-the-art tool ecFactory⁴⁵. Specifically, EnzymeTuning correctly prioritized high-value candidates within the direct biosynthetic pathway, including HOM3 (aspartokinase), HOM2 (aspartate-semialdehyde dehydrogenase), and THR1 (homoserine kinase). Notably, HOM3 encodes the key rate-limiting enzyme governing the entry of carbon flux into the aspartate family pathway, and its overexpression is a well-established strategy for enhancing threonine production⁴⁶. Additionally, EnzymeTuning uniquely highlighted critical upstream targets that were missed by the Bayesian approach, such as PYC1 (pyruvate carboxylase). This finding aligns with the fact that enhancing precursor supply via PYC1 is crucial for high-yield threonine production⁴⁷. This capability to simultaneously identify direct biosynthetic and distal precursor-supply targets demonstrated that EnzymeTuning offered a comprehensive and mechanistically sound roadmap for rational strain design.

Discussion

In this study, we developed a GAN-based framework, EnzymeTuning, to optimize k_cat parameter sets in ecGEMs. Compared with Bayesian posterior sampling approaches, the EnzymeTuning framework significantly improved the accuracy of protein abundance predictions while maintaining robust phenotype predictions¹¹. This demonstrated the potential of GANs to capture complex, nonlinear k_cat distributions and to simultaneously optimize multiple biological objectives⁴⁸. Unlike Bayesian inference, which yields maximum a posterior estimates of k_cat values based on prior assumptions, the GAN-based approach can learn parameter distributions driven jointly by global constraints (e.g., phenotype fidelity) and local evaluation (e.g., reduction of extreme enzyme burden, correlation with proteomics). We demonstrated the generalizability and robustness of the framework by extending its application from Crabtree-positive S. cerevisiae to three Crabtree-negative yeasts (K. lactis, K. marxianus, and Y. lipolytica) and the bacterium E. coli.

Nevertheless, extreme enzyme predictions were still concentrated in complex regulatory pathways such as oxidative phosphorylation. These cases may reflect inherent limitations of the framework, including the lack of cellular compartmentalized constraints, isoenzyme-level differentiation, and post-translational regulatory information^49,50. In addition, training GANs for high-dimensional enzyme networks remains computationally intensive, and the interpretability of the generated parameter distributions is limited. To alleviate bottlenecks in protein predictability, we incorporated the protein synthesis rate (v_syn), which was inferred from protein degradation coefficients (k_deg), as auxiliary constraints, increasing the predictable enzyme coverage in the ecGEM of S. cerevisiae from 331 to 379 (Fig. 4c)^23,51. To further explore the physiological mechanisms underlying condition-specific enzyme utilization, we applied EnzymeTuning to proteomics datasets collected under carbon-limited conditions and nitrogen-limited conditions. By analyzing in vivo enzyme catalytic efficiency through the $k_{cat}/k_{cat}^{\max }$ ratio, we revealed adaptive enzyme usage patterns consistent with nutrient-dependent resource allocation strategies. While these consistencies substantiate the biological relevance of ecGEM, future experimental validation remains essential to fully corroborate the inferred catalytic plasticity. We propose that specific enzymatic activity assays should be conducted on key responsive enzymes (e.g., GPD2, ARG8) with controlled C/N gradients. Such experimental validation would allow for the direct observation of the predicted continuous shifts in enzyme usage, thus establishing a definitive link between computational inferences and in vivo physiological adaptations. Moreover, integrating EnzymeTuning into high-throughput design-build-test-learn cycles offers the potential to accelerate industrial strain development. Together, these developments point toward a comprehensive and dynamic framework for quantitative, context-specific metabolic modeling.

