The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD To quantitatively analyze available in vivo experimental data and predict nonmeasurable dynamic responses, we developed a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics. The model is developed here from our previous model of cellular metabolism and energetics in skeletal muscle Skeletal muscle plays a major role in the regulation of whole-body substrates and energy metabolism, especially under changing physiological conditions such as ischemia (reduced blood flow), hypoxia (reduced oxygen supply), and exercise (increased energy demand). Current experimental techniques provide relatively little in vivo experimental data—with an objective of achieving a quantitative understanding of the system to physiological perturbations—is a challenging task. Such a modeling approach requires information about the general structural features and catalytic mechanisms of the associated transporters and enzymes, subcellular metabolic pathways and fluxes and their control mechanisms, and tissue/organ specific metabolic characteristics. Such a modeling approach also requires mechanistic models for key functional components of the system  to be first individually developed and validated and then integrated to emulate the systems behavior at the molecular, subcellular, cellular, and tissue/organ levels. To avoid this complex approach and facilitate analysis of available sparse in vivo experimental data to understand dynamic responses of the system to physiological stresses, approximations are often made to obtain a simplified model of the system that includes key functional components regulating cellular metabolic processes at the desired level of complexity.Developing a mechanistic computational model of substrates and energy metabolism in complex, multi-scale metabolic systems, such as skeletal muscle, using a detailed, bottom-up systems approach with sparse in vivo metabolic systems that incorporate primary substrates and key intermediate metabolites with coupled metabolic energy controllers ATP-ADP and NADH-NAD+in vivo experimental data. To estimate these unknown parameters, constraint-based, robust nonlinear optimization methods are needed, as established in our previous work A top-down systems approach is an alternative approach which has been previously applied to determine and integrate a representative set of lumped biochemical reactions in vivo experimental data and predict dynamic metabolic responses to physiological stimuli in subcellular compartments, such as mitochondria. Previous models have incorporated some aspects of glycolysis, TCA cycle, oxidative phosphorylation, and fatty acid β-oxidation in vivo at whole-organ level. While our recently developed models of skeletal muscle cellular metabolism and energetics + that modulate several key metabolic reactions in the cytosol and mitochondria have different concentrations in these two subcellular domains To date, no physiologically-based, whole-organ level model of skeletal muscle cellular metabolism and energetics has been developed that can be applied to analyze available 2 and CO2 transport in the blood and cells. The inter-domain species transport processes are considered either by passive diffusion or by carrier-mediated (facilitated) transport. The metabolic reaction fluxes in the cytosolic and mitochondrial domains are represented by a general phenomenological Michaelis-Menten equation involving the compartmentalized ATP/ADP and NADH/NAD+ energy controller ratios. The phenomenological kinetic parameters of the model are estimated by using our recently developed constraint-based, robust nonlinear optimization approach in vivo dynamic data on glycolytic and energetic metabolite concentrations from experiments in humans with muscle ischemia previously published In this paper, a physiologically-based, whole-organ level model of skeletal muscle cellular metabolism and energetics is developed and applied to study dynamic cellular metabolic responses to reduced blood flow and oxygen supply to mitochondria (muscle ischemia). The model, which is extended from our previous model + whose ratios are known to modulate (fine tune) the reaction fluxes G) is high and negative in favor of product formation in vivo metabolic systems (nonequilibrium open systems), the reversible reactions like lactate dehydrogenase (LDH), creatine kinase (CK), and adenylate kinase (AK) were decomposed into two separate irreversible reactions with distinct kinetics The first step in our development of a multi-scale, top-down computational model of cellular metabolism and energetics in skeletal muscle was to identify the key intermediate metabolites and regulatory enzymes in the cellular metabolic pathways of skeletal muscle. We then integrated available information on cellular metabolic pathways and fluxes, cellular metabolic control mechanisms, catalytic enzyme kinetic mechanisms, subcellular compartmentation and metabolites volumes of distributions, inter-domain transport mechanisms, and skeletal muscle tissue-specific metabolic characteristics. A simplified map of the compartmentalized cellular metabolic pathways in skeletal muscle is shown in mit,jC(t) = j.Ccyt,jσ(t), where jσ is the equilibrium concentration ratio (or partition coefficient) of species j between mitochondria and cytosol. In the present model, a total of 10 chemical species  are considered to exist in both the cytosolic and mitochondrial compartments with negligible transport flux between the compartments.The dynamic mass balance equations are based on a multi-domain model structure for skeletal muscle consisting of a spatially-lumped capillary blood domain which exchanges nutrients and metabolic waste products with a spatially-lumped domain of tissue cells . Althougj in the spatially-lumped blood domain has the following general form:art,jC is the arterial species concentration; bl,jC is the capillary blood species concentration ; bl,jV and isf,jV are the volumes of distribution of species j in blood and ISF, and Q is the regional blood flow; bl↔cyt,jJ is the net transport flux (mass per unit time) across the blood-cytosol exchange barrier .The dynamic mass balance of a chemical species The dynamic mass balance of the chemical species j in the spatially-lumped tissue cells domain (cytosol and/or mitochondria) has the following general forms:x,jC is the species concentration in domain x (cytosol/mitochondria); x,jV is the volume of distribution of species j in domain x; x,jP and x,jU are the production and utilization of species j in domain x; x,pφ and x,uφ are the reaction fluxes of the reactions processes that produce and utilize species j in domain x; x,j,pβ and x,j,uβ are the corresponding stoichiometric coefficients. For chemical species which are in the tissue cells (cytosol and/or mitochondria) but not in the capillary blood, the transport flux bl↔cyt,jJ is zero.Here 2 and CO2 in these domains are developed by considering their distinct transport and binding mechanisms 2 and CO2, are provided in The dynamic mass balance equations for all the chemical species in blood, cytosol and mitochondrial domains can be rewritten from our previous model of skeletal muscle metabolism bl↔cyt,jJ (mass per unit time) of the species j across the blood-cytosol exchange barrier is related to the concentrations bl,jC and cyt,jC bybl↔cyt,jλ is the effective permeability surface area product for diffusive mass transport across the barrier (for passive transport); bl↔cyt,jT is the maximal transport flux across the barrier (Tmax) and bl↔cyt,jM is the corresponding Michaelis-Menten (M-M) constant (mM) (for facilitated transport). The flux expressions (3) satisfy the thermodynamic equilibrium conditions across the barrier.The reversible transport flux 2, and O2  is considered to be passive. For the 10 species that exist in both cytosol and mitochondria, the inter-domain transport flux cyt↔mit,jJ is zero.The species involved in the blood-cytosol exchange are glucose, lactate, pyruvate, alanine, glycerol, free fatty acid, CO, and O2 . The tra1 and P2 are ATP and ADP or vice-versa (PS±:1 and R2 are NADH and NAD+ and vice-versa (RS±: redox state). The corresponding coupled phosphorylation and redox reactions are ATP→ADP (PS+) and/or NADH→NAD+ (RS+) or vice-versa (PS- and RS-). Assuming a phenomenological, single-step enzyme kinetic mechanism Vmax and mK are the phenomenological maximal/limiting velocity and M-M parameter of the reaction; P1/CP2 is the phosphorylation ratio: CATP/CADP (PS+) or CADP/CATP (PS-), and CR1/CR2 is the redox ratio: CNADH/CNAD+ (RS+) or CNAD+/CNADH (RS-). So the reaction fluxes are explicitly regulated by the coupled energy controller ratios CP1/CP2 and/or CR1/CR2 (if coupled).The lumped metabolic reactions of skeletal muscle cellular metabolism and energetics can be considered as special cases of a general, irreversible, multi-reactant multi-product enzymatic reaction coupled with the metabolic energy controller pairs: +. The details are provided in The flux expressions for all the lumped metabolic reactions in the subcellular compartments of cytosol and mitochondria can be rewritten from our previous model of skeletal muscle metabolism bl↔cyt,jJ transport fluxes characterized by 4 λ, 4 Tmax and 4 Mm parameters, and 26 φ reaction fluxes characterized by 26 Vmax, 27 Km . Therefore, the present model is characterized by a total of 99 unknown parameters that need to be estimated to fit the model outputs to the available in vivo experimental data. For convenience, the transport and reaction fluxes are written here in vector form: λ, 4 Tmax and 4 Mm) can be estimated here uniquely from the resting, steady-state transport flux-concentration relationships (σ) can be estimated uniquely from the resting, steady-state species concentration ratios between the mitochondria and cytosol   in the tissue cells