Synechocystis sp. PCC 6803, we applied stoichiometric metabolic modelling. Our network-wide analysis indicates that the rate of NAD(P)H regeneration, rather than of ATP, controls ATP/NADPH ratio, and thereby bioproduction. The simulation also implies that energy and redox balance is interconnected with carbon and nitrogen metabolism. Furthermore, we show that an auxiliary pathway, composed of serine, one-carbon and glycine metabolism, supports cellular redox homeostasis and ATP cycling. The study revealed non-intuitive metabolic pathways required to enhance alkene production, which are mainly driven by a few key reactions carrying a high flux. We envision that the presented comparative in-silico metabolic analysis will guide the rational design of Synechocystis as a photobiological production platform of target chemicals.Understanding energy and redox homeostasis and carbon partitioning is crucial for systems metabolic engineering of cell factories. Carbon metabolism alone cannot achieve maximal accumulation of metabolites in production hosts, since an efficient production of target molecules requires energy and redox balance, in addition to carbon flow. The interplay between cofactor regeneration and heterologous production in photosynthetic microorganisms is not fully explored. To investigate the optimality of energy and redox metabolism, while overproducing alkenes—isobutene, isoprene, ethylene and 1-undecene, in the cyanobacterium  In the past years, the unicellular cyanobacterium Synechocystis sp. PCC 6803 (hereafter Synechocystis) has been successfully used as a cell factory for the production of commodity chemicals, including, n-butanol2, bisabolene3 and phenylpropanoids4. Besides autotrophy, cyanobacteria are able to grow under mixotrophic conditions. Mixotrophic metabolism allows the cells to catabolize organic carbon parallel to CO2 being assimilated photosynthetically. Addition of organic substrates in light growth conditions, though increasing the risk of contamination and cost, is considered as a promising cultivation strategy for the commercialization of cyanobacteria6, owing to enhanced biomass7 and chemical yield9.Cyanobacteria are photosynthetic microbes that serve as an attractive platform for the sustainable production of chemicals and fuels, mainly due to their capability of converting atmospheric carbon dioxide into organic compounds by using solar energy, their relative rapid growth rate, and the readily available genetic toolbox for various species10. The different glycolytic routes and the TCA cycle generate reducing agent in the form of NADH. In addition, transhydrogenases catalyze the interconversion between NADH and NADPH11.The biosynthesis of various cell metabolites involves biochemical reactions, which require cofactors, such as adenosine triphosphate (ATP) and reduced nicotinamide adenine dinucleotides [NAD(P)H]. ATP is the major energy carrier in the cell, driving numerous metabolic pathways. The pyridine nucleotides NADH and NADPH serve as reducing equivalents in redox reactions. While NADH participates mainly in catabolic reactions, NADPH plays a role in anabolic reactions. In cyanobacteria, the photosynthetic electron transport chain is the major source for ATP and NADPH generation, when grown under light conditions12. The photosynthetic linear electron flow (LEF) in Synechocystis generates an ATP/NADPH ratio of approximately 1.28, which is less than required for CO2 fixation by the Calvin–Benson–Bassham (CBB) cycle and downstream biochemical pathways12. To deal with this imbalance, alternative pathways contributing to ATP production exist14. In addition, re-oxidation of NAD(P)H to NAD(P)+ and phosphorylation-dephosphorylation of reducing equivalents are important for balancing the ATP/NADPH budget and maintaining redox homeostasis15. Despite the importance of meeting the energy and redox requirement to achieve an efficient cellular performance17, only few metabolic engineering efforts of Synechocystis have targeted this designing strategy18, while most studies are concerned with controlling carbon partitioning1.Optimal performance of photosynthesis requires that the light-energy conversion by the photosystems and the downstream metabolic pathways are fine-tuned, to support the ATP/NADPH output ratio and the cellular energy economySynechocystis, for which several detailed genome-scale metabolic reconstructions are available25. CBM is based on imposing of a set of constraints that govern the operation of a metabolic network at steady state. These include, for example, the stoichiometry of the biochemical reactions, mass balance and thermodynamic laws. Flux balance analysis (FBA) is a common CBM-based approach to calculate, under given constraints, the intracellular flux distributions within the stoichiometric network, by optimizing an objective function26. As such, FBA can be used to predict the maximum (or minimum) growth rate or the production of desired metabolites, as well as to identify genetic interventions that force carbon flux toward chosen compound. Case studies demonstrating model-driven metabolic engineering of Synechocystis include the overproduction production of isoprene27, n-butanol28 and ethanol29.Constraint-based modelling (CBM) has been employed for the characterization of physiological capabilities of 30. The development of gas-to-liquid technologies, enabling the oligomerization of small gaseous substrates into liquid chemicals, together with the environmental concerns associated with the use of fossil fuels and carbon dioxide emissions31, are driving the necessity for an environmentally-friendly, yet economically-feasible, manufacturing process of bio-alkenes33.In this work, we focus on alkenes, commercially valuable platform chemicals, which are traditionally used as detergents, lubricants and rubbers. In addition, they are compatible hydrocarbon fuels, due to their high energy contentSynechocystis balances its anabolic-catabolic processes, with respect to central cofactor metabolites [ATP and NAD(P)H], during growth under autotrophic and mixotrophic conditions. To this end, we employed genome-scale metabolic modelling, and analyzed the metabolism of Synechocystis strains overproducing alkenes as a case study.We addressed the question of how the model cyanobacterium Synechocystis strains, and assess the resulting energy and redox (im)balance, we chose four alkenes whose production using cyanobacteria has been previously demonstrated: isoprene34, isobutene35, ethylene36 and 1-undecene37. The four alkenes stem from different metabolic routes and possess different cofactors requirements  and product synthesis. Predicted maximal alkene production rates resulted in zero biomass accumulation, and vice-versa , and ATP (turnover rate of 7.24–8.61 mmol/gDW/h) was observed, as compare to the usage of NADH (turnover rate of 0.01–0.49 mmol/gDW/h) 42. A higher cofactor availability of NAD(P)H could be achieved by the introduction of non-native NADH-dependent oxidoreductases, or protein engineering of enzymes for swapped cofactor-dependency43.Since the overall consumption and production rates are equal, under the steady-state assumption, the flux-sum serves as a proxy of the metabolite pool size in the system, by which the cellular ATP/NADPH ratio could be examined. The analysis revealed a narrow range of intracellular ATP pool Table . In cont45. These differences could be justified by that: (i) Here, we considered flux in the entire metabolic network, whereas previous studies mainly considered photosynthetic reactions . (ii) Different metabolic network sized were examined, covering different number of reactions acting on ATP and NAD(P)H: 760 reactions44, 780 reactions45, and 883 reactions in this study. (iii) We simulated a synergistic interaction between biomass formation (10%) and alkene biosynthesis, whereas earlier studies modelled 0%44 or 75%45 of growth, which affected the evaluation of ATP/NAD(P)H demand.It should be noted that, the ATP/NADPH ratios presented here slightly differ from earlier published resultsSynechocystis could be recognized. We would like to note that FBA and 13C-metabolic flux analysis (MFA) are two different approaches to determine the intracellular fluxes46. Further, our model does not include information regarding cellular regulation or enzyme kinetics, which influence the conclusion on the flow of carbon in the cell.In order to identify the metabolic reactions contributing to the computed turnover rates, we employed a reaction-centric approach by using pFBA. By comparing biomass and alkene-overproducing strains, potential reactions whose metabolic fluxes constrain alkenes synthesis in Synechocystis is active also during light, albeit at low capacity47. Isoprene and ethylene production required a higher contribution of respiratory oxidative phosphorylation, whereas for isobutene, pyruvate kinase (PYK), from lower glycolysis, contributed to ATP generation  Table . Under aon Table .Table 3PSynechocystis49. Our data also revealed specific flux distributions depending on the objective function. For ethylene production, the ATP-consuming reactions were within nitrogen metabolism pathways , whereas for isoprene production, the terpenoid biosynthesis pathways contributed the most to ATP consumption. Bicarbonate transport (BCT1_syn) exhibited a large ATP consumption for production of isoprene and 1-undecene. Acetyl coenzyme A (acetyl-CoA) carboxylase (ACCOAC) was mainly involved in 1-undecene accumulation, probably due to high amount of carbon assimilated during the elongation process of fatty acyl chain for 1-undecene synthesis.Reactions involved in ATP consumption were more diverse than for ATP generation and differed between growth conditions. Under autotrophic growth, ATP consumption was dictated by reactions within CBB cycle and glycolysis/gluconeogenesis  for all strains Table . EarlierSynechocystis49. Our data also revealed specific flux distributions depending on the objective function. For ethylene production, the ATP-consuming reactions were within nitrogen metabolism pathways , whereas for isoprene production, the terpenoid biosynthesis pathways contributed the most to ATP consumption. Bicarbonate transport (BCT1_syn) exhibited a large ATP consumption for production of isoprene and 1-undecene. Acetyl coenzyme A (acetyl-CoA) carboxylase (ACCOAC) was mainly involved in 1-undecene accumulation, probably due to high amount of carbon assimilated during the elongation process of fatty-acyl chain for 1-undecene synthesis.Reactions involved in ATP consumption were more diverse than for ATP generation and differed between growth conditions. Under autotrophic growth, ATP consumption was dictated by reactions within CBB cycle and glycolysis/gluconeogenesis  for all strains Table . EarlierUnder mixotrophic conditions, the ATP consumption was mainly governed by cyanophycin metabolism  during biomass, isobutene and 1-undecene synthesis Table . For isoWe additionally investigated how the ATP precursors  are recycled within the metabolic network Fig. –19. The