Methods

Dataset resources

The genome-scale metabolic models (GEMs) for S. cerevisiae, Y. lipolytica, K. lactis, and K. marxianus used in this study were derived from a yeast pan-GEM using the modeling framework developed by Lu et al.⁵². These GEMs were obtained as pre-reconstructed versions, and no further structural modifications were made to these models in this work. Experimental growth phenotypes, exchange flux rates, and the absolute quantitative proteomics data for S. cerevisiae under 23 steady-state chemostat cultures, including 9 carbon-limited and 14 nitrogen-limited chemostat conditions, were collected from the literatures^22,35. The experimental data for the other three yeasts were collected from the literatures^53,54. Condition-specific proteomic data for S. cerevisiae under varying C/N ratios were also obtained from the literature²⁹. In this study, all cultures were maintained at a dilution rate of 0.2 h⁻¹, and the nitrogen availability was progressively reduced by decreasing ammonium concentration while keeping glucose constant. A C/N ratio of 3 corresponds to a carbon-limited condition, while C/N $\ge$ 5 reflects a nitrogen-limited state²⁹. The GEM of E. coli used in this study was based on the reconstruction of eciML1515⁵⁵. For E. coli, the experimentally measured growth phenotypes and quantitative proteomics data were obtained from the literature⁵⁶. In addition to the publicly available datasets, we further incorporated an independent proteomics dataset collected within our research group as an external validation set. This dataset comprised absolute quantitative proteomics data obtained under carbon-limited chemostat conditions at varying dilution rates, including both aerobic and anaerobic conditions.

Sensitivity analysis

In this study, the enzyme-constrained genome-scale metabolic model (ecGEM) of S. cerevisiae comprised 4354 k_cat parameters. While Li et al. previously optimized these parameters for phenotype predictions¹¹, we aimed to improve protein abundance prediction accuracy while maintaining phenotype fidelity. Thus, we introduced a sensitivity analysis-based refinement strategy as an optional step prior to global optimization. This step allowed for targeted improvement of protein abundance prediction when phenotype optimization was not required. We evaluated protein abundance prediction performance from two complementary aspects: (1) the correlation between predicted and measured abundance, assessed by the PCC; and (2) the physiological plausibility of enzyme allocation, quantified by the number of extreme enzymes. Here, the extreme enzymes were defined as those with predicted/measured protein abundance ratios outside a predefined range. Enzymes with a fold change greater than 100 or less than 0.01 were considered extreme, with the thresholds determined empirically and described earlier in the manuscript. In this study, predictable enzymes were defined as the subset of enzymes for which both non-zero predicted protein abundances (derived from non-zero protein exchange fluxes) and experimentally measured protein abundances were available under identical conditions. All PCCs were calculated using log₁₀-transformed abundance values. We employed SALib (Sensitivity Analysis Library in Python) to systematically identify critical k_cat parameters²¹. Each k_cat value was perturbed across seven intervals (1–3%, 10–30%, 50–70%, 90–110%, 110–130%, 150–170%, and 900–1100% of their nominal values). Sampling was performed via the Sobol method to ensure quasi-random coverage of the parameter space. The prediction under these perturbations yielded growth rates and exchange fluxes, with the accuracy quantified by the RMSE between predicted and experimental datasets (Eq. 5).

$$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i},\mathrm{pre}}-{\mathrm{y}}_{\mathrm{i},\exp }\right)}^2}$$ 5

Here, $y_{i,pre}$ and $y_{i,\exp }$ represent the predicted and experimentally measured values, respectively. n is the number of experimentally measured phenotypic variables, such as the specific growth rate and exchange fluxes for ethanol, glycerol, carbon dioxide and oxygen. To access parameter sensitivity, the first-order (S1) and the total-order (ST) indices were computed. Through the S1 and ST results across seven perturbation ranges, a pre-optimized k_cat dataset was generated.

ecGEM reconstruction based on Bayesian methods

A sequential Monte Carlo-based approximate Bayesian computation (SMC-ABC) approach was employed for sampling k_cat values⁵⁷. Each k_cat value was described as a log-normal distribution, which was progressively updated by sampling 126 parameter sets per generation and retaining the top 100 with the smallest phenotype prediction errors¹¹. This process continued until the distance between experimental and predicted phenotypes was less than one (RMSE < 1), yielding the final posterior distribution. The posterior mean of the sampled k_cat distribution was then used to parameterize the ecGEM, resulting in the posterior-mean-ecGEM.