domain (cytosol and mitochondria) is 30, which participate in 26 metabolic reactions. The number of chemical species that exist in both blood and cells is 8, and that in both cytosol and mitochondria is 10. Accordingly, the model includes 8 ionships  [1]. The/Ccyt,j) .https://computation.llnl.gov/casc/odepack/odepack_home.html; http://www.netlib.org/odepack; −10 guarantees high accuracy and convergence of the iterative solutions of the ODEs. The DLSODES solver is usually very fast; a typical simulation of this problem using the DLSODES solver in a standard desktop computer (Intel Xeon or Core 2 Duo CPU 5160 @ 3 GHz) takes only about 5 seconds of the CPU time. As a check, the numerical solutions of the initial value problem were also obtained using the ODE15S solver in MATLAB (http://www.mathworks.com) with the similar tolerance levels. These solutions were of comparable accuracy with that obtained using the DLSODES solver.With specified parameter values, the mathematical model is solved numerically to simulate dynamic responses of the system to ischemia produced by reducing muscle blood flow. Typically, the initial conditions: ionships  and 2. Tin vivo experimental data of Katz Q = 0.9 L/min at rest (t<0 min) to Q = Qisch (unknown) at the onset of ischemia (0≤t≤30 min), and then increased to the starting level at the onset of recovery (t>30 min). The active muscle volume (Vmus) and ischemic muscle blood flow (Qisch) responsible for the predicted metabolic dynamics in skeletal muscle during ischemia and recovery were not known from the experimental study of Katz Vmus and Qisch are also included as the unknown parameters for estimation, making the total number of unknown parameters in the model to 101. This is an increase of 10 unknown parameters (10 σ) from our previous model The large number of unknown parameters of this model are estimated by comparing model outputs to jσ = mit,jC/cyt,jC)  . In the /Ccyt,j)  and 4.in vivo metabolic systems. The efficiency and robustness of this parameter estimation approach was tested with parameter sensitivity analysis as well as with repeated parameter estimation with various initial parameter estimates . Various estimates of the more sensitive model parameters spanned in a small neighborhood of the optimal parameter estimates (see Ref. Vmus+Qisch) are effectively estimated from the dynamic data.A detailed description of this robust estimation approach for obtaining optimal parameter estimates from species concentration dynamics during muscle ischemia and recovery is presented in Ref. λ,Tmax,mM), partition coefficients (σ), active muscle volume and ischemic muscle blood flow , and reaction parameters Vmus and Qisch corresponding to the experimental data were ∼4.0 L  and ∼0.216 L/min . These optimal parameter values were used for model simulations during the resting, ischemia and recovery periods. The blood flow reduction levels of Qisch = 0.18, 0.27 and 0.36 L/min  were used for simulating severe to moderate to mild ischemic conditions.The optimal estimates of the transport parameters  and cytosolic [LAC]/[PYR] and [PCR]/[CR] ratios are shown in Qisch = 0.216 L/min corresponds to the experimental data of Katz The correspondence of model simulations and experimental data is demonstrated through The model simulations of cellular glucose (GLC), glucose-6-phosphate (G6P), pyruvate (PYR), and lactate (LAC) concentrations at the end of 76% ischemia and reperfusion are in close agreement with the experimental data , Table 5+]) and redox potentials ([NAD+]/[NADH] ratios) were all similar having biphasic behaviors during the ischemia and reperfusion periods  as ischemia progressed, in agreement with the data /([PYR][NADH]) decreased considerably from a resting level of ∼8856 to ∼5585 during 76% ischemia. At different levels of blood flow reductions, the model-predicted changes were not proportional. The changes were negligible below 70% blood flow reduction levels and significant above 76% blood flow reduction levels.Both cellular [LAC] and [PYR] increased by ∼125% during 76% ischemia and almost returned to the resting levels after 30 minutes of reperfusion. However, the dynamic response of [PYR] was different from that of [LAC]. During ischemia, [PYR] first decreased and then increased, but during reperfusion, [PYR] first sharply increased and then rapidly decreased to the resting level. On the other hand, [LAC] slowly  increased during ischemia and slowly  decreased during reperfusion. Blood [LAC] had the similar dynamics as that of cellular [LAC] (not shown). These differential dynamics of cellular [LAC] and [PYR] characterize the dynamics of cellular or cytosolic [LAC]/[PYR] ratio. The dynamics of cytosolic [LAC]/[PYR] ratio and cytosolic and mitochondrial redox states ([NADH] and  decreased slightly during ischemia which resulted in appropriate increases in muscle [ADP] and [AMP] . A 76% bisch = 0.18, 0.216, 0.27 and 0.36 L/min) are shown in in vivo at the whole tissue-organ level. However, the present compartmentalized model is able to simulate the dynamic responses of these subcellular metabolites to physiological stresses such as muscle ischemia. Model simulations show that the changes in these metabolites concentrations during muscle ischemia are not simply proportional to the extent of blood flow reduction. The changes are negligible during the mild 60% and moderate 70% blood flow reduction levels, but significant above the severe 76% blood flow reduction level.The model-simulated dynamic responses of mitochondrial FAC, ACoA, CIT, AKG, SCoA, SUC, MAL and OXA during the ischemia and recovery periods with blood flow reduction levels of 80%, 76%, 70% and 60% (Q+]/[NADH]. The accumulation of ACoA is primarily attributed to a biphasic increase in free [CoA] and a sharp 80-fold decrease in [OXA] (+]/[NADH]. The TCA cycle reaction fluxes decreased from a resting level of ∼0.82 to ∼0.62 mmol/min (∼25%) with a 76% blood flow reduction (not shown).The model-simulated dynamic responses of mitochondrial and TCA cycle intermediate metabolites to muscle ischemia differ from each other . During in [OXA]  resultin2, and O2) during the resting steady-state (t<0 min), ischemia (0≤t≤30 min), and recovery (t>30 min) periods with a blood flow reduction level of 76% (Qisch = 0.216 L/min) are shown in 2 and CO2 are shown in jUR = Q) and net blood-tissue cells exchange rates cl,jR = cl,jP−cl,jU) in the tissue cells (cytosol and/or mitochondria). Most of these model predictions are similar to those from our previous model Qisch = 0.216 vs. previous Qisch = 0.135).The model-simulated dynamic responses of transport and reaction rates associated with the blood-tissue cells exchangeable substrates  changes sharply (decreases/increases) at the onset of ischemia/recovery due to a step change (decrease/increase) in muscle blood flow, while the net glucose uptake by muscle tissue cells  remains fairly constant during ischemia and recovery. This results in a fast adjustment (decrease/increase) in the venous glucose concentration and glucose A–V difference and a rapid recovery in muscle net glucose uptake. The net glucose utilization  through the hexokinase reaction decreases/increases quickly during ischemia/recovery due to the increase/decrease of [G6P] and G6P inhibition of hexokinase reaction. This is reflected in the predicted elevated cellular [GLC] during recovery  first decreases when muscle blood flow is reduced and then increases steadily (linearly) slightly above the baseline value during the remaining ischemic period. During recovery, the opposite, but more pronounced, trend occurs. The net lactate production  increased quickly at the onset of ischemia and reached a new steady-state level within the first 10 minutes of ischemia. At the onset of recovery, the net lactate production decreased quickly to the baseline value  decreased quickly at the onset of ischemia and then increased rapidly towards the baseline value during ischemia (biphasic behavior); the opposite trend occurred during the recovery period. The net utilization of FFA  had exactly the opposite behavior of FFAUR and bl↔cyt,FFAJ rates. The dynamics of CO2 release and FFA uptake were similar , except at the onset of ischemia and recovery, where the muscle O2 uptake decreased/increased sharply with the step change (decrease/increase) in muscle blood flow and returned to the new steady state levels as ischemia progressed  in the muscle tissue cells decreased from 25 mmHg to ∼0.5 mmHg , while the corresponding CO2 partial pressure (PCO2) increased from 46 mmHg to ∼52 mmHg during the 76% ischemia period (2 content in the capillary blood (venous blood) decreased from ∼6.6 mM (∼36 mmHg) to ∼0.4 mM (∼8 mmHg) and the total CO2 content in the blood increased from ∼25.5 mM (∼43.6 mmHg) to ∼29.6 mM (∼51 mmHg) (2 consumption was maintained by the reduced O2 supply during ischemia.ogressed . The O2 a period . Accordi51 mmHg) . These mt<0 min), ischemia (0≤t≤30 min) and recovery (t>30 min) periods with a blood flow reduction level of 76% (Qisch = 0.216 L/min) are shown in 2 consumption) in mitochondria and creatine kinase buffer reaction in cytosol.The model-simulated dynamic responses of metabolic fluxes associated with the production and utilization of ACoA and ATP during the resting steady-state . During recovery, the trend was opposite . The pro2 utilization) rapidly decreased (as a step) by about 22% during 76% ischemia (2 delivery to mitochondria by capillary blood flow (+] (2 consumption) reaction was about 5 minutes. Thus, in contrast to our previous model The rate of ATP utilization in cytosol through ATP hydrolysis slowly decreased  by about 20% during 76% ischemia and returned to its baseline level during the recovery period . Howeverischemia  due to aood flow , in spitflow (+]  and phosflow (+]  (the actflow (+]  was mostflow (+] . The ATPin vivo in response to reduced blood