Saccharomyces cerevisiae50, and could explain the low ethylene production found experimentally in Synechocystis36.The enhanced ADK1 flux during biomass Fig.  and 10 a51, we suggest that a combinatorial metabolic engineering, with the aim to form an efficient ATP cycling for fueling the CBB cycle, could be based on the ATP-consuming enzymes , and on the ATP-producing enzymes . In addition a high ATP turnover would be beneficial for the heterologous production of alkenes, and probably other products, in Synechocystis, as previously confirmed for E. coli42.Based on our studies and others52.We propose that, under mixotrophic conditions, the regeneration of cellular nitrogenous polymers  is essential for optimized nitrogen and energy metabolism in the cell. The data are in agreement with previous studies, arguing that the transition in growth conditions affects nitrogen metabolism through cyanophycin53, the flux analysis revealed that, under both autotrophic and mixotrophic growth, the photosynthetic ferredoxin-NADP+ reductase (FNOR) contributed largely to the supply of NADPH  was significantly higher than that in the other modeled strains Table –7. We suThe flux distribution of reactions catalyzing NADPH consumption revealed that for all objectives, NADPH was mainly consumed by glyceraldehyde-3-phosphate dehydrogenase (GAPDi_nadp), a key enzyme within the CBB cycle and gluconeogenesis Table . As coulThough carrying low flux under both growth conditions, production of NADH were distributed among BCAA biosynthesis pathway , TCA cycle  and L-arginine and L-proline metabolism  Table .Fig. 5MeWe observed that under autotrophy, for all objectives but 1-undecene, the photosynthesis (NAD(P)H dehydrogenase, NDH1_2u) is the main NADH consumer Table . For 1-uThe data imply that the regeneration of the NADH pool in the system is facilitated mainly by amino acids metabolism. The reduction of nitrate to ammonia requires a considerable amount of NADPH. We suggest that designing an alternative NADH-dependent pathway for ammonium assimilation (for example by introducing ALAD_L) could reduce the competition for NADPH. Hence, increasing the potential for NADPH-dependent product formation Fig. , while s+ consumption phosphorylating enzymes, and identified that NAD kinase (NADK) had a negligible contribution to the overall flux of NAD+, rather than by the regeneration of ATP. Our data are consistent with a previous study, demonstrating that, under steady-state photosynthesis, CO2 assimilation is not limited by the availability of ATP, but by the rate of NADPH formation57.Considering the large variation in NADPH turnover rates . We identified that, under autotrophic conditions, carbon is channeled back to the Embden-Meyerhof-Parnas (EMP) pathway to synthetize glycogen through glucose-1-phosphate adenylyltransferase (GLGC) and glycogen synthase (GLCS1) reactions Fig. , 4, 6. I63, ME2 functions as an additional route for synthesizing pyruvate in Synechocystis7. Fluxomic studies pinpointed that PYK reaction represents a bottleneck for isobutyraldehyde production in Synechococcus elongatus PCC 7942, which was overcome by heterologous overproduction of PYK64. Under mixotrophic conditions, the Entner–Doudoroff pathway also provided pyruvate for biomass synthesis (Supplementary Table Synechocystis for hydrocarbon production. The CO2 released by ME2 can be further assimilated by phosphoenolpyruvate carboxylase (PPC)  and Malic enzyme (ME2) are the major contributors to pyruvate synthesis, although at distinct ratios, depending on the objective function  function as an auxiliary pathway to regenerate ATP, NADPH and NADH in ion Fig. –19. The Synechocystis metabolism is governed by several high-flux core reactions, which probably allows the cell to adapt rapidly to perturbations in environmental conditions and genetic modifications. We also show that assessment of ATP and NAD(P)H balance can neither be done in isolation from each other and their precursors, nor from carbon and nitrogen metabolism. Even though the predictions are yet to be validated in vivo, our results provide hints for strain design strategies enabling efficient bioproduction of valuable compounds derived from core metabolic pathways in Synechocystis.To conclude, we demonstrate the significance of high flexibility in activity of energy- and carbon-converting enzymes in order to achieve the required ATP/NADPH output ratio. It was apparent that the overall activity of the 69 was employed on COBRApy v0.20.070 using the commercial solver Gurobi v10.0.1  in Python v3.8.5, using the packages Pandas v1.3.0, NumPy v1.19.4, Matplotlib v3.3.3 and Pickle v4.0. Model consistency was tested with MEMOTE v0.12.071. Visualization of the metabolic reaction network and the obtained fluxes was done using the Escher web-tool72.Parsimonious enzyme usage FBA (pFBA)Synechocystis sp. PCC 680319, downloaded from the BiGG database73, was used for the computational analysis. The model reconstruction includes 622 genes, 863 reactions and 795 metabolites. iJN678 also contains three different biomass compositions, allowing for simulating autotrophic, mixotrophic, and heterotrophic growth conditions, in addition to constraining the appropriate carbon and photon uptake rates.The iJN678 genome-scale metabolic model of 76, addition of the phosphoketolase reactions77, addition of the Entner–Doudoroff (ED) pathway78, addition of the light-independent L-serine biosynthesis pathway79, addition of prephenate transaminase, prephenate dehydratase and arogenate dehydrogenase80, transhydrogenase (NADTRHD) was changed to a reversible reaction11, addition of NADH dehydrogenase 2, alternative respiratory terminal oxidase, and flavodiiron proteins 2 and 4, and constraining cytochrome b6f, cytochrome c oxidase and NAD(P)H dehydrogenase to zero81. In addition, non-growth associated ATP maintenance (ATPM)83 reaction was added to the model. The ATPM coefficient is represented by a pseudo-reaction that degrades ATP into ADP and orthophosphate (Pi) , irreversible leucine transaminase (LEUTAi) and glycine cleavage system (GLYCL and GLYCL_2). It was reported earlier that, the transhydrogenase reaction was poorly resolved by 13C measurements87. Therefore, we chose to model redox balance without an active NADTRHD, as previously suggested88. At the same time, we could learn how the entire metabolic network balances between NADPH/NADH. In addition, the upper and lower bounds of LEUTAi and GLYCL and GLYCL_2 were constrained to zero, and the glycine cleavage system was modeled by introducing three separate reactions 89. In addition, we coupled our analysis to FVA.In order to avoid thermodynamic infeasible cycles, the “add_loopless” function in COBRApy was applied, that makes thermodynamically infeasible loops impossible90, autotrophic metabolism was simulated by constraining the carbon dioxide, bicarbonate and glucose uptake rates to 0, 3.7 and 0 mmol/gDW/h, respectively. Mixotrophic metabolism was simulated by constraining the inorganic carbon (carbon dioxide and bicarbonate) uptake rates to 0 and glucose uptake rate to 0.38, respectively. For both trophic conditions, the photon uptake rate to was set to 45 mmol/gDW/h, to simulate a light-limited condition. These settings resulted in maximum specific growth rates of 0.082 h−1 and 0.056 h−1, under autotrophic and mixotrophic conditions, respectively, which are in agreement with experimental growth values22. In addition, the biomass objective function91 was set to BIOMASS_Ec_SynAuto, BIOMASS_Ec_SynMixo, depending on the simulated growth conditions, to account for changes in macromolecular composition.According to previous studies93, showing that a feasible overproduction of hydrocarbons in Synechocystis entails a carbon partitioning to biomass of 10%, we simulated a scenario where the cellular growth is limited, while achieving a high alkene production rate. We used a two-step optimization strategy, where, first, the biomass objective function was maximized. Then, the minimum flux through the biomass objective function was set to 10% of the obtained value, followed by the maximization of alkene production.Following earlier studies38 was carried out.For providing a global perspective on the relation between growth rate and alkene production a phenotypic phase plane analysis39. The flux-sum values for a metabolite represent the sum of flux in all the reactions that consume or produce it, multiplied by the corresponding stoichiometric coefficients  produced per c-mole of substrate consumed.The theoretical maximum productivity is expressed hFurther information on research design is available in the Supplementary materialReporting Summary


Escherichia coli cells. Surprisingly, the ATP generated during the biosynthesis of building blocks from glucose almost balances the demand from protein synthesis, the largest energy expenditure known for growing cells. This leaves the bulk of the energy generated by fermentation and respiration unaccounted for, thus challenging the common notion that energy is a key growth-limiting resource. Moreover, FDM together with proteomics enables the quantification of enzymes contributing towards each metabolic function, allowing for a first-principle formulation of a coarse-grained model of global protein allocation based on the structure of the metabolic network.Quantifying the contribution of individual molecular components to complex cellular processes is a grand challenge in systems biology. Here we establish a general theoretical framework  to quantify the contribution of every metabolic reaction to metabolic functions, e.g. the synthesis of biomass building blocks. FDM allowed for a detailed quantification of the energy and biosynthesis budget for growing  Quantifying the contribution of individual molecular components to complex cellular processes is a grand challenge in systems biology. Here, the authors present a general theoretical framework  to quantify the contribution of every metabolic reaction to metabolic functions, e.g. the synthesis of biomass building blocks. In order to integrate genome-scale data of metabolic fluxes and protein abundances, metabolic models are increasingly used as multi-omics platforms15. The inference of intracellular fluxes based on mass-balance constraints and optimization principles is a mature subject16, with Flux Balance Analysis (FBA) being the most celebrated framework for studying the metabolic capabilities of a wide variety of organisms17. Extensions of FBA have been developed to predict how global protein allocation impacts metabolic activities of the cell and vice-versa23. Despite the need of inferring a large number of unknown molecular parameters26, these models were able to recapitulate known metabolic features, e.g. the emergence of overflow metabolism27, or the global utilization of the proteome28, in relation to cell growth.Living cells perform thousands of distinct metabolic reactions in order to grow, maintain homeostasis, and respond to environmental stimuli. Understanding the coordination of these reactions, their