The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches.The online version of this article (doi:10.1186/s12918-016-0283-2) contains supplementary material, which is available to authorized users. Specifically within metabolism, kinetic models have the potential to elucidate the control mechanisms underlying metabolic homeostasis and regulatory responses [Kinetic models of biochemical networks continue to grow in scope and scale –7. The pesponses –10, as wesponses . To dateesponses , 13, metThe primary challenge in kinetic modeling of metabolism is dealing with the frequent cases where data to construct detailed kinetic models is lacking . This chHere, we construct a set of kinetic models of red blood cell (RBC) metabolism using various approximate rate laws, such that their parameters are equivalent to those of the fully-described enzyme mechanistic model. We choose the red blood cell due to the large amount of available data, enabling us to use physiological enzyme kinetic parameters, reaction fluxes, metabolite concentrations, and reaction equilibrium constants. Thus, we can examine the practical importance of rate law approximations against the backdrop of a realistic system.We utilize these models to study the effect of simplifying assumptions to the rate laws on system dynamics through simulating the network response to small transient perturbations. We additionally discuss theoretical differences in the kinetic behavior of these rate laws. Finally, we iteratively replace approximate rate laws with mechanistic enzyme kinetics to examine whether we can anticipate general dynamic effects of certain types of approximations. We purposefully chose a simple perturbation approach with mathematical response properties as output metrics, as opposed to physiological prediction accuracy, in order to simplify the task of understanding any observed correlations or lack of correlations.ms) and catalytic constants (kcats) to parameterize the system, as well as metabolomics data, Keqs of biochemical reactions, and enzyme concentrations. The conditions for validity of the assumptions underlying this rate law have been examined in great detail [In preparation for investigating rate law effects through model simulation, we first discuss the assumptions underlying the different approximate rate laws. Perhaps the most well-known kinetic assumption is the QSS assumption, normally associated with Michaelis-Menten kinetics but originated by Briggs and Haldane . This ast detail –27.Fig. m values. Previously it has been shown experimentally that enzyme Km values tend to be similar to the in vivo concentrations of corresponding metabolites [m = x assumption to parameterize rate laws. If we additionally lack of knowledge about the enzyme reaction mechanism as well, the form of the QSS rate law equation into which parameters will be inserted is unclear. To deal with this, we can add a further assumption that the reaction follows a rapid equilibrium random order mechanism [If sufficient kinetic data is lacking, but reproducing enzyme saturation behavior is desired, an additional assumption can be made to approximate the Kabolites . To deteechanism , followim < < x for substrates and activators while Km > > x for products and inhibitors). This assumption effectively removes enzyme-specific parameters from the rate law and leads to a thermodynamics-driven rate law similar to what has been termed Q-linear kinetics  the ability of the rate law to exhibit the ‘saturation’ behavior that is characteristic of enzyme kinetics, and 2) the properties of the first derivative of the rate law, which defines the local dynamic behavior of the system.max as x approaches infinity. A mass action enzyme module exhibits the same behavior due to the constant total enzyme, placing a constraining relationship between the fluxes of individual reaction steps. The manner in which saturation is achieved between a full mass action enzyme module and the Michaelis-Menten kinetics is thus mathematically different.Each rate law exhibits different behavior as metabolite concentrations approach infinity. For example, the Michaelis-Menten kinetics with measured properties exhibit the well-known saturation behavior due to the hyperbolic form, such that v = vmax if the substrate concentration is maximized, but will incorrectly have a minimum of negative infinity if the product concentration is maximized. This asymmetry is known and proponents of the rate law suggest that the rate law only be used in a range near equilibrium [In contrast to Michaelis-Menten kinetics with measured properties and enzyme module of mass action rate laws, the non-module mass action and Q-linear rate laws do not exhibit saturation behavior. Mass action kinetics will approach positive or negative infinity as substrate or product concentrations, respectively, approach infinity. Meanwhile, Q-linear kinetics exhibit asymmetrical saturation properties. The flux v will correctly have a maximum of vilibrium , which iExamining the first derivatives of the reactions is a straightforward analytical approach to anticipating dynamic differences between the rate laws Fig. . From theqs), enzyme concentrations, and rate constants of individual enzymatic reaction steps, to fully describe the dynamics of the system. We used these ten enzyme modules as a ‘gold standard’ for later comparison with approximate rate laws.We first constructed enzyme ‘modules,’ consisting of full mass action descriptions of enzymatic reaction mechanisms, for ten key enzymes in RBC central metabolism utilizing measured data for these enzymes Fig. , Table 1m values being approximated as equal to the concentrations of corresponding metabolites, to simulate the effect of unknown data, mechanisms, and regulation, 3) a rate law previously, termed Q-linear kinetics [In this study, we examined four approximate rate laws to compare to the fully-described enzyme modules. Those four rate laws are: 1) Michaelis-Menten kinetics based on the quasi-steady state (QSS) assumption for the true enzyme module with measured enzyme parameters, 2) an assumed rapid-equilibrium random-order Michaelis-Menten rate law ignoring regulation and with Kkinetics , containkinetics .We first constructed a cell-scale model of RBC metabolism using approximate Q-linear rate laws to serve as a scaffold model for analysis. Our approach was to insert the ten constructed enzyme modules into this scaffold, and compare this model behavior to that of models generated with different approximate rate laws substituted into those same ten reactions. The model was constructed using steady-state metabolite levels from plasma and intracellular erythrocyte metabolomics data from a fasting state . The modi at the same time to simulate the hydrolysis of ATP in the system.A straightforward way to estimate the similarity of behavior between different rate laws is to simulate the response of each model to perturbation. A perturbation in this case denotes the change of certain metabolite concentrations at time t = 0, after which the system is allowed to simulate through a long enough time such that the original steady state is once again reached. For example, we perturbed the concentrations of ATP, ADP and PTwo key decisions in such an analysis are the choice of perturbation and the choice of output variable to observe. In this study, we perturbed both metabolites directly involved in as well as distant from the constructed enzyme modules. The list of perturbations can be found in Fig. One final decision in the simulation workflow is the size of the perturbation to use. As mentioned previously, the rate laws chosen differ in both saturation properties, which are non-linear features of the rate laws, and local dynamic properties, which are linear features of the rate law. It appeared to be a trivial result that saturating and non-saturating rate laws will exhibit very different behavior for large deviations where non-linear effects play a significant role. However, understanding the origin and nuances of such deviations is complex, and we sought to achieve a simpler goal as a baseline investigation. To avoid such obvious effects dominating our findings, we intentionally chose small perturbations to minimize saturation effects and instead focus on determining the importance of the linear/local differences between rate laws.m = x assumption (x being the concentration of the corresponding ligand) is not sufficiently correct to capture the dynamics of the original enzyme module. Notably we did not include known regulation of these enzymes in this approximate rate law, and further investigation of the behavior of models with the addition of these regulatory events with an analogous Kd = x assumption may be warranted. We note that these conclusions regarding the suitability of approximate rate laws are not due to the choice of model underlying the analyses.The final workflow was to perform nine different small perturbations on the system with different rate laws and characterized the response of metabolites in terms of RT and MP Fig. –b. CalcuWe repeated these analyses on a previously published model of the red blood cell, smaller scale but composed entirely of mechanistic enzyme mechanisms . We iternd law of thermodynamics [One key control in the study is to determine whether uncertainty in parameters significantly impacts the conclusions of analyses. To address this, we conducted Markov chain Monte Carlo (MCMC) convex sampling of steady-state fluxes given physiological ranges on metabolite uptakes and secretions . Similardynamics . We thenSince the simplified rate laws introduces noticeable discrepancies in dynamic behavior, we wanted to determine whether these discrepancies would continue to increase as simplified rate laws are applied to more reactions until the correlation completely disappears, or whether the approximate model behavior would stabilize at some positive correlation to the true model. Based on the previous observation that Michaelis-Menten kinetics with measured properties closely resembled the true model, we set up a simple test case with as many reactions specified with Michaelis-Menten kinetics as possible (38 out of 168 reactions ) and theWe then investigated the source of the positive correlation between fully approximate models and the true model. As both models share the same initial steady state, in terms of reaction