flow and oxygen supply to mitochondria (ischemia) is limited by available in vivo experimental data. Relatively few in vivo measurements can be obtained of metabolite concentrations and metabolic fluxes in subcellular compartments, such as mitochondria. As a complementary approach to experimental measurements and as a framework for quantitatively analyzing available in vivo data, a physiologically-based, whole-organ level model of skeletal muscle cellular metabolism and energetics is developed. This model emphasizes a multi-scale, top-down systems approach in vitro experimental studies are applicable to in vivo conditions is uncertain, our multi-scale, top-down modeling approach provides a unified, systematic framework for modeling and analysis of in vivo complex metabolic systems. A major improvement of the present model over our previous model +] ratios  and incorporates metabolic reactions and transport processes of key chemical species, including glucose, lactate, pyruvate, free fatty acid, oxygen and carbon dioxide  in these three domains The governing model equations are based on dynamic mass balances of chemical species in spatially-lumped, capillary blood-interstitial fluid domain and two distinct intracellular cytosolic and mitochondrial domains . These i+ whose ratios  modulate (or fine tune) the reaction fluxes in the subcellular domains G) is large and negative in favor of product formation are considered irreversible in vivo metabolic systems are nonequilibrium open systems and the biochemical reactions usually operate far from true equilibrium under physiological stimuli . Besides, the consideration of the law of microscopic reversibility (thermodynamics) requires a detailed knowledge of proton handling in cytosol and mitochondria +] energy controller ratios. These flux expressions characterize the behavior of saturable enzyme kinetics and in vivo control mechanisms observed experimentally in vivo at the whole-organ level.In this model, the compartmentalized lumped biochemical reactions along the cellular metabolic pathways are the stoichiometrically coupled sequential elementary reactions, which include the compartmentalized metabolic energy controller pairs ATP-ADP and NADH-NADin vivo studies on muscle ischemia λ, 4 Tmax and 4 Mm) and 10 partition coefficients (10 σ), resulting in a reduction of 22 kinetic parameters for estimation from the dynamic experimental data from muscle ischemia.A major challenge of this work was to evaluate a large number of unknown model parameters  with relatively sparse experimental data from φnet.ΔG≤0 Vmus) and ischemic blood flow (Qisch) . Such constraints also reduced uncertainty and enhanced accuracy in the estimated parameter values.The key to success of our parameter estimation approach for obtaining the remaining 79 kinetic parameters (second step) was the incorporation of constraint information to the maximum extent in the GRG2 optimization algorithm Since the available experimental data Vmus≈4 L and ischemic muscle blood flow Qisch≈0.216 L/min (Vmus≈5 L and Qisch≈0.135 L/min), when scaled to one leg with a resting blood flow of 0.45 L/min, the estimated Vmus value becomes ∼2 L which lies well within the experimental range of 1.5–3 L for one leg quadriceps femoris muscle This physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics can simulate dynamic metabolic changes in cellular and subcellular compartments and provide quantitative analysis of the mechanisms of metabolic regulation during physiological stresses . Model simulations based on the estimated optimal parameter values correspond well to the experimental data on muscle ischemia of Katz 16 L/min  indicateThe model simulations of cellular [GLC], [G6P], [LAC], [PYR], and [LAC]/[PYR] with ∼76% ischemia corresponded well with the experimental data . To simuThe model-simulated muscle [PCR], [CR], [PCR]/[CR], [PI], [ATP], [ADP], [ATP]/[ADP], and [AMP] with ∼76% ischemia were in close agreement with the experimental data . One of We tested fitting the model to the data using alternative flux expressions for the CK and AK  reversible reactions satisfying the Haldane relationship and thermodynamic equilibrium conditions. However, we were unable to achieve good fittings for the high-energy metabolites. This may be due to the limitations in the present model, or may be the fact that the data do not support thermodynamic equilibrium of the CK reaction during ischemia/recovery. It is evident from the data of Katz + cotransporter, and exchange of TCA cycle substrates/intermediates +]/[CR] ratio for maintaining the thermodynamic equilibrium of the CK reaction. This information will be the mechanistic basis for the extension of the current model which can be used to analyze the data on high-energy phosphate metabolites.This issue may be resolved by including the dynamics and buffering of cytosolic and mitochondrial pH With the estimated optimal parameter values, the present model is able to correctly simulate the dynamic metabolic responses of compartmentalized cytosolic and mitochondrial phosphorylation and redox potentials , key mit+]  –from the oxygen consumption point of view– is considered to have the same oxygen cost as carbohydrates for ATP production.Our compartmentalized model simulations show that the metabolic changes were negligible with respect to the extent of blood flow reduction up to ∼70%, beyond which a profound derangement in substrate and energy metabolism occurred due to reduced supply of oxygen to mitochondria. The metabolic changes during severe ischemia (∼76% and beyond) include (1) a switch from a net pyruvate uptake and utilization to a net pyruvate production and release  and 7B; +]  accompan+]  and mito+] ; (3) an +]  accompan+] . In genemit,jC = j.Ccyt,jσ, with the partition coefficients jσ constant). This is projected in the model-simulated dynamic responses of cytosolic and mitochondrial phosphorylation and redox potentials   metabolism and cellular respiration during physiological perturbations, such as ischemia, hypoxia, and exercise. Furthermore, the inclusion of FADH2 as a reducing equivalent (produced through oxidation of fatty acids) is essential when investigating the relative contribution of carbohydrate and fat oxidations in the synthesis of ATP in mitochondria.In this multi-scale, multi-compartmental, top-down integrated model of cellular metabolism and energetics in skeletal muscle, the substrate and cation transport mechanisms between cytosol and mitochondria are not incorporated. Instead, these two domains are assumed to be in fast equilibrium with each other with the common metabolites having the similar dynamics  . This as2Another limitation in the present model is that the model does not account for blood flow heterogeneity and fiber type distributions associated with skeletal muscle cellular metabolism. Specifically, the capillary blood domain is considered spatially-lumped and the advective-diffusive transport of chemical species in capillary blood is ignored. Such compartmental modeling may not account for situations where important gradients of chemical species exist . In skeletal muscle, where the blood flow is highly heterogeneous due to complex capillarization and fiber type distributions, more than 70% of arterial oxygen is extracted from the blood before it leaves the microcirculation Finally, in the present model most of the lumped biochemical reactions in the cellular metabolic pathways are considered irreversible in the direction of product formation. Although the flux in the reverse direction is almost one order of magnitude smaller than the flux in the forward direction under normal, resting steady-state conditions, their magnitudes may change during physiological perturbations such as ischemia, hypoxia or exercise. Therefore, it would be advantageous to consider all the biochemical reactions to be reversible and their fluxes to satisfy the thermodynamic equilibrium constraints Including the substrate and cation transport mechanisms between cytosol and mitochondria and distinguishing common metabolites dynamics within these subcellular domains would be important in the analysis of dynamic cellular metabolic responses to high intensity exercise. The subcellular compartmentalization could account for distinct volumes of metabolites distribution, for example, metabolic channeling for glycolysis 2 as a reducing equivalent, the advanced model of cellular metabolism and energetics in skeletal muscle can be used to analyze physiological responses to exercise (increased energy demand). Specifically, the model can assist in providing insight into long-standing or paradoxical questions, such as the extent of control that mitochondrial oxygen concentration and redox state exert over the rate of lactate production in the cytosol during heavy intensity exercise. In general, a multi-scale computational model of cellular metabolism and energetics in tissue/organ systems within the body that incorporate sufficient mechanistic processes can be used to (1) analyze and interpret in vivo experimental data; (2) provide new hypotheses as well as suggest how to test a given hypothesis; (3) design critical experiments; (4) quantify and predict dynamic responses to physiological stimuli that can not be directly measured; (5) evaluate relative importance of metabolic pathways and fluxes and their regulatory mechanisms under both normal and pathological conditions; and (6) provide the mechanistic basis for simulating integrated effects of altering enzyme activities and substrate concentrations through pharmacological agents and/or dietary inputs.With these enhancements and with additional metabolic pathways similar to those of the models of cellular metabolism and energetics in cardiac muscle Materials S1(0.34 MB DOC)Click here for additional data file.Materials S2(0.43 MB DOC)Click here for additional data file.