associated costs, and their contribution to cellular fitness are grand challenges of systems biology. Protein allocation has been established to be a key factor determining bacterial growth, owing to constraints in protein synthesis for rapidly growing bacteria29. For example, central carbon pathways such as glycolysis and the TCA cycle are not only tasked with the production of metabolic precursors for biomass building blocks, but also with balancing the currency metabolites, e.g. ATP and NAD(P)H30, consumed by each biosynthetic pathway. Thus, it can be difficult to associate reaction fluxes, and the corresponding enzyme concentrations, to individual metabolic functions. Indeed, the intuitive notion of individual metabolic pathways is largely concocted, as the production and consumption of currency metabolites have to be balanced across conditions, thus effectively coupling the fluxes through all pathways. Thus, the calculation of costs and yields for the production of individual metabolites are often performed by making use of coarse-grained metabolic networks in which the balance of currency metabolites or pathway byproducts is simplified or neglected32.Given the global constraint in protein synthesis, knowledge of the amount of protein needed for specific metabolic functions, e.g. the synthesis of a specific amino acid, is important for quantifying the link between metabolism and cell growth. However, the deeply interconnected nature of the metabolic networks also complicates its decomposition into individual componentsEscherichia coli cells grown in carbon minimal media, under translational-limiting antibiotics, and in anaerobic growth. The resulting functional characterization of the metabolic reactions allowed us to analyze in detail how cells allocate nutrients towards biosynthesis and energy generation, as well as the metabolic costs and yields of the production of different biomolecules. Together with experimental protein abundances, FDM allowed us to quantify the total amount of enzymes allocated to each function. Finally, FDM enabled a genome-wide classification of the proteome according to metabolic function, and the formulation of a coarse-grained model of protein allocation which quantitatively captures the global changes of the proteome across conditions.Here, we sought to develop a systematic computational method to define the metabolic costs and the enzyme amounts associated with each metabolic function, thus cutting through the complexity of the network. We introduce a Functional Decomposition of Metabolism (FDM) based on the decomposition of metabolic fluxes into a set of flux components, each associated with a metabolic function. Being based on properties of optimal flux pattern such those obtained with FBA, FDM is generally applicable to any metabolic network, and does not require additional parameters. We applied FDM to the study of 33. The prototypical use of GEMs is the inference of intracellular fluxes by using a combination of empirical constraints and optimization, an approach that is generally termed Flux Balance Analysis (FBA)17. In brief, growing cells accumulate biomass building blocks (e.g. amino acids and nucleotides) at rates set by the cellular biomass composition and the growth rate, while also regenerating the ATP required for homeostasis and growth   enable the quantitative modeling of cellular metabolism by including information on thousands of cellular metabolites and reactions, as well as on the cellular biomass composition and the enzyme-reaction assignationγ, e.g. how much of the carbon intake flux is used for the production of a given amino acid, or how much of the flux through a given glycolytic reaction is associated with the regeneration of ATP. Answering these questions is tantamount to expressing the metabolic fluxes in the network in terms of the consumption (demand) fluxes of biomass building blocks or the production of energy in each growth condition.Given a flux pattern obtained via FBA, we sought a general method to quantify how much a given metabolic reaction contributes to another metabolic process v, which has entries vi for each reaction i, to the demand fluxes Jγ. The set of the demand fluxes appearing in such expression is not arbitrary and it depends on the specific FBA formulation used to model the metabolic fluxes. As discussed in depth in Supplementary Note 23 as a linear combination of the demand fluxes Jγ:Jγ, and allows to analyze how the flux v changes in response to perturbations of the demand fluxes. The terms ξ γ)( and vγ) by a fraction vi. This is illustrated in Fig. In the context of metabolic networks, the production of biomass and energy represent natural definitions of biological functions which the cell has to perform in order to survive and grow. This offers a biological interpretation of the linear relation, Eq. , betweenmentclass2pt{minimE. coli cells in carbon minimal media. However, we will first highlight two challenges that emerge when applying the method on realistic networks, and how both issues are solved by adjusting the set of biological functions used to define the functional decomposition.We term the definition of function-specific shares for individual metabolic reactions  Functional Decomposition of Metabolism (FDM). In the next sections we will discuss the application of FDM to the concrete case of exponentially growing E. coli cells even in presence of oxygen, but FBA fails to model overflow metabolism without additional constraints. The simplest approach to improve FBA’s ability to model the intracellular fluxes is to set the acetate production to a non-zero value Jac determined experimentally across growth conditions. This constraint leads to the appearance in Eq. , or by inhibiting protein synthesis using sublethal doses of chloramphenicol (R-limitation).  includeore Fig. b, c. TheAs mentioned above, the flux to the Pentose Phosphate Pathway (PPP) is mostly associated with biomass production, but has a large mixed component The functional decomposition of the network fluxes allowed us to study in detail the energetic metabolism of the cell. The maintenance ATP hydrolysis flux models the energetic requirements of homeostasis and growth in metabolic models. As a result of our flux coupling procedure, each flux component has an associated net ATP hydrolysis flux, which is balanced through the ATP maintenance reaction. Depending on its sign, we refer to this flux as the ATP/energy production or consumption associated with the flux component; for flux modes, this flux represents the ATP/energy cost or yield associated with the metabolic function.37, at 4 ATP equivalents per residue. The estimated ATP demand is shown as green bar in Fig. 38.Protein synthesis (tRNA charging and AA polymerization) is generally thought to be the major energetic burden to the cellDW/h in the reference condition, is associated with the respiration and fermentation pathways . In slow, C-limited growth, only the respiration pathway is active, and the ATP flux is reduced  is close to the energetic demand associated with protein synthesis (in green). Even under fast-growth conditions, it seems that most of the flux through the respiration and fermentation pathways, which are solely dedicated to ATP synthesis, is not needed to power the known energy-consuming processes.39. FBA fluxes are obtained under the assumption of minimal carbon consumption, which leads to the use of the efficient NDH-I protein complex (nuo genes). On the other hand, quantitative proteomics data40 showed that the concentration of NDH-I varied across conditions. Instead, the concentration of the inefficient NADH dehydrogenase II  showed trends to those of NDH-I opposite trend across conditions, and became comparable at either fast or slow, R-limited growth , and thus the overall production of ATP by oxidative phosphorylation, by expressing different NADH dehydrogenase enzymesnuo− strain), both the energetic yield of reduced electron carriers through the ETC, and the efficiency of both respiration and fermentation pathways were reduced , and used the data to model the intracellular fluxes with FBA  or groups of amino acids ; these modules match well known biosynthetic pathways and superpathways41. As expected, TCA cycle reactions are mostly associated with energy production, while other reactions from the central carbon pathways, such as those included in upper/lower glycolysis, electron transport chain and pentose phosphate pathway, have more broadly distributed functions associated with the synthesis of several amino acids and/or energy. In sum, these results indicate that our approach is able to recapitulate the known biological functions of the metabolic network of E. coli.We then turned to the analysis of the global structure of the flux and functional decomposition. From this point on, we focused on the flux solutions obtained in aerobic conditions with the high-efficiency NDH-I enzyme. We first considered the functional decomposition in the reference condition, Each flux component, Eq. , describ31. These costs are computed for each pathway starting from carbon precursors, rather than from the external carbon source. In order to compare to these costs, we removed from the flux components all reactions belonging to the central carbon pathways, and computed the energetic balance for the biosynthetic reactions only. Reassuringly, the resulting energy costs were positive and matched well those reported in ref. 31 . After computing the functional decomposition in each growth condition, we made use of the gene-protein-reaction matrix of the iML1515 model to associate the reactions to expressed proteins. Overall, 412 proteins were both associated with flux-carrying reactions and detected in the reference condition; the numbers are similar for the other growth conditions. For these reactions, the joint use of the experimental protein abundances and of the functional decomposition allowed us to quantify the contribution of each enzyme to the various metabolic functions, as illustrated in Fig. The functional decomposition described above defined functional shares for each flux-carrying metabolic reaction in the cell. In turn, these functional shares can be used to generate a functional decomposition for the corresponding metabolic proteins. To do so, we made use of highly accurate experimental protein abundancesoli Fig. a, expres23, increasing from about 8% to 12% of the total proteome  of the linear relations  and arginine (R) stand out as the amino acids whose associated proteome had the largest offsets  and translation sectors respond specifically to changes in the carbon quality and in the translation capacity, respectively. Expression of the biomass sector is linearly related to growth rate, while the housekeeping sector is constant. Finally, we assumed a regulatory constraint setting the energy sector in response to carbon starvation and translational limitation of the following form:κC and κR determine change in protein allocation in response to the specific growth limitation. As