Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and regulatory processes at the genome scale, such as the S. cerevisiae system presented here.Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes  without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)–based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporating kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism  Cellular systems comprise many diverse components and component interactions spanning signal transduction, transcriptional regulation, and metabolism. Although signaling, metabolic, and regulatory activities are often investigated independently of one another, there is growing evidence that considerable interplay occurs among them, and that the malfunctioning of this interplay is associated with disease. The computational analysis of integrated networks has been challenging because of the varying time scales involved as well as the sheer magnitude of such systems . To this end, we developed a novel computational framework called integrated dynamic flux balance analysis (idFBA) that generates quantitative, dynamic predictions of species concentrations spanning signaling, regulatory, and metabolic processes. idFBA extends an existing approach called flux balance analysis (FBA) in that it couples “fast” and “slow” reactions, thereby facilitating the study of whole-cell phenotypes and not just sub-cellular network properties. We applied this framework to a prototypic integrated system derived from literature as well as a representative integrated yeast module (the high-osmolarity glycerol [HOG] pathway) and generated time-course predictions that matched with available experimental data. By extending this framework to larger-scale systems, phenotypic profiles of whole-cell systems could be attained expeditiously. Intracellular biochemical networks are comprised of signaling, metabolic, and regulatory processes.  Until recently, computational analyses focused independently on signaling, metabolic, and regulatory networks. However, high-throughput experimental data coupled with computational systems analysis techniques have elucidated multifunctional components involved in fundamental disease processes Dynamic integrated systems is that time scales of intracellular biochemical networks generally span multiple orders of magnitude. Signaling and metabolic reactions typically occur rapidly. For example, kinase/phosphatase reactions, protein conformational changes, and most metabolic reactions occur on the order of fractions of a second to seconds An additional challenge to the modeling of Saccharomyces cerevisiae and Escherichia coliS. cerevisiae to osmotic shock Some preliminary dynamic analyses of integrated systems have been completed. Integrated analyses of regulatory and metabolic networks revealed novel mechanisms in S. cerevisiae as a validation of our approach. idFBA allowed for quantitative, dynamic analysis of systemic effects of extracellular cues on phenotypes of these systems and generated comparable time-course predictions when contrasted with kinetic models. Ultimately, we demonstrate how idFBA enables genome-scale quantitative, dynamic analysis of integrated systems.The purpose of this study was to develop a FBA-based computational framework, termed integrated dynamic Flux Balance Analysis (idFBA), for the quantitative, dynamic analysis of cellular behaviors arising from signaling, metabolic, and regulatory networks at the genome-scale. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system with topological features characteristic of those observed in existing signaling, metabolic, and regulatory network reconstructions as well as kinetic parameters reported in literature. Additionally, we applied in a similar manner the idFBA framework to a representative module in The idFBA framework facilitates the dynamic analysis of cellular phenotypes on the genome scale arising from extracellular cues. The systems evaluated as part of this study, including an integrated prototype spanning signaling, metabolism, and regulation, and a representative module from yeast are described here. The implementation details of the framework are also delineated.In order to assess the efficacy of idFBA, a prototypic integrated system was constructed with characteristics typical of those observed in published reconstructions of signaling, metabolic, and regulatory networks see  and 2. S1, L2, and L3) bind to receptors  to form ligand-receptor complexes . These complexes are subsequently either internalized or involved in phosphorylation events. Phosphorylation of signaling components takes place through a series of reactions involving ATP and other activated components. Any one signaling component can also activate multiple other signaling components; this activity represents the type of multi-functionality  that is often found in biological systems 1p, T2p, and T3p), that are representative of phosphorylated proteins are the downstream effector molecules