A novel yeast hybrid modeling framework integrating Boolean and enzyme-constrained networks enables exploration of the interplay between signaling and metabolism

The interplay between nutrient-induced signaling and metabolism plays an important role in maintaining homeostasis and its malfunction has been implicated in many different human diseases such as obesity, type 2 diabetes, cancer, and neurological disorders. Therefore, unraveling the role of nutrients as signaling molecules and metabolites together with their interconnectivity may provide a deeper understanding of how these conditions occur. Both signaling and metabolism have been extensively studied using various systems biology approaches. However, they are mainly studied individually and in addition, current models lack both the complexity of the dynamics and the effects of the crosstalk in the signaling system. To gain a better understanding of the interconnectivity between nutrient signaling and metabolism in yeast cells, we developed a hybrid model, combining a Boolean module, describing the main pathways of glucose and nitrogen signaling, and an enzyme-constrained model accounting for the central carbon metabolism of Saccharomyces cerevisiae, using a regulatory network as a link. The resulting hybrid model was able to capture a diverse utalization of isoenzymes and to our knowledge outperforms constraint-based models in the prediction of individual enzymes for both respiratory and mixed metabolism. The model showed that during fermentation, enzyme utilization has a major contribution in governing protein allocation, while in low glucose conditions robustness and control are prioritized. In addition, the model was capable of reproducing the regulatory effects that are associated with the Crabtree effect and glucose repression, as well as regulatory effects associated with lifespan increase during caloric restriction. Overall, we show that our hybrid model provides a comprehensive framework for the study of the non-trivial effects of the interplay between signaling and metabolism, suggesting connections between the Snf1 signaling pathways and processes that have been related to chronological lifespan of yeast cells.

The interplay between nutrient-induced signaling and metabolism plays an important role in 16 maintaining homeostasis and its malfunction has been implicated in many different human diseases 17 such as obesity, type 2 diabetes, cancer and neurological disorders. Therefore, unravelling the role of 18 nutrients as signaling molecules and metabolites as well as their interconnectivity may provide a 19 deeper understanding of how these conditions occur. Both signalling and metabolism have been 20 extensively studied using various systems biology approaches. However, they are mainly studied 21 individually and in addition current models lack both the complexity of the dynamics and the effects 22 of the crosstalk in the signaling system. To gain a better understanding of the interconnectivity 23 between nutrient signaling and metabolism, we developed a hybrid model, combining Boolean 24 model, describing the signalling layer and the enzyme constraint model accounting for metabolism 25 using a regulatory network as a link. The model was capable of reproducing the regulatory effects 26 that are associated with the Crabtree effect and glucose repression. We show that using this 27 methodology one can investigat intrinsically different systems, such as signaling and metabolism, in 28 the same model and gain insight into how the interplay between them can have non-trivial effects by 29 showing a connection between Snf1 signaling and chronological lifespan by the regulation of NDE 30 and NDI usage in respiring conditions. In addition, the model showed that during fermentation, 31 enzyme utilization is the more important factor governing the protein allocation, while in low glucose 32 conditions robustness and control is prioritized. 33 34 Author summary 35 Elucidating the complex relationship between nutrient-induced signaling and metabolism represents a 36 key in understanding the onset of many different human diseases like obesity, type 3 diabetes, cancer 37 and many neurological disorders. In this work we proposed a hybrid modeling approach, combining 38 Boolean representation of singaling pathways, like Snf11, TORC1 and PKA with the enzyme 39 constrained model of metabolism linking them via the regulatory network. This allowed us to 40 improve individual model predictions and elucidate how single components in the dynamic signaling 41 layer affect the steady-state metabolism. The model has been tested under respiration and 42 fermentation, reveling novel connections and further reproducing the regulatory effects that are 43 associated with the Crabtree effect and glucose repression. Finally, we show a connection between 44 Snf1 signaling and chronological lifespan by the regulation of NDE and NDI usage in 45 respiring conditions. 