detailed in Supplementary Note ϕE generate an ATP flux in proportion to their proteome share  for studying cellular metabolism and protein allocation based on the decomposition of metabolic fluxes into distinct functional components. This framework allowed us to comprehensively evaluate metabolic costs and protein burdens associated with each metabolic function, a feat impossible to achieve from the analysis of single reactions or protein abundances because of the deeply interconnected nature of metabolic networks.The flux decomposition at the core of FDM is fundamentally derived from mathematical properties of FBA solutions. Furthermore, it does not rely on parameters such as kinetic constants, nor requires simplifying hypothesis on the structure of the metabolic network: FDM can be generally applied to any network, as long as the application of FBA (or other optimization approaches) estimates correctly the intracellular fluxes. At the core of FDM is a quantitative definition of system-level metabolic functions for each reaction and protein. Each of these metabolic functions can be associated with multiple activities, e.g. synthesis of amino acid and ATP production, when these are tightly coupled. Furthermore, flux constraints are often applied to the network in order to improve the agreement with experimentally determined fluxes; these constraints are fully accounted for by the flux decomposition, at the cost of introducing associated metabolic functions, as shown in Fig. 48.One of the most immediate results enabled by FDM was the calculation of specific ATP and carbon costs for the biosynthesis of individual biomass component, as well as the ATP yields of the energetic pathways. These were generally uncorrelated with the rate of aerobic growth, although we noticed that gluconeogenic carbon sources tended to yield less energy and allow for slower growth rates compared to the best glycolytic carbon sources  to the estimated consumption. In anaerobic conditions, when the electron transport chain is not used, the predicted ATP production matches the costs , while being independent on the actual energetic demand; the latter could be matched instead by modulating the ATP yield of the energetic pathways, in agreement with the analysis discussed above.We suspect that both possibilities might hold true in the conditions studied here. The opposite changes observed in the levels of the two NADH dehydrogenases NDH-I and NDH-II across conditions . The design of a systematic procedure to functionally classify all of the expressed proteome across conditions  FBA framework, but it also provides a concrete interpretation of marginal costs as flux modes. The complete decomposition of fluxes into the complete set of components, Eq. ,,58 quantEscherichiacoli K-12 NCM372264 and listed in Supplementary Table All strains used in this work are derived from 7. The phosphate-based growth media used for anaerobic growth and for other control samples in aerobic conditions contained 10 mM glucose, 80 mM K2HPO4, 20 mM KH2PO4, 10 mM NaCl, 10 mM NH4Cl, 0.5 mM Na2SO4, a phosphate buffer and a 1000x micronutrient solution. The 1000x micronutrient solution contained 20 mM FeSO4, 500 mM MgCl2, 1 mM MnCl2.4H2O, 1 mM CoCl2.6H2O, 1 mM ZnSO4.7H2O, 1 mM H24Mo7N6O24.4H2O, 1 mM NiSO4.6H2O, 1 mM CuSO4.5H2O, 1 mM SeO2, 1 mM H3BO4, 1 mM CaCl2, and 1 mM MgCl2 dissolved in a 0.1 M HCl solution. Carbon limitation was implemented by titrating 3-methyl-benzylalcohol (3MBA) concentration in strains NQ1243, NQ1448, and NQ1554 as well as by growing strain NQ1261 (ptsG deletion) in glucose. Translational limitation was obtained by adding sublethal doses of chloramphenicol. Concentrations of nutrients, 3MBA and chloramphenicol in each experiment are reported in Supplementary Data The growth media for aerobic growth is the MOPS-buffered minimal medium from ref. 5. Briefly, exponential cell growth was performed in a 37 °C water bath shaker at 240 rpm. Cultures were grown in the following three steps: seed culture, pre-culture, and experimental culture. Cells were first grown as seed cultures in LB broth for several hours, then as pre-cultures overnight in an identical medium to the experimental culture. Experimental cultures were started by diluting the exponentially growing pre-culture to an optical density at wavelength 600 nm (OD600) of ~ 0.01–0.02. Growth rates were calculated from at least seven OD600 points within a range of OD600 of ~ 0.04–0.4.Growth measurements for aerobic culture were performed as in ref. 600 measured through the Hungate tubes was equivalent to the OD600 measured through a cuvette for the range of 0.04–0.5.Anaerobic growth was performed similarly to aerobic growth with a few exceptions. All transfers were performed with disposable syringes to avoid oxygen contamination. Aerobic seed cultures were diluted into Hungate tubes for preculture. After overnight growth, the precultures were diluted into fresh Hungate tubes for experimental culture. To avoid atmospheric exposure from removing samples, OD measurements were performed with a Thermo Genesys 20 modified to hold Hungate tubes in place of cuvettes. The culture temperature was kept stable during OD measurements by removing and replacing the Hungate tubes from the water bath shaker within 30 seconds. The OD65. Four samples of 200 μL were pipetted from culture tubes at regularly spaced ODs during exponential growth. For anoxically grown cultures, samples were removed with tuberculin syringes inserted into the rubber stopper. Samples were then transferred to 0.22 μm nylon filter centrifuge tubes (Corning Costar Spin-X Centrifuge Tubes) and quickly filtered by centrifugation. Samples were then stored at −20 °C until HPLC analysis, which was performed using the Rezex RoA (H+) organic acid column with 10 mM H2SO4 as the mobile phase.Metabolites were prepared and quantified as in ref. 67 and the GUROBI solver . In order to estimate the numerical derivatives reliably, we set the following GUROBI parameters: maximum iteration to 1000, “BarConvTol” and “BarQCPConvTol” to 10−12, “FeasibilityTol” and “OptimalityTol” to 10−9. Additionally, COBRApy version 0.26.3 was used to parse the metabolic models. Details on the implementation of FBA and of the functional decomposition are provided in Supplementary Notes The formulation of the FBA and FDM optimization problems is described in detail in Supplementary Note −4 mmol/gDW/h and only considering the metabolic functions associated with energy production, biosynthesis of amino acid and nucleotides, plus the mixed functional component; clusters were determined based on the cityblock distance among the functional shares The hierarchical clustering in Fig. E. coli proteins which were not categorized using the functional decomposition .Best fit parameters for the ATP maintenance flux were obtained by minimizing the squared residuals between the experimental and modeled glucose intake fluxes, Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary Files - NEWSupplementary Dataset 1Supplementary Dataset 2Supplementary Dataset 3Supplementary Dataset 4Supplementary Dataset 5Supplementary Dataset 6Supplementary Dataset 7Supplementary Dataset 8Reporting Summary


Escherichia coli, engineering gut commensals is gaining traction owing to their innate capacity to survive and stably propagate in the intestine for an extended duration. Although limited genetic tractability has been a major roadblock, recent advances in systems and synthetic biology have unlocked our ability to effectively harness native gut commensals for therapeutic and diagnostic purposes, ranging from the rational design of synthetic microbial consortia to the construction of synthetic cells that execute “sense-and-respond” logic operations that allow real-time detection and therapeutic payload delivery in response to specific signals in the intestine. In this review, we outline the current progress and latest updates on microbial therapeutics, with particular emphasis on gut commensal engineering driven by synthetic biology and systems understanding of their molecular phenotypes. Finally, the challenges and prospects of engineering gut commensals for therapeutic applications are discussed.The past decade has seen growing interest in bacterial engineering for therapeutically relevant applications. While early efforts focused on repurposing genetically tractable model strains, such as  The emeDecades of omics biology research on the human gut microbiome have uncovered the complex interplay of host–microbe interactions at the molecular level, allowing us to consider the implications of such dynamics on the health of the host. In the past decades, many efforts have been devoted to characterizing the composition and patterns of the gut microbiota that correlate with specific host status, such as diet and age , obesityin silico modeling frameworks serves as an effective approach for revealing the implicit dynamics of host-microbe interactions. Briefly, the collective understanding of microbial genetics, genomics, and biochemistry is put into a single computational framework, the genome-scale metabolic model (GEM), which is a mathematical framework featuring a matrix of biochemical reactions that allows the prediction of metabolic flux distribution using linear programming. The optimization technique, flux balance analysis (FBA), calculates the most feasible metabolic state that maximizes a given objective function such as biomass generation or target metabolite production , was approved by the Food and Drug Administration for clinical use . This wain vivo  such as deoxycholic and lithocholic acids, which render the intestine highly prone to CDI . The humin vivo . With redB toxin . Thus, tdB toxin . TherefoClostridium scindens, a species that retains a complete secondary BA biosynthetic pathway  varied considerably in their metabolic capacity to produce secondary BAs compared with healthy controls .Systems biology has shed light on the therapeutic potential of gut microbiota editing for thwarting recurring CDI. In one study, authors identified native species of gut microbiota that contributed significantly to CDI resistance . Importa pathway , confers pathway . Interescontrols . Taken tRecent progress in etiological characterization of celiac disease (CD) driven by-multi-omics analysis is also worth notable mentions . CD is aListeria monocytogenes and potent anti-tumor effects without observable adverse effects , which has clinically relevant antimicrobial and immunomodulatory properties , requires a robust chassis strain with the ability to survive, thrive, and drive the production and delivery of the desired payloads in vivo . Furtheroperties . Since toperties .Despite the reported efficacy and valid conceptual basis for its therapeutic effects , probiotin vivo -induced signals at the receiving end of the DNA-binding regulator ThsR. Phosphorylated ThsR, in turn, activates its cognate promoter PphsA and expression of the downstream reporter gene superfolder GFP (sfGFP) to transform the ligand-binding signal into