fluxes, metabolite concentrations, and reaction equilibrium constants, we sought to determine whether these values were essential to the dynamic consistency we observed across rate laws. The flux and concentration state of the cell play a role in determining the dynamic structure of the network. For example, large metabolite pools will be changed slowly by small fluxes, and vice versa, giving some expectation of fast and slow dynamics within the network. We wanted to investigate the degree to which network dynamics are determined by the initial flux and concentration state, as opposed to the choice of rate law. To this end, we sampled reaction fluxes and metabolite concentration within physiological ranges, and then in wider ranges. In contrast to changing rate laws, we found that widening the sampling range on fluxes and concentrations greatly impacted the dynamic response of metabolite throughout the network. For example, metabolite MP and RT subject to ATP hydrolysis perturbation showed weaker correlations within models sampled with wider concentration and flux ranges compared to those from models sampled with physiological concentration and flux ranges Fig. –b. We alDPGASE and DPGM are thermodynamically in an irreversible state but the high concentration of 23DPG creates a large slow moving pool that causes the dynamics of the network to be insensitive to the choice of rate law for these enzymes . For example, the relative metabolite concentrations across different levels of G6PDH activity were the same between enzyme module and Michaelis-Menten rate law with measured properties, while other rate laws showed noticeable differences  often incomplete and measured under non-physiological conditions, but there is a separate issue with the additional parameters that are required to parameterize a mass action mechanistic description of a reaction (which we term an enzyme module). Full specification of kinetic parameters is experimentally intensive but theoretically possible, and some enzymes such as PFK have been characterized in great detail in particular organisms, including pH and temperature dependence of parameters. However, the difficulty in determining these parameters and uncertain immediate value of the data, evidenced by lack of practical applications of resulting kinetic models, is likely the main reason these data are not routinely being generated. In this study, we show both the value of fully-defined enzyme mechanism as well as rate law approximations, and thus it appears that the appropriate rate law to use should continue to be determined by the goals of the modeler.Obtaining enzyme kinetic parameters continues to be a core issue hindering the development of practical large-scale kinetic models of metabolism. Databases such as BRENDA  continueOn the note of the design of this study, we note that kinetic models can be analyzed from numerous angles. Much work thus far has focus on the dynamic control of metabolic states. This goal is of great importance, but due to the non-linear and complex nature of such control, we targeted our investigation on a simpler task of understanding transient responses to small perturbations in the metabolic network. Experimentally measuring such transients, i.e., dynamics of metabolite concentrations, is challenging and fundamentally limited by sampling frequency and metabolism quenching time. However, we chose to focus on these perturbations as they are the most simple to understand mathematically. Further studies looking at the effect of rate law approximations on more intricate dynamic properties, such as the non-linear control of steady-state changes following enzyme inactivation, are extremely desirable if they can be conducted in a rigorous way.ms for corresponding enzymes [In our comparison of rate laws, we showed that the Michaelis-Menten kinetics with measured properties gives a good approximate of the full system when comparing the relaxation time and maximum perturbation of the metabolites. Thus, discrepancies due to ignoring dynamics of individual enzyme forms do not appear to be a significant issue. This success in approximation is likely due to the combination of the small concentrations of most enzyme forms relative to metabolite concentrations, a requirement for the validity of the QSS assumption , as well enzymes , which cWe showed that adding a module can bring qualitative effects to the dynamics of related metabolites. However, the quantitative effects have to be examined in a context specific manner, possibly due to the associated reaction property or network connectivity. We also showed that the addition of regulations, such as feedback inhibition and feedforward activation, can cause dynamic behavioral changes different from those of simple genetic circuits. Taken together, we would advise a detailed mechanistic description for enzyme catalyzed reaction is likely a necessity for predicting system dynamics with reasonable accuracy.ms, vmax and Kds. However, those data are not sufficient to solve for the rate constants of specific enzymatic steps in the module. Thus, a good fitting approach is necessary to obtain a set of rate constants that accurately recapitulate the existing experimental data. The second problem is associated with the simulation of the system containing multiple modules. A possible stiffness issue can occur when integrating the ODE equations during dynamic simulations. This might be due to the large difference in orders of magnitude between metabolite concentrations and enzyme intermediate concentrations. In this case, we would advise normalizing the enzyme concentrations to the same level as metabolite concentrations and adjust the corresponding rate constants. However, one needs to be careful with the magnitude of change in enzyme concentrations as we found that different changes can cause different dynamic responses. Looking forward, addressing these issues will be essential to make progress toward bottom-up construction of kinetic models of metabolism.There are two additional possible issues associated with modeling enzyme kinetics using an enzymatic mass action approach. The first is the estimation of kinetic parameters within the module. The current available experimental data on the enzyme include KThe work here explored the validity of using approximate rate laws with varying levels of assumptions in the context of a cell-scale RBC kinetic model. We found that the Michaelis-Menten rate law based on quasi-steady state assumption was able to recapitulate the dynamic behaviors of the mechanistic model consistently as long as measured parameters were used. Rate laws that are derived from further approximations on Michaelis-Menten kinetics or ignore the role of the enzyme showed substantial discrepancies in dynamic behaviors compared to the mechanistic model. However, we found that the errors associated in these approximate models appeared to stabilize as more reactions were replaced by approximate rate laws, suggesting that even fully approximate models can contain useful information. This appears to be due to the dominant effect that the order of magnitude differences in reaction fluxes and metabolite concentrations have on the dynamic structure of the network. Still, we also found that replacing approximate models with the detailed mechanistic enzyme module can bring unpredictable quantitative effects to the system, suggesting a clear benefit of constructing mechanistically detailed enzyme modules when possible. The work here should aid the choice of rate laws and parameterization approaches in future kinetic modeling efforts.https://github.com/opencobra/MASS-Toolbox) for model construction and simulation. The RBC metabolic network with enzyme modules incorporated is available in Mathematica file format.All work was done in Mathematica. We used the MASS Toolbox kinetic modeling package  is bound to a particular enzyme form.The data used for module construction can be found in Additional file PFK module), all the reactions in the module were added into the metabolic network and the original metabolic reaction (PFK reaction) was removed.The constructed modules were added into the RBC metabolic network  for furtBefore dynamic simulations, the steady state metabolite concentrations were set as the initial conditions of the system. For a particular perturbation, a change on certain metabolite concentrations were applied at time 0 and the subsequent simulation was conducted through numerical integration of the ODE equations. The system was allowed to simulate to over 100,000 h to regain the steady state concentrations.Given a concentration profile from simulation, the maximum perturbation is the largest percent change in concentration compared to the steady state concentration for a particular metabolite. The relaxation time is defined as the last time point at which the deviation from the steady state concentration is 5 % of the maximum perturbation. Specifically, when calculating the relaxation time, we traced backwards by starting from the concentration at a ‘long enough’ time  and calculated the difference between the concentration at a particular time and the steady state concentration until the relaxation time was identified.https://github.com/opencobra/MASS-Toolbox). There are extra 13 reactions in the model that we did not build enzyme modules for. They are export/import reactions, generic metabolic reaction without specific reference to an enzyme and reactions with zero flux. Specifically, they are AMP export reaction, AMP import reaction, CO2 export reaction, glucose import reaction, proton export reaction, water export reaction, lactate export reaction, O2 export reaction, pyruvate export reaction, ATP hydrolysis reaction, glutathione redox reaction, NADH redox reaction, adenylate kinase reaction.We used the scope  were compared across rate laws and verified against physiological studies. All simulations were performed on the model constructed based on Mulquiney et al [The metabolic state of the system was simulated with different levels of enzyme activities, for the three enzymes ey et al .We started with the model constructed based on Mulquiney et al  (containTo test the effect of replacing single module on the network dynamics, we started with the model constructed based on Mulquiney et al  (containWe used the model constructed by Bordbar et al  for paraTo compare the dynamic