## Introduction

Bacillus subtilis is the best-studied Gram-positive bacterium and has promising industrial applications1. The organism has been widely used in industrial applications, including for the production of antibiotics, enzymes, and vitamins2. Furthermore, B. subtilis serves as a model in studies of gut3 and soil microbiome4, for our understanding of sporulation and cell differentiation, biofilm formation, as well as to unravel pathogenicity in related pathogens5,6.

The tremendous amount of omics and physiological data available for B. subtilis allowed reconstructing one of the first bacterial genome-scale metabolic models (M-models)7. The M-model consists of a network of all known metabolic reactions, resulting in high prediction accuracy of gene essentiality, growth on different carbon and nitrogen substrates, and gene-knockout phenotypes8. Even though this network can accurately predict metabolic responses to nutrient levels and gene knockouts9,10, enzyme production costs, and protein secretion are out of the scope of the M-model. Moreover, the biomass composition is a constraint in M-models, thus limiting predictions about variations of biomass precursor abundances11. Therefore, it is impracticable to simulate stress conditions that involve shifts in gene expression or alterations in biomass composition with the M-model. While M-model coupling with metabolomics data has been successfully employed to analyze variations in biomass composition12,13, no a priori prediction of these shifts has been possible with bacterial M-models.

A new generation of computational models enables linking gene expression mechanisms to metabolic reactions14. The models of metabolism and gene expression (ME-models) link enzyme production profiles with metabolic reaction fluxes, thus assigning additional protein biosynthetic costs to metabolism. Now, predicted metabolic fluxes account for optimal proteome composition at specific growth conditions. ME-models can also be associated with the chaperones framework to simulate changes in the proteome in response to temperature or metal availability15,16,17,18. The first ME model was reconstructed for Thermotoga maritima18, with explicit definitions of necessary coupling constraints for complex usage, transcription, translation, and mRNA degradation. The next ME-models were reconstructed for Escherichia coli, the first being published by Thiele et al.19, which then underwent three subsequent updates, namely iOL1650-ME14, iJL1678-ME17, and iJL1678b-ME20. The last of these was released with a new standard on ME-model reconstruction, called COBRAme, upon which this work was based.

Here, we reconstructed the ME model of B. subtilis str. 168, iJT964-ME, based on the available M-model iYO8447, gene annotation in BsubCyc21, and extensive manual curation of transporters and secretory pathways. We show the increased predictive capability of iJT964-ME to simulate gene essentiality, stress-induced biomass composition variation, and shifts in gene expression. Furthermore, we deployed the ME model to accurately predict enzyme production under various conditions, showcasing its ability to assist protein production strategies.

## Results

### Properties and benchmarking of the metabolic and gene expression model of B. subtilis, iJT964-ME

Reconstruction of iJT964-ME was performed by adapting the available metabolic modeling packages COBRAme20, COBRApy22, and ECOLIme20. COBRAme functions were altered to be compatible with Bacillus subtilis gene and protein nomenclature used in GenBank, FASTA, and other files (Table 1). The resulting pipeline expanded the existing B. subtilis M-model iYO844 with non-metabolic reactions, including translation, transcription, tRNA charging, and post-translational modification20. The final ME model (iJT964-ME) contains 964 genes, 6282 reactions, and 4208 metabolites (Fig. 1d). A detailed breakdown of metabolite and reaction types is shown in Fig. 1a, b. The ME-model components that are inherited from the M-model’s metabolic network are called “metabolic”, such as the “metabolic reaction” and “metabolite” in Fig. 1a, b. In this study, we used iYO844 as a template M-model, with modifications following updated information on transport reactions and gene-protein-reaction associations. A complete list of updates is provided in Supplementary Table 1. Approximately 28% of the network in iJT964-ME comprises metabolic reactions, with 23% of metabolites resulting from these metabolic reactions. Note that the number of metabolic reactions in iJT964-ME is far greater (5023 additional reactions) than in iYO844, since reversible reactions are split into forward and reverse subreactions.

iJT964-ME includes new transcription and translation reactions, which correspond to 28% of the total reactions. An additional 23% of reactions represent complex formation (including generic complexes), post-translational modification, and tRNA charging, and the remaining reactions (21%) account for exchange and demand reactions. While most exchange reactions are kept the same as in iYO844, 1,081 new demand reactions were added to account for RNA degradation. To test the quality of the ME-metabolic network, we ran a high-throughput phenotypic analysis of 87 carbon sources based on experimental results from ref. 7, which were initially used to validate iYO844. iJT964-ME and iYO844 simulations achieved a Matthews Correlation Coefficient (MCC) of 0.454. Considering the base metabolic network of the model is fully inherited from iYO844, it is expected that growth calls on different substrates varies little to none. Major changes, however, are to be expected in predictions at the level of gene expression and protein synthesis. Complete lists of flux distributions for the M- and ME- models are provided in Supplementary Data 1.