that result from the signaling pathways.Signal transduction pathways govern a cell's response to extracellular stimuli, including, e.g., how a cell adapts its transcriptional regulatory program in response to specific environmental cues. The prototypic signaling network is comprised of a set of reactions that attempts to mimic what is typical of biological signaling pathways such as phosphorelay and kinase cascade modules. As shown in The model of signal transduction consists of a total of 45 reactions. As previously described, the rate constants for these reactions are based on values observed for similar signaling reactions in literature 1 and H2 are representative of amino acids and F and G are representative of metabolites.uSmax, was set to 10.5 mmol/(g(dry weight)•h) as in Metabolic pathways produce energy, amino acids, and other precursors required for the growth and maintenance of a cell. The metabolic reactions in the prototypic system comprise pathways representative of glycolysis and amino acid synthesis  Transcriptional regulatory networks control the transcription state of a genome. In general, they describe the connections between environmental cues and transcriptional responses These networks have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals Studies on the dynamic behavior of regulation have involved constructing mass-balanced models of messenger RNA (mRNA) transcripts, ribosomes, and proteasomes in order to quantitatively predict protein synthesis 1 and H2 (polyk[H1][H2]), and the kinetic parameter polyk was estimated by considering a typical time constant for protein production based on polyk .The goal of the idFBA approach presented here, therefore, is to quantitatively account for the production and use of proteins throughout the cell. The transcriptional regulatory network is comprised of transcription factors that associate with specific genes, leading to the activation or inactivation of gene transcription. Activated genes yield proteins that participate in various intracellular signaling, metabolic, and regulatory reactions. Additionally, we considered amino acid requirements for protein synthesis: typically 30–80 moles of amino acids were required for every mole of protein, as shown in 3 is expressed only if both T1p and T2p are present.The prototypic transcriptional regulatory network presented here is comprised of 18 genes see , bottom.in vivo.As previously described, a cellular phenotype ultimately arises from complex interactions of network components across signaling, metabolism, and regulation. The prototypic integrated system described above was designed to exhibit the interconnectedness seen in actual cellular systems, as illustrated by the input/output relationships between the three functional modules of signaling, metabolism, and regulation see . FurtherS. cerevisiae, the prototypic single-cell eukaryote, was investigated. This module was comprised of key aspects of yeast osmoregulation, i.e., the active processes with which yeast cells monitor and adjust pressure and control their shape, turgor, and water content in response to extracellular conditions To assess the applicability of idFBA to actual biological systems, a representative integrated module in S. cerevisiae, from existing literature. The HOG MAP kinase pathway plays a pivotal role in the adaptation of S. cerevisiae to conditions of high external osmolarity Specifically, we reconstructed a portion of the high-osmolarity glycerol response (HOG) pathway, one of four major mitogen-activated protein (MAP) kinase cascades in As this model serves an illustrative purpose here, the HOG pathway was restricted to the key set of reactions necessary for its phenotypic function. Specifically, 26 reactions spanning 48 components were assimilated in stoichiometric matrix form, including 16 reactions across 33 components in signaling; a single transcription factor activating three regulated genes; and seven reactions across 12 components in metabolism. Inputs of this module included osmotic shock  and glucose (metabolism), and outputs included glycerol (metabolism). Key reactions connecting the underlying signaling, metabolic, and regulatory processes were the translocation of the kinase Hog1 into the nucleus for the activation of transcription factor Hot1 , and the synthesis of metabolic enzymes Stl1, Gpd1, and Gpp2 for reactions involved in the conversion of glucose to glycerol . Other reactions in the HOG pathway as previously experimentally characterized  were excluded from the reconstruction used here for simplicity.As with the prototypic system, the representative integrated yeast module was implemented using the idFBA framework as well as a kinetic model similar to the one in One modeling technique for evaluating cellular phenotypes is called flux balance analysis (FBA). FBA is a constraints-based approach that attempts to derive a phenotype in the form of a steady-state flux distribution for the reactions in a given biological