behavior of models with different sets of parameters, concentrations and fluxes, we performed three different perturbations on the 300 sampled models. The three perturbations were: changing ATP, ADP, Pi concentrations, changing NAD/NADH concentrations and changing FDP concentration. It was worth noting that only 63 models were able to achieve stable steady states after the perturbations. The RT and MP of the metabolites in those models were calculated from the perturbation profiles. We then selected metabolites with MP over 5 % and compared the dynamic response across models.PFK, GAPDH and ALD [We used the model constructed based on Mulquiney et al  (contain and ALD . We replADK, adenylate kinase; ADP, adenosine diphosphate; ALD, aldolase; AMP, adenosine monophosphate; ATP, adenosine triphosphate; CO2, carbon dioxide; DHAP, dihydroxyacetone phosphate; DPGASE, bisphosphoglycerate phosphatase; DPGM, bisphosphoglycerate mutase; ENO, enolase; F6P, D-Fructose 6-phosphate; FDP, D-Fructose 1,6-bisphosphate; G3P, glyceraldehyde 3-phosphate; G6P, D-Glucose 6-phosphate; G6PDH, glucose 6-phosphate dehydrogenase; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; GLC-D, D-Glucose; GND, phosphogluconate dehydrogenase; GSSGR, glutathione reductase; H+, hydrogen ion; HEX1, hexokinase; LAC-L, L-Lactate; LDH, lactate dehydrogenase; MAN6P, D-Mannose 6-phosphate; MP, maximum perturbation; NAD, Nicotinamide adenine dinucleotide; NADH, Nicotinamide adenine dinucleotide - reduced; NADP, nicotinamide adenine dinucleotide phosphate; NADPH, nicotinamide adenine dinucleotide phosphate - reduced; O2, oxygen; PEP, phosphoenolpyruvate; PFK, phosphofructokinase; PGI, glucose 6-phosphate isomerase; PGK, phosphoglycerate kinase; PGLASE, 6-phosphogluconolactonase; PGLM, phosphoglycerate mutase; Pi, orthophosphate; PK, pyruvate kinase; PRPP, 5-Phospho-alpha-D-ribose 1-diphosphate; PYR, pyruvate; QSS, quasi-steady state; R5P, alpha-D-Ribose 5-phosphate; R5PE, ribulose 5-phosphate epimerase; R5PI, ribulose 5-phosphate isomerase; RBC, red blood cell; RT, relaxation time; RU5P-D, D-Ribulose 5-phosphate; TALA, transaldolase; TKI/TKII, transketolase; TPI, triose phosphate isomerase13DPG, 3-Phospho-D-glyceroyl phosphate; 23DPG, 2,3-diphosphoglycerate; 2PG, 2-Phospho-D-glycerate; 3PG, 3-Phospho-D-glycerate; 6PGC, 6-Phospho-D-gluconate; 6PGL, 6-phospho- D-glucono-1,5-lactone;


B. thuringiensis culture. However, this culture is a time dependent dynamic process where cells physiology suffers several changes depending on the changes in the cell environment. Therefore, through its culture, B. thuringiensis presents three phases related with the predominance of three major metabolic pathways: vegetative growth (Embded-Meyerhof-Parnas pathway), transition (γ-aminobutiric cycle) and sporulation (tricarboxylic acid cycle). There is not available a mathematical model that relates the different stages of cultivation with the metabolic pathway active on each one of them. Therefore, in the present study, and based on published data, a biodynamic model was generated to describe the dynamic of the three different phases based on their major metabolic pathways. The biodynamic model is used to study the interrelation between the different culture phases and their relationship with the Cry protein production. The model consists of three interconnected modules where each module represents one culture phase and its principal metabolic pathway. For model validation four new fermentations were done showing that the model constructed describes reasonably well the dynamic of the three phases. The main results of this model imply that poly-β-hydroxybutyrate is crucial for endospore and Cry protein production. According to the yields of dipicolinic acid and Cry from poly-β-hydroxybutyrate, calculated with the model, the endospore and Cry protein production are not just simultaneous and parallel processes they are also competitive processes.Mathematical models have been used from growth kinetic simulation to gen regulatory networks prediction for The online version of this article (doi:10.1186/s13568-014-0079-y) contains supplementary material, which is available to authorized users. Bacillus thuringiensis (B. thuringiensis) is a Gram-positive endospore-forming bacterium isolated from soil that synthesizes a crystalline δ-endotoxin protein, named Cry protein . The mao et al. ). It haso et al. ). Cry pra et al. ; Navarroa et al. ; Ozcan ea et al. ; Zhuang a et al. ). Also, nd Moser ; Liu andnd Moser ; Popovicnd Moser ; Rivera nd Moser ; Starzaknd Moser ).B. thuringiensis culture is a time dependent dynamic process where the physiology of cells suffers several changes. During the culture the number of cells increase causing changes in the environment and subsequently the cells respond to those changes modifying their activity. This dynamics continues until the death of the cells when active entomopathogenic products (endospores and Cry protein) are obtained. The response of the cell to the environmental changes is a complicated process that involves cell metabolism, cell cycle regulation, signaling and gene regulatory networks and gene expression. As result of the response of the cell to the environmental changes, the culture typically shows three different phases related with the predominance of one of three major metabolic pathways , transition-γ-aminobutiric cycle (GABA) and sporulation-tricarboxylic acid cycle (TCA) .Figure B. thuringiensis culture, specifically: the vegetative growth phase  and thend Moser ). These nd Moser ) model cB. thuringiensis culture. Also, it was used to study the interrelation between the different culture phases and its relationship with the Cry protein production. The considerations for the construction of the model were: a) each phase of B. thuringiensis culture can be represented by its principal metabolic pathways ; and b) each pathway can be follow with its key compound .In the present study, a biodynamic model was constructed to describe the complete evolution of the B. thuringiensis culture. It is not straightforward to compare the cells/biomass and PHB kinetics data reported in the literature because different conditions and analytic techniques were used. Thus, in order to be able to compare these data a normalization was done  PHB affects positively the Cry production; ii) Yield of DPA, Cry protein and PHB from biomass are independent from initial substrate concentration; iii) Embded-Meyerhof-Parnas, γ-aminobutyric acid cycle and tricarboxylic acid cycle are the main pathways for vegetative growth, transition and sporulation phases, respectively; iv) Every metabolic change has a key compound associated and can be represented by: cells, poly-β-hydroxybutyrate (PHB) and DPA-Cry protein.2 is released due to the respiration process. During transition the substrate is accumulated as PHB. While during sporulation: there is no substrate consumption; PHB is consumed; the vegetative cell is transformed into endospore; and in the same period of time the Cry protein is produced from protein turnover . The PHPhase: Vegetative growth; metabolic pathway: Embded-Meyerhof-Parnas pathway; key compound: cells. The vegetative cell evolution requires a two-term equation: growth and dead Equation . The firPhase: Transition; metabolic pathway: γ-aminobutyric acid cycle; key compound: Poly-β-hydroxybutyrate. The PHB also requires a two-term equation: production and consumption Equation . In the Phase: Sporulation; metabolic pathway: tricarboxylic acid cycle; key compound: Cry protein and DPA. DPA and Cry protein production are assumed as simultaneous and parallel processes both represented by the Gompertz model, Cry protein Equation  and DPA The biodynamic model constructed . These fermentations were done using the same culture media, carbon:nitrogen relation, operating condition and bioreactor. In order to establish the relationship between the carbon source and the biomass and Cry protein production, different concentration of the substrates in the culture media were used in each run.Bacillus thuringiensis var. kurstaki HD-73 (ATCC-35866), which produces a 133.3 kDa Cry1A(c) insecticidal crystal protein, was obtained from the USDA Insect Pathology Research Unit, Brownsville, Texas. The microorganism conservation was made in endospore filter-paper disk and the inoculum for fermentation was prepared in two stages, according to Navarro et al. .The media was adjusted for all the fermentations to a carbon:nitrogen ratio of 7:1; to achieve this ratio several glucose-soybean meal concentrations were used Table . AdditioB. thuringiensis cell is 2.3 pg  under dark field illumination, with a 40 X objective and 10 X ocular lenses, as previously described . In ordla Torre ).The PHB concentration was determined in a FID gas chromatograph  equipped with an AT-1000 column . Each vThe concentration of Cry protein was determined by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). Bovine serum albumin (BSA) was used as protein standard. The samples preparation was done according to Navarro et al. . The soBacillus and Clostridium genus. In order to obtain more accurate result, endospore kinetics was follow by DPA photoluminescence technique  is a unique constituent of all endospores of o et al. ). The phThe normalized data from the literature show that the cells/biomass and PHB kinetics .0); stage II, the first hour; stage III, 1 h after t0; stage IV, 2 h after t0; stage V, 4 h after t0; stage VI, 5 h after t0; and stage VII, more than 5 h after t0. Figure Stage I starts at the beginning of the sporulation process  agree with the experimental and the reported ones (Tables max) and growth yield coefficients (YX/S) have been reported for different culture conditions , 1 C-mol of glucose (CH2O) and no respiration process (no formation of CO2). Then, the growth yield coefficient for aerobic growth must be always below 0.863 g of biomass/g glucose and values greater than 0.863 imply that glucose is not the limiting substrate. In the present study, the μmax and the YX/S values obtained agree with previously reported  formation through YDPA/X. In the same way, the PHB consumption is related with DPA-Cry production through YDPA/PHB and YCry/PHB. These yields were calculated with the model  is used in the Cry protein formation. There is not data available in the literature to compare these results and further experiments have to be