46 47 Introduction 48 Biological systems are of complex nature comprising numerous dynamical processes and 49 networks on different functional, spatial and temporal levels, while being highly 50 interconnected (Walpole et al., 2013). The field of systems biology faces the great challenge 51 of elucidating how these interconnected systems work both separately and together to 52 prime organisms for survival. One of such phenomena is the cells ability to sense and respond to 53 environmental conditions such as nutrient availability. In order to coordinate cellular metabolism and 54 strategize, the cell needs an exact perception of the dynamics of intra-and extra-cellular 55 metabolites (Y. P. Wang & Lei, 2018 unravelling the role of nutrients as signaling molecules and metabolites as well as their 59 interconnectivity may provide a deeper understanding of how these conditions occur. 60 61 Yeast has long been used as a model organism for studying nutrient-induced signaling (Conrad et al.,62 2014a). Two major classes of nutrients include carbon and nitrogen. Carbon-induced signaling acts 63 mainly through the PKA and SNF1 pathway while nitrogen-induced signaling acts through the 64 mTOR pathway. The PKA pathway plays a major role in regulating growth by inducing ribosome 65 biogenesis genes and inhibiting stress response genes (Broach, 2012). The SNF1 pathway is mainly 66 active in low glucose conditions where it promotes respiratory metabolism, glycogen accumulation, 67 gluconeogenesis and utilization of alternative carbon sources but it also controls cellular 68 developmental processes such as meiosis and ageing (Ashrafi et al., 2000;Conrad et al., 2014a;69 Hedbacker & Carlson, 2008). The strongly conserved TORC1 pathway plays a crucial role in 70 promoting anabolic processes and cell growth in response to nitrogen availability (Broach, 2012 been shown that glucose signaling is related to metabolism however the nature of this relationship 77 remains unknown (Welkenhuysen et al., 2017). Numerous crosstalk mechanisms between these 78 pathways have been described (Shashkova et al., 2015) and depending on their activity, they may 79 influence the overall effect of the signaling process and thus the interaction with the 80 metabolism (Welkenhuysen et al., 2019). In order to better understand the impact of cell signaling on 81 metabolism, a systems biology approach is often implemented (Nielsen, 2017 Notably, a method to account for enzyme constraints, genome-scale models using kinetics and omics 107 (GECKO) (Sánchez et al., 2017)has been developed. GECKO incorporates constraints on metabolic 108 fluxes given by the maximum activity of enzymes, which are also constrained by a limited pool of 109 protein in the cell. This method has refined predictions for growth on diverse environments, cellular 110 response to genetic perturbations, and even predicted the Crabtree effect in S. cerevisiae's 111 metabolism, but also proven to be a helpful tool for probing protein allocation and enabled the 112 integration of condition-dependent absolute proteomics data into metabolic networks (Massaiu et al.,113 2019; Sánchez et al., 2017). 114 Following the holistic view of systems biology, hybrid models allow us to take the next step and 115 combine many different formalisms to study the interconnectivity and crosstalk spanning different 116 scales and/or systems. For example, to quantify the contribution of the regulatory constraints of 117 an E.coli genome-scale model, a steady-state regulatory flux balance analysis (SR-FBA) has been 118 developed (Shlomi et al., 2007), further the diauxic shift in S. cerevisiae has been studied by 119 CoRegFlux workflow integrating metabolic models and gene regulatory networks (Banos et al.,120 2017). To bypass the need for kinetic parameters, a FlexFlux tool has been developed where 121 metabolic flux analyses using FBA have been constrained with steady-state values resulting from the 122 regulatory network (Marmiesse et al., 2015). This strategy has also been used in a hybrid model of 123 the Mycobacterium tuberculosis where the gene regulatory network was used to constrain the 124 metabolic model to study the adaptation to the intra-host hypoxic environment (Bose et al., 2018). 