Coupling transcription and translation rates to metabolic fluxes allows the ME model to deal with artificially high fluxes and metabolic loops. In M-models, artificial loops are inevitably predicted as a way for the model to maximize the metabolite transport and energy production. By linking protein biosynthesis pathways to fluxes, ME-models penalize unrealistic fluxes and can predict biologically relevant alternatives. An example of this is depicted in Fig. 1f. A handful of reactions showed artificially high fluxes in the M-model (~106), which is not the case for iJT964-ME. On the other hand, the rest of the predicted metabolic fluxes are distributed similarly across the network in both iYO844, with each reaction carrying a comparable flux in both models, yielding an overall Pearson correlation coefficient (R2) of 0.81 (Fig. 1g).

The addition of gene expression reactions into the network of B. subtilis resulted in a 14% increase in genome coverage (total 964 genes out of 4443 coding genes), with 32% of them being essential in the growth on glucose as predicted by iJT964-ME (Fig. 1e). The extensive manual curation performed for iJT964-ME significantly increased the prediction scores of gene essentiality. In some cases, prediction scores surpass those predicted for the E. coli M- and ME-models. Interestingly, just a 14% increase in gene content allowed iJT964-ME to predict essentiality with increases of 34% in the Matthews Correlation Coefficient (MCC) and 40% in Precision. The superior performance achieved by ME-models can be explained by the emergent metabolite-metabolite and metabolite-protein dependencies that arise when flux in the network is permitted to alter gene expression profiles.

Figure 1c shows that genes associated with transport reactions compose the most considerable portion of non-essential genes. B. subtilis is a versatile organism that can metabolize a wide range of different carbon and nitrogen sources. This results in the model containing many transporters, though most of them are not active under specific growth conditions. For example, if glucose is supplemented in minimal medium the transporter for glucose-6-phosphate will be prioritized. The next significant groups of non-essential genes correspond to carbohydrate and amino acid metabolism. Even though both biomass precursors are essential for growth, B. subtilis contains several alternative pathways to synthesize them. This is especially the case for carbohydrate metabolism, as only 6% of its genes were predicted to be essential and relate mostly to the pentose phosphate pathway (PPP) and glycolysis reactions. In a similar way, alternative pathways render some reactions in nucleotide metabolism, lipid metabolism, membrane synthesis, and cell wall synthesis non-essential.

As biomass precursor synthesis reactions were split into essential and non-essential, cofactors associated with those reactions fell into both categories accordingly (“Coenzymes” in Fig. 1c). Almost a third of genes encoding for cofactor metabolism were found to be essential. Furthermore, a significant portion of essential genes (21%) is related to amino acid synthesis for protein synthesis and growth (“Amino acids” in Fig. 1c). Notably, the entirety of the gene expression machinery was predicted to be essential, which includes ribosome formation (21.5%), transcription (5.7%), translation (3.4%), and tRNA charging (7.4%). It is worthy to note that essentiality is overestimated in ME-models for gene expression machinery, as all complexes in this category are formed by a fixed number of subunits that must be complete to have a nonzero production flux and ultimately growth. For example, rpsT was observed to not be essential23; however, since it is annotated as a subunit of the ribosome, it is essential to carry out translation in the ME-model. As a result of this limitation, false positives are higher among the core expression machinery (Supplementary Fig. 1) and the TNR scores decrease by 6.0 and 7.5% in iJT964-ME and iJL1678-ME, respectively (Fig. 1e).

### Predicting upregulation of tryptophan synthesis under ethanol stress

Stress by increased concentrations of fermentation products, e.g., alcohols or short-chain fatty acids, is one of the principal stresses to overcome in industrial settings24. A machine learning algorithm was recently applied to identify groups of genes in B. subtilis with significant differential expression in experimental transcriptomics datasets across several stress conditions25. The results highlighted a group of significantly co-regulated genes associated with an 8–20% upregulation of tryptophan biosynthetic genes under ethanol stress (4% v/v). The trp operon (trpEDCFBA-hisC-tyrA-aroE) codes for enzymes that carry out tryptophan biosynthesis. It has been suggested that trp upregulation is caused by ethanol inducing a decrease in tryptophan concentrations25, although it has not been fully explained yet. We performed simulations to predict ethanol stress and give a mechanistic insight into gene expression phenomena in B. subtilis.

iJT964-ME contains transport reactions that simulate the flow of ethanol through the cell membrane via diffusion as experimentally observed. We simulated ethanol diffusion rates between (0 and 0.5 mmol/gDW/h). In agreement with the recent differential expression results25, the model predicted the increase in tryptophan synthesis due to increased ethanol uptake (Fig. 2a). In our simulations, transcription of trp genes was predicted to increase due to ethanol uptake, although translation rates varied, as shown in detail in Fig. 2b. While trpE and trpF translation was downregulated (Supplementary Fig. 2), expression of the proteins trpD, trpC, trpB, and trpA was upregulated to increase fluxes through anthranilate phosphoribosyltransferase (trpD), indole-3-glycerol-phosphate synthase (trpC), and tryptophan synthase (trpBA). Similarly, aroE and tyrA expression increased as a response to a higher demand for shikimate dehydrogenase (aroE) and prephenate dehydrogenase (tyrA). When we used the same constraints in the M-model iYO844 predictions yielded no variation in tryptophan synthesis (Fig. 2a).