S. cerevisiae was constructed from iFF708, an existing Flux Balance Analysis (FBA) model, and augmented with information from the KEGG online pathway database. The use of predicate logic as the knowledge representation for modelling enables an explicit representation of the structure of the metabolic network, and enables logical inference techniques to be used for model identification/improvement.A logical model of the known metabolic processes in Compared to the FBA model, the logical model has information on an additional 263 putative genes and 247 additional reactions. The correctness of this model was evaluated by comparison with iND750 (an updated FBA model closely related to iFF708) by evaluating the performance of both models on predicting empirical minimal medium growth data/essential gene listings.ROC analysis and other statistical studies revealed that use of the simpler logical form and larger coverage results in no significant degradation of performance compared to iND750. Saccharomyces cerevisiae). The model outlines the relationships between Open Reading Frames (ORFs), enzymes and reactions comprising the metabolic pathways in yeast, presenting the knowledge as facts in a restricted form of First Order Logic (FOL). This representation allows the model to behave as a deductive  database, as well as a model for the study of metabolic behaviour.This paper describes the construction and application of a logical model of known metabolic processes in bakers' yeast  and 750 represents the number of genes included in the model). Both models have also been compared with the predicted growth outcomes generated by a simple majority class classifier, as well as the probability that prediction success was purely random.To evaluate the correctness of the model we have used it to predict the results of empirical growth experiments of knockout mutants growing on defined minimal medium . AlthougiND750   Quantitative methods that aim to capture the changes in the quantities of metabolites and enzymes etc. by representing cellular processes, e.g. reaction kinetics, in detail2) Qualitative methods that aim simply model the presence of interactions, e.g. reactions are modelled as chemical transformations, with no representation of reaction kineticsThe two most important quantitative methods are ODE  and FBA . ODEs are the most established modelling representation in science. In using ODEs to model metabolism the concentration of each metabolite is calculated by a single ODE encapsulating all the reactions where the metabolite is synthesised or consumed, with fluxes determining the transformations to and from other metabolites in the network. The use of ODE models is the main technique of the quantitative sciences. There are also now a number of specialised ODE modelling packages for metabolism, e.g. Gepasi/Copasi -17 and eS. cerevisiae [E. coli [Flux Balance Analysis (FBA) ,6,19-21 revisiae ,6 and E.[E. coli  and rece[E. coli . HoweverE. coli, ROOM had an accuracy of 85%, which is comparable to the standard FBA approach. Elementary mode analysis [et al [E. coli, where lethal mutants mostly have an empty set of elementary modes, and non-lethal mutants have at least one elementary mode with an overall positive growth rate. Stelling et al [A number of flux based alternatives to FBA have been developed that address the changes in fluxes that occur after major environmental or other perturbations such as gene knockouts: MOMA (Minimisation of Metabolic Adjustment)  and ROOManalysis  determins [et al  use elemng et al  observedet al [E. coli and have used it to analyse how much damage the absence of each enzyme causes to the metabolic network. Metabolic damage is defined as the number of metabolites that can no longer be produced by the organism. They show that only 9% of enzymes prevent production of 5 or more metabolites, but that more than 50% of essential enzymes are to be found in this group.Logical and Graph (LG) based models ,11-13 aret al ,27 have et al [Logical models may use computationally efficient forms of both propositional and FOL (Prolog) as their representation language . As in get al ,27, unliet al [The BIOCHAM system  is a dedet al  used thiet al used QR to model the Glycolysis pathway [et al found 27,254 possible states for the Glycolysis model.The use of qualitative reasoning (QR)  is an in pathway . Rather  pathway  are usedet al [To test the utility of our "aber" model we compared it with the iND750 FBA model, and a majority classifier that assigns each prediction to the most commonly occurring classification (in this case continued growth of the strains). Although iND750 and the aber model have both been constructed from iFF708 , subsequet al : iND750 Two different cases of gene knockout sensitivity on MMD+ura+hist+leu were considered, 1) genes found to be significantly sensitive after 5 generations and 2) genes found to be significantly sensitive after 5 generations that remain significantly sensitive after 15 generations. As for iND750, the metabolic network and the starting media definitions used by the aber model were altered to reflect the additional requirements for uracil, histidine and leucine. An additional comparison was also made with the iND750 results where a preprocessing step was used to identify borderline cases of retarded growth in the sensitive/refractory data. This preprocessing step used all of the sensitivity results for each ORF, ignoring any refractory scores for ORFs, therefore all of the sensitivity data is used rather than focusing only on ORFs found to be sensitive in both Giaever experiment sets (The iND750 results may include ORFs not found to be sensitive in both sets). The imbalance of prediction counts also results in a shortfall of experiment results from the iND750 preprocessing step  were used for comparison of the aber model and iND750. The shared ORFs and aber ORF sources were used for the comparison of the aber model and the majority classifier. The iND750 ORFs and shared ORFs sources were used for the comparison of iND750 and the majority classifier. The McNemar test analyses the proportions of mistakes for predictions common to both models. To enable comparison of equivalent numbers the majority class was used to obtain predictions for ORFs not found in either model (i.e. the 40 ORFs from iND750 not found in the aber model and the 299 ORFs in the aber model not found in iND750). Significance for the McNemar tests was determined for p > 0.05 and the direction of the test result was collected (i.e. which model outperforms the other if a significant difference is observed). The following equation defines the McNemar test used, where b is the number of predictions found to be correct by model 1 and incorrect by model 2 and c is the converse (incorrect by model 2 and correct by model 1). A Cumulative binomial test was also used to determine the probability of generating the predictions of the aber model by chance.A McNemar χet al [phenotype) of a knockout strain depends on both its genotype (what gene(s) have been removed) and the environment. To use a model of metabolism to predict gene essentiality, it is therefore necessary to know the composition of the growth medium (the environment). This makes the use of "wet" results using the most common growth medium for yeast, YPD, problematic because its exact composition is undefined. This is why we have focused on using the Giaever et al data [We use the ability of a metabolic network models to predict the essentiality of a gene as a measure of model quality. Gene essentiality results have been presented for iFF708, the prime source of knowledge for the aber model and the precursor to iND750, to which the aber model is compared. Förster et al  report a al data  for growTable This indicates that use of the more complicated formalism of FBA does not improve the prediction of healthy/retarded growth compared to logical modelling. However this observation must be tempered by the fact that a fully direct comparison between the FBA prediction technique and the logical model prediction technique has not been possible, because the network corresponding to the shared ORFs is incomplete. The results from the McNemar tests also indicate that expanding the coverage of the model by adding information from KEGG has not significantly compromised the performance of the component of the model originating from iFF708. Indeed, it has been possible to increase the coverage of the metabolic network by around 30% without a significant degradation of performance. There was also no significant difference between both the aber model and iND750 on comparison set B – the more stringent definition of sensitive growth. This is partly because of the skewed nature of the experimental results  and partly because of the generally high false positive rates (variation from 0.55 to 0.86), therefore both iND750 and the aber model make more incorrect predictions for growth.Table r..n, where r = 889: the number of predictions for growth and n is the total number of predictions made (growth + no growth: 940):A cumulative binomial test was used to evaluate the probability that the predictions made by the logical model could have been made by chance. This test calculates the significance of deviations from the binomial distribution of observations falling into two categories (predictions of growth and no growth), assuming a random binomial model that assigns genes to essential/retarded growth and non essential/healthy growth categories by chance. The probability is calculated for the range p = 0.82, the proportion of ORFs that result in experimental growth and q = 1 - p . This test resulted in a probability, P(X ≥ 889)bin = 8.81 × 10-32: a very low probability that the predictions were generated by chance.where et al [Comparison of our logical model with iND750 demonstrated that there is no significant difference in the performance of any of the models on the prediction of gene essentiality. A significant increase in performance was observed for both the aber model and iND750 w.r.t the majority classifier on predicting growth outcome on defined growth medium, for all except the most stringent definition of growth from Giaever et al . There wThe high number of inaccuracies in the prediction of growth for all models indicates that much important information remains to be discovered about yeast metabolism.A major motivation for our use of a logical formalism is that it enables the exploitation of techniques from the large research area of Inductive Logic Programming (ILP) and related first-order learning methods . This isThe formation of hypotheses from the outcomes of the selected experiments was performed by a limited form of abductive theory completion , performThe use of this restricted form of FOL allows all components of the scientific discovery task to be described using the same knowledge representation, indeed the complexity of the entities and relationships required for accurate description of enzymes, reactions, experiments, and hypotheses etc can only be expressed by FOL or an equivalently expressive knowledge representation . Abduction of hypotheses relating ORFs, enzymes and reactions also requires that the machine learning program has FOL as it's representation language, hence the use of programs from ILP. The Robot Scientist concept therefore represents a close integration of logical inference techniques used for scientific discovery and an automated laboratory that can perform experiments. The previous work on the AAA Biosynthesis pathway was a proof of principle study. Recently the original robot hardware has been replaced by a state-of-the-art automated laboratory that substantially increases the throughput of the Robot Scientist S. cerevisiae: "aber". The core of the aber model is the FBA model iFF708 [This paper presents a logic based model of the metabolic processes in l iFF708 . Added tl iFF708 ,12. The The Logical model of Yeast metabolism has been constructed from two main sources:et al [1) iFF708 – the Genome Scale Metabolic Network produced by Forster et al 2) The Kyoto Encyclopaedia of Genes and Genomes (KEGG) ,12S. cerevisiae and a set of open reading frames (ORFs) that encode the gene products that catalyse the reactions. The gene products also belong to enzyme classes, defined by the Enzyme Commission. Forster et al used online database sources  the organelles in the yeast cell. There are 2 compartments – 3 if the immediate external environment (e.g. growth medium) is thought of as another compartment. The internal compartments are the cytosol and the mitochondrion. The resulting reaction list included reactions confined to each of the cell compartments and transport reactions across membranes between the external environment and the cytosol and the cytosol and mitochondrion.iFF708 consists of a set of reactions for which there exists biochemical evidence in es  andS [et al  estimateet al used the flux balance analysis to simulate various phenotypic and metabolic behaviours. These included the models capability to manufacture key precursor metabolites such as the amino acids, and the ATP related costs of synthesising macromolecules and ultimately biomass from precursors. The latter method was used to validate the model: by comparing the predicted results to previous experimental results from aerobic and anaerobic chemostat cultivation, and investigation of the flux distributions and shadow price calculations allowed the reaction list to be corrected (by hand) – so the predictions from the final model were in agreement with the experimental results. iFF708 has also been validated by comparing growth to a list of essential genes (see section 2).Forster The logical model and iFF708 both include ORFs, enzymes and reactions found to be part of yeast metabolism. An ORF corresponds to the DNA sequence that is removed or replaced to create each knockout mutant. Enzymes types are the Enzyme Commission number used to classify gene products corresponding to a particular enzyme function, and the reactions are the individual chemical transformation steps that, when taken together represent yeast metabolism. In its original form iFF708 treats the relationships between these components as if they corresponded to a single relational database table, resulting in much duplication of components. For example, with isoenzymes, where the gene products from two or more unique ORFs catalyse the same reaction, the reaction will be repeated in the table as many times as there are isoenzymes. This can lead to confusion when defining the various unique entities or components. Adapting iFF708 to a logical model enables the separation of entities and components into many linked database tables, which is a more natural way to represent the components and their relationships. The current logical model represents a first step – the reactions have been placed in a separate table allowing each reaction to be defined uniquely, with links to the ORF/enzyme components that code/catalyse the reaction. However, there remains much work to be done to extend this representation to allow for additional complexities such as multimeric reactions and protein complexes . Table 9Two sets of relations lie at the core of the logical representation of the metabolic network:1. orf_fact.This relation corresponds to a single mapping between one ORF, its Enzyme Commission number ; the corresponding Gene name; a (brief) description of the function