125 However, to further study the impact of signaling on the metabolism, the complexity of the signaling 126 systems itself and the crosstalk between interacting pathways need to be represented in a coherent 127 manner. 128 129 To better understand the complex relationship between metabolism and signaling pathways, 130 we created a hybrid model consisting of a Boolean module integrating the PKA, TORC1 and the 131 Snf1 pathways as well as the known crosstalk between them and an enzyme-constrained module of S. 132 cerevisiae's central carbon and energy metabolism (Figure 1). The backbone of the presented model 133 is a framework for utilizing the complex Boolean representation of large-scale signaling systems to 134 further constrain an enzyme-constrained model (ecModel), where the activity of the transcription 135 factors resulting from the Boolean module was used to constrain an ecModel of the central carbon 136 metabolism. The proposed hybrid model is capable of reproducing the regulatory effects that are 137 associated with the Crabtree effect and glucose repression and have further showed a connection 138 between glucose signaling and chronological lifespan by the regulation of NDE and NDI usage in 139 respiring conditions. In addition, the model showed that during fermentation, enzyme utilization is 140 the more important factor governing the protein allocation, while in low glucose conditions 141 robustness and control is prioritized. 142 143 were simulated from nitrogen and glucose starved conditions to nutrient rich conditions. The PKA 154 pathway was activated upon glucose abundance via the small G proteins Ras and Gpa2. These 155 proteins, in turn, activated the adenylate cyclase (AC) that induced processes leading to the activation 156 of the catalytic subunit of PKA. Active PKA phosphorylated and therefore inactivated Rim15, thus 157 the transcription factors Gis1, Msn2 and Msn4 became inactive. 158 The SNF1 pathway is active when glucose is limited, while the addition of glucose causes Snf1 159 inactivation resulting in the activation of the transcriptional repressor Mig1 and the deactivation of 160 Adr1, Cat8 and Sip4. However, the inactivation of Adr1 happened prior to Snf1 inactivation. This is 161 due to the implemented crosstalk with the PKA pathway, where activated PKA inhibits Adr1 activity 162 (Cherry et al., 1989). 163 Nutrient availability activates the TOR complex 1 which in turn phosphorylates Sch9 and Sfp1 164 resulting in the repression of Rim15 phosphorylation and the expression of ribosomal genes 165 respectively. No change was observed in the activity of PP2A-regulated transcription factors Rtg1, 166 Rtg3, Gat2 and Gln2. However, during the 8 th iteration, PP2A was active. In addition, Sch9 was not 167 the main regulator of Rim15 activity in our simulations since PKA was activated prior to Sch9 and 168 acted independently to regulate Rim15, either due to a gap in the model or a lack of complexity in 169 our understanding of the signalling system (Supplementary Information S1). 170 To further investigate the impact of crosstalk in the Boolean model, knockouts of main components 177 of each pathway (Snf1, Reg1, Tpk1-3 and Tor1,2) were simulated and compared to the wildtype in 178 glc|nitr = 1|1 and glc|nitr = 0|0, see Figure S2. In nutrient-depleted conditions, only the Snf1 knockout 179 had a significant impact. In the Snf1 pathway, Snf1 knockout affected all downstream targets leading 180 to a transcription factor activity pattern that is usually observed in wildtype strains when glucose is 181 available (Conrad et al., 2014b). It has been previously described that the phenotype of Snf1 mutants 182 resembles the phenotype observed when the cAMP/PKA pathway is over-activated (Thompson-183 Jaeger The effects of Tor1 and 2 knockouts only affected the TORC1 signaling pathway. The simulated 203 phenotype equalled the phenotype that is expected upon nitrogen depletion and glucose abundance 204 and was therefore similar to the phenotype observed when simulating the Snf1 knockout in nutrient-205 starved cells. Besides, experimental observations revealed that impairing Tor1 and 2 function results 206 in growth arrest in the early G1 phase of the cell cycle, as well as inhibition of translation initiation 207 which are characteristics of nutrient, depleted cells entering stationary phase (Barbet et al., 1996). 208 The fact that inactivation of TORC1 results in the inactivation of Sfp1 that regulates the expression 209 of genes required for ribosomal biogenesis could be an indicator of this observation; however other 210 TORC1-associated signaling mechanisms inducing translation initiation may likely be involved 211 (Barbet et al., 1996). 212