luminescence readouts in a dose-dependent manner  induction. This rather simple tweak in transcription regulation led to prolonged in vivo survival by allowing programmable evasion of the host immune response, consequently augmenting the antitumor efficacy of LBT by ten-fold , enzymes, or nucleic acids, regulate gene expression. The mode of action of a genetic biosensor typically entails a conformational change upon ligand binding, followed by the activation of orthogonal transcription machinery. Using a two-component signal transduction system (TCS) as an example, the membrane-bound sensor histidine kinase ThsS phosphorelays thiosulfate (St manner . To dateanner (2 . The senten-fold . The intten-fold .4O62−) and nitrate (NO3−) are proxies for two distinct etiologies of IBD , L-arabinose (PBAD) or anaerobic-inducible (PfnrS) manner  and assimilate the aforementioned engineering and optimization principles, which are worthy of a detailed discussion . The orinase pma  (Isabellnase pma . To achi) manner . The in primates , and wasprimates .trans-cinnamate (TCA), a product of PAL, in a concentration-dependent manner. The stlA mutant library was designed considering the enzyme phylogeny, co-evolution, and structural attributes to infer enzyme residues for targeted engineering. To avoid cross-talk between different TCA producer strains  in the pooled library, an oil-emulsion-assisted microculture followed by a fluorescence-activated cell sorting (FACS) strategy was adopted to effectively isolate high TCA-producing mutants (stlA* or mPAL) carrying five mutations  with Vmax and KM two to three folds higher compared to that of wild-type PAL. The SYNB1618-derivative that expresses stlA*, designated SYNB 1934, showed an approximately 2-fold increase in in vivo phenylalanine conversion capacity compared to SYNB1618 , and a phase III trial of SYNB 1934 (NCT05764239) is underway in June 2023.In a follow-up study aimed at further augmenting the phenylalanine-degrading capacity of LBT, PAL was no longer rate-limiting, hence calling for efforts to optimize the performance of PAL . In this mutants   engineering highlights the “technological readiness level” of engineering gut commensals that is nearly on par with that of other model species , which together account for nearly 18% of the whole genome   , furtherarticles .a priori understanding of the cellular systems precedes their rational design and engineering. In the case of gut commensals, factors such as the genetic determinants of strain fitness within the intestinal niche provide important engineering considerations for in vivo applications. However, conventional approaches to characterize genetic functions, such as gene knockout, are highly effective but limited in scale and require considerable labor and resources . The deletion of genes that encode ECF-σs embedded within O-glycan-responsive PULs led to a significant in vivo deficit, elucidating yet another essential genetic determinant of in vivo fitness, along with the regulatory elements that impart transcriptional control , is a common strategy for analyzing condition-specific changes in mRNA transcript abundance. Variations in transcriptome sequencing technologies allow the characterization of distinct transcriptome landscapes across species that reflect unique ecological features and provide an important system-level inference that translates into engineering applications. For example, investigation of  control . Transcr control , which haomicron .B. thetaiotaomicron genome-wide led to the discovery of more than 4 3 transcription start sites corresponding to putative promoters with conserved motifs, conserved ribosome binding sites (RBSs) in the downstream vicinity, and putative riboswitches , and different RBS strength rules that limit the use of standard synthetic biology tools , human keratinocyte growth factor-2 (hKGF-2), and human transforming growth factor-β (hTGF-β) using a xylanase-inducible promoter in pre-clinical models of gut inflammation  showed an increase in colonic secretion and a shortened gut transit time , which promoted goblet cell differentiation (Ruminococcus gnavus encoding a subset of the 3β-hydroxydeoxycholic acid (isoDCA) biosynthetic pathway, hydroxysteroid dehydrogenases, were heterologously expressed in model Bacteroides species  with proposed immunomodulatory properties. While the strain failed to produce butyrate in the wild-type background, a round of metabolic engineering informed by the Optknock simulation redirected the cellular metabolic flux toward non-native butyrate biosynthesis, albeit at a much lower concentration than the native SCFA products , paving the way toward the clinical use of commensal-based LBTs that have hitherto been prospective.Taken together, these studies demonstrate that prominent gut commensal species can be engineered to functionally express exogenous compounds at a sufficient dosage to elicit the desired changes B. thetaiotaomicron in the expansion of enteric pathogens in genetically-predisposed hosts (dapA encoding 4-hydroxy-tetrahydrodipicolinate synthase was inactivated and required exogenous diaminopimelate (DAP) supplementation for survival  of artificial genetic elements into native ecosystems. In addition, aberrant behaviors of chassis strains such as ed hosts  and invoed hosts  call forsurvival . Other psurvival . Similarsurvival   therapy, which raised safety flags and was haunted by the weak reproducibility of its therapeutic efficacy. The rational design of synthetic microbial consortia based on a systems biology-driven understanding can selectively screen candidate microbial species and their combinations for maximum therapeutic potency . Potentiin vivo. One prospect of the LBT lies in its ability to administer the correct drug dosage at the right time and place, which is expected to significantly improve treatment efficiency while minimizing side effects that are not uncommon in current therapeutic regimens , paving the way toward real-life applications of commensal-based therapeutics that have long remained prospective. However, a recent report showed a distinct approach to circumvent the existing hurdles in probiotic (E. coli)-based LBTs to isolate and engineer native gut-resident E. coli which engrafts perpetually upon reintroduction  regimens . Furtheroduction . This isLiving cells constantly undergo evolution, similar to that of LBTs. SYNB1618, the original Phe-degrading LBT that passed a phase 1 trial (NCT03516487), was upgraded using a catalytically superior mutant PAL enzyme discovered through high-throughput screening . In anot


Cycling of co-substrates, whereby a metabolite is converted among alternate forms via different reactions, is ubiquitous in metabolism. Several cycled co-substrates are well known as energy and electron carriers (e.g. ATP and NAD(P)H), but there are also other metabolites that act as cycled co-substrates in different parts of central metabolism. Here, we develop a mathematical framework to analyse the effect of co-substrate cycling on metabolic flux. In the cases of a single reaction and linear pathways, we find that co-substrate cycling imposes an additional flux limit on a reaction, distinct to the limit imposed by the kinetics of the primary enzyme catalysing that reaction. Using analytical methods, we show that this additional limit is a function of the total pool size and turnover rate of the cycled co-substrate. Expanding from this insight and using simulations, we show that regulation of these two parameters can allow regulation of flux dynamics in branched and coupled pathways. To support these theoretical insights, we analysed existing flux measurements and enzyme levels from the central carbon metabolism and identified several reactions that could be limited by the dynamics of co-substrate cycling. We discuss how the limitations imposed by co-substrate cycling provide experimentally testable hypotheses on specific metabolic phenotypes. We conclude that measuring and controlling co-substrate dynamics is crucial for understanding and engineering metabolic fluxes in cells. Metabolism powers individual cells and ultimately the body. It comprises a sequence of chemical reactions that cells use to break down substances and generate energy. These reactions are catalyzed by enzymes, which are proteins that speed up the rate of the reaction. Many reactions also involve co-substrates, which are themselves transformed by individual reactions but are eventually converted back into their original form in a series of steps. This process is known as co-substrate cycling.Scientists have long been interested in understanding what controls the rate at which metabolic reactions and metabolic pathways convert a substance into a final product. This is a difficult subject to study because of the complexity of the metabolic pathways, with their branched, linear or coupled structures. In the past, researchers have looked at the influence of enzymes on the rate of a metabolic pathway, but less has been known about the effect of co-substrate cycling.To find out more, West, Delattre et al. developed a series of mathematical models to describe different types of metabolic pathways in terms of the number of metabolites that enter and leave it, including the influence of co-substrates.They found that co-substrate cycling, when involved in a metabolic reaction, limits the speed with which the reaction happens. This is distinct from the limit that enzymes impose on the speed of the reaction. It depends on the total amount of co-substrates in the cell: changing the number of co-substrates in the cell influences the speed at which the metabolic reaction takes place.This study has increased our understanding of how metabolic pathways work, and what controls the speed at which reactions take place. It opens up a new potential method for explaining how cells control metabolic reaction rates and how metabolic substrates can be directed across different pathways. This research is likely to inspire future research into the influence of co-substrates in different cell types and conditions. Dynamics of cell metabolism directly influences individual and population-level cellular responses. Examples include metabolic oscillations underpinning the cell cycle  and metamaximal value of the apparent activities  . However enzymes .Another conceptual framework emphasized the importance of cyclic reaction motifs, particularly those involving so-called co-substrate pairs, such as ATP / ADP or NAD(P)H / NAD(P)dynamics . This frdynamics . For exadynamics . Inspiredynamics , and thadynamics . Specifidynamics . Taken tTowards better understanding the role of co-substrate cycling in cell metabolism dynamics, we undertook here an analytical and simulation-based mathematical study together with analyses of measured fluxes. We created models of enzymatic reaction systems featuring co-substrate cycling, abstracted from real metabolic systems such as glycolysis, nitrogen-assimilation, and central carbon metabolism. We found that co-substrate cycling introduces a fundamental constraint on reaction flux. In the case of single reaction and short linear pathways, we were able to derive a mathematical expression of the constraint, showing that it relates to the pool size and turnover rate of the co-substrate. Analysing measured fluxes, we find that several of the co-substrate featuring reactions in central carbon metabolism carry lower fluxes than expected from the kinetics of their primary enzymes, suggesting that these reactions might be limited by co-substrate cycling. In addition to its possible constraining role, we show that co-substrate cycling can also act as a regulatory element, where control of co-substrate pool size can allow control of flux dynamics across connected or branching pathways. Together, these findings show that co-substrate cycling can act both as a constraint and a regulatory element in cellular metabolism. The resulting theory provides testable hypotheses on how to manipulate metabolic fluxes and cell physiology through the control of co-substrate pool sizes and turnover dynamics, and can be expanded to explain dynamic measurements of metabolite concentrations in different perturbation experiments.