of the gene; and the reaction catalysed by the gene product. The second relation defines the reactions in the logical model:2. reaction.ReactionNumber is a unique number by which the reaction is identified, Direction is either "forwards" (->) or "reversible" (<->) and Substrate and Product are lists of metabolites together with the cell compartment where the metabolite is found or added to. The stoichiometry of the reaction is also recorded, although the reaction mechanism used to predict the outcome of experiments does not currently make use of this information. Figure where reactantCompoundID is the unique ID from the KEGG database – where conversion from the notation used in the iFF708 was possible (>90% of metabolites). Compartment is one of {external, cytosol, mitochondrion}. The Orf/Enzyme/Reaction relations corresponding to the aber logical model are available as Additional file where the The Reaction Mechanism model used to predict the outcome of knockout mutant experiments is essentially the same mechanism as that used in . To relaReactions are processed by checking whether the metabolites on one side of the reaction were present in the cell and adding the metabolites on the other side. Each reaction was processed until no further reactions could be executed and the final complement of cell compounds was used to evaluate the growth outcome for that particular growth experiment. This basic approach has now been altered to incorporate the cell compartments used by the iFF708. KEGG does not specify cell compartments, hence the network components added from KEGG are assumed to be located in the cytosol. Figure 1) The metabolites comprising the minimal growth medium MMD+ura+hist+leu. These are the minimum set of compounds required by the wild yeast for continued growth – as well as the additional nutritional requirements of Uracil, L-Histidine and L-Leucine2) The ORF(s) knocked out to form the mutant strain3) Any additional nutrients added to identify possible reactions removed from the metabolic network by knocking out the ORF.4) Metabolites deemed "ubiquitous" – deemed to be always present in the cell. These include co-factors such as NADPH, NADH, ATP, ADP etc. The full list of ubiquitous compounds is given in Table 5) The reactions and ORFs/enzymes defined aboveLists corresponding to the three compartments defined in the iFF708 are created: the lists corresponding to the cytosol and mitochondrion compartments are initially set to contain the minimal medium compounds, and the ubiquitous compounds. The first task of the reaction mechanism is to identify all reactions that can no longer proceed because they are uniquely catalysed by the gene products produced by the ORF(s) removed to create the knockout strain. These reactions are removed from the network before processing by the reaction mechanism proper. The remaining reactions are analysed in turn to see whether the following conditions allowing the reaction to proceed have been met:iff (if and only if) all reactants in the substrate are present in the correct cell compartments. When the reaction runs, all reactants found in the product list are added to the compartment specified.1) Irreversible reactions can proceed iff all reactants in the products list are found in the correct compartments, the reactants in the substrate list are added to the specified compartments.2) Reversible reactions are processed similarly to irreversible reactions, but can also be processed in the reverse direction i.e. Each reaction is processed in turn and is processed at most once. Currently the logical model simply records the presence or absence of a metabolite and no calculation of the quantities produced is undertaken. This approach is sufficient for the simple continued/arrested growth predictions currently generated, but it will be revised when the model is modified to generate quantitative growth predictions. The mechanism processes all reactions in a cyclical manner as long as 1 or more reactions in the previous cycle have executed. This process ensures that all possible reactions can be processed and as many metabolites as possible are added to each cell compartment.After processing by the reaction mechanism, determination of continued or arrested growth is made by comparing the final complement of metabolites with a list of compounds deemed essential for healthy cell growth: these include amino acids, nucleic acids, compounds such as D-Glucose 1-phosphate that are essential to the formation of polysaccharides, compounds such as choline that are essential to the formation of membranes, and important intermediary compounds such as pyruvate. The complete list of essential compounds is given in Table iff ∀1) Continued growth is predicted if ∃2) Arrested growth is predicted However, including components only found in the iFF708 was not sufficient to predict growth as the network did not include enough reactions to enable synthesis of all the compounds deemed to be essential. However, this is because the aber model is focussed on modelling the viability of metabolism. This means that our end-points are metabolites considered to be essential for life. The end-points of a flux balance analysis model are metabolites that are important in cell biomass. The two sets of end-point metabolite are therefore not necessarily the same. For example, it would seem clear that a cell must be able to synthesise the immediate nucleotide precursors of RNA and DNA, but these are not all end-points in the iFF708 model. Inclusion of the knowledge representing additions to yeast biology in the KEGG database and added subsequent to the completion of iFF708; as well as an additional reaction, also from KEGG, not yet documented in yeast, but essential for the production of Palmitate, allowed the graph traversal algorithm to reach all essential compounds. . ConTable The relations corresponding to the 247 additional reactions belong to 47 pathways described in KEGG, however the largest proportion of these relations correspond to reactions that are not included in KEGG pathways. Purine metabolism (33 reactions), Fatty acid biosynthesis (path 1) (32 reactions) and Pyrimidine metabolism (29 reactions) have the largest numbers of reaction assignments; Purine metabolism (71 ORFs), Pyrimidine metabolism (68 ORFs) and RNA polymerase (31 ORFs) have the largest numbers of ORF assignments. There is no simple relationship between the numbers of ORFs in a pathway and the number of reactions, e.g. the 32 new reactions added to the Fatty acid biosynthesis (path 1) pathway are all coded for by a single ORF.Model validation  is a vitet al [sensitive and those growing faster as refractory. Growth data for each particular strain corresponds to the relative abundance of strain-specific DNA tags found by hybridisation to a custom high density oligonucleotide array, and take the form of continuously valued relative fitness scores, which are expressed as "units of deleterious growth" [et al used a sensitivity score cut off of >20 units of deleterious growth to identify strains with a significant deleterious phenotype after 5 generations, rising to >100 for 15 generations, reflecting the observation that strains found to be sensitive earlier would represent genes that are more important for cell growth. Giaever et al [essential strains that did not grow on YPD. Model validation therefore assessed the models' performance on predictions of gene essentiality as well as on a more comprehensive analysis of growth predictions which combine the essential gene listings with the results from the most relevant defined medium. This was a minimal medium (MMD+ura+hist+leu), which contains the minimum sets of compounds required for wild type growth as well as additional nutritional requirements for uracil, histidine and leucine.It is possible to use the second method to obtain some measurements of the validity of metabolic models of yeast by comparing the predicted outcomes of auxotrophy experiments to the results of a whole genome gene-deletion study undertaken by Giaever et al . This st growth" . There aer et al  also comRDK initiated the logical modelling concept and constructed the prototype model. KW constructed the logical model and carried out the validation experiments and the statistical tests. RDK and KW wrote and revised the manuscript.ORF, Enzyme and Reaction Relations. This file contains Prolog facts corresponding to the relationships between ORFs, Enzyme Commission Numbers and Reactions for the Logical Model of Yeast Metabolism.Click here for fileReactions. This file contains Prolog facts corresponding to Substrate and Product information for Reactions in the Logical Model of Yeast Metabolism.Click here for file


A report of the meeting "Challenges in experimental data integration within genome-scale metabolic models", Institut Henri Poincaré, Paris, October 10-11 2009, organized by the CNRS-MPG joint program in Systems Biology. Instances of such methods were presented by Maranas, who developed with his colleagues novel algorithms including GapFill and GapFind [While the number of fully sequenced genomes continues to grow at an exponential rate, the number of published reconstructions of metabolic models  is drama GapFind  to fill S. cerevisiae from the Charlie Boone Lab [in silico enumeration of all lethal gene pairs, triplets and quartets using FBA is computationally intractable for any genome-scale metabolic model; instead, Maranas presented a heuristic method based on a bi-level optimization approach which improves considerably the computational time to obtain lethal triplets and quartets  as candidates for further assessment of the genetic interactions predicted by the model [While single gene-deletion mutants are considered a prominent source of data for assessing the quality of reconstructed models, datasets including the phenotypes of double gene-deletion mutants appeared recently. Balázs Papp  presented unpublished results where such a dataset obtained in yeast oone Lab  was usedhe model .Tomer Shlomi  also showed that reconstructing a model may involve further challenges, pertaining for instance to the proper account of cellular compartments in absence of prior knowledge of enzyme localization. In particular, he presented a novel algorithm to predict sub-cellular localization of enzymes based on their embedding metabolic network, relying on a parsimony principle which minimizes the number of cross-membrane metabolite transporters .in silico and in vivo single mutant growth phenotypes by suitably modifying the static biomass composition under different environmental conditions. Shlomi presented a method, Metabolite-dilution FBA (MD-FBA), which systematically accounts for the growth demand of synthesizing all intermediate metabolites required for balancing their growth dilution, leading to improved metabolic phenotype predictions [While the static composition of the biomass as a component of a metabolic model is known to influence the results of FBA predictions, little had been proposed to date in order to overcome this limitation of the framework. Maranas presented the GrowMatch  method tdictions .13C labeling experiments followed by nuclear magnetic resonance (NMR) or mass spectrometry (MS) analysis have generated experimental data for a number of intracellular fluxes and metabolite concentrations [Condition-dependent refinements of metabolic models can also be fed by further experimental observations. Recently, trations . Such extrations  which syS. cerevisiae and Lactobacilli where the two maximizations are not equivalent. He compared the two cases with the experimentally observed solution corresponding to maximization of rate [Another criticism often addressed to FBA pertains to the use of an optimality principle to obtain a single biologically relevant flux distribution. Stefan Schuster  emphasized that FBA predicts a flux distribution that strictly maximizes biomass yield rather than biomass flux or growth rate. Although, in most situations, maximization of rate and yield give equivalent solutions, Schuster presented interesting examples in  of rate . In cont of rate  cannot b of rate  closely The reconstruction of metabolic networks for several organisms spread across the tree of life and that thrive in diverse habitats has enabled investigations aimed at understanding the role of the environment in determining the structure of metabolic networks of different organisms. Oliver Ebenhöh  presented a simple heuristic based on the principle of forward propagation called network expansion  which usBuchnera aphidicola receives from its host.Marie-France Sagot  presented ongoing work in her group to improve the network expansion algorithm by appropriately differentiating self-regenerating metabolites   from nutE. coli metabolic network, Martin and colleagues showed that the E. coli network is atypically robust to mutations.Several studies in the past have been focused towards understanding the relation between structure and function of metabolic networks. However, little is known about the variation in reaction content of the different possible metabolic networks having the same phenotype. Olivier Martin  presented a new method based on Markov Chain Monte Carlo (MCMC) sampling which can be used to uniformly sample the space of metabolic networks with a given phenotype and fixed number of reactions in a global reaction set . Using tE. coli was identified. Modeling this process allowed him to further characterize qualitatively different regimes.While the investigation of statistically overrepresented motifs in gene regulatory networks has resulted in the identification of qualitative features of the associated dynamics , similarAs an alternative to traditional optimization-based predictions, Daniela Calvetti  presented a probabilistic extension of both kinetic and steady state models of metabolism that she introduced with her colleague E. Somersalo . RelyingWolfram Liebermeister  presented various methods leveraging such mathematical theories to integrate experimental data within metabolic models. He provided the audience with a thorough review of the methods he developed with his colleagues to induce quantitative relationships between enzyme levels, metabolite concentrations and metabolic fluxes, while properly accounting for physical laws and allosteric regulation ,23. EmphAlthough the detailed modelling of human metabolism was initiated almost ten years ago, to date it has been restricted to specific cell-types and organelles. In parallel, comprehensive datasets of the genes involved and biochemical activities in human cells have been gathered, allowing Duarte and colleagues to publish the first global map of human metabolism in 2007 . BuildinKiran Patil  tackled the challenge of modeling several other metabolic processes in humans. He specifically investigated the metabolic and regulatory underpinnings of diabetes, combining the knowledge on regulatory and metabolic mechanisms to pinpoint biomarkers of diabetes with the help of several case-studies pertaining to this particular disease. An analysis of the enrichment in binding sites of transcription factors in upstream regions of the enzymatic genes relevant to this study allowed him to uncover the potential of various transcription factors as drug targets .The authors declare that they have no competing interests.All authors contributed equally to this manuscript. All authors have read and approved the manuscript.