Our simulations show that the higher tryptophan demand can be caused solely by an increase in the demand for ethanol processing and acetate secretion enzymes (Fig. 2a). According to in silico experiments, ethanol was converted to acetate through alcohol dehydrogenase (adhA) and aldehyde dehydrogenase (aldX), which was then secreted through a sodium-dependent acetate symporter (ywcA). The translation of ywcA caused ~65% of the total increment in tryptophan synthesis rate, 6.5% by adhA, and aldX. In comparison, the remaining 28.5% was distributed almost evenly across gene and protein expression machinery, e.g., RNA polymerase and ribosomes.

Under the hypothesis that tryptophan concentration driving trp expression25, the flux of its precursor chorismate would be redirected to synthesize folate, which is consumed by ethanol oxidation byproducts. This mechanism has not yet been well-described26. However, model simulations of folate depletion showed a significant increase in trp transcription (Fig. 2b). Transcription of trp was predicted to increase due to higher demand of aroE for chorismate synthesis, despite tryptophan synthesis decreasing.

### iJT964-ME reproduces regulation of gene expression under salt stress

The ability to overcome osmotic stress defines how competitive an organism is in under high salinity. Salt stress in B. subtilis is an ongoing research area, with the primary objective of understanding how cells are affected by excess ions and how they adapt to it. Both biophysical and metabolic responses have been identified27 with repercussions at the industrial scale28. We deployed iJT964-ME to unravel metabolic mechanisms to overcome osmotic stress. We used transcriptomics data of B. subtilis growing under salt stress29 to evaluate the predicted flux distributions at the genome scale. We modeled salt stress with excess sodium uptake (see “Methods”). Sodium is moved through the membrane via active transport, so transport fluxes in the model trigger transporter expression. However, sodium importers are downregulated (Fig. 3a), while sodium exporters are upregulated to help pump out the excess ion and maintain internal homeostasis (Fig. 3a). Therefore, to model salt stress, we forced an excess influx of sodium with no coupled enzymatic expression, while secretion was left coupled to the synthesis of its transporter.

Figure 3b shows the differential expression of active genes as predicted by iJT964-ME and reported in SubtiWiki. iJT964-ME accurately captured the regulation of 60.4% of differentially expressed genes. The model accurately captures the response of most genes associated with the main metabolic pathways, such as amino acid synthesis, ribosome formation, and nucleotide synthesis. These pathways are accurately captured since their activity is related to the organism’s core metabolic response to stress. However, some genes of core metabolism were incorrectly predicted, though they correspond to a minority within their respective subsystems. For example, 79% of amino acid synthetic genes and 70% of ribosome formation genes were accurately captured. On the other hand, most incorrectly predicted genes correspond to secondary metabolism, such as carbohydrate metabolism, cell wall synthesis, and the transcription of the genes involved in those reactions. More specifically, 74 and 33% (Supplementary Fig. 3) of downregulated and upregulated genes were predicted correctly, respectively. The decrease in accuracy in upregulated genes is largely caused by incorrectly predicted carbohydrate-related genes (Fig. 3b). In M- and ME-models, the prediction of differential expression of storage compounds, e.g., carbohydrates and lipids, is particularly complicated, as storage is largely linked to sub-optimal growth and transition to dormancy30. Under stress conditions, storage compound biosynthetic pathways are directed by complex regulatory signals, which are currently out of the capabilities of a metabolic model.

Our predictions of differential expression agree with the recent observations in transcriptomics25, which described an unexpected and previously unexplained downregulation of arginine synthesis under salt stress conditions. As shown in Fig. 3c, our model accurately predicts the decrease in expression of the arg operon when excess sodium enters the cell. This reduction is explained by the model as a part of a general downregulation of all amino acid synthesis, resulting from a salt-induced decreased capacity of protein synthesis.

### Optimization of protein secretion

B. subtilis, classified as Generally Recognized as Safe (GRAS) by the FDA5, is a widely used cell factory for the production of proteins due to its accelerated metabolism and highly efficient secretory pathways. One of the most prominent biotechnological application of B. subtilis is the production of amylase for a variety of materials and detergents industries31. Amylase production and secretion in this organism has been extensively optimized, mainly through random mutagenesis and variation in starch-feeding strategies31,32.