done. Also, the biodynamic model simulation results indicate that the Cry protein production is a function of development of the three fermentation phases, and that endospore and Cry protein production are competitive processes. Therefore, the optimization of each phase cannot be done independently. The reports in the literature usually do not take into account the transition phase neither the PHB production as important variables for Cry production. However, the biodynamic model implies that PHB is crucial for endospore and Cry protein production.The biodynamic model represents the evolution of the el Table  and theyB. thuringiensis fermentation and it can be used as a tool to understand the complex processes related to the physiology of the bacilli. Besides, it can be applied for fermentation with different production systems, operating conditions and culture media. Also, it can be used to study other dynamic processes that occur during fermentation as the cell cycle regulation, the signaling and gen regulatory networks and the changes in gene expression, between others. Although, the biodynamic model is the first model that represents the entire fermentation of B. thuringiensis and it is also the first one that links each phase of the culture with its predominantly active metabolic pathway. This model is a powerful tool to study the dynamics of the B. thuringiensis culture and the interrelation between their phases. Also, the model can be used to know the physiological phase during the fermentation. From the simulation results it can be concluded that the PHB is crucial for endospore and Cry protein production; and that those processes are simultaneous, parallel and competitive. In terms of the DPA and Cry yield from PHB, the endospore formation is preferred over the Cry protein synthesis.In summary, the new biodynamic model reported here represents well the dynamic of the Normalization of cells/biomass and PHB kinetics fromB. thuringiensisculture. Figure S1. Normalization of the biomass kinetics from reported data. The data correspond to different culture systems, different operating conditions, different culture media, different bioreactors, etc., and biomass concentrations were measured using different techniques. The line represents an average biomass kinetic for B. thuringiensis var. kurstaki HD-73. Figure S2. Normalization of the Poly-β-hidroxybutyrate kinetics from reported data. The data correspond to different culture systems, different operating conditions, different culture media, different bioreactors, etc. and Poly-β-hidroxybutyrate concentrations were determined using different techniques. The line represents an average PHB kinetic for B. thuringiensis var. kurstaki HD-73. Figure S3. Effect of the glucose concentration on the Xmax for B. thuringiensis culture (bibliographic data). Figure S4. Effect of the glucose concentration on the tcx for B. thuringiensis culture (bibliographic data). Figure S5. Effect of the glucose concentration on the PHBmax and for B. thuringiensis culture (bibliographic data). Figure S6. Effect of the glucose concentration on the tcp for B. thuringiensis culture (bibliographic data). (PDF 9 MB)Additional file 1: Authors’ original file for figure 1Authors’ original file for figure 2Authors’ original file for figure 3Authors’ original file for figure 4Authors’ original file for figure 5Authors’ original file for figure 6Authors’ original file for figure 7Authors’ original file for figure 8Authors’ original file for figure 9Below are the links to the authors’ original submitted files for images.


Saccharomyces cerevisiae, S. paradoxus, S. mikatae, and S. bayanus) by integrating metabolic network simulations with RNA sequencing (RNA‐seq) datasets. We generated high‐resolution transcriptome maps of four yeast species through de novo assembly and genome‐guided approaches. The transcriptomes were annotated and applied to build the consensus metabolic network, which was verified using independent RNA‐seq experiments. The expression profiles reveal that the genes involved in amino acid and lipid metabolism are highly coexpressed. The diverse phenotypic characteristics, such as cellular growth and gene deletions, can be simulated using the metabolic model. We also explored the applications of the consensus model in metabolic engineering using yeast‐specific reactions and biofuel production as examples. Similar strategies will benefit communities studying genome‐scale metabolic networks of other organisms.One practical application of genome‐scale metabolic reconstructions is to interrogate multispecies relationships. Here, we report a consensus metabolic model in four yeast species ( DEGDifferentially Expressed GenesFBAFlux Balance AnalysisGDLSGenetic Design through Local SearchlMOMALinear Minimization Of Metabolic AdjustmentMOMAMinimization Of Metabolic AdjustmentPCCPearson's correlation coefficientPYRDCPyruvate decarboxylaseRPKMReads Per Kilobase of exon per Million readset al. The metabolic network reconstructions can be applied in diverse aspects, such as metabolic engineering for biotechnological productions de novo assembly) de novo assembly is suitable for the accurate reconstructions.However, the majority of the current metabolic networks are reconstructed based on the prior knowledge (knowledge‐driven) and focused on network topologies or characteristics of components in the model, ignoring the actual states of the metabolic networks Saccharomyces cerevisiae, Saccharomyces paradoxus, Saccharomyces mikatae, and Saccharomyces bayanus) to generate a ‘consensus’ metabolic network. First, we generated high‐resolution transcriptome maps of four yeast species through de novo assembly and genome‐guided approach. We then produced a consensus metabolic network and validated the model using an independent RNA‐seq study. By quantifying the gene expression level in the model, we estimated the conservation and divergence of metabolic pathways. We also discussed the practical applications of the metabolic model.In the study, we carried out an integration analysis of RNA‐seq expression profiles from four yeast species  reconstruction of consensus metabolic model; and (d) model annotations, simulations, and validation.The process, explained in detail below and illustrated in Fig. S. cerevisiae, S. paradoxus, S. mikatae, and S. bayanus) was downloaded from the NCBI GEO database (NCBI GEO accession: GSE32679) et al.'s study The raw RNA‐seq data from four yeast species (S. cerevisiae iND750 metabolic network (hereinafter referred to as ‘iND750′) was retrieved from Schellenberger et al.'s work S. cerevisiae genes. The model is available as a systems biology markup language (SBML) The S. cerevisiae were obtained from the Saccharomyces Genome Database (http://www.yeastgenome.org/). Genome, annotations, and orthology mappings for the other species were from Kellis et al.'s work mosaik alignment program  allowing for a threshold of two mismatches between each 35‐base pair read and the reference genome. The alignment output was parsed using the bamtools API The reference genome and annotations for de novo assemblies were run with oases (version 0.2.08) velvet (version 1.2.07) All the blastn (version 2.2.23) program was used to map all the metabolic genes in S. cerevisiae model to the transcriptomes reconstructed through genome‐guided approach and de novo assembly, with e‐value threshold set at 10−4. We then overlapped all the positive results from four species to obtain a consensus metabolic gene dataset.In the process, the S. cerevisiae metabolic network using two commonly used algorithms of top–down metabolic reconstructions, including GIMME S. cerevisiae metabolic network, and (b) the high‐quality transcriptomes in four species based on the genome‐guided and de novo methods above.We derived a consensus metabolic model from the bioconductordeseq (version 1.1.11) P‐value cutoff of 0.05 and fold‐change < 0.5 or > 2, that is, fold‐change < −1 or > 1 after log transformation) were retained for further analysis. We also applied reads per KB per million reads (RPKM) to detect gene expression levels We identified differentially expressed genes (DEGs) using a free S. bayanus included in the further analysis as an outgroup. If a DEG between S. bayanus and the other three species show the same tendency , the gene was considered to form divergent expression patterns.To reduce the bias induced by randomization, we introduced the phastCons tree model GSE38875), with two replicates for S. paradoxus, S. mikatae, and S. bayanus, and six replicates for S. cerevisiaeDe Novo assembly methods, and (b) the consensus metabolic model was built using GIMME S. cerevisiae iND750 To validate our metabolic model, we introduced another independent RNA‐seq dataset  were filtered. We then adopted the Pearson's correlation coefficient (PCCs) of gene expression patterns to measure the gene coexpression. To make the result solid, we set |Pearson's r| ≥ 0.90.The metabolic models were analyzed by using multiple methods in COBRA toolbox (V 2.0.2) These methods provide important tools for harnessing the knowledge encoded in the reconstructed metabolic model. FBA predicts metabolic flux distributions at steady state by using linear programming while the method of minimization of metabolic adjustment (MOMA) employs quadratic programming to identify a point in flux space, which is closest to the wild‐type point, compatibly with the gene deletion constraint. FBA and MOMA of the metabolic network were used to calculate the impact of gene deletions on maximum biomass production rate (a proxy for fitness). We set both the upper and lower flux bounds of the reaction(s) involving the deleted gene to zero. The gene‐reaction associations in the model are indicated by logical relationships between metabolic genes and their corresponding reactions. That is, if a single gene participates in multiple reactions, the gene deletion will result in the removal of all associated reactions. On the other hand, if a reaction involves multiple noninteracting genes, it will not be silenced in a single gene deletion. We categorized the simulation results from a single gene deletion into nonlethal and lethal, which correspond to unchanged maximal growth (defined as mutant growing at > 99.9% of the wild‐type growth rate) and reduced maximal growth or no growth separately. We can obtain valuable information by exploring the