The hybrid model improves predictions of individual proteins and reveals a connection 213 between regulation and chronological ageing 214
To verify the ecModel performance, the predictions of exchange reaction fluxes at increasing dilution 215 rates were compared against experimental data (Van Hoek et al., 1998) ( Figure S3), predictions 216 showed a median relative error of 9.82% in the whole range of dilution rates from 0 to 0.4 h -1 , 217 spanning both respiratory and fermentative metabolic regimes. The hybrid model, including 218 regulation, was further compared with the ecModel in their ability to predict protein abundances by 219 comparing the predicted abundances to proteomics data from the literature in both respiratory and 220 fermentative conditions (Doughty et al., 2020;Paulo et al., 2016). By adding the regulation layer, the 221 prediction accuracy of individual protein abundances was drastically improved, reducing the mean 222 absolute log 10 -transformed ratio between predicted and measured values (r) from 2.62 to 1.55 for 223 respiration and from 3.56 to 2.32 for fermentation (Figure 3), which represents an average 224 improvement in protein predictions by more than one order of magnitude for both conditions. 225 Moreover, two sample Kolmogorov-Smirnov tests did not show significant statistical differences 226 between model predictions and the available proteomics datasets. This large improvement is 227 predominantly resulting from the utilization of more than one isoform for some reactions in the 228 hybrid model in contrast to a pure ecModel, in which just the most efficient enzyme for a given 229 reaction is used. 230 Pathway enrichment analysis of the proteins miss-predicted by more than one order of magnitude, by 231 the hybrid model has been performed and showed that the superpathway of glucose fermentation was 232 underpredicted for both respiration and fermentation (p-value of 1.398426e-7 and 7.002912e-5, 233 respectively). Additionally, the superpathway of TCA cycle and glyoxylate cycle was underpredicted 234 (p-value = 0.036267), whilst aerobic respiration and electron transport chain were significantly 235 overpredicted (p-value = 2.857451e-23) in the fermentative state and the pentose phosphate pathway 236 (p-value= 2.863892e-4) as well as glucose-6-phosphate biosynthesis (p-value= 0.019529) were 237 underpredicted in respiration. A detailed comparison between the models as well as in-depth results 238 from the protein predictions are available in Data file S1 and Supplementary Information S1. 239 To better understand which pathways and reactions are most affected by regulation, the metabolic  which is turned on, implying that the Snf1 pathway is responsible for changing the acetate production 320 via ALD6 to acetate production via ALD2, resulting in increased production of cytosolic NADH to 321 the expense of the NADPH, which is compensated by increasing the flux through the pentose 322 phosphate pathway as well as the additional use of NDE. 323

Discussion 324
The effects of nutrient-induced signaling on metabolism play an important role in maintaining 325 organismal homeostasis and consequently understanding human disease and ageing. To gain a better 326 understanding of the interconnectivity between nutrient signaling and metabolism, we have 327 developed a hybrid model by combining the Boolean and the enzyme constraint models using a 328 regulatory network as a link. More specifically, we have implemented a Boolean signaling network 329 that is responsive to glucose and nitrogen and an ecModel of yeast's central carbon metabolism. The 330 proposed framework has been validated using available experimental data resulting in an increased 331 predictive power on individual protein abundances in comparison to individual models alone. Further 332 we were able to characterize the cells deviation from the optimal protein allocation and flux 333 distribution profiles. The model is capable of reproducing the regulatory effects that are associated 334 with the Crabtree effect and glucose repression. The model showed a connection between 335 SNF1 signaling and chronological lifespan by the regulation of NDE and NDI usage in 336 respiring conditions. In addition, the model showed that during fermentation, enzyme utilization is 337 the more important factor governing the protein allocation, while in low glucose conditions 338 robustness and control is prioritized. 