system. FBA is based on the principle that all expressed phenotypes of a given biological system must satisfy basic constraints that are imposed on the functions of all cells S, where S is of size m components×n reactions and is comprised of stoichiometric coefficients that capture the underlying reactions of the biochemical network.FBA requires a stoichiometric reconstruction of the biochemical network of interest. An annotated genome cataloging which reactions specific enzymes catalyze is the basis for a detailed description of a network's components and interactions C over time t across all reactions within the system must be zero. Consequently, mass balance is defined in terms of the flux through each reaction and the stoichiometry of that reaction, and a set of coupled ordinary differential equations relating the roles of reactions with components may be written in the form of Equation 3.S denotes the m×n matrix of stoichiometric coefficients and v denotes the vector of n reaction fluxes, with each element (row) of the n-row vector v corresponding to the flux in the associated reaction (column) in S. The vector C is a m-row vector defining the concentrations of the m components within the system. This mass balance represents the principal constraint in FBA and defines a feasible solution space for the set of fluxes. Additional constraints such as thermodynamics can be incorporated into FBA as well, further narrowing the possible distribution of fluxes After the network is reconstructed, fluxes are calculated by deriving a dynamic mass balance for all the components within the system c is the vector that defines the coefficients, or weights, for each of the fluxes in vZ, wherein the elements of c can be easily manipulated, enables the formulation of many diverse objectives. Common choices for cellular objective functions in models of metabolic networks include biomass production Equation 3 generally leads to an under-determined system because the number of components tends to be far fewer than the number of reactions. Even with additional constraints, FBA usually requires performing an optimization with linear programming (LP) to identify a particular flux distribution. In other words, FBA involves optimizing the set of fluxes such that the flux through a particular cellular reaction is maximized (or minimized). A cellular objective represents what a given biological system has optimized toward through evolutionary pressures v that optimizes Z while lying in the bounded solution space defined by a set of physio-chemical, topological, and environmental constraints.vlb and vub are the lower and upper bounds on the reaction fluxes, respectively. For example, thermodynamic constraints or reaction directionalities can be incorporated by setting a given lbv = 0.Ultimately, FBA attempts to solve the LP problem in Equation 5 to find a physiologically-relevant cellular phenotype in the form of a flux distribution Though the steady-state assumption of FBA precludes the calculation of dynamic concentrations of the network components, dynamic profiles of cellular phenotypes  have been successfully predicted with a quasi-steady-state assumption Applications of FBA to dynamic simulations have focused on metabolic networks because time constants of metabolic transients are typically very rapid when contrasted with time constants characterizing whole-cell phenotypic changes. Exceptions include the incorporation of gene regulatory events, which are much slower than metabolic reactions, into FBA for time-course simulation of metabolic reactions As previously described, the stoichiometric reconstruction enforces explicit, chemically-consistent accounting of the components and reactions underlying a biochemical network, and facilitates the systematic analysis of fundamental network properties with FBA and associated analysis techniques Therefore, integrating signaling reactions with metabolic and regulatory reactions using FBA can facilitate the dynamic analysis of cellular phenotypes arising from environmental cues and provide a complete snapshot of cellular sysems. However, as previously described, applying FBA directly to integrated networks is challenging. First, unlike metabolic systems in which objectives for the FBA formulation are often experimentally characterized , objectives of signaling and regulatory systems are not well-defined. Second, integrated networks are comprised of reactions with mixed time scales , and FBA has previously been applied only to fast reactions for which steady-state assumptions hold.Here we describe the idFBA framework, including how we address these challenges. We use the prototypic integrated system as the basis for this discussion.1p consistently yields zero fluxes for the key pathway reactions denoted by dashed lines, including receptor internalization, pathway inhibition, and transcription factor degradation.As previously described, we represent signaling networks using a stoichiometric