effect of reducing flux through a single reaction on growth, for example, predicting the haploinsufficient phenotypes in yeasts. Moreover, robustness analysis of the metabolic network tells us how growth rate changes as the flux through a specific reaction of interest varies in magnitude in silico production of desired metabolites. GDLS is a computational design tool for metabolic engineering, which uses an efficient, low‐complexity local search approach to identify favorable genetic designs from flux balance metabolic models −1 h−1−1 h−1).The GDLS algorithm Saccharomyces Genome Deletion Project (http://www-sequence.stanford.edu/group/yeast_deletion_project), which generates more than 20000 strains with the overall goal of assigning function to the ORFs through phenotypic analysis of the mutants We retrieved the essential genes for yeast growth from t‐test was performed to compare the gene expression levels between metabolic genes.All the Gene Ontology enrichment analyses were assessed using ClueGO, a Gene Ontology‐based tool as functionally grouped networks S. cerevisiae. Of these consensus genes, 545 were found to be metabolic genes in S. cerevisiae metabolic genes. Meanwhile, molecular function enrichment analysis with Gene Ontology annotation reveals that the transcripts not included in consensus dataset from S. cerevisiae are enriched with DNA‐binding (GO:00036770), protein kinase activity (GO:00046720), and transcription factor binding (GO:00081340) and other important function categories , which are crucial for cell growth. KEGG pathway analysis shows that the metabolic genes not included in the consensus dataset were enriched with basic metabolic pathways . Besides, the transcripts retrieved from 19‐mer performed best in the following BLAST analysis, which were therefore used for the further analysis. Oases assembles 71429 transcripts in four yeast species, with two replicates in each species merged into one transcriptome  to reconstruct a consensus metabolic network. It shows that the two methods produced the equivalent network, containing 992 metabolites, which participate in 1104 reactions, catalyzed by 604 metabolic genes (TEXT S1). The model was written in systems biology markup language and could be divided into 47 subsystems . It is observed that different gene‐protein‐reaction (GPR) relationships are adopted in different subsystems. For example, reactions in oxidative phosphorylation are often catalyzed by multiple genes while genes in fatty acid biosynthesis correspond to multiple reactions.de novo assembly approach. A total of 602 consensus metabolic genes were found from the transcriptomes. A metabolic model containing 992 metabolites, 1104 reactions, and 604 metabolic genes was obtained. It shows that the model contains the same GPR relationships as the one in TEXT S1, suggesting that the reconstructed model is robust. Moreover, compared to the manually curated metabolic networks Using an independent RNA‐seq dataset S. bayanus, most of which show high expression in other three species. By setting stringent criteria , we identified seven genes divergent in gene expression. Among these seven genes, gene FAS2  shows up‐regulated patterns while the other six genes  show down‐regulated patterns between S. bayanus and the other three species. It shows that the protein encoded by S. bayanus FAS2 is much longer than the orthologous proteins in the other species, with large deletions/insertions in the multiple sequence alignment. We also detected FAS2 with positive selection on coding region (P < 10−5), using the Nei–Gojobori method Gene expression is a sensitive measure to observe the molecular change We also wondered whether the metabolic genes in the model displayed the same patterns in expression profiles with each other. As a result, we built up a coexpression network based on the intra‐ and interspecies expression variation Fig. ; MethodsS. cerevisiae metabolic network .Using the metabolic model, we could predict phenotypes of yeast metabolic genes. In the previous studies, one of the most important phenotypic predictions is the simulation of cellular growth We performed a genome‐scale single gene deletion study using both FBA and linearMOMA methods in COBRA toolbox EC 4.1.1) participates in Pyruvate Metabolism while the gene YKL060C  catalyzed Glycolysis/Gluconeogenesis. The growth rate is sustained near the optimal value over a range of fluxes for Pyruvate Metabolism  while the growth rate for Glycolysis/Gluconeogenesis  is sharply reduced after optimal value, indicating network robustness with respect to flux changes in PYRDC . However, a complete deletion of the PYRDC reaction would lead to a lethal phenotype, whereas deletion of the fructose‐bisphosphate aldolase reaction exhibits no change in growth.We wondered the effects of reducing flux through reactions catalyzed by the highly expressed genes in consensus metabolic model. As a result, we studied the effect of decreasing the expression level of the top two genes  on the growth rate to predict haploinsufficient phenotypes. The gene YLR044C  using metabolic genes in the metabolic model and identified 54 yeast‐specific reactions (Table S1). We set the minimal medium composition of the metabolic model aerobic and contain a glucose supply (20 mmol gDW−1 h−1) and predicted a list of candidate reactions for deletion to optimize product formation of these yeast‐specific reactions  are increasingly common complications in critically ill patients worldwide and are frequently fatal Despite our experimental and statistical rigor, our dataset does have some limitations. We used two RNA‐seq datasets with 20 samples to reconstruct the coexpression network, which may not cover the entire temporal differentially expressed genes. Besides, the reconstructed metabolic model is not robust to the changing flux through a single reaction. Some of the links between reactions or nodes  might be missing. The future work should focus on the filling gaps in metabolic pathways.In this study, we reconstructed a consensus metabolic model in four yeast species based on RNA‐Seq datasets. The metabolic model can be applied to metabolic engineering and benefit communities studying genome‐scale metabolic networks of other organisms.YZ, YW carried out the RNA‐seq data analysis, network simulations, and drafted the manuscript. LZ performed all the statistical analysis, and helped draft the paper. JH conceived of the study, and helped to draft the manuscript. All authors read and approved the final manuscript.Fig. S1. The phastCons tree model for four yeast species.Fig. S2. The Gene Ontology molecular functions enrichment of transcripts Saccharomyces cerevisiae not included in the consensus dataset.Fig. S3. The compartmentalization of the consensus metabolic model.Fig. S4. Network simulation of phenotypic characteristics.Table S1. Yeast‐specific reactions in consensus metabolic model.Click here for additional data file.Text S1. The consensus metabolic model for four yeast species in Systems Biology Markup Language.Click here for additional data file.


E. coli data and time-dependent S. oneidensis fluxes inferred from gene expression, we apply our inverse approach to flux measurements in long-term evolved E. coli strains, revealing objective functions that provide insight into metabolic adaptation trajectories.Genome-scale flux balance models of metabolism provide testable predictions of all metabolic rates in an organism, by assuming that the cell is optimizing a metabolic goal known as the objective function. We introduce an efficient inverse flux balance analysis (invFBA) approach, based on linear programming duality, to characterize the space of possible objective functions compatible with measured fluxes. After testing our algorithm on simulated The online version of this article (doi:10.1186/s13059-016-0968-2) contains supplementary material, which is available to authorized users. Metabolism, the chemical network that transforms nutrients supplied by the environment into energy and molecular building blocks, is one of the few cellular subsystems for which systems biology approaches can provide quantitative, testable predictions at a genomic scale. Flux balance analysis (FBA), in particular, makes it possible to simulate reaction fluxes through a stoichiometric constraint-based model of metabolism  show promising results, but also a range of serious limitations, mainly stemming from the non-convexity of the proposed formulations, which lead to computationally expensive solution approaches that fail to guarantee global optimality , 9. An a13C-labeled substrates. Our invFBA formulation, based on linear optimization, guarantees global optimality and can be solved in polynomial time, unlike ,,13C-labec, whose elements represent the extent to which individual fluxes tend to be maximized or minimized in the resource allocation problem that the cell tries to solve. Mathematically, the linear combination of fluxes being maximized or minimized is expressed in the form ∑j = 1ncjxj, where n is the total number of reactions in the model. The problem addressed by invFBA is to infer, from measurements of the fluxes through a cell’s metabolism under a given condition, the vector c that best represents its objective. Most FBA calculations include only one non-zero element in c, corresponding to the biomass production flux. In our invFBA approach, we want to assume that more complex c vectors may better capture the objective function implied by experimentally measured fluxes. The intuition behind invFBA is also described through a simple toy model in Fig. The objective function in FBA Fig.  is encodin silico fluxes simulated by FBA with a known objective. Using the iJO1366 metabolic model for E. coli  in Additional file Part of the optimal solution of the problem in Eq. An important observation is that both problems in Eqs. https://dx.doi.org/10.6084/m9.figshare.3181504.v1). The directory contains subdirectories for specific figures and general algorithms (including the InvFBA function). The scripts are in Matlab (.m) and use datafiles in Matlab binary format (.mat). Paths pointing to the optimization software  need to be updated by the user.All data and scripts used to generate the figures presented in this work are available under an MIT open access license in a zipped directory at Figshare (No ethical approval was required for this study.