GeneForce, to identify incorrect regulatory rules and gene-protein-reaction associations in integrated metabolic and regulatory models. We applied the algorithm to refine integrated models of Escherichia coli and Salmonella typhimurium, and experimentally validated some of the algorithm's suggested refinements. The adjusted E. coli model showed improved accuracy (∼80.0%) for predicting growth phenotypes for 50,557 cases . In addition to identifying needed model corrections, the algorithm was used to identify native E. coli genes that, if over-expressed, would allow E. coli to grow in new environments. We envision that this approach will enable the rapid development and assessment of genome-scale metabolic and regulatory network models for less characterized organisms, as such models can be constructed from genome annotations and cis-regulatory network predictions.Integrated constraint-based metabolic and regulatory models can accurately predict cellular growth phenotypes arising from genetic and environmental perturbations. Challenges in constructing such models involve the limited availability of information about transcription factor—gene target interactions and computational methods to quickly refine models based on additional datasets. In this study, we developed an algorithm,  GeneForce) that automatically corrects integrated metabolic and transcriptional regulatory network models. To illustrate the utility of the approach, we applied the developed method to well-curated models of E. coli metabolism and regulation. We found that the approach significantly improved the accuracy of phenotype predictions and suggested changes needed to the metabolic and/or regulatory models. We also used the approach to identify rescue non-growth phenotypes and to evaluate the conservation of transcriptional regulatory interactions between E. coli and S. typhimurium. The developed approach helps reconcile discrepancies between model predictions and experimental data by hypothesizing required network changes, and helps facilitate the development of new genome-scale models.Computational models of biological networks are useful for explaining experimental observations and predicting phenotypic behaviors. The construction of genome-scale metabolic and regulatory models is still a labor-intensive process, even with the availability of genome sequences and high-throughput datasets. Since our knowledge about biological systems is incomplete, these models are iteratively refined and validated as we discover new connections in biological networks, and eliminate inconsistencies between model predictions and experimental observations. To enable researchers to quickly determine what causes discrepancies between observed phenotypes and model predictions, we developed a new approach ( E. coli and Saccharomyces cerevisiae, inferred or indirect regulatory interactions have to be included in genome-scale transcriptional regulatory reconstructions due to existing knowledge gaps in how genes are transcriptionally regulated cis-regulatory networks, and may include incorrect interactions. As such, methods for iterative validation and refinement of regulatory reconstructions are needed in order to assess new experimental datasets as they emerge A current challenge in systems biology is reconstructing transcriptional regulatory networks from experimental data , due to the complexity of interactions in these networks and the limited information on network components and interactions for most organisms While there are many types of regulatory modeling approaches (reviewed in GeneForce) to reconcile integrated regulatory and metabolic model predictions with experimental data, by automatically identifying and overriding transcriptional regulatory rules that cause inconsistencies between model predictions and experimental observations. The approach can be used in cases where both the experimental data and an un-regulated metabolic model agree on a positive growth phenotype (cells can grow), but the integrated metabolic and regulatory model predicts a non-growth phenotype (cells cannot grow). In these cases, the GeneForce algorithm allows the integrated metabolic and regulatory model to achieve growth by violating regulatory rules as needed, while minimizing the total number of regulatory violations in order to maximally preserve the original regulatory interactions present in the regulatory network reconstruction. These rule violations indicate that regulatory rules describing gene expression are incorrect or that isozymes or alternative pathways are present in the metabolic network.In this work, we developed an algorithm  in certain growth environments. Finally, we applied the GeneForce method to investigate the conservation of transcriptional regulatory interactions between E. coli and S. typhimurium. The E. coli transcriptional regulatory rules were integrated with a metabolic model for S. typhimurium that included metabolic genes and reactions from a recent metabolic reconstruction iRR1083 GeneForce suggested a small set of rule corrections for this hybrid network model were needed, based on analysis of S. typhimurium growth phenotyping data, suggesting that regulation may be highly conserved between these two organisms. While the approach has been used here to correct Boolean representations of transcriptional regulation, it could easily be extended to consider non-Boolean approaches to modeling transcriptional regulation as they are developed.We first applied the GeneForce, to identify problematic Boolean regulatory rules in an integrated metabolic and transcriptional regulatory model. The method identifies regulatory rules that prevent the models from predicting cellular growth in conditions, which are capable of supporting growth experimentally. The approach can be used when the integrated metabolic and regulatory model does not predict growth, but experimental data and metabolic model predictions (without any regulatory constraints) indicate growth occurs.We developed an automated MILP approach, GeneForce algorithm is to allow the integrated metabolic and regulatory model to violate a minimal set of transcriptional regulatory rules so that growth can occur in a particular condition. The algorithm therefore adds an additional constraint that the model must satisfy a minimal threshold growth rate. The algorithm uses a set of ‘rule-violation’ equations (see Supporting Information g) that can differ in value from the gene expression indicators (yg), the latter of which are determined by Boolean regulatory rules. Normally in the integrated metabolic and regulatory model a flux is constrained to be zero if the necessary metabolic genes are determined to be un-expressed (yg = 0). In the GeneForce algorithm, the bounds on the metabolic fluxes are dependent on y′g instead of yg. The reaction dependence on y′g then allows the model to override a minimum number of gene expression indicators (where yg = 0 but y′g = 1) so that the threshold growth rate can be achieved.The basic idea of the GeneForce algorithm uses the rule violation technique to achieve non-zero growth in an integrated metabolic and regulatory model in agreement with the metabolic model predictions. As shown in the xt, whereas the integrated metabolic and regulatory model predicts no growth due to the regulatory interactions between gene G1 and transcription factor TF1  was not overruled (yG2′ = yG2 = 0), even though yG2′ could also take the value 1 instead of 0. This is because the algorithm minimizes the sum of the distances between the surrogate and the original gene expression indicators,  to give the final version of the regulatory model iMC105ABC. Here we consider the regulatory models  to be just the regulatory part of the integrated models .We used the iJR904 with Lrp-modified iMC104 regulatory rules allowed comparison of 32,050 growth phenotype predictions to experimental data  were needed to correct predictions for growth on L-serine as a nitrogen source or the ΔsdaB mutant. These 3,079 cases correspond to cases where a zero growth prediction by the integrated metabolic and regulatory model contradicted both the experimental data and the metabolic model prediction . Not all regulatory rules identified by the algorithm in the 3,079 cases were adjusted, as they may cause new incorrect predictions in other conditions. Instead, corrections were made for regulatory rules that were frequently identified as problematic for a particular knockout mutant or growth environment  were corrected in the first regulatory model refinement, iMC105A. Two gene-protein-reaction (GPR) associations were also corrected in the metabolic model for two amino acid transport reactions (L-methionine and D-serine). These model adjustments led to an ∼8% improvement in the overall accuracy of the integrated model from 73.9% to 81.5%  associated with cases where arginine is the nitrogen source, but also introduced 297 new errors (−/+/− changed to −/+/+) for cases where arginine is the carbon source. To correct these new errors we subsequently refined the rules for the astCADBE operon and speA gene, in addition to argD, to reconcile the model with both arginine conditions. The prediction accuracy of the integrated metabolic and regulatory model (iAF1260+iMC105A) was 78.1% before all eleven rule corrections were made, and with this additional second set of regulatory refinements, the iMC105AB model could achieve a slightly higher accuracy, 79.9% (The second set of refinements (refinement step B), occurred when the y, 79.9%  and withiMC105AB, was tested by comparing predictions to newly acquired experimental data for three transcription factor knockout mutants . The five transcription factors in iMC105AB with the most metabolic gene targets are Crp, Fnr, ArcA, PurR and Lrp. Experimental data was already available for knockout mutants for two of these transcription factors (Crp and Fnr), however, growth phenotyping data for ΔarcA, ΔpurR, and Δlrp mutants was not available. Therefore, growth experiments on phenotype microarrays  were conducted for the three mutant strains ΔarcA, ΔpurR, and Δlrp. The GeneForce algorithm identified an additional nine genes needing regulatory rule corrections  in model accuracy over the previous version iMC105AB .In the third set of refinements, the refined regulatory model, iMC105AB  when evaGeneForce algorithm was determined. The distribution of the number of rule corrections needed for the +/+/− cases is