formalism, and we calculate a flux distribution with FBA (see Equation 5). Transcription factors activate transcriptional regulatory programs in response to extracellular cues. Consequently, one choice for the objective of a signaling network is maximizing the activation of transcription factors. However, as illustrated for the prototypic signaling network depicted in I. I indicates whether reaction iR is to be included in the system at time t, given an underlying network objective. It is constructed on the basis of a set of rules and other parameters  that a user specifies as consistent with data about the given system. For a given reaction iR at time t, I is multiplied by the upper bound of the associated reaction flux iv. If a particular reaction is included in the network at time t based on the user-defined rules and parameters , the binary parameters I for the reactions sharing components with the included reaction are set to zero at that time point and/or at future time points, depending on the specified time delays, indicating that they are not included in the network. Multiplying these zero-values by the upper bounds of the associated reaction fluxes nets a new upper bound of zero. As a consequence, fluxes through the reactions sharing components with an included reaction are set to zero at specific times in order to drive all the flux through the included reaction. In this way, the hypothesized network objective is maximized, all the while ensuring that flux is driven through all “active” reactions. For example, in 1R1 → L1R1,int) implies that the binary variables for the reactions (L1R1+S1 → L1R1 · S1) and (L1R1 → L1+R1) are set to zero. In this manner, a feasible flux distribution for a signaling network is obtained by maximizing for the activation of transcription factors. Importantly, the binary parameter I can take into account time delays associated with “slow” reactions, as described below.To address this challenge, we model the objective of a signaling network by introducing a binary parameter, represented as the matrix delay), indicating after what time a “slow” reaction is considered an “active” steady-state constraint in the stoichiometric matrix; and reaction duration (τduration), indicating how long the “slow” reaction remains as the effective constraint once it is activated. In the prototypic integrated system, “slow” reactions include protein degradation, pathway inhibition, and receptor internalization in the signaling network; the uptake of a carbon source and production of biomass in the metabolic network; and the synthesis of proteins in the transcriptional regulatory network.In addition, to characterize mixed time-scale phenomena using FBA, we implement idFBA by assuming quasi-steady-state conditions for “fast” reactions and incorporating “slow” reactions into the stoichiometric matrix in a time-delayed manner as in The optimized flux distribution that results from FBA is used to predict the time-course of phenotypic variables. The time-scale separation between “slow” and “fast” reactions is determined by the discretization of the time domain. Specifically, a reaction that reaches steady state or that produces a product at a specified threshold concentration within a single time step is considered “fast.” “Slow” reactions are those that take longer than the unit time interval to attain steady state.Ultimately, the implementation of the idFBA framework can be described as a seven-step process see :t. For example, in the case of the prototypic integrated system, the time step was specified as 0.1 h as described in “Discretize the time window into small steps, ΔsR×Nt incidence matrix (I) denoting which reactions participate during which time steps (Equation 6). Here sR represents the number of reactions within the system and Nt the number of time intervals (see Equation 6).I denotes a reaction iR, and each column denotes a time step Δt. The coefficients of I, at the intersection of reactions and time steps, are binary parameters indicating whether a given reaction participates during a given time step. A “0” denotes that a given reaction does not participate in the system at the specified time step, whereas a “1” denotes that the reaction does participate in the system at that time step. Although I is difficult to generate for an actual biological system given the limitations of available experimental technologies, it facilitates a best-guess of the system dynamics based on available literature. For example, for any given system, I can be derived from experimental data and assumptions inputted into the idFBA framework.Initialize a iR, multiply the corresponding coefficient I by the flux bounds of the reaction. By specifying I = 0 for excluded reactions, the fluxes of these reactions are set to zero when a “slow” reaction is included. For example, consider the signaling network shown in 1R1] →  is included and “active” and the objective of the network is maximizing the production of the activated transcription