+ / NADH pair is cycled by the enzymes glutamine oxoglutarate aminotransferase and glutamate dehydrogenase  are given by:To explore the effect of co-substrate cycling on pathway fluxes, we first consider a didactic case of a single reaction. This reaction converts an arbitrary metabolite  cycling . For co-kin and kout denote the rate of in-flux of M0, and out-flux of M1, either in-and-out of the cell or from other pathways, and A0 and A1 in A0 and M0 into A1 and M1 (enzyme E0), and the turnover of A1 into A0 . The term kin, and the Michaelis-Menten coefficients and the A0 and A1, are given in Appendix 3. The steady state solutions of these alternative models are structurally akin to  (see Why does (1) show this specific form, leading to these limits? We find that this is a direct consequence of the steady state condition, where metabolite production and consumption rates need to be the same at steady state. In the case of co-substrate cycling, the production rate of given in  and showple) see . We alsoTo conclude this section, we re-iterate its main result. The flux of a reaction involving co-substrate cycling is limited either by the kinetics of the primary enzyme mediating that reaction, or by the turnover rate of the co-substrate. The latter is determined by the co-substrate pool size and the kinetics of the enzyme(s) mediating its turnover.We next considered a generalised, linear pathway model with ycolysis . In thisycolysis , while tkin is above a threshold value, the metabolite M0 accumulates towards infinity and the system does not have a steady state . In An analytical expression for the threshold for shown in , could nWe also considered several variants of this generalised linear pathway model, corresponding to biologically relevant cases as shown in Escherichia coli are shown to have lower flux than expected from the kinetics of their immediate enzymes . The flux and enzyme concentration data were from other studies which measured them during the exponential phase in E. coli growing on minimal media supplemented with various carbon sources , we can conclude from the fact that there were no observed substrate accumulation in these reactions, as an indication for the analysed reactions carrying fluxes below the first limit identified above in , many reactions from the central carbon metabolism of the model organism e. Vmax) . This fi sources . If we cabove in . There ckcat values with full experimental data and 259 combinations with only FBA-predicted flux values. We compared the flux values that would be expected from the primary enzyme limit identified above, under all conditions analysed  . This shMDH), linked with NADH pool, phosphoglycerate kinase (PGK), linked with the ATP pool, and glucose-6-phosphate dehydrogenase (G6PDH) linked with the NADPH pool.We have also checked the relation between fluxes and co-substrate pool sizes. Co-substrate pool sizes do change between different conditions, and we note that such changes cannot be due to flux changes in co-substrate utilising reactions. But, on the other hand, changes in pool size can affect flux in those reactions, where co-substrate dynamics is limiting (as predicted by the theory). For both measured and FBA-predicted fluxes, we find that several reactions show significant correlation between flux and co-substrate pool size see . In the could indicate co-substrate pool sizes and/or co-substrate cycling dynamics being a limiting factor for flux. We can not state this as a certainty, however, as there are possibly other factors acting as the extra limitation, including thermodynamic effects. These points call for further experimental analysis of co-substrate cycling within the study of metabolic system dynamics.In summary, these results show that for reactions involving co-substrate cycling (1) measured fluxes are lower than those predicted by kinetics of the primary enzyme (i.e. enzyme involved in substrate conversion) alone, and (2) there is – for some reactions – a correlation between flux and co-substrate pool size. Both observations In addition to its possible constraining effects on fluxes, we wondered if co-substrate dynamics can offer a regulatory element in cellular metabolism. In particular, co-substrate cycling can commonly interconnect two independent pathways, or pathways branching from the same upstream metabolite, where it could influence flux distributions among those pathways. To explore this idea, we considered a model of a branching pathway, with each branch involving a different co-substrate, kin values, but the threshold effect is still present with high enough kin values leading to loss of steady state and metabolite build up. In that case, the resulting metabolite build-up can affect either branch depending on which co-substrate has the lower pool size . In other words, for two pathways coupled via co-substrate cycling, the cycling-dependent flux limit for each is not determined by their own influx but rather on how different this is to the coupled pathways’ influx .To test the second hypothesis about the output coupling, we considered the correlation of the steady-state outputs of the pathways with random fluctuations in their influx . We founEa=0 see . As we it values .These results show that coupling by co-substrate cycling can introduce a limit on influxes of independent pathways or metabolic processes. Furthermore, such coupling can allow high correlation in the pathway outputs, despite significant noise in the inputs of those pathways. These effects are most readily seen where the turnover of the coupling co-substrate by other processes is low. We note that an example case for such a scenario is the coupling of respiration and oxidative phosphorylation, where transmembrane proton cycling takes the role of the cycled co-substrate .kin, approaches a threshold value, the steady state concentrations of metabolites that are upstream of a reaction linked to co-substrate cycling, increase towards infinity and the system cannot reach steady state. Specifically, for reactions involving co-substrates, there are two thresholds on influx rate, one relating to the kinetics of the enzyme directly mediating that reaction, and another relating to the kinetics of the enzymes mediating the turnover of the co-substrate and the pool size of that co-substrate.We presented a mathematical analysis of metabolic systems featuring co-substrate cycling and showed that such cycling introduces a threshold effect on system dynamics. As the pathway’s influx rate, kin values across various pathways, their metabolic systems can be close to the threshold presented here. While both kin and This second, additional constraint arising from co-substrate cycling can be directly relevant for cell physiology. We particularly note that this threshold can be highly dynamic, and condition- and cell-dependent. When cells have a permanently or occasionally lowered total co-substrate pool size , malate dehydrogenase (MDH), and glucose-6-phosphate dehydrogenase (G6PDH) and linked to ATP, NADH, and NADPH pools. Possible flux limitation of these reactions by co-substrate dynamics can also be subjected to further experimental study -– as we discuss further below.Comparing measured flux data against estimated flux values based on measured enzyme levels from proteomics and enzyme kinetics from urements . DespiteE. coli populations  and controlling their expression. It would also be possible to monitor co-substrate pool sizes in cells in real time by using fluorescent sensors on key metabolites such as ATP or glutamate, or by measuring autofluorescence of certain pool metabolites, such as NAD(P)H, under alterations to influx rate of glucose or ammonium.Besides acting as a flux constraint, we find that co-substrate pools can also allow for regulation of pathway fluxes through regulation of pool size or turnover dynamics. We find that such regulation can take the form of balancing inter-connected pathways, thereby ensuring correlation between outputs of different metabolic processes, or regulating flux across branch points. Regulation of fluxes through co-substrate pools can act to adjust metabolic fluxes at time scales shorter than possible via gene regulation, and possibly at similar time scales as with allosteric regulation – especially when considering pool size alterations through exchange among connected pools. Possibility of such a regulatory role has been indicated experimentally, where total ATP pool size is found to change when yeast cells are confronted with a sudden increase in glucose influx rate . In thatThe metabolic system shown in A1 and A0, mediated through other enzymatic reactions. The parameters kin, and kout denote the in- and out- flux of M0 and M1 respectively, from and to other pathways or across cell boundary. The ordinary differential equations (ODEs) for the system shown in  feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, including Babak Momeni as Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Aleksandra Walczak as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Jonas Cremer (Reviewer #2); Silvio Waschina (Reviewer #3).Thank you for submitting your article "Dynamics of co-substrate pools can constrain and regulate metabolic fluxes" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:1) Please include the terminology and basic concepts in the introduction to improve the accessibility of the paper.2) Please revise the manuscript to explicitly include the relevant model assumptions and details of the setups .3) Please further address the limitations of the study in the Discussion section (see comments from Reviewer #3).Reviewer #1 (Recommendations for the authors):1. Although the definition of cycling is somewhat intuitive, I do not think the formal definition offered in lines 84 and 85 is accurate. I'd suggest revising it .2. One of the main theses in this manuscript is that limitations by