Escherichia coli when grown on glucose and show that only one LTCS shows the required phenotypical properties. Using our method, we find that in our E. coli model < 10% of all EFMs are thermodynamically relevant.Elementary flux modes (EFMs) are non‐decomposable steady‐state fluxes through metabolic networks. Every possible flux through a network can be described as a superposition of EFMs. The definition of EFMs is based on the stoichiometry of the network, and it has been shown previously that not all EFMs are thermodynamically feasible. These infeasible EFMs cannot contribute to a biologically meaningful flux distribution. In this work, we show that a set of thermodynamically feasible EFMs need not be thermodynamically consistent. We use first principles of thermodynamics to define the feasibility of a flux distribution and present a method to compute the largest thermodynamically consistent sets (LTCSs) of EFMs. An LTCS contains the maximum number of EFMs that can be combined to form a thermodynamically feasible flux distribution. As a case study we analyze all LTCSs found in  ATPadenosine triphosphateEFMelementary flux modeEFMAEFM analysisLTCSlargest thermodynamically consistent setMILPmixed integer linear programtEFMAthermodynamic EFMATFthermodynamically feasiblewithout cancelations [S. Müller and G. Regensburger, unpublished results;Elementary flux mode analysis (EFMA) is a key concept in constraint‐based modeling, which allows a metabolic network to be decomposed into irreducible functional building blocks, called elementary flux modes (EFMs). An EFM corresponds to a minimal set of reactions that can operate at steady state, thereby using all irreversible reactions in the appropriate direction From a systems‐biology point of view, the advantage of an unbiased decomposition of a metabolic network into EFMs lies in the ability to fully characterize the metabolic capabilities of an organism. This can be used, for instance, to analyze cellular robustness Phaeodactylum tricornutum with 318 reactions et al. et al. However, a complete EFMA is currently limited to medium‐scale metabolic models since the number of EFMs explodes with the size of the metabolic network Here, we expand on our earlier work on the thermodynamics of EFMs Escherichia coliS∈Rm×r with m = 76 internal metabolites and r = 101 reactions of which 48 are reversible. The network contains ntot = 169 916 EFMs of which n = 32 374 EFMs are TF. Reactions and intracellular metabolites are thermodynamically characterized by their Gibbs free energy of reaction ΔrG and their standard transformed Gibbs energy of formation ΔfG′0, respectively. The latter is estimated using a pH of 7 and an ionic strength I = 0.15 m at a temperature T = 310.15 K (37°C), according to Alberty We consider a metabolic core model of et al. ei is TF if and only if all reactions j which support ei proceed in the direction of negative Gibbs free energy rGj < 0 for all reactions j with eji>0. Based on this fundamental property, tEFMA avoids the calculation of thermodynamically infeasible EFMs, which drastically reduces the computational burden of an EFMA and makes the analysis of large scale metabolic networks feasible without losing any biologically relevant information Thermodynamic constraints are often utilized to augment classical constraint‐based approaches n TF EFMs of a network. However, not every set of TF EFMs is necessarily thermodynamically consistent. For example, two EFMs that utilize the same reversible reaction in different directions cannot be active simultaneously. This is illustrated in the simple example network in Fig. rG cannot be smaller than zero for both directions of the reversible reaction R3. In other words, thermodynamics implies the no‐cancelation rule mentioned in the introduction. In this example, the sets {EFM1, EFM2, EFM4} and {EFM1, EFM3, EFM4} are the LTCSs, and its elements can contribute to a TF steady‐state flux.tEFMA computes all vT =  = . Obviously, the flux can be decomposed as v = EFM2 + 2 × EFM3  belowWe first determine an LTCS ℒ1 of maximal cardinality is an optimal solution to the MILPAn LTCS ℒ1 to denote its association with the LTCS ℒ1. Briefly, λ1 indicates the presence (λi1=1) or absence (λi1=0) of EFM ei in the LTCS ℒ1, and we maximize ∑i=1nλi1, that is, the cardinality of ℒ1, by varying the contributing EFMs and the (logarithms of the) metabolite concentrations ck, as stated in Eqn We use the superscript in λij indicates if EFM ei is supported by reaction j, and ρj counts the number of EFMs supported by reaction j, as stated in Eqns aint Eqn . Equivalj, given the (logarithms of the) metabolite concentrations. Thereby, Skj denotes the elements of the stoichiometry matrix. The inequalities  can be found by successively excluding already existing solutions λj with j ∈ {1,…,l−1} from the MILP Alternative optima and suboptimal solutions λThe process terminates when the MILP becomes infeasible, and no further solutions are found.E. coli grown on minimal medium with glucose as the sole carbon source. Subsequently, we narrowed down the number of LTCSs to one by successively considering additional yield, expression and flux data.In the following, we computed all LTCSs for E. coli grown on minimal medium with glucose as the sole carbon source. The largest LTCS contains 15 560 EFMs. This corresponds to only 9% of all EFMs or 47% of the TF EFMs  appeared to be more stable than the average number of EFMs per LTCS (4316 ± 86%).E. coli, under the conditions specified in the model. To characterize these capabilities, we used maximum yield parameters Yxi/glc. Yxi/glc was defined as the maximum of the yields of all EFMs in an LTCS for a specific product xi. To identify the biologically relevant LTCSs, we used typical growth parameters obtained by Andersen and Meyenburg An LTCS represents the metabolic capabilities of Figure u counts the number of EFMs that have a certain minimal yield of metabolite u, cf. Eqn iu indicates if EFM i has the required yield for metabolite u, cf. Eqn Here σ8,ℒ12,ℒ15,ℒ16,ℒ21 and ℒ38, had an active fumarate reductase (FrdABCD), but had an inactive succinate dehydrogenase (SdhCDAB) in all their EFMs. This is in contrast to experimental findings since, under aerobic conditions, sdhCDAB is optimally expressed 1,ℒ3,ℒ5,ℒ6,ℒ7 and ℒ18, were found to be consistent with the data.We further analyzed the remaining 12 LTCSs, using expression data. Six LTCSs, ℒ3 and ℒ18 due to their lack of overlap with the other LTCSs (see the next section for a mechanistic characterization of these sets). In contrast to ℒ3 and ℒ18, the four remaining LTCSs share some core functionality, represented by a large fraction of common EFMs (segment A). We investigated if these EFMs were characterized by their supports and observed that on average shared EFMs  were shorter than EFMs unique to an LTCS .All EFMs in the segments D, E and J  could be distinguished by the directions of reversible reactions. In particular, we analyzed the flux across transketolase  and found that all EFMs in the segments A and B carried no flux, whereas all EFMs in the segments C, F, I, K and L had a reverse flux and all EFMs in G and H had a forward flux. Under the standard growth conditions investigated here, transketolase is forward active 1 (as in every other LTCS) all reversible reactions have a fixed direction (due to the no‐cancelation rule). The predicted directions were fully consistent with independent 13C flux data In ℒ1 was consistent with all data. ℒ1 contains 15 559 TF EFMs, which represent only 9% of all EFMs. More specifically, 4486 EFMs produce biomass, 2024 produce maintenance energy, and 54 produce both. In fact, ℒ1 is composed of several segments: all EFMs in segment A do not invoke the pentose phosphate pathway and do not produce biomass, but are responsible for the production of maintenance energy; all EFMs in segment B produce biomass without invoking TktA or TktB; all EFMs in segment G do not carry flux across Pgi, but are able to produce biomass and/or maintenance energy. Finally, EFMs in segment H are not characterized by a single common property.To summarize, we found that from 40 LTCSs only ℒE. coli as an example, we outlined a procedure that narrowed down the feasible solution space and eventually identified a single LTCS. The success of such an analysis is dependent on the quality of the measured metabolome. However, the general concept of LTCSs is not affected by the metabolome's quality. In fact, we can find LTCSs even if the metabolome is unknown. As soon as a network contains at least two EFMs that are supported by a reversible reaction carrying fluxes in opposite directions, different LTCSs exist. Moreover, the cardinalities of these LTCSs are always smaller than the total number of EFMs in a system . Thus even in the absence of a measured metabolome it is useful to look at LTCSs, as only then is a thermodynamically consistent understanding guaranteed. Although an LTCS is less complex than the complete set of EFMs, one now has to analyze multiple LTCSs. In general the number of LTCSs scales combinatorially with the number of reversible reactions in a network. Practically, that is why an accurately measured metabolome is essential.Using Every intercellular flux distribution is TF and can be decomposed into TF EFMs. However, the reverse is not necessarily true. That is, the conformal superposition of any two TF EFMs is itself not necessarily TF.Here we developed a method that identifies the largest sets of TF EFMs that are thermodynamically consistent (LTCSs). Within an LTCS every nonnegative linear combination of its elements results in a TF flux distribution. A necessary condition for an LTCS is that all reactions supporting the EFMs of an LTCS operate in the same direction. This is known as the no‐cancelation rule Geometrically, an LTCS spans a TF subcone of the flux cone see Fig. . In factWe found that shorter TF EFMs are more likely to be elements in multiple LTCSs than longer TF EFMs. More specifically, we found that segment A in Fig. Every metabolic phenotype can be described by an LTCS. Conversely, if an EFM is not part of an LTCS, it is biologically irrelevant, since it does not contribute to a thermodynamically consistent decomposition of a TF flux distribution. In