factor T1p, fluxes of the excluded reactions [L1R1]+[S1] → [L1R1 · S1] and [L1R1] → [L1]+[R1] are set to zero at the associated time steps.For each reaction in the system v, with the updated constraints, for the start of the current time step, currentt.Solve Equation 5 for the optimized flux vector, currentt, integrate the phenotype variable, pX, over the time step Δt (Equation 7).X) and substrate concentration (cS). These terms are given by Equations 8 and 9, where μ is a specific growth rate, and uS is the uptake rate for the carbon source.Given the optimized flux vector for I based on v at the current time step currentt given the time-delay and reaction duration parameters  (Equation 10).delay and τduration approximate the progression of “slow” reactions as steady-state constraints in the idFBA framework. The parameter τdelay describes when a particular “slow” reaction appears as a steady-state constraint in the stoichiometric matrix and instantaneously becomes an “active” reaction. The parameter τduration indicates how long the “slow” reaction is kept as a constraint in the stoichiometric matrix and maintained active. For example, in the transcriptional regulatory network, if the reaction flux of a transcription factor exceeds a specified threshold, the transcription of its target gene is incorporated into the matrix after a defined time (τdelay) , and the protein is assumed to remain in the system until it degrades (a period of time captured by τduration).Update v, at the current time step currentt imposes new constraints on the internal fluxes of the next time step. These constraints include ligand binding rates, carbon uptake rate, and protein production rates.Repeat steps 3 through 6. The optimized flux vector, As described above, implementing the idFBA framework in this manner dynamically simulates cellular phenotypes arising from integrated biochemical networks. We describe the results for a prototypic integrated system as well as a representative yeast module below.Technical implementation details. idFBA was implemented on the prototypic and yeast integrated systems in MATLAB v. 7.5 (part of the MathWorks R2007b release package).iC of the thi compound within a system may be described as in Equation 11 below ijS is the stoichiometric coefficient, jv is the rate of the thj reaction, and n is the total number of reactions in the network. Reactions that produce or consume the thi compound have non-zero stoichiometric coefficients and are therefore included in the thi differential equation.v, are functions of component concentrations, such as the concentrations of enzymes , as well as parameters including kinetic constants. These rates are described by different types of kinetic laws. For example, Michaelis-Menten expressions can be used to model enzyme kinetics To validate the results of the idFBA framework, we developed kinetic models of the prototypic integrated system and the representative integrated yeast module. As previously stated, kinetic models describe the temporal changes of compound concentrations due to production, degradation, modification, or transport Our ODE models of the prototypic integrated system and representative integrated yeast module were constructed from the underlying reaction network, with rate constants  obtained from literature. The systems of ODEs were continuously solved over the time window of interest . Details of these models, including the kinetic equations, kinetic constants, and ordinary differential equations, are presented in It is important to note that idFBA and kinetic modeling constitute two independent approaches. The idFBA framework involves performing an optimization, over multiple discretized time steps, to approximate the dynamics of a system with time-delay information from strictly stoichiometric constraints. By contrast, a kinetic model requires all of the kinetic parameters and, by continuously solving a set of ordinary differential equations, yields a more detailed portrait of the system dynamics. We attempt to illustrate here how the idFBA framework, with significantly fewer parameters, approximates the system dynamics observed through much more detailed ODE models.Technical implementation details. The kinetic models of the integrated prototypic system and representative integrated yeast module were implemented using the ode23tb ODE solver in MATLAB v. 7.5 (part of the MathWorks R2007b release package). The ode23tb solver is an implementation of an implicit Runge-Kutta formula, comprised of a trapezoidal rule followed by a backward differentiation formula of order two. The solver compromises efficiency for crude tolerances Using the prototypic integrated system shown in The specific implementation of the idFBA framework on the prototypic integrated system is detailed below.t, was set to 0.1 h as in The sample time, ΔE. coliThe maximum carbon uptake rate, Constraints on the uptake of substrates from the extracellular environment were required in order to