M-models have successfully been used to identify critical mutations and growth medium compositions to optimize the production of metabolism of interest, e.g., lipids in microalgae33. While M-models can accurately capture the biosynthetic mechanism of metabolic compounds, optimization of enzyme synthesis is not feasible by these models. ME-models on the other hand have great potential for the simulation and optimization of protein synthesis and secretion. In this work, we manually curated the translocation pathways of B. subtilis (Table 1). Thereupon, we illustrate the ability of the ME model iJT964-ME to predict and optimize the production and secretion of amylase.

First, we collected two available datasets describing the time-course biomass and amylase concentrations at low (0.04 h−1)31 and high (0.195 h−1) growth rate32. Simulations were then performed with starch as the carbon source, which triggers the secretion of amyE in the model. Starch uptake rates were set to fit the experimental growth rate described in the mentioned kinetic studies. Then, we sampled the solution space close to the optimal solution (above 90% the optimal growth rate) to generate a distribution representing biologically relevant secretion rates robustly12,34 (see “Methods”). The predicted secretion rates at both conditions were compared with the experimental data (Fig. 4a).

Under low growth, the model overestimates the amylase secretion rate, while iJT964-ME predicts secretion rates within the reported experimental ranges at high growth rate. The discrepancy at the low growth rate condition is not surprising, as metabolic models inherently cannot capture several regulatory processes under sub-optimal growth35. Nonetheless, the model can predict a steep increment in amylase secretion rates necessary to sustain a higher growth rate. To illustrate the biological insight that iJT964-ME can provide, we performed a Principal Component Analysis (PCA) on the simulated data. As expected, both growth conditions cluster tidily in the PCA plot shown in Fig. 4b. The largest principal component (PC1) that was identified explained 30% of the variance, with the most significant contributions coming from nucleotide, organic carbon breakdown, and energy metabolism reactions, e.g., cytidilate kinase (CYTK2), phosphomannomutase (PNANM), ubiquinol-cytochrome oxidoreductase (CYOR), and ATP synthase (ATPS4r) (Fig. 4c). Since both conditions occur at two very different metabolic activities, it is expected that the difference in the fluxes of biomass precursor synthesis, organic carbon assimilation, and energy production describes the most considerable portion of the variance. While the reactions with significant contribution to PC1 could be targeted with mutations for the optimization of B. subtilis growth and amylase secretion in starch, we further designed an in silico experiment to isolate the effect of amyE expression at a constant growth rate.

We tested what groups of reactions would significantly drive the overexpression of amyE by fixing the growth rate at the lowest of the high growth conditions and forcing amyE overproduction until reaching the highest secretion rate. With this new sampling dataset, we performed a PCA that generated a profound insight into the effect of amyE overexpression on the network. The two largest components (PC1 and PC2 in Fig. 4d) described a strikingly higher portion of the variance (69%). As expected, both components mostly consist of amino acid synthesis reactions (Fig. 4d). PC1 is described by valine, leucine, isoleucine, alanine, aspartate, arginine, and proline. On the other hand, PC2 consists of glutamate, glycine, serine, tyrosine, tryptophan, and phenylalanine. Interestingly, these 11 amino acids do not correspond to those with the highest composition in the amylase primary structure (Fig. 5a). For example, the most influential amino acid in PC1 is glutamate, though its composition is less than half (3.5%) than alanine (8.8%). A similar trend is observed in PC2, where the highest-ranking amino acids are valine, leucine, and isoleucine, which lie only among the top 10 (5%, 6.5%, 5.15%, respectively). This indicates that, although their composition in the protein is not nearly as high as alanine, their biosynthetic pathways might pose a bottleneck to target in the overexpression and industrial production of amylase.

Figure 5a shows the individual effect of amylase overexpression on the synthesis of amino acids and shows its correlation with the molar fraction in the protein structure. Glutamine, glutamate, leucine, and aspartate stand out as outliers from this expected trend. Discarding these outliers, the molar fraction showed a significant correlation with predicted sensitivity (R2 = 0.5, P = 0.02). A few more amino acids are called in Fig. 5b as outliers, such as serine and alanine, although their deviation is orders of magnitude less than the previous outliers.

We aimed to test the effect of outliers in Fig. 5a that were predicted to influence amylase overexpression in a way that does not follow the expected trend linked to molar fraction in amylase (Fig. 5b). B. subtilis was grown in M9 medium supplemented with starch and different amino acids (see “Methods”), and the resulting amylase expression was quantified using enzymatic activity as a proxy for protein content (see “Methods”), as described in the previous studies36. A complete summary of sensitivity, composition, and experimental values is provided in Supplementary Data 2. Raw measurements of amylase activity (OD405) and biomass concentration (OD600) are provided in Supplementary Data 3 and Supplementary Data 5, respectively.