shown for the first two refinement steps in For each +/+/− case the minimum number of genes whose regulatory rules had been violated by the GeneForce problem. The number of +/+/− cases for which alternative optimal solutions exist can be found in Supporting Information ilvA, metH, sdaC and thrA). For other cases described below , we performed additional growth phenotyping experiments to determine the final set of corrections. Overall application of the GeneForce algorithm to correct +/+/− cases led to (i) changes in the regulatory rules for metabolic genes  (ii) changes in the rules for TF activities (e.g. RpiR), or (iii) changes in the gene-protein-reaction (GPR) associations in the metabolic network (e.g. dsdX). Some examples from the different types of changes are presented below, and in some cases additional mutant phenotypes were screened by experiments to confirm the necessary model changes identified by GeneForce.Alternative optimal solutions were generated for each refinement step by adding integer-cut constraints and re-solving the glmU by the NagC transcription factor was identified as the most problematic rule, causing approximately one third of the total incorrect zero growth predictions by the Lrp-modified iMC104+iJR904 integrated model. GeneForce identified the regulatory rule for glmU gene as needing a correction for most mutants grown in conditions where any of the three amino sugars, N-acetylglucosamine (GlcNAc), N-acetylneuraminate, and N-acetylmannosamine were present. GlmU catalyzes two consecutive reactions producing an essential precursor UDP-N-acetyl-glucosamine (UDP-GlcNAc) for the cell wall of E. coliE. coliGeneForce's prediction that the regulatory rule for glmU is incorrect.In our analysis, the regulatory rule describing the regulation of iMC104 precluded the gene from being expressed in the integrated model under certain conditions: ‘NagC is active if NOT (GlcNAc OR glucosamine-6-phosphate)’ and ‘glmU is expressed if NagC is active’. The first rule prohibited NagC from being active in the presence of any of the three amino sugars because glucosamine-6-phosphate is a common intermediate in their degradation pathways. The inactivity of NagC subsequently prohibited the expression of glmU in the integrated model, resulting in a non-growth phenotype prediction. GeneForce violated the glmU regulatory rule so that GlmU can carry out the two essential reactions. Although the regulatory rules shown above were in agreement with experimental data reported in the literature, the Boolean representation of the regulatory interaction was too stringent in the model. The glmU gene contains two upstream promoters P1 and P2, and the transcription factor NagC is shown to induce expression using the promoter P1 in the absence of any of the three amino sugars glmU promoter, P2, is weakly induced in presence of N-acetylglucosamine, suggesting that the activating role of NagC could be dispensable for this promoter glmU is not completely abolished when NagC is inactive, and that the low level of induction at P2 is still sufficient to allow for the production of UDP-GlcNAc. Since glmU is required for growth in other environments as well, it is always expressed in the refined set of regulatory rules.The following two regulatory rules in lrp mutant in a few different conditions, including growth on glucose, gluconate, and L-malate as sole carbon sources. For the glucose and gluconate conditions, GeneForce found that either ilvHI or ilvBN needed to be expressed since these two isozymes are used for the synthesis of branched chain amino acids. To evaluate which of these isozymes is used by the cells, we screened a number of Lrp double mutants for growth on glucose and found that only ΔlrpΔilvB is unable to grow; however, ΔlrpΔilvN, ΔlrpΔilvH, and ΔlrpΔilvI were all capable of growing in glucose minimal media (ilvB and ilvI) are still active in the absence of the smaller regulatory subunits  lrp mutant grown on malate, GeneForce needed to override the regulatory rule for one of the malate transporters in E. coli. We subsequently found that ΔdctA and ΔlrpΔdctA mutants did not grow on L-malate, while the Δlrp mutant grew  catalyzes the reversible conversion of ribose-5-phosphate to ribulose-5-phosphate in the pentose phosphate pathway. Two RPIs have been identified in D-ribose , while nD-allose . The oricycA based on the utilization of D-alanine and D-serine. In this case the algorithm helped lead to improvements in GPR associations in the metabolic network as well as the regulatory rule for cycA. The integrated model incorrectly predicted that these compounds could not be used as carbon and nitrogen sources, which GeneForce attributed to the expression rule for the CycA transporter. We subsequently measured growth of ΔcycA, ΔdsdX, and ΔcycAΔdsdX mutants, and found that the ΔcycA and ΔcycAΔdsdX mutant were unable to grow with D-alanine as a carbon source , since the model changes were not intended to affect these conditions. We found that the model changes had no significant effect on the predicted wildtype fluxes for the 84 and 112 conditions examined , except for the two conditions with L-malate and D,L-malate as carbon sources. In these two conditions, the regulatory rule change for dctA in Refinement C allows D-malate to be transported and L-malate to be transported with a more energetically efficient transporter. As a result higher growth rates can be achieved for these two conditions and the optimal flux distributions will change significantly.To investigate the effects the model corrections have in other conditions we evaluated how many new false positives were introduced (i.e. −/+/− cases became −/+/+) for each refinement step  E. coli strains. In each of these nutritional states: (i) the majority of the E. coli knockout mutants were unable to grow, (ii) the metabolic model incorrectly predicts growth, and (iii) the integrated metabolic and regulatory model correctly predicts no growth. In seven out of the ten aerobic conditions, either a single gene or a single operon was needed to be expressed in violation of the regulatory rules to allow for growth. This list included citT, xylA, allC, fucO, atoDAEB, ttdAB, and nirBD, which correspond to the different medium conditions listed in In our analysis of ∼32,000 mutant phenotypes using citT, fucO and atoDAEB rescuing the inability of wild-type E. coli to grow aerobically on citrate, 1,2-propanediol, and butyrate, respectively citT gene encodes a citrate transporter, and Pos et al. have shown that plasmid mediated over-expression of citT allows for aerobic growth on citrate fucO leads to an ability to grow on 1,2-propanediol aerobically E. coli is unable to utilize saturated short chain fatty acids, such as butyrate, and studies have shown that the constitutive expression of atoC, an activator of the atoDAEB operon, instills the ability to grow on butyrate We subsequently looked for experimental evidence in the literature that would corroborate the algorithm's predictions of genes whose overexpression can rescue non-growth phenotypes. We found direct evidence in support of allC  and ttrAB (L-tartrate) but these genes encode enzymes in the catabolic pathways for these substrates. Wild-type E. coli can utilize allantoin as a sole nitrogen source anaerobically, but not as a sole carbon source allS, which is an activator of the allantoin regulon containing allCallC would allow for utilization of allantoin in an oxic environment. Similar strategies may also be proposed for the ttrAB operon, which is also repressed in the presence of oxygen thereby preventing aerobic growth on L-tartrate, a substrate that can be used anaerobically We were unable to find direct evidence in support of S. typhimurium LT2 and E. coli K-12 MG1655 are closely related and both organisms have been well studied experimentally and modeled. However, the transcriptional regulatory network of S. typhimurium is less characterized experimentally, than E. coli's, and a genome-scale transcriptional regulatory model for S. typhimurium is not available. Recently, a metabolic network model, (iRR1083) for S. typhimurium was published E. coli transcriptional regulatory interactions in S. typhimurium by superimposing the E. coli regulatory constraints on the Salmonella metabolic network. The regulatory model iMC105A was integrated with the metabolic model iRR1083, and we evaluated whether this chimeric model was consistent with growth phenotypes for S. typhimurium. The expectation was that if the transcriptional regulatory networks were highly conserved few regulatory rule violations would be needed to correctly predict growth.The two bacterial strains, iMC105A for E. coli genes to their orthologs in S. typhimurium, and used the GPR association in the S. typhimurium metabolic network to constrain fluxes through the metabolic reactions. Among the 1,083 S. typhimurium genes included in iRR1083, 782 genes had orthologs in E. coli that were included in iJR904 . Additionally, among the 105 E. coli transcription factors in iMC105A, we found 86 had orthologs in S. typhimurium which were incorporated into the chimeric model. These differences in conservation of metabolic and regulatory genes allowed us to transfer approximately 83% of the regulatory rules in iMC105A, while discarding the remaining rules associated with metabolic genes not present in S. typhimurium or regulatory rules involving transcription factors present only in E. coli. Any metabolic ortholog present in S. typhimurium but regulated by transcription factors without orthologs in S. typhimurium were kept unregulated in the chimeric model.We transferred the regulatory rules in GeneForce algorithm to this hybrid E. coli regulatory-S. typhimurium metabolic model and evaluated model predictions against wild-type S. typhimurium growth phenotypes in 196 medium conditions  also needed rule corrections in subsequent refinements of the E. coli integrated model as well  was also identified as requiring a rule correction in S. typhimurium but not in E. coli for growth on glucose and D-gluconate medium. This difference is primarily attributed to differences in the GPR association for glutamine synthetase between the two metabolic networks, where glnA encodes a sole enzyme for glutamine synthesis in S. typhimurium, whereas in the E. coli models an additional isozyme YcjK can catalyze the same reaction when glnA expression is suppressed. Recently, however the YcjK has been shown to be