identify an optimal flux distribution through the metabolic network. These constraints are detailed in delay and τduration) were specified to account for “slow” reactions. The “slow” reactions were allowed to participate in the reaction network after a delay τdelay and with duration τduration. The following rules were applied at time t:Temporal parameters  corresponding to the reaction iR describing the synthesis of a particular protein was set to 1 (indicating the reaction was “active”) if the flux of the activated transcription factor exceeded a specified threshold . All these data support the use of flux thresholds in idFBA, and these types of measurements would serve as inputs to the idFBA framework in future implementations.The binary variable d  as in . BecauseI for inhibition and degradation of the component were set to 1 (indicating these reactions were “active”) after specified time delays (τdelay) and with durations (τduration) of one sample time. This particular τduration was chosen since the steady-state constraints of these reactions impose complete depletion of available reactants within the current sample time currentt. Similarly, elements of I for the internalization of ligand-receptor complexes were set to 0 (indicating these reactions were “inactive”) after a time delay accounting for the time it takes for the complexes to become internalized.If the flux of a phosphorylated component was not zero , elements of ia and ib are specified in The objective functions of the resultant FBA formulations included maximizing the production of: (1) activated transcription factors in the signaling network; (2) the set of metabolites that produce biomass in the metabolic network; and (3) the amino acids, in relative ratios, that are necessary for the synthesis of proteins by the transcriptional regulatory network. The fluxes for the activation of transcription factors are  see . BiomassThe optimized fluxes for the production of activated transcription factors  of 10.5 mM. The production of the amino acid H2 was catalyzed by the enzyme delay = 40 min, and consequently, cellular growth was sluggish during this initial period. Two periods of no growth  corresponded to times when enzymes that catalyze metabolic reactions and protein synthesis were unavailable. For example, the first phase of no growth at t = 7 h was due to the degradation (and therefore inactivity) of transcription factors regulating key factors involved in biomass production, and the second at t = 8.25 h was caused by the degradation of phosphorylated proteins  that activate transcription factors leading to protein synthesis. Although these types of on/off descriptions are not precise, they serve as useful approximations of the phenotypic behavior over an entire time course.We first simulated the case in which the concentration of all three ligands was 2.0 µM. The results are shown in t≤6.5 h. Consequently, a no-growth period was observed at about 7 h. All transcription factors generated before t = 6 h were degraded by this time, preventing the amino acid H2 from being synthesized for a period of 0.5 h . The cell also stopped growing at about t = 8.2 h. The transcription factor T3p, which activates the synthesis of enzyme 1. Additionally, the simultaneous absence of all ligands led to the inactivation of S1p (S1) and the consequent lack of phosphorylation of T3 as illustrated in 1p and T2p have additional activation pathways . The inactive T1 can also be phosphorylated via a series of reactions initiated by ligand L2 if T1 is present in the system. 1 is present, approximately 15 percent more biomass is produced . This result makes sense since L1 initiates greater production of T1 than L2, which is involved in the synthesis of both T1 and T2. Eventually, both cases failed to produce biomass or uptake carbon after t = 4 h: in case 1, the absence of T2p and T3p meant that key receptors for the uptake of carbon were not expressed; and in case 2 (red dotted lines), the absence of T1p meant that the enzyme synthesizing the key amino acid H2 was no longer expressed. These types of dynamic characteristics of complex ligand availabilities are as expected yet are difficult to analyze without considering all the interactions in an integrated, quantitative manner such as the one implemented by idFBA.As illustrated in 1p and T2p together, and not T1p or T2p individually, are required for the production of the protein F was incorporated into the regulatory network. Again, two scenarios were simulated. In the first one, no ligand was available to the cell at 5≤t≤7 h. In the second one, the transcription factor T3p was not synthesized at 5≤t≤7 h. With these exceptions, the concentration of all ligands was maintained at 2 µM. 1p and T2p are available, the carbon supply is exhausted and maximum biomass is attained at t = 6.7 h, down from t = 8.7 h under the original regulatory program (blue solid line). By contrast, when no ligand is present during the two hours, the cellular