Predicted low-sensitivity amino acids, such as tryptophan, phenylalanine, tyrosine, valine, and isoleucine, were also observed to induce a significantly lower increase in amylase activity. Interestingly, the model predicted that cysteine would have a negative effect of −0.23 (mmol Cys) (mmol Amylase)−1, it being the only amino acid with a negative predicted effect. The observed amylase activity (Fig. 5c) with added cysteine was lower than the control with only starch, which confirms the prediction of this amino acid being the only one that decreases amylase activity. We performed sampling at high- and low- amylase secretion rates and assessed the cysteine synthesis flux to ensure that the negative signal of our predictions was robust. Flux sampling results at low and high-amylase secretion are presented in Supplementary Data 4. Figure 5d shows that the cysteine synthesis is significantly negatively correlated with amylase secretion (P = 1.24e-8), with a mean ratio of −0.227 (mmol Cys) (mmol Amylase)−1, which is in sync with the single optimum shown in Fig. 5a.

On the other hand, high-sensitivity amino acids with a medium-level composition, such as glutamate and aspartate, were shown to have some of the highest and most statistically significant effects on amylase activity. Moreover, the colorimetric assay confirmed that glutamine would show a remarkable effect despite having an average abundance in the composition of amylase. In some cases, supplementation effect agrees with growth rate changes, as some high-sensitivity amino acids induced a significantly higher growth rate and vice versa (Supplementary Fig. 4). Therefore, the effect could sometimes be explained by the nutritional value of the amino acids to B. subtilis, in terms of energetic level and macronutrient content. It can also be argued that higher amylase secretion rates favor the uptake of starch, and thus, biomass production. However, this is not the case for the negative effect of cysteine, which indicates it is not related with its nutritional value. Further, aspartate, glutamine and glutamate, showed an amylase secretion effect comparable to asparagine (Fig. 5c) but their growth rate effects were significantly lower (Supplementary Fig. 4). These results show that iJT964-ME can capture effects of supplementation on protein secretion beyond the individual effects of the composition trend (Fig. 5b), as well as the nutritional value of the supplementation.

Inevitably, discrepancies were encountered between model simulations and observed amylase activity variations. Out of four predicted outliers, leucine did not show a significant influence on amylase secretion (P = 0.76). While ME-models are the first generation of models with the ability to predict adapted amino acid synthesis profiles, numerous biological processes at the level of kinetics and regulation are not considered. Leucine is one of the amino acids with the lowest solubility in water, which significantly decreased the amount of amino acid that we could supplement in the samples, and thus reduces the driving force for its uptake in vivo. This physical limitation of leucine might have impacted the amylase activity increase.

## Discussion

Here, we constructed the iJT964-ME model of Bacillus subtilis and demonstrated its usefulness through gene essentiality predictions and three biologically and industrially relevant examples. The model contains 964 genes, 6282 reactions, and 4208 metabolites, and it captures the interdependence of genes, proteins, and metabolites, making it a significant improvement over the existing iYO844 M-model. iJT964-ME’s significantly expanded scope and more realistic expression framework led to a 40% increase in the precision of gene essentiality predictions, the removal of unrealistically high loop fluxes that plague unconstrained M-models, and an ability to model changes in amino acid metabolism and biomass functions.

ME-models can improve the prediction of flux distributions while overcoming inherent issues present in M-models. One of these issues that are most difficult to overcome is the prediction of metabolic loops with fluxes above biologically relevant ranges. In previous studies, loops have been addressed by coupling thermodynamic constraints37 and multi-step loopless algorithms38. In ME-models, both high and cyclic fluxes are penalized, as each unit of flux carries gene transcription, translation, and post-translational processing20. As a result, iJT964-ME eliminates previously present metabolic loops in the template M-model iYO844. This was shown for the simulated growth conditions and can be expected for any other simulation conditions. Moreover, ME-model architecture allows for a mechanistic interdependence between metabolic pathways. New reactions are essential due to new mechanisms in the network, and biomass precursor requirements adapt to different growth conditions. Thereupon, iJT964-ME was shown to improve gene essentiality predictions by 40% (MCC) as compared to iYO844.

Recent advances in transcriptomic analysis using machine learning tools have led to hypotheses about amino acid metabolism, which presented excellent questions for us to explore with our model. The study by Rychel et al.25 computed and characterized sets of co-regulated genes across a microarray dataset and identified signals with a lack of prior literature: (i) activation of tryptophan synthesis by ethanol stress and (ii) downregulation of arginine synthesis by salt shock. By simulating these conditions, we demonstrate that our model recapitulates these effects, without adding further constrains to the model, such as varying biomass reaction coefficients12 or condition-specific flux constraints13. With regard to (i), our model supports potential mechanisms involving increased amino acid synthesis for ethanol processing and efflux enzymes, and a potential role of folate degradation. For (ii), we observed decreased arginine synthesis as a result of overall downregulation for amino acid synthesis as expression flux shifts toward carbohydrate metabolism. It is worthy to note that in all cases, iYO844 could not capture any change in amino acid metabolism due to it being directly constrained by the fixed requirements in the biomass reaction.