Construction of EnzymeTuning

The GAN-based optimization named EnzymeTuning was implemented in three steps to refine enzyme turnover numbers (k_cat) and enhance the predictive performance of ecGEMs (Fig. 1). The process was initiated with k_cat parameter sets obtained from a Bayesian inference framework¹¹. In the first step (Step 1: preparation of training data), each parameter set was systematically evaluated for its ability to simultaneously reproduce two cellular features: (1) growth phenotypes and (2) quantitative protein abundance profiles. The initial parameter sets were selected using the criteria of RMSE < 2 and PCC > 0.4, which served as an empirical reference of Bayesian-derived parameter sets. Subsequently, these selected parameter sets were assigned a discriminator score that integrated growth phenotype prediction and protein abundance prediction performance, as described in Eqs. 2–4, where lower scores correspond to superior predictive accuracy. Parameter sets with the lowest scores were classified as the high-performance group, whereas those with higher scores were designated as the low-performance group. When sensitivity analysis was applied prior to global optimization, only protein abundance prediction accuracy was considered. In this context, the high-performance sets were defined solely by their agreement with measured protein abundance profiles. This classification produced a labeled dataset with clear performance-based categories, which was subsequently used for supervised generative modeling.

In the second step, using the labeled dataset, a cGAN was trained to learn the distribution of high-performance k_cat parameter sets (Step 2: training the adversarial networks)²⁰. The cGAN consisted of two fully connected neural networks: a generator and a discriminator, both of which were conditioned on the labels during training. The discriminator consisted of three dense layers of increasing complexity: the three layers contained 32 units, 64 units, and 128 units, each followed by a Dropout layer (rate = 0.5). The generator network comprised three dense layers with progressive depth and regularization: 128 units, 256 units, and 512 units, each followed by batch normalization and dropout (rate = 0.5). All models were implemented using Keras with a TensorFlow-GPU backend. Both the generator and discriminator were trained using binary cross-entropy as the loss function and optimized with the Adam optimizer using a fixed learning rate of 2 × 10^–4 and a batch size of 50.

After each training generation, the generator produced new k_cat parameter sets, which were integrated into the ecGEM and re-evaluated for growth phenotypes and protein abundance predictions. The top 100 k_cat parameter sets, ranked according to the performance criteria described above, were retained and used as input for the subsequent training generations. This loop was repeated for 50 generations, progressively converging toward high-performing k_cat distributions.

The final trained generator was used to produce k_cat parameter sets for performance evaluation under multiple environmental conditions (Step 3: validation). Model performance was assessed by predicting protein abundances of S. cerevisiae under carbon-limited chemostat conditions and comparing them with experimental measurements. To further assess the robustness and generalizability, the optimized k_cat parameter sets were validated under nitrogen limitation and three alternative nitrogen sources, including glutamate, isoleucine, and phenylalanine.

V_syn estimation based on the degradation rates

Assuming steady-state intracellular protein levels, we applied the principle of protein mass conservation to estimate the protein synthesis rate (v_syn)⁵⁸. According to this principle, for each enzyme, the rate of protein synthesis must balance the sum of degradation and dilution rates (Eqs. 6–9).