339 The integration of regulation constraints is resulting in a highly constrained hybrid model. The 340 downside of this approach is connected to the lack of information regarding the regulatory effects of 341 transcription factor activation. In this work we assume a uniform proportional action for all gene 342 targets, together with the other constraints of the model, resulting in a rather low effect on the 343 regulatory action. Despite this, the hybrid model shows improved protein abundance predictive 344 power and can qualitatively reproduce regulatory effects associated with glucose repression in 345 fermentation conditions, suggesting that with this framework we can gain novel insight into the 346 interplay between signaling pathways and metabolism, however, any quantitively or definitive 347 statements should be avoided. Another limitation is the inclusion of only the central carbon 348 metabolism, a potential extension of this work would include the addition of pathways responsive to 349 glucose signaling, like glycerol metabolism and fatty acid synthesis, enabling also the study of the 350 regulatory effect on these pathways specifically with relatively few modifications in the hybrid 351 model. 352 The hybrid model shows that under regulation the NADH to support the electron transport chain is 353 partly  indicate their important role as modulators of flux balance between glycolysis, PPP and fermentative 390 pathways at highly demanding conditions, suggesting that when entering fermentation, the cell 391 sacrifices robustness to favor enzyme utilization. 392 Comparison of enzyme usage and flux distributions between models and across conditions reveals 393 that the effects of regulation are generally stronger for the respiratory condition, causing the arisen of 394 more and higher futile fluxes; turning on reaction steps that are not required by optimal metabolic 395 allocation (purely ecModel); and inducing higher fold-changes into fluxes. These findings suggest 396 that metabolic phenotypes are majorly shaped by regulatory constraints in low glucose conditions, 397 whilst enzymatic constraints play a major role when glucose is not the limiting resource. 398 It was also found that the regulatory layer diminishes the strong flux control that hexokinase isoforms 399 have over glucose consumption in both low and high glucose conditions to 0. indicating the components' activity, allowing a better graphical depiction. In total, the model 452 comprises 5 metabolites, 10 groups of target genes, 6 enzymes whose activity is altered upon nutrient 453 signaling and 46 proteins belonging to PKA/cAMP, the SNF1 and the TORC1 pathway, for detailed 454 description, see Supplementary Information S1 and Table S1-S6. 455 Availability of glucose and nitrogen was used as an input to the model and is implemented as one 456 vector of binary values for each nutrient. This input enables to simulate the induction of signaling 457 under different nutrient conditions, for instance the addition of glucose and nitrogen to starved cells 458 is represented by the vector 0|1 for both nutrients respectively. Here, 0 represent the starved or low 459 nutrient condition and 1 the nutrient-rich condition. Based on this input and the formulation of the 460 Boolean rules, a cascade of state transitions is induced. The simulation was conducted using a 461 synchronous updating scheme meaning that at each iteration, the state vectors are updated 462 simultaneously. The algorithm stops if a Boolean steady state is reached at which no operation causes 463 a change in the state vectors. This process is repeated for each pair of glucose and nitrogen 464 availabilities whereby the reached steady state for each nutrient condition serves as an initial 465 condition for the next nutrient condition. 466 Since for many of the included processes, no information on the mechanisms causing reversibility 467 was available, especially a lack in the knowledge on phosphatases reverting phosphorylation was 468 observed ( carbon and energy  478  metabolism, including metabolites, reactions, genes and their interactions accounting for glycolysis,  479  TCA cycle, oxidative phosphorylation, pentose phosphate, Leloir and anaerobic excretion pathways,  480 together with a representation of biomass formation, was taken as a network scaffold (Nilsson &  481 Nielsen, 2016). The metabolic model was further enhanced with enzyme constraints using the 482 GECKO toolbox v1.3.5 (Sánchez et al., 2017), which considers enzymes as part of metabolic 483 reactions, as they are occupied by