In a final analysis, we assessed whether iJT964-ME could be employed to predict protein secretion at different growth conditions. For this, we reproduced two previous reports of amylase secretion at high32 and low31 growth rate conditions in silico. The model successfully predicted the secretion rate of amylase within the experimental reported range, though the secretion rate under low growth was overestimated. Overall, the dependence of growth rate on the required secretion rate of amylase was accurately captured. We performed a PCA to identify critical drivers of the metabolic change between these two conditions. As expected, the response to a higher expression of amylase was mixed with the global increase in metabolic activity. This showed the main drivers to be essential reactions related to biomass precursor synthesis, energy metabolism, and carbon source breakdown.

Thereupon, we isolated the response of amylase overproduction by simulating an increase in amylase secretion at a fixed growth rate. The new PCA unraveled key metabolic pathways directly related to amylase composition, with the biosynthetic pathways of the most abundant amino acids in its sequence having the highest weights in the principal components. However, the link between composition and weight in the principal component was not direct, as the amino acids with the highest weight were not always the most abundant. Out of the four predicted outliers with outstanding effect on amylase secretion, only one observation diverged from the simulations. Further, low-sensitivity amino acids were correctly predicted, with the notable case of cysteine, which was correctly predicted to negatively affect amylase secretion.

The iJT964-ME model represents a significant advancement in the metabolic modeling of B. subtilis. Its wide scope and ability to capture expression changes have improved gene essentiality predictions, shed light on recent hypotheses relating amino acid metabolism and stress, and explored the capacity to secrete industrially relevant proteins. This model can serve as the basis for unraveling further questions about metabolism and has the potential to be the foundation on which to optimize heterologous protein expression in this important model organism and cell factory.

## Methods

### Model reconstruction

Reconstruction was performed in Python 3.6, using the reconstruction packages cobrapy 0.5.422 and COBRAme20. Models were solved using the package SOLVEme39. The E. coli reconstruction package ECOLIme20 was adapted with B. subtilis gene expression machinery, complexes, and translocation pathways. In brief, every reaction in a template core metabolic network (M-model) is coupled with the consumption of the enzyme that catalyzes it. Similarly, enzyme production pathways (transcription, translation, post-translational modification) are coupled with the corresponding catalyzing enzymes. The link of the reactions is performed with coupling coefficients, which represent the usage requirement of the catalyzing enzyme per unit flux of reaction.

The core metabolic network was taken from the available M-model iYO844, along with its gene-reaction rules (with updates presented in Supplementary Table 1). The used information is summarized and shown in Table 1.

### Flux prediction

Metabolic and gene expression flux distribution was predicted following the same protocol and software used in the reconstruction of the E. coli ME model iJL1678-ME20. Like an M-model, iJT964-ME is solved by finding a vector of flux rates, v, that maximizes biomass production while satisfying $$S \ast v = 0$$, where S is a matrix of dimensions $$\left| M \right| \times \left| R \right|$$ containing the stoichiometric coefficients of all metabolites in M in every reaction in R. The formulation of ME-models represents a nonlinear programming problem, which must be solved iteratively40. We solved flux distributions in iJT964-ME with SOLVEme39, which uses a binary search algorithm that looks for the maximum possible growth rate that is feasible. In each iteration, a growth rate was assumed and substituted in all symbolic expressions to yield a linear programming problem (LP). Then, the QuadMINOS40 solver was called to solve the LP and assess feasibility in quad-precision.

### Carbon substrate analysis

As a way of checking the sanity of the metabolic network, we reproduced the carbon substrate analysis performed by Oh et al.7 with the template M-model iYO844. Only those carbon substrates that were already present in the model were included in this analysis, which leaves 88 carbon substrates. Detailed results are shown in Supplementary Data 1.

### Gene essentiality analysis

Single gene knockouts were modeled by closing their respective translation reactions. Genes were deemed essential when the single knockouts resulted in a growth rate of zero. Results were validated with a list of essential genes reported by Juhas et al.41 for B. subtilis and EcoCyc42 for E. coli. Gene functions were assigned as annotated in the subsystem of the reaction they catalyze. Metabolic subsystem annotation was taken from iYO844, and gene expression subsystems were assigned according to the catalyzed reaction types (as shown in the reaction breakdown in Fig. 1b).