conserved pools in cycles will impact the overall metabolite dynamics. It would be nice to have an estimate of how often cycles will impose a limitation and where they should be expected in the metabolic network. Figure 3 and associated supplementary figures perhaps contain this information, but if possible, a more explicit estimate would be informative.3. In Figure 3B-D, I do not think that the correct model for the relation between the pool size and the normalized flux is a linear dependency . Should this be taken into account instead of a regression line (and RMSE) for representing whether the model fits the existing data?4. On lines 245-245, I think the second hypothesis should be phrased more explicitly. It is not immediately clear what "balancing" means.5. In Figure 5, a simpler configuration can be imagined in which there is no direct reaction between A0 and A1. Presumably such a configuration creates an even stronger dependency between the two pathways through cycling A0 to A1 and vice versa. I am curious why the authors did not choose such a configuration. Alternatively, with the A0 <-> A1 reaction included, what is the impact of the rate of this reaction on the correlation between the two pathways?Reviewer #2 (Recommendations for the authors):– Overall, the paper is well written and I was able to follow. However, it also assumes that readers are familiar with a lot of different terminology/examples of metabolic analysis. Below are some remarks that the authors might want to consider. For example, I think the introduction would benefit from a more detailed introduction of terms. For example, a clearer definition of co-substrates in the introduction would be helpful. Similarly, a better introduction of the term flux would help and yield is not introduced such that it remains unclear for readers to see what the tradeoffs are.– line 46 onwards: What is the evidence? Can a sentence or two be added to clarify?– line 84 onwards: It seems this paragraph is still part of the introduction.– Too early reference to Figure 1A . Better to show a summary figure illustrating the different co-substrates mentioned?– line 101 onwards: paragraph could be better embedded and it is currently hard to follow what the authors want to stress when the following discussion is primarily about steady state.– line 113 onwards: I think it would be helpful to spell out in the main text what α is.in and Vmax), so how can one establish that kin < Vmax?– line 180 onwards: I am missing background to understand the statement. It was always my impression that it is in general very hard to reliably measure reaction rates in-vivo .– It is also important to introduce in more detail the different experimental conditions for which the variation in ATP precursors has been observed. Could it be that ATP levels are merely changing because of the way the conditions change and not because fluxes vary as well?Reviewer #3 (Recommendations for the authors):Mathematical equations, transformations, resulting constraints, and conclusions are generally very clearly explained, which allows readers, who might be less-accustomed to kinetic modeling, to follow the line of arguments. One suggestion I have is to provide units of variables that are used in equations also in the text, or perhaps as a (supplementary) table. Specifically, I noticed that this could help readers already at equations (1). Here, the steady-state concentration of m1 is given by the ratio of the two rate parameters k[in] and k[out]. Since in the text, both parameters are only referred to as "flux rates", one could assume that both have the same unit, which would make their ratio (=m1 concentration) unit-less. Only with the units that appear later in figure 2  it becomes clear that the two parameters have different units.In addition, I understand that the authors claim, that flux-governing and -regulation through means of co-substrate cycling could be a general 'design principle' that is not limited to a specific group of organisms. However, I would suggest to provide more detail on the experimental/FBA data  that is used for the comparison with the model predictions. For instance, details on the organisms behind the experimental data that is mentioned e.g. in lines 187-208 and in Figure 3 could be added. This would help readers to put the authors' results in more biological context. Along those lines, the discussion could include a paragraph that addresses current limitations to further evaluate the developed mathematical framework. For instance, from which organisms do we have experimental data to study the potential role of co-substrate cycling using the developed framework? What future experiments/data types will further help to test the mathematical framework? Essential revisions:1) Please include the terminology and basic concepts in the introduction to improve the accessibility of the paper.This point is addressed. See revised text and also reply to recommendation 1 from reviewer 2, and recommendation 1 from reviewer 3.2) Please revise the manuscript to explicitly include the relevant model assumptions and details of the setups .This point is addressed. See revised text and specific replies to recommendations 4-6 from reviewer 1, recommendations 1 and 2 from reviewer 3, and recommendations 2, 7-9 from reviewer 2.3) Please further address the limitations of the study in the Discussion section (see comments from Reviewer #3).This point is addressed. See revised text and specific replies to reviewer 3 and the replies to general summary by reviewer 2 and their recommendation 9.Reviewer #1 (Recommendations for the authors):1. Although the definition of cycling is somewhat intuitive, I do not think the formal definition offered in lines 84 and 85 is accurate. I'd suggest revising it .We thank the reviewer for this comment. We have revised the definition, as:“Certain pairs of metabolites can be interconverted via different reactions in the cell, thereby resulting in their ‘cycling’.”2. One of the main theses in this manuscript is that limitations by conserved pools in cycles will impact the overall metabolite dynamics. It would be nice to have an estimate of how often cycles will impose a limitation and where they should be expected in the metabolic network. Figure 3 and associated supplementary figures perhaps contain this information, but if possible, a more explicit estimate would be informative.E. coli, where flux seems linked to co-substrate pool size. Further predictions would require more data, specifically for co-substrate related reactions. We also note that our analytical solutions provide an inequality of system parameters, which when satisfied will indicate flux limitation due to co-substrate cycling. These parameters, especially enzyme levels and co-substrate pool size will be condition dependent.We thank the reviewer for this suggestion. We explicitly stated that 80% of the analysed co-substrate linked reactions are possibly constrained by co-substrate dynamics. We have further highlighted three specific reactions in We have now included elements of this reply in the revised manuscript. See also reply to 2nd recommendation by reviewer 3.3. In Figure 3B-D, I do not think that the correct model for the relation between the pool size and the normalized flux is a linear dependency . Should this be taken into account instead of a regression line (and RMSE) for representing whether the model fits the existing data?totA) while the rest of the system is unchanged. In Figure 3B-D, we compare data points of the measured reaction flux at different environmental condition (carbon sources) which are likely to affect other system parameters in Equation 1. Therefore, it is difficult to describe the relationship quantitatively and we thus chose to look at correlations as a proxy. See also our replies to public review and recommendation 9 by reviewer 2.We agree with the reviewer that the dependency between the maximal flux and the pool size is not a linear relationship, but a saturating one as shown in Figure 1. We would expect this relation to hold if the only controlled parameter was the pool size  the co-substrate related limit to relate to difference in pathway influxes, rather than the influx into one pathway, and (2) a coupling of the pathway output fluxes against influx fluctuations, such that the output fluxes remain correlated to each other, despite differences in influx levels.”5. In Figure 5, a simpler configuration can be imagined in which there is no direct reaction between A0 and A1. Presumably such a configuration creates an even stronger dependency between the two pathways through cycling A0 to A1 and vice versa. I am curious why the authors did not choose such a configuration. Alternatively, with the A0 <-> A1 reaction included, what is the impact of the rate of this reaction on the correlation between the two pathways?0 to A1 reaction, which we called "pathway-independent turnover of the co-substrate” and labelled its rate as max,EaV. This analysis had not considered the reaction rate being zero, i.e. no pathway-independent turnover. We have now extended this analysis to include this case, and also included a section in the results, summarising the findings from it .We thank the reviewer for this comment. We had already analysed the effect of the rate of the AtotA) despite fluctuations in their inputs. We also found that as totA gets smaller, the two pathway outputs shift from being highly anti-correlated  to being highly correlated . This 'correlated outputs regime' is further split into two sub-regimes, where the pathways are `responsive' or `unresponsive' to fluctuations in the inputs, as shown in Figure 5C/D.In brief, we had shown in Figure 5B that the pathway outputs are coupled (i.e. correlated) for a range of pool sizes  causes a reduction in the totA value for which a transition to the highly correlated regime happens . The case for max,EaV = 0 remains qualitatively the same as analysed in Figure 5. We have also checked that the systems remain 'responsive' to changes in the input as max,EaV increase .We found that an increase in the rate of the pathway-independent turnover (We have now included these results in the main text in the corresponding section.Reviewer #2 (Recommendations for the authors):– Overall, the paper is well written and I was able to follow. However, it also assumes that readers are familiar with a lot of different terminology/examples of metabolic analysis. Below are some remarks that the authors might want to consider. For example, I think the introduction would benefit from a more detailed introduction of terms. For example, a clearer definition of co-substrates in the introduction would be helpful. Similarly, a better introduction of the term flux would help and yield is not introduced such that it remains unclear for readers to see what the tradeoffs are.We thank the reviewer for this useful comment. We have now revised the introduction section to better introduce the relevant terms. See also reply to second recommendation of reviewer 1.