metabolites for a given amount of time that is inversely 484 proportional to the enzyme's turnover number (k cat ). Therefore, enzymes are incorporated as new 485 "pseudo metabolites" and usage pseudo reactions are also introduced in order to represent their 486 connection to a limited pool of protein mass available for metabolic enzymes. Moreover, all 487 reversible reactions are split into two reactions with opposite directionalities in the ecModel, in order 488 to account for the enzyme demands of backwards fluxes. Several size metrics for the Boolean model, 489 the metabolic network and its enzyme-constrained version (ecModel) are shown in Table 1. between reaction fluxes and enzyme demands, which are constrained by the aforementioned pool of 506 metabolic enzymes 507 is the turnover number of the enzyme j for the i-th reaction, as in some cases several 508 enzymes can catalize the same reaction (isoenzymes); ݁ , is the usage rate for the enzyme j in 509 mmol/gDw h -1 ; ‫ܯ‬ ‫ݓ‬ , represents the molecular weight of the enzyme j, in mmol/g; ܲ ௧ ௧ , is the total 510 protein content in a yeast cell, corresponding to a value of 0.46 g prot /gDw (Famili et al., 2003); ݂ , is 511 the fraction of the total cell proteome that is accounted for in our ecModel, 0.1732 when using the 512 integrated dataset for S. cerevisiae in paxDB as a reference (M. Wang  This simple modelling formalism enables the incorporation of complex enzyme-reaction relations 521 into the ecModel due to its matrix formulation, such as isoenzymes, which are different enzymes able 522 to catalyse the same reaction; promiscuous enzymes, enzymes that can catalyze more than one 523 reaction; and enzyme complexes, several enzyme subunits all needed to catalyse a given reaction. 524

ecModel curation 525
As the ecModel was generated by the automated pipeline of the GECKO toolbox, several of its 526 components were curated in order to achieve predictions that are in agreement with experimental data 527 at different dilution rates. Data on exchange reaction fluxes at increasing dilution rates, spanning both 528 respiration and fermentative metabolic regimes (Van Hoek et al., 1998) was used as a comparison 529 basis. Additionally, all unused genes in the original metabolic network were removed and gene rules 530 for lactose and galactose metabolism were corrected according to manually curated entries for S. 531 cerevisiae available at the Swiss-Prot database (Bateman, 2019). Gene rules and metabolites 532 stoichiometries (P/O ratio) in the oxidative phosphorylation pathway were also corrected according 533 to the consensus genome-scale network reconstruction, Yeast8 (Lu et al., 2019). 534 The average saturation factor for the enzymes in the model was fitted to a value of 0.48, which 535 allows the prediction of the experimental critical dilution rate (i.e. the onset of fermentative 536 metabolism) at 0.285 h -1 . ATP requirements for biomass production were fitted by minimization of 537 the median relative error in the prediction of exchange fluxes for glucose, oxygen, CO 2 and ethanol 538 across dilution rates (0 -0.4 h -1 ), resulting in a linear relation depending on biomass formation from 539 18 to 25 mmol per gDw for respiratory conditions and from 25 to 30 mmol per gDw for the 540 fermentative regime. 541

Hybrid model 542
A hybrid model consists of the Boolean model connected with the ecModel trough a transcriptional 543 layer that regulates its constraints on protein allocation (Figure 1). , is a parsimonious usage for enzyme i for a given growth and 552 glucose uptake rates; ܴ ‫ܨ‬ , corresponds to a regulation factor between 0 and 1; ݁ ௫ and ݁ are the 553 maximum and minimum allowable usages for enzyme i under the specified conditions. 554 A distribution of parsimonious enzyme usages is obtained by applying the rationale of the 555 parsimonious FBA technique (Lewis et al., 2010), which explicitly minimizes the total protein 556 burden that sustains a given metabolic state (i.e. fixed growth and nutrient uptake rates). 557 To connect the transcription factor activity with gene regulation we extracted regulation information 558 from YEASTRACT and set a regulation level of 5% of the enzyme usage variability range for the 559 simulations. When several transcription factors affect the same gene, the effects are summed up and 560 the resulting sum is used as a basis for constraint. For example, if a gene is downregulated by two 561 transcription factors (-2) and upregulated by one transcription factor (+1), the net sum would be (-1), 562 thus the gene will be downregulated. In our model, an absolute sum higher than 1 will not cause a 563 stronger regulation, as this additive process is just implemented to define the directionality of a 564 regulatory effect. 565