Scores used to assess the performance of the gene essentiality predictions are True Positive Rate (TPR), True Negative Rate (TNR), False Discovery Rate (FDR), Matthews Correlation Coefficient (MCC), Precision, and Coverage. The definitions were as follows:

$${{{\mathrm{TPR}}}} = \frac{{{{{\mathrm{TP}}}}}}{{{{{\mathrm{TP}}}} + {{{\mathrm{FN}}}}}}$$
(1)
$${{{\mathrm{TNR}}}} = \frac{{{{{\mathrm{TN}}}}}}{{{{{\mathrm{TN}}}} + {{{\mathrm{FP}}}}}}$$
(2)
$${{{\mathrm{FDR}}}} = \frac{{{{{\mathrm{FP}}}}}}{{{{{\mathrm{FP}}}} + {{{\mathrm{TP}}}}}}$$
(3)
$${{{\mathrm{MCC}}}} = \frac{{\left( {{{{\mathrm{TP}}}} \ast {{{\mathrm{TN}}}} - {{{\mathrm{FP}}}} \ast {{{\mathrm{FN}}}}} \right)}}{{\left( {{{{\mathrm{TP}}}} + {{{\mathrm{FP}}}}} \right) \ast \left( {{{{\mathrm{TP}}}} + {{{\mathrm{FN}}}}} \right) \ast \left( {{{{\mathrm{TN}}}} + {{{\mathrm{FP}}}}} \right) \ast \left( {{{{\mathrm{TN}}}} + {{{\mathrm{FN}}}}} \right)}}$$
(4)
$${{{\mathrm{Precision}}}} = \frac{{{{{\mathrm{TP}}}}}}{{{{{\mathrm{TP}}}} + {{{\mathrm{FP}}}}}}$$
(5)
$${{{\mathrm{Coverage}}}} = \frac{{{{{\mathrm{Number}}}}\,{{{\mathrm{of}}}}\,{{{\mathrm{genes}}}}\,{{{\mathrm{in}}}}\,{{{\mathrm{model}}}}}}{{{{{\mathrm{Total}}}}\,{{{\mathrm{number}}}}\,{{{\mathrm{of}}}}\,{{{\mathrm{genes}}}}\,{{{\mathrm{in}}}}\,{{{\mathrm{database}}}}}}$$
(6)

### Modeling ethanol stress

Ethanol is a small polar molecule that can readily diffuse through the cell membrane. Therefore, ethanol uptake was modeled with no enzymatic coupling. The exchange reaction of ethanol was opened with lower and upper bounds equal to a defined uptake rate (see uptake rates in Fig. 2a), while all other exchange constraints were left unchanged as defined in ref. 7. Transcription and translation levels were defined as a ratio of the flux at a specific condition to the maximal flux in the whole dataset to normalize and highlight trends.

### Modeling salt stress

As opposed to ethanol, salt is transported through the membrane by a series of complexes. Transcriptomics data under salt stress showed that salt importers were downregulated, implying that an increased flux of salt occurs without a higher expression of transporters. Therefore, salt stress was modeled by an artificial uptake of salt uncoupled to any transporter so that higher uptakes did not falsely trigger importer expression in the model. Secretion complexes were left unchanged and coupled to salt secretion pathways. As in the simulation of ethanol stress, sodium uptake bound was defined as the different uptake rates, while all other constraints were left unchanged as defined in iYO8447.

### Modeling and validating amylase secretion rates

In the model, amyE is transcribed (transcription_TU8J2_1134_from_BSU25200-MONOMER), translated (translation_BSU25200), secreted through the sec pathway (translocation_BSU03040), and finally used in the hydrolysis of extracellular starch (AAMYL_1_FWD_BSU03040-MONOMER). Secretion rates, in units of mmol gDW−1 h−1, correspond to the flux through translocation_BSU03040. Random sampling of the solution space was performed from 90 to 100% of the optimal growth rate at the simulation conditions, in order to generate a robust distribution of biologically relevant fluxes12,34. First, the model was solved at low and high-amylase expression conditions to obtain lower and upper bounds of all exchange reactions in the model, thus yielding ranges of exchange reactions that ensure model feasibility (see “Flux prediction”). Then, exchange reactions were constrained with random values within the calculated bounds in every sampling iteration. This solution space was sampled 100 times.

Validation of secretion rates was performed in data collected from two previously reported experimental datasets, at a high32 and low31 growth rate. In both studies, the authors reported time-course biomass, X (g L−1), and amylase activity, A (mU mL−1). Amylase activity required conversion to mass concentration for direct comparison with model predictions. Thus, we converted activity to amylase concentration, C (mg mL−1), using a typical range for B. subtilis’ amylase specific activity43 of 153.7 (minimum) to 245 (maximum) U mg−1. Then, growth and amylase secretion rates were obtained using a linearized model.