– line 46 onwards: What is the evidence? Can a sentence or two be added to clarify?We thank the reviewer for this useful comment. We have now expanded this section to read:app,max) of an enzyme, derived using measured enzyme levels and fluxes under different conditions, was a good estimate for the specific activity of that enzyme in vitro (kcat). However, individual estimates from each condition  were commonly lower than the specific activity – suggesting that the flux is limited by something other than enzyme levels under those conditions. Other studies have shown that metabolic flux changes, caused by perturbations in media conditions, are not explained solely by changes in expression levels of enzymes .”“There are, however, increasing number of studies suggesting that enzyme levels alone might not be sufficient to explain observed flux levels. For example, in Davidi et al. 2016, the maximal value of the apparent activities . Better to show a summary figure illustrating the different co-substrates mentioned?We agree with the reviewer and have removed this reference to Figure 1A at the end of the first paragraph. See also next reply.– line 101 onwards: paragraph could be better embedded and it is currently hard to follow what the authors want to stress when the following discussion is primarily about steady state.We thank the reviewer for this comment. In light of it, we have revised this section and combined it with the previous section (the title of which is changed to: Co-substrate cycling represents a ubiquitous motif in metabolism with co-substrate pools acting as ‘conserved moieties’).The point we wanted to highlight is that the pool size can still be defined by a constant, even under consideration of biosynthesis and uptake. We revised this section to read:“We notice here that many of the co-substrate involving, cycling reactions can be abstracted as a simplified motif as shown in Figure 1A. This abstract representation highlights the fact that the total pool-size involving all the different forms of a cycled metabolite can become a conserved quantity. This would be the case even when we consider biosynthesis or environmental uptake of co-substrates, as the total concentration of a cycled metabolite across its different forms at steady state would then be given by a constant defined by the ratio of the influx and outflux rates . In other words, the cycled metabolite would become a ‘conserved moiety’ for the rest of the metabolic system and can have a constant ‘pool size’. Supporting this, temporal measurement of specific co-substrate pool sizes shows that ATP and GTP pools are constant under stable metabolic conditions, but can rapidly change in response to external perturbations, possibly through inter-conversions among pools rather than through biosynthesis .”– line 113 onwards: I think it would be helpful to spell out in the main text what α is.We have now done so for the case presented in the main text . For other models considered, we referred to the relevant Appendix section.in and Vmax), so how can one establish that kin < Vmax?– line 180 onwards: I am missing background to understand the statement. It was always my impression that it is in general very hard to reliably measure reaction rates in-vivo  and measured expression level of enzymes (i.e. totE from proteomics datasets). While there is no direct measurement of ink, the measured flux can be used as proxy for it, since the two will be equal at steady state. The fact that there is no observed accumulation of metabolites in the measured reactions, suggest that the analytically derived inequality holds and the influx into, and across, each reaction is below the analytically obtained limits. We have now revised this section as follows, to make this point more clear:We thank the reviewer for this comment, which highlights that this section is not written clearly. The utilised experimental / FBA-based data does not include Escherichia coli are shown to have lower flux than expected from the kinetics of their immediate enzymes (i.e. Vmax) [Davidi et al. (2016)]. This finding is based on calculating Vmax from in vitro measured kcat values of specific enzymes and their in vivo levels based on proteomics studies in E. coli (see Methods). The flux and enzyme concentration data were from other studies which measured them during the exponential phase in E. coli, growing on minimal media supplemented with various carbon sources . If we consider measured fluxes for each reaction as a proxy for kin , we can conclude from the fact that there were no observed substrate accumulation in these reactions, as the analysed reactions carrying fluxes below the first limit identified above in Equation 2. There could be several explanations for this observation of measured fluxes being lower than the limit set by measured enzyme kinetics and level. One simple explanation could be that there is a discrepancy between in vitro measured enzyme kinetics and in vivo realised ones. Alternatively, this discrepancy can be low, but the lower flux could be arising because there are additional limiting factors other than the enzymes mediating the main reaction. Among such additional limiting factors, substrate limitation and thermodynamic effects are shown to partially explain observed lower fluxes in some reactions [Davidi et al. (2016)]. Here, we highlight that the presented theory shows that an additional possible limitation could be the co-substrate pool size and turnover dynamics.”“Based on flux values that are either experimentally measured or predicted by flux balance analysis (FBA), many reactions from the central carbon metabolism of the model organism – ll 187 onwards: some essential details are missing to understand the type of dataset used (see above).We agree with the reviewer and added the relevant details to the text (see the answer to previous comment).– It is also important to introduce in more detail the different experimental conditions for which the variation in ATP precursors has been observed. Could it be that ATP levels are merely changing because of the way the conditions change and not because fluxes vary as well?We are not clear what the reviewer is suggesting about ATP precursors. We don't assume anything regarding changes to ATP precursors, but only use the measured values to show that there is a change in total ATP pool with changing conditions. We do not speculate about the reasons for this, however, we note that the changes in the total ATP pool size cannot be due to flux changes in reactions using the ATP pool members as co-substrates. The changes in pool size, however, can affect flux in those reactions, where co-substrate dynamics is limiting (as predicted by the theory). If this was the case, then we would expect a change in flux in those reactions with changing pool size. This is what we wanted to explore / show with Figure 3B-D. Indeed, there seems to be some reactions where this is the case. We also recognise that we cannot rule out other effects arising from pool size changes.We have now included elements of this response in the revised text to make this point clear. Reviewer #3 (Recommendations for the authors):Mathematical equations, transformations, resulting constraints, and conclusions are generally very clearly explained, which allows readers, who might be less-accustomed to kinetic modeling, to follow the line of arguments. One suggestion I have is to provide units of variables that are used in equations also in the text, or perhaps as a (supplementary) table. Specifically, I noticed that this could help readers already at equations (1). Here, the steady-state concentration of m1 is given by the ratio of the two rate parameters k[in] and k[out]. Since in the text, both parameters are only referred to as "flux rates", one could assume that both have the same unit, which would make their ratio (=m1 concentration) unit-less. Only with the units that appear later in figure 2  it becomes clear that the two parameters have different units.We thank the reviewer for this useful comment. We have now included a table, Appendix – Table 2, listing the units of all the parameters, and referred to it in the Methods section of the main text.In addition, I understand that the authors claim, that flux-governing and -regulation through means of co-substrate cycling could be a general 'design principle' that is not limited to a specific group of organisms. However, I would suggest to provide more detail on the experimental/FBA data  that is used for the comparison with the model predictions. For instance, details on the organisms behind the experimental data that is mentioned e.g. in lines 187-208 and in Figure 3 could be added. This would help readers to put the authors' results in more biological context. Along those lines, the discussion could include a paragraph that addresses current limitations to further evaluate the developed mathematical framework. For instance, from which organisms do we have experimental data to study the potential role of co-substrate cycling using the developed framework? What future experiments/data types will further help to test the mathematical framework?Escherichia coli. We have now included this information both in the Methods and the Results sections. See also reply to recommendation 7 by reviewer 2.We thank the reviewer for these useful comments. The source organisms for the data used was the model bacterium Additionally, we have included the following paragraph in the Discussion section to make the current limitations in the available data clear, and to highlight future experimental avenues possible:E. coli and is limited even for this organism due to limited flux and proteomics data. For example, the data compiled here contained 14 co-substrate reactions with experimentally measured fluxes, but only half of these could be used due to lack of measurement on enzyme concentrations. We hope that the presented theory will provide motivation to further expand the available data sets, especially for reactions relating to co-substrate linked reactions. In this quest, we expect that the expansion of measurements to eukaryotic cells to be particularly challenging due to organelle-specific pools, but some progress is being made to achieve at least mitochondrial and cytosolic measurements [Chen et al. 2016]. Despite the current limitations, our data-based analyses highlighted three key reactions mediated by phosphoglycerate kinase (PGK), malate dehydrogenase (MDH), and glucose-6-phosphate dehydrogenase (G6PDH) and linking to ATP, NADH, and NADPH pools. Possible flux limitation of these reactions by co-substrate dynamics can also be subjected to further experimental study – as we discuss further below.”“Comparing measured flux data against estimated flux values based on measured enzyme levels from proteomics and enzyme kinetics from in vitro studies, we have provided support that fluxes in co-substrate linked reactions could indeed by limited by co-substrate pool dynamics under physiological conditions. This analysis was based on the model organism