The initial v_syn values were derived from literature-reported protein degradation constants (k_deg), which were collected from two independent large-scale proteome turnover studies employing distinct computational strategies^23,24. These two studies obtained k_deg constants by fitting the temporal profiles of labeling incorporation (relative isotope abundance, RIA) to an exponential equation. However, one study defined the k_deg constants on protein turnover rates inferred from dynamic labeling experiments, whereas the other estimated the k_deg constants by explicitly subtracting growth-rate-dependent dilution effects. To account for methodological heterogeneity between these two k_deg parameter sets, we did not treat k_deg-derived v_syn values as fixed parameters. Instead, for each protein, we computed the lower and upper bounds (v_syn,min, v_syn,max) using Eq. 9, thereby defining a biologically plausible range that captures uncertainty arising from different degradation rate estimation methods. To determine an appropriate scale for introducing v_syn constraints into the ecGEM, we systematically evaluated multiple constraint sizes. Specifically, enzymes with predicted protein abundance equal to zero were first ranked by experimentally measured protein abundance, and 100 proteins were selected for comparative analysis. The bounds of the corresponding protein exchange reactions in the ecGEM were parameterized using these v_syn estimates. Finally, the EnzymeTuning framework was applied to systematically calibrate the protein synthesis rates, with the optimized values being integrated into the ecGEM. Importantly, within the EnzymeTuning framework, v_syn constraints were treated as flexible and updatable priors. As additional or more consistent k_deg measurements become available, the v_syn bounds can be readily updated without altering the overall modeling workflow.

$$v_{syn}=v_{\mathrm{deg}}+v_{dil}$$ 6

$$v_{\mathrm{deg}}=k_{\mathrm{deg}}\bullet \left[E\right]$$ 7

$$v_{dil}=\mu \bullet \left[E\right]$$ 8

$$v_{syn}=\left(k_{\mathrm{deg}}+\mu \right)\bullet \left[E\right]$$ 9

Here, Eq. 6 defined the total protein synthesis rate (v_syn). Each protein could be degraded (v_deg, Eq. 7) and be diluted by growth rate (v_dil, Eq. 8). Equation 7 described the protein degradation as a first-order process, with k_deg denoting the protein-specific degradation constant and $\left[E\right]$ representing the intracellular protein concentration. Equation 8 captured the dilution effect of biomass growth, where $\mu$ was the specific growth rate. By combining Eqs. 6–8, Eq. 9 provided a unified expression for the protein synthesis rate, which integrated both degradation and dilution effects.

Computational environment

The EnzymeTuning framework was implemented in Python, with enzyme-constrained model reconstruction, training, and evaluation. The execution of the EnzymeTuning framework required approximately 1 day to complete. The computations in this paper were run on the Siyuan-1 cluster supported by the Center for High Performance Computing at Shanghai Jiao Tong University and a workstation equipped with an Intel Core i7-12700H CPU and an NVIDIA GeForce RTX 3050 Ti GPU, operating on Windows 11.

Statistics and reproducibility

Proteomics data in this study were acquired independently with three biological replicates. P value was calculated using a two-sided t-test. No statistical method was used to predetermine sample size. No data were excluded from the analyses. The experiments were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

H.L., and G.W. designed the research. X.W. wrote the manuscript and performed data analyses and algorithm development. Y.W. provided the quantitative proteomic datasets for the validation in S. cerevisiae under anaerobic chemostat cultivation, performed the omics data analysis, and contributed to the drafting and revision of the manuscript. H.L., G.W., Y.Z., X.W., and Y.W. revised the manuscript. H.L., and G.W. supervised the study. All authors contributed to the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

All GEMs, ecGEMs, and collected proteome data are available in the GitHub repository [https://github.com/hongzhonglu/EnzymeTuning]. Other collected datasets, such as experimental growth phenotypes are available in the GitHub repository [https://github.com/hongzhonglu/EnzymeTuning/tree/main/data/growthdata.xlsx]. The protein degradation constants used in this work are obtained from [10.1016/j.celrep.2014.10.065] and [10.1016/j.cels.2017.08.008]. The proteome raw data have been uploaded to the iProX database [https://www.iprox.cn/page/home.html]^59,60. Project ID is IPX0015844000, and ProteomeXchange ID is PXD074934. All data supporting the findings and for reproducing all figures of this study are provided in the Source data file and in the GitHub repository⁶¹. Source data are provided with this paper.

Code availability

All code and detailed instructions are available in a GitHub repository [https://github.com/hongzhonglu/EnzymeTuning]⁶¹.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains Supplementary material available at 10.1038/s41467-026-73744-3.