Equations (7) and (8) are the mass balance equations for biomass (X) and amylase (C) in batch culture, where μ is the growth rate and v is the amylase secretion rate. Integration for $${{{\mathrm{X}}}}\left( {{{\mathrm{t}}}} \right)$$ in Eq. (7) yields the linearized model $$\log \left( {{{\mathrm{X}}}} \right) = \mu {{{\mathrm{t}}}} + {{{\mathrm{k}}}}$$. Growth rate was then estimated by fitting the datapoints during exponential growth to the linearized model. The Pearson correlation coefficients of the linear regressions for the datasets at high32 and low31 growth rate conditions were 0.81 and 0.98, respectively. For the amylase secretion rate (ν), integration for $$\left. {{{{\mathrm{C}}}}\left( {{{\mathrm{t}}}} \right)} \right|_{t_0}^{t_f}$$ and solving for ν in Eq. (8) yields Eq. (9).

$$\frac{{{{{\mathrm{dX}}}}}}{{{{{\mathrm{dt}}}}}} = \mu {{{\mathrm{X}}}}$$
(7)
$$\frac{{{{{\mathrm{dC}}}}}}{{{{{\mathrm{dt}}}}}} = \nu {{{\mathrm{X}}}}$$
(8)
$$\nu = \frac{{{\mathrm{C}}_{\mathrm{f}} - {\mathrm{C}}_0}}{{\mathop {\int }\nolimits_{{\mathrm{t}}_0}^{{\mathrm{t}}_{\mathrm{f}}} {{{\mathrm{Xdt}}}}}}$$
(9)

### Modeling the overexpression of amylase

Amylase overexpression was performed by setting the growth rate constant at the minimum rate exhibited in the distribution of samples at a high growth ($$0.17\,{{{\mathrm{h}}}}^{ - 1}$$). Then, amylase secretion rate was randomly forced within the range from the base requirement at $$0.17\,{{{\mathrm{h}}}}^{ - 1}$$ until the requirement the model would predict for $$0.195\,{{{\mathrm{h}}}}^{ - 1}$$. This solution space was sampled 100 times.

### Principal component analysis to identify critical reactions

Principal Component Analysis (PCA) is a resourceful unsupervised machine learning method that identifies key underlying variables that drive the variance in the samples. We used PCA to identify key reactions that explain the variance between high and low growth, as well as within the samples at different levels of amylase overexpression. The flux data were pre-processed by calculating z-scores and then fed to the scikit-learn method sklearn.decomposition.PCA.

### Growth of B. subtilis and amylase activity

B. subtilis strain 168 was struck out on LB agar plate overnight. One colony was inoculated in LB medium for 16 h at 37 °C, pelleted and resuspended in M9 medium. For amylase production testing, the cell resuspension was inoculated into M9, M9 + 0.2% starch (through 0.22uM filter), and M9 + 0.2% starch + amino acid in a 96-well plate at the starting inoculum of OD600 = 0.07 and final volume of 200ul. All amino acid concentrations were at 20 mM when possible, based on solubility data provided by the manufacturer (Millipore Sigma). Exceptions are Asp (3.4 mM), Glu (5.8 mM), Ile (14 mM), Leu (3.8 mm), Phe (16.3 mM), Trp (6.6 mM), Try (0.3 mM). All growth conditions were set up in triplicates. After 24 h at 37 °C, amylase activity and production were determined using the Sigma-Aldrich® Amylase Activity Assay Kit (MAK009). The protocol was followed exactly as suggested by the assay kit manufacturer. OD405 was measured at 24 h, and the value of the starch-only sample was subtracted from the value of each amino acid- supplemented sample. Amylase activity was reported as nmole/min/mL (milliunits), considering that one unit of amylase is the amount of amylase that cleaves ethylidene-pNP-G7 to generate 1.0 mmole of p-nitrophenol per minute at 25 °C.

### Sampling of cysteine synthesis rates

Sampling was performed in two different amylase secretion conditions, corresponding to amylase secretion rates calculated from ref. 31 (low amylase secretion) and ref. 32 (high-amylase secretion). Accordingly, amylase secretion rates were centered around 1.36e-8 and 4.4e-7 mmol Amylase gDW−1 h−1, allowing for a 10% variation. Sampling was performed with 100 points, and outliers were removed with 95% confidence. Significance in the change of cysteine synthesis rate distributions across both conditions was assessed with a two-tailed t test. The sensitivity of cysteine synthesis to amylase expression, in units of $${{{\mathrm{mmol}}}}\,{{{\mathrm{Cys}}}} \ast {{{\mathrm{mmol}}}}\,{{{\mathrm{Amylase}}}}^{ - 1}$$, was calculated as shown in Eq. (10). In this equation, $$\bar x_{high}$$ and $$\bar x_{low}$$ represent the means of cysteine secretion rates in the distribution of fluxes at the high and low amylase expression conditions, respectively. Similarly, $$r_{high}$$ and $$r_{low}$$ represent the rates of amylase expression at the high and low amylase expression conditions, respectively.

$$sensitivity = \frac{{change\,in\,cysteine\,synthesis}}{{change\,in\,amylase\,expression}} = \frac{{\bar x_{high} - \bar x_{low}}}{{r_{high} - r_{low}}}$$
(10)