incapable of synthesizing glutamine from glutamate and ammonia so the regulatory rule for glnA and GPR association for glutamine synthetase needs to be updated in the E. coli model as well focA gene encodes the sole formate transporter in S. typhimurium but has an alternative gene focB in E. coli, which explains why the focA regulatory rule was not problematic in our analysis of E. coli growth phenotypes.The S. typhimurium, when tested against the wild-type S. typhimurium growth phenotypic data in 196 medium conditions was 77% accurate. The unregulated metabolic model (unregulated iRR1083) was 82% accurate against the same growth phenotyping data. After introducing the refined rules  refine existing transcriptional regulatory and metabolic models of E. coli and suggest regulatory rule corrections, (ii) explain how transcriptional regulation prevents cellular growth in certain conditions and identify genes which can rescue non-growth phenotypes if expressed, and (iii) construct and refine a new integrated regulatory and metabolic model for S. typhimurium.In this work we developed a new optimization-based approach, E. coliiAF1260 metabolic model was used, flux balance analysis (FBA) was ∼76.5% accurate and minimization of metabolic adjustment (MOMA) iAF1260+iMC105ABC) was ∼79.6% accurate when predictions were made for the metabolic gene knockouts. The integration of metabolic and regulatory network models is thus important for being able to more accurately predict behavior of metabolic mutants, as well as, transcription factor mutants.We showed that even well curated transcriptional regulatory and metabolic models for GeneForce can also be used to evaluate correct model predictions of non-growth conditions to explain how regulation prevents the use of particular nutrients since the needed enzymes are encoded in the genome. We used the approach to suggest a set of genes which if expressed can rescue non-growth phenotypes of mutant and wildtype strains. Experimental testing of these hypotheses would validate that particular metabolic transformations occur and could be used to engineer novel growth phenotypes in an organism.In addition to fixing incorrect model predictions, we showed that GeneForce approach to already developed and refined metabolic and regulatory E. coli models, we also applied it to a new integrated model for S. typhimurium. We constructed an initial transcriptional regulatory model for S. typhimurium, by transferring the regulatory network from a closely related organism. We then applied the approach to correct regulatory rules in the integrated metabolic and regulatory model of S. typhimuriumE. coli is highly consistent with the growth phenotypes of S. typhimurium, indicating that the regulatory networks in these two organisms may be highly conserved between these two organisms. A similar observation was found previously by Babu et al., where ∼90% of E. coli regulatory interactions were predicted to be conserved in S. typhimurium based on the presence of orthologs of transcription factors and their target genes in S. typhimuriumS. typhimurium, additional work is still needed to expand this initial regulatory model to include organism-specific regulatory interactions .In addition to applying the E. coliS. cerevisiaeGeneForce approach can be very useful for validating and refining transcriptional regulatory models against new experimental data, as well as for developing new regulatory models where initial models often yield a number of predictions that are inconsistent with experimental data. In the past, the identification of regulatory rules causing inconsistencies between model predictions and experimental observations was done through a time intensive, trial and error process The number of available metabolic reconstructions is rapidly increasing, which is made possible by the increased number of genome sequences GeneForce algorithm could be easily extended to consider other types of integrated metabolic and regulatory models as they are developed, where the number of genes needing expression levels higher than those predicted by the regulatory models could be minimized. As such, the approach would still reconcile integrated metabolic and regulatory network models with observed growth phenotypes and suggest improvements of such models. Other approaches have been developed for metabolic models that use experimentally determined flux distributions as a means to refine metabolic models GeneForce algorithm could be extended to compare more quantitative data including biomass yields (where the measured yields are used to determine the minimum growth rate threshold) and measured fluxes  as such quantitative data become available at a large-scale.Other types of non-Boolean methods are needed to integrate genome-scale metabolic and regulatory models, since Boolean approaches cannot capture all transcriptional regulatory interactions  and gene expression and metabolic fluxes have variable levels that cannot be reflected using ‘On/Off’ variables. Modeling methods are available to predict gene expression levels cis-regulatory networks, based on genomic analysis and/or experimental data, can be translated into Boolean regulatory models that can be rapidly refined using our developed approach. The identified refinements can then suggest further experiments and lead to a re-evaluation of cis-regulatory networks. By integrating models of metabolism and regulation, phenotypic data can be evaluated against regulatory network predictions (which is difficult to do without a metabolic model), thereby expanding the types of datasets  that can be used to reconstruct transcriptional regulatory networks.Although automated approaches for refining metabolic models have been developed E. coli K-12 BW25113 (the parent strain of the Keio collection) were used to confirm the model changes identified by GeneForce. The kanamycin resistant gene (kan) was removed from the single-deletion strains before screening mutant phenotypes in the microplate reader  were generated using P1 transduction . Briefly, strains were grown on BUG+B agar plates and resuspended in inoculating fluid containing Dye A and loaded onto plates. Plates were incubated at 30°C and absorbance readings were taken at 600nm at 24 and 48 hours. Other strains were screened for growth in triplicate at 37°C in a Tecan Infinite 200 microplate reader . Optical density measurements at 600 nm were taken by the microplate reader every 15 minutes. The Tecan OD measurements (ODTecan)were converted to an OD value in a spectrophotometer with a 1cm pathlength (OD600), using a predetermined linear relationship, OD600 = (2.566)ODTecan+0.0028. Strains were pre-cultured overnight in 2 g/liter glucose-supplemented M9 minimal medium, except for a few strains  supplemented with 2 g/liter of carbon source.Phenotype microarray (PM) experiments were conducted for the E. coli from the ASAP database E. coliarcA, ΔpurR, and Δlrp) was generated in this study using the phenotype microarrays  as described above. In this study, we have excluded the phenotypic data for cells grown on formate and L-serine as carbon sources, and xanthine and xanthosine as nitrogen sources, as they are likely false positives in the PM datasets  data for iJR904 iAF1260 iMC104v1E. coli were integrated and used in this study. First, regulatory interactions for the global transcription factor, Lrp, were updated in the regulatory rules represented in the iMC104 model based on the recent regulatory reconstruction from analysis of gene expression and ChIP-chip data iAF1260 instead of iJR904, another set of preliminary rule corrections were needed for the eight genes that are essential only in iAF1260, due primarily to changes in the biomass equation. These fifteen preliminary rule corrections were made before the integrated model was compared to mutant phenotypes, and thus they are not listed in The genome-scale models of metabolism  GeneForce identifies the minimal set of genes that are required for growth, but are unexpressed in a given condition due to transcriptional regulatory constraints. In the GeneForce formulation, unexpressed genes are allowed to violate the regulatory rules, and the number of violations is minimized to prevent unnecessary rule violations. A rule violation is implemented by introducing surrogate gene expression indicator variables (y′g) to allow flux through reactions whose associated genes are not expressed according to the Boolean regulatory rules. A minimum growth rate requirement is introduced by setting the lower bound for growth rate to a minimum threshold value, and the threshold value was set to 10% of the maximum growth rate predicted by the metabolic model in this study. The algorithm was relatively insensitive to threshold values between 5 and 50% . If a certain set of regulatory rules were repeatedly violated in the Figure S1Histograms of OD600 measurement in Biolog Phenotype Microarrays (PM).(0.19 MB PDF)Click here for additional data file.Figure S2iJR904 and iMC104 (with Lrp modified regulatory rules) for postive and negative experimental growth phenotypes.Histograms of relative growth rate predictions by (0.07 MB PDF)Click here for additional data file.Table S1iJR904 and iMC104 (with Lrp modified regulatory rules).Phenotype-model comparison using (0.51 MB XLS)Click here for additional data file.Table S2iAF1260 and iMC105A.Phenotype-model comparison using (0.77 MB XLS)Click here for additional data file.Table S3iAF1260 and iMC105AB/iMC105ABC for ΔarcA, ΔpurR, and Δlrp mutants.Phenotype-model comparison using (0.03 MB XLS)Click here for additional data file.Table S4Detailed statistics of model-data comparisons and alternative optimal solutions for each refinement step.(0.03 MB XLS)Click here for additional data file.Table S5iRR1083  and iMC105A.Phenotype-model comparison using (0.03 MB XLS)Click here for additional data file.Table S6iAF1260.Preliminary analysis for integrating the new Lrp reconstruction and metabolic model (0.05 MB XLS)Click here for additional data file.Table S7Simulation conditions for Biolog Phenotype Microarrays (PM) and GN2-Microplate.(0.06 MB XLS)Click here for additional data file.Table S8iJR904 and iMC104 (with Lrp modified regulatory rules).Sensitivity analysis for different values of minimum growth rate requirement using (0.03 MB XLS)Click here for additional data file.Text S1GeneForce formulation.Detailed description of the (0.05 MB DOC)Click here for additional data file.