Enzyme usage variability analysis 566
As metabolic networks are highly redundant and interconnected, the use of purely stoichiometric 567 constraints usually leads to an underdetermined system with infinite solutions (Kauffman et al.,  568 2003), in a typical FBA problem it is common that even for an optimal value of the objective 569 function, several reactions in the network can take any value within a "feasible" range, such ranges 570 can be explored by flux variability analysis (Mahadevan & Schilling, 2003). 571 In this study, enzyme usage variability ranges for all of the individual enzymes are calculated by 572 fixing a minimal glucose uptake flux, for a given fixed dilution rate, and then running sequential 573 maximization and minimization for each enzyme usage pseudo reaction. 574 This approach allows the identification of enzymes that are either tightly constrained, highly variable 577 or even not usable at optimal levels of biomass yield. 578 Simulations 579 Cellular growth on chemostat conditions, at varying dilution rates from 0 to 0.4 h -1 , was simulated 580 with the multiscale model by the following sequence of steps: 581 1. Initially, the desired dilution rate is set as both lower and upper bounds for the growth pseudo 582 reaction and the glucose uptake rate is minimized, assuming that cells maximize biomass production 583 yield when glucose is limited ( represents the minimum uptake rate allowed by the stoichiometric and enzymatic 588 constraints of the metabolic network, possible deviations from optimal behaviour may be induced by 589 regulatory circuits. In order to allow the Boolean model to reallocate enzyme levels a suboptimality 590 factor ‫)ܨܵ(‬ of 15% was used to set an upper bound for ‫ݒ‬ ீ ಿ . 591 3. The ecModel is connected to the glucose-sensing Boolean model through the glucose uptake rate. 592 At the critical dilution rate, the glucose uptake rate obtained by the ecModel is 3.2914 mmol/gDw h, 593 this value is used as a threshold to define a "low" or "high" glucose level input in the Boolean model, 594 represented as 0 and 1, respectively. For each dilution rate, the initial value of ‫ݒ‬ ீ ಿ is calculated and 595 fed to the regulatory network, which runs a series of synchronous update steps until a steady-state is 596 reached. 597 4. At steady state, the regulatory network indicates the enzyme usages that should be up and 598 downregulated, for which new usage bounds are set as described above. 599 5. A final FBA simulation is run by minimizing the glucose uptake rate, subject to a fixed dilution 600 rate and the newly regulated enzyme usage bounds. 601 Gene deletions can also be set in the Boolean module and will result in activation or inactivation of 602 transcription factors which then affect the constraints on the FBA model. We ran four simulations of 603 deletion strains as follows: TOR1 and TOR2 (TOR deletion), Snf1 (SNF1 deletion), Tpk1, Tpk2 and 604 Tpk3 (PKA deletion) and Reg1(Reg1 deletion). 605

Proteomics analysis 606
Protein abundance data on respiratory and fermentative conditions were compared to protein usage 607 predictions by the hybrid model in order to assess its performance. For the respiration phase, absolute 608 protein abundances were taken from a study of yeast growing under glucose-limited chemostat 609 conditions at 30°C on minimal mineral medium with a dilution rate of 0.1 h −1 (Doughty et al., 2020). 610 For the fermentation phase, a proteomics dataset was taken from a batch culture using minimal media 611 with 2% glucose and harvested at an optical density (OD) of 0.6 (Paulo et al., 2016). The dataset 612 given as relative abundances was then rescaled to relative protein abundances in the whole-cell 613 according to integrated data available for S. cerevisiae in PaxDB (M. Wang, Herrmann, Simonovic, 614 Szklarczyk, & von Mering, 2015), and finally converted to absolute units of mmol/gDw using the 615 "total protein approach" (Wiśniewski & Rakus, 2014). 616 We used three metrics for comparing the simulations with the proteomics data, the Pearson 617 correlation coefficient (PCC), two-sample Kolmogorov-Smirnov (KS) test and the mean of the 618 absolute log 10 -transformed ratios between predicted and measured values (r). The PCC and the 619 significance of the PCC were determined by a permutation test of n=2000. Pathway enrichments 620 were done using YeastMine (Balakrishnan et al., 2012)