general, decompositions into EFMs are not unique, and several methods have been proposed 1, ℒ2, ℒ31, and ℒ36), and a comparison with growth parameters would have identified ℒ1, the same LTCS as before. However, for less studied organisms detailed data may not be available. In this case, an analysis of phenotypical properties like in Tables We outlined a systematic procedure to identify biologically relevant LTCSs. Based on the integration of additional (omics) data, we successively narrowed down the number of LTCSs. In fact, most LTCSs were found to be inconsistent with commonly available growth parameters. Further consideration of expression and flux data eventually identified a single LTCS that characterizes the phenotype. The additional information could have been used to adapt the network first. Doing so would have reduced the number of LTCSs from 40 to four (ℒOur method is able to compute LTCSs if all TF EFMs are known, and we showed that the set of TF EFMs characterizing a phenotype is smaller than the set of all TF EFMs. However, currently our method does not allow computation of LTCSs directly. It would be desirable to enumerate only the biologically relevant EFMs, which would facilitate an unbiased analysis of metabolic systems even on a genome‐scale level. Recent progress enabled the selective calculation of subsets of EFMs efmaE. colickmin=10−7m and ckmax=1m. ΔfG0 values were obtained from the online version of equilibratorfG values were available. Reactions to which those metabolites contributed were not checked for thermodynamic feasibility to avoid false conclusions We used the software package tilog cplex Optimization Studio, version 12.5. A Perl‐script that sets up the systems equations and invokes the cplex lp solver, and the metabolic model and all data used in this study are available at https://github.com/mpgerstl/ltcsCalculator. Note that cplex is a commercial software product although free academic licenses are available.The set of Eqns J.Z. conceived the study; all authors contributed to the development of the theory; J.Z. and M.P.G. designed the study; M.P.G. developed the software and performed the analyses; all authors wrote, read and approved the final manuscript.


New antimycotic drugs are challenging to find, as potential target proteins may have close human orthologs. We here focus on identifying metabolic targets that are critical for fungal growth and have minimal similarity to targets among human proteins. We compare and combine here: (I) direct metabolic network modeling using elementary mode analysis and flux estimates approximations using expression data, (II) targeting metabolic genes by transcriptome analysis of condition-specific highly expressed enzymes, and (III) analysis of enzyme structure, enzyme interconnectedness (“hubs”), and identification of pathogen-specific enzymes using orthology relations. We have identified 64 targets including metabolic enzymes involved in vitamin synthesis, lipid, and amino acid biosynthesis including 18 targets validated from the literature, two validated and five currently examined in own genetic experiments, and 38 further promising novel target proteins which are non-orthologous to human proteins, involved in metabolism and are highly ranked drug targets from these pipelines. Aspergillus fumigatus is challenging  metabolic modeling  vitamin synthesis, (b) lipid biosynthesis, and (c) amino acids biosynthesis, we developed a pipeline that integrates and compares results from all three bioinformatics approaches (I-III) to reduce and focus the target list to the most promising candidate genes.Each of these approaches has its strengths and limitations, however, their combination offers a powerful tool to reveal metabolic targets for later drug development. Based on the resulting candidates we suggest a prioritized list of target genes that are important for A. fumigatus but can also be easily transferred to other pathogens which are similar challenging to target.These candidate proteins for targeting fungal metabolism by antimycotics were in part validated according to literature evidence, several are currently tested and evaluated experimentally while others are still available for targeting. Additional information can be incorporated for further refinement and iterations of our combined target screening pipeline. Our workflow is not restricted to Figure A. fumigatus enzymes involved in the different pathways.: For this we used biochemical databanks such as KEGG , nucleotide biosynthesis, amino acid biosynthesis and degradation, and fermentation pathways.As a first step we apply a process of pathway reconstruction that identifies the Furthermore, cofactors and cell wall synthesis were also taken into account. Moreover, we created sub-networks for vitamins and fatty acid metabolism. For these additional components we looked only at selective reactions and pathways, which we considered particularly promising for targeting and being absent in humans. Accordingly, we selected basic fatty acid metabolism, ergosterol, and glucan metabolism, as well as vitamin metabolism with focus on riboflavin and thiamine.A method to identify metabolic pathways that might be crucial for growth is the elementary mode analysis. A flux mode is a set of enzymes, which balance all metabolites within a metabolic network such that these “internal metabolites” do not accumulate or are diminished . Those flux modes (combinations of enzymes) which cannot be decomposed further without affecting this balance are called elementary modes. We computed these elementary modes using the Metatool program  or as they carry a strong metabolic flux, either constantly (housekeeping enzymes) or in the relevant situation of invasion and infection.GSE19430); Schrettl et al. (GSE22052); Willger et al. (GSE12376). These data sets were available from Gene Expression Omnibus .A. fumigatus genes involved in virulence. Such genes have to be induced by appropriate conditions, we found the following datasets: changes during invasion initiation -values as well as A. fumigatus metabolic enzymes; later enriched subsets) to receive the relative expression of those target genes in comparison to control conditions.In the next step, the resulting list of differential expressed genes was matched onto the list of potential targets .A. fumigatus growth under this condition, thus indicating potential antimycotic targets. Additionally we compared those up-regulated target genes with the metabolic simulation data to specify the quality of each suggested target.Furthermore, we analyzed the resulting expression list of target genes with respect to increased transcript level since up-regulated genes (URGs) are considered important genes for in silico screening  using the DDI containing databases DOMINE  is in a network. It counts the number of shortest paths from all vertices to all others that pass through that node. The degree rank just counts how well connected a protein target is by counting all edges leading to one of the vertex (so how many interactions converge on this protein). Further details are found in Thadakamalla et al. .The newly ranked protein were further compared in their sequence against the human proteome and the proteins showing significant similarity with human were discarded from the potential drug target list. The KEGG   structure template.Furthermore, the A. fumigatus, first all metabolic reactions were mapped using the orthology information from the already available metabolic models of Aspergillus oryzae, Aspergillus niger, and Aspergillus nidulans  as a key simplification, and to avoid combinatorial explosion during elementary mode calculation, we selected very few enzymes for any linear stretch while considering the metabolites which are similar; (v) the pace-maker  enzymes for long linear pathways were generally included; (vi) finally, pathway annotation was done for this list and only the reactions which participate in primary metabolic pathway were further considered to find the drug targets in primary metabolism. Moreover, we calculated the RhumPDB score  genes that were highly expressed at many independent time points were given top priority  over the genes highly expressed at fewer time points. A top expression rank represents a higher expression of a gene at all time points during invasive infection (ii) the final priority order was decided based on the minimum of RhumPDB , central enzyme nodes , unique pathways and reactions, which are similar as “choke points”  as predicted just according to the gene expression data  then their calculated flux; see Supplementary Files Recent studies have shown that the fungus a et al.  for compa et al.  and the a et al. . That coAccording to the metabolic modeling we performed, pathways differentially regulated correlating with the biofilm gene expression datasets include: glycolysis (down-regulated) and gluconeogenesis ; down-regulatedlipid, fatty acid, and isoprenoid metabolism up-regulated, in particular ergosterol and cell wall synthesis, pentose phosphate cycle, nucleotide metabolism , amino acid metabolism up-regulated and vitamin and cofactor metabolism down-regulated, several degradation pathways upregulated Table . Such stWe next show the flow chart for the enzyme regulation-based strategy Figure . First, p < 0.05, multiple testing condition) up- (red) or down-regulated (green) under these condition  and only strongly regulated genes (logFC > 1) and ranking all genes and potential targets accordingly.The following top enzyme targets were predicted from this approach, zooming in on lipid metabolism and amino acid metabolism and considering only significantly differentially expressed genes  are down-regulated in vivo, while they are up-regulated under hypoxia adaptation. Furthermore, in vitamin metabolism, thiamin biosynthesis proteins stand out, showing a negative regulation under in vivo condition . Finally, several cell wall carbohydrate metabolism genes stand out as strongly regulated and induced both for invasion and under hypoxia, such as glutathione S-transferase and the vacuolar transporter chaperone (Vtc4).Fatty acid synthases are down-regulated In summary, in this pipeline we show only targets according to one simple but clear criterion: High expression under infection-associated conditions as detailed above. However, other criteria help to identify alternative targets. As detailed in methods, we are currently screening for new targets with constant and high expression under several conditions, representing so-called housekeeping genes. As this involves analysis of much more transcriptome data sets, a definite list of metabolic target enzymes will be generated during future efforts.As a third line of research we considered an interactome-based approach. Figure A. fumigatus after considering the domain-domain interaction database (DDI) and localization filtering consists of 1903 nodes and 4743 PPIs and its interactome relation is given in Supplementary Table The final interactome of After consideration of the added Ranking scores from Degree Rank and Betweenness Rank and sorting of the resulting list we re-ranked the genes regarding their position. The five best hits include (1) 1,3-beta-glucosyltranferase Gel2 (AFUA_6G11390), (2) phosphate transporter , (3) DUF6 domain protein (AFUA_1G09310), (4) pyruvate decarboxylase PdcA (AFUA_3G11070) as well as (5) high osmolarity signaling protein Sho1 (AFUA_5G08420).In the subsequent analysis we determined a further ranking based on RhumPDB data and expression by calculation of the RhumPDB Score Table . The comHence, a total of 65 proteins were predicted to be important based on orthology with DEG-derived proteins.A. fumigatus homolog. For the A. fumigatus genes we hence used DEG only to identify functionally conserved and probably important metabolic genes. Two preliminary targets identified in this way include the 50S ribosomal protein (AFUA_4G10480) and a cytochrome c oxidase family protein (AFUA_3G14440) that participates in oxidative phosphorylation.Genes in the DEG database were included if they had scored to be essential for one organism under a specific condition. In general, essentiality depends very much on the environmental condition tested. Instead, the sequence similarity to the DEG entry can be determined by objective criteria. It is thus hard to predict essentiality of the A. fumigatus proteins were identified and subsequently parsed and prioritized regarding contained top targets . The gene expression of predicted potential targets in the infection condition , participates in biofilm formation, which is represented by data from Muszkieta et al. . PdcA isThe RhumPDB rank of this gene is 55, however, the protein is downregulated during invasive aspergillosis conditions and upregulated under iron limiting conditions, henceforth it might be possibly represent a valid target. AFUA_3G04210 (FasA Fatty acid synthase A) and AFUA_3G04220 (FasB Fatty acid synthase beta subunit) with RhumPDB rank of 1 and 4, respectively, significant expression changes, up-regulation in iron limiting condition and downregulation during invasion might be further promising targets. AFUA_3G14440 (cytochrome c oxidase family protein) from DEG can be examined as supported by expression changes under both tested conditions. These proteins would be the most interesting ones from this refined interaction-based pipeline to identify targets in the pathogen metabolism network , or using combined degree rank and betweenness rank (top five targets given) as well as functional important, non-orthologous genes in the interactome (top two targets included).A. fumigatus differs in these pathways significantly from the host, which is of course a simplified search for metabolic targets. However, for a direct comparison of the three pipelines (and sub-pipelines) this focus is valid as it allows to combine and compare results from all three approaches pertaining to the same pathways  vitamin synthesis, (b) lipid synthesis, and (c) biosynthesis of amino acids. This focus was chosen as ys Table . The topys Table . All of Furthermore, we selected the top five of the resulting genes from network analysis strategy. Two of them are also known to participate in metabolic pathways. This methods accuracy is highly depending on the network structure to calculate valid targets but nevertheless could give two new metabolic targets Table .The remaining method of the pipeline is relevant for the assessment of essential genes with no human orthologs. The two best hits can be easily assigned to a metabolic pathway , we used a stringent cutoff of a p-value of 0.05 and a logarithmic fold change of >1.0 or respective < −1.0  are shown in the list. We also included two essential genes, AFUA_3G14440 and AFUA_4G10480. Additionally we considered enzymes which have metabolic pathway neighborhood to already known  promising antimycotic targets, as targeting further members of such a known pathway promising to be targeted by an antimycotic may yield further attractive targets . The results of the metabolic model simulations are shown in an additional column, listing the pathway annotations of the proteins (as far as known) as well as their predicted activation . We show only the targets with a top rank which were still (after filtering as above) considered by our analysis to be worth testing experimentally. This list of 64 targets is thus not further ranked as in the interactome pipeline (ranking see above) but rather the top targets from all approaches are considered equally.Table in vivo growth and can be considered as promising potential drug targets , a protein participating in inorganic phosphate acquisition. In fact, Pho88 was already studied in A. nidulans as well as in A. fumigatus   morphology, so its absence results in altered LD size  with a typical virulence-factor like expression during infection. Most components of the pathway, except this protein, are shared in all organisms; yet, this gene itself is an essential gene target and might be explored further.In contrast, the vacuolar transporter chaperone  is a vacuolar membrane polyphosphate polymerase; from A. nidulans was studied by Tao et al.  is a major component of pulmonary surfactant, and may provide an alternative source of phospholipids.Furthermore, some members of the phospholipid biosynthesis like cho1 (AFUA_4G13680), cho2 (AFUA_2G15970), and choC (AFUA_1G09050)  should inhibit A. fumigatus growth.Finally, for this phospholipid pathway a promising, not yet explored strategy would be to target the connected enzyme flippase. Phosphatidylserine(s) are actively held facing the cytosolic (inner) side of the cell membrane by the enzyme. Specific blocking of flippase  the metabolic approach can be pushed much further to identify new pathways  was discarded as a potential drug target, only central metabolism was targeted and so on. Such an approach is good for delivering certified, strong targets and can be used to validate the different pipelines by knowledge . However, as the results confirm, this yields also several targets that have already been identified or are currently tested.A. fumigatus infection.Hence, this has to be extended in future by more subtle approaches. A first measure will be to loosen the strict requirement of absent orthology to human proteins, allowing distant homologs. Furthermore, primary metabolism is defined by its connection and requirement for cellular growth (reason to pick it for antimycotic design), however, it needs not to be central in the metabolic web. In particular further areas connected to cell wall metabolism, virulence or, for instance, iron utilization can and will be scrutinized further. Finally, the metabolic calculations in particular, but also interaction screens and transcriptomics allow more refined screening methods: this includes synthetic lethality , and exerting the full power of the transcriptomic approach by looking at ten or more conditions to identify all metabolic genes that are at least expressed under some specific condition. Furthermore, there can be better targeting of auxotrophic mutants, for instance by knowledge-based approaches and creating toxic metabolic intermediates which stop fungal growth in the fungus without harming the human patient. We believe that these more sophisticated approaches will allow an even better view on new antifungal strategies against A. fumigatus in this respect. They validate potential targets from metabolism according to their importance in flux control and metabolic pathways, as key regulated enzymes under different challenging conditions or as central metabolic hubs with known protein structure, different from man, and, if possible, with some drug to target it. Together, these produced important targets, as validated by previous publications and currently ongoing experimental tests for about half of these. The others are made public here to allow further research and investigations. However, we followed a conservative approach demanding no homology to human proteins and avoiding more complex considerations such as targeting the same pathway twice or producing toxic intermediates. Future, more detailed analyses will follow up also these more sophisticated options. Additionally, the software and criteria applied can (and will) next be applied to other parts of the metabolic map in A. fumigatus and can also handle any other organism of interest if protein sequences are sufficiently comprehensively known.Metabolism is interesting to target by novel antimycotic substances. Three different pipelines are made available here to investigate A. fumigatus expertise and experimental expertise on all protein targets suggested. TD analyzed data, lead and guided the study. MK and TD drafted and finalized the manuscript, all authors contributed expert advice, gave own comments, and agreed to the final submitted version of the manuscript.MK analyzed and calculated transcriptome and enzyme regulation data. MS and SG analyzed and calculated interactome-based data. CL calculated and analyzed metabolic fluxes and elementary modes. HH, NO, and SK and their PhD students AD, ZM, and JB, respectively, provided This study was supported by the German Federal Ministry of Education and Research (FKZ 031A408B to TD and 031A408A to SK), the Austrian Science Fund (FWF grant I1616 to HH), and the Israel Ministry of Health (MOH 3-0000-11080 to NO) by funding the AspMetNet consortium during the first call of the Infect-ERA research co-ordination action.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.