machinery is unable to consume all of the carbon supply and instead the amount of biomass it synthesizes is reduced by over 33% .Additionally, robustness analyses can systematically establish S. cerevisiae HOG pathway was similar to that of the prototypic integrated system described above. Key aspects of this implementation are detailed below.The implementation of the idFBA framework on the t, was set to 0.1 h as in The sample time, ΔS. cerevisiaeThe maximum carbon uptake rate, To obtain optimal flux distributions in metabolism and signaling , rates for the uptake of carbon and signal transduction of osmotic stress were chosen based on known experimental values delay and τduration) were specified to account for “slow” reactions as in the idFBA implementation of the prototype. Briefly, “slow” reactions were allowed to participate in the reaction network after a delay τdelay and with duration τduration. At any given time t, the binary variable I governed whether a particular protein was present based on the flux of activated transcription factor Hot1 Temporal parameters (namely τThe objective functions of the FBA formulations for the yeast system included maximizing the production of: (1) the activated transcription factor in the signaling network; (2) the metabolite that produces biomass  in the metabolic network; and (3) the amino acids (assumed to be derived from glycerol in relative ratios) that are necessary for the synthesis of the three proteins Stl1, Gpd2, and Gpp1 by the transcriptional regulatory network. The flux for the activation of the single transcription factor Hot1 is The optimized flux for the activation of transcription factor Hot1  a sensitivity analysis of the model parameters and (2) an evaluation of the effects of network perturbations, such as single- or double-gene (reaction) knockouts. This type of analysis at the whole-cell level bridges the gap in knowledge of how systemic phenotypes arise in response to extracellular conditions.Ultimately, this validation of the idFBA-based implementation of the representative integrated yeast module implies that it may be used to further probe the The integrated dynamic Flux Balance Analysis (idFBA) framework presented here couples stoichiometric reconstructions of signaling, metabolic, and transcriptional regulatory networks with Flux Balance Analysis (FBA) to predict dynamic profiles of cellular phenotypes as a function of extracellular stimuli. Instantaneous inclusion of “slow” reactions in a time-delayed fashion accounted for network interactions occurring over a wide range of time scales. Previous approaches based on FBA have only addressed the coupling of regulatory structure with metabolic systems v = 0) on their counterparts, as described in “Conceptual Methods and Framework.”The key features and results described here include: (1) an explicit accounting of the protein synthesis demands of a transcriptional regulatory network in the context of signaling and metabolic functions; (2) a quasi-steady-state description of cellular signaling events, readily interfaced with metabolic and regulatory networks; (3) similar dynamic profiles of phenotypic variables  between the idFBA framework presented here and an explicit kinetic model; and (4) applicability of the idFBA framework to actual biological systems through an illustrative example using yeast osmoregulation and agreement with published values. To implement idFBA, the objective function for the underlying optimization problem included, for signaling networks, the reactions associated with the activation of transcription factors. The subsequent analysis resulted in “excluded reaction fluxes” . These reactions were specified as “active” to denote their participation in the reaction network by imposing simple constraints .jw is the weight associated with the objective after jT sample times.The idFBA framework optimizes the system at the current time step, currentt is determined such that it maximizes a cellular objective within a certain future time period of interest. The resulting optimization problem, including a Boolean representation of the transcriptional regulatory network, becomes a multi-horizon, mixed-integer linear programming problem. Though the solution of such a problem needs further development for its scalability to large-scale systems The main assumption of a multi-horizon formulation is that the flux distribution at in silico flux distribution for the integrated system, a key step in the idFBA framework.Recently, a method called Biological Objective Solution Search (BOSS) was developed for the inference of an objective function for a biological system from its underlying network stoichiometry as well as experimentally-measured flux distributions The fact that different reactions occur on different time scales  is readily handled within the idFBA framework. Reactions with time constants of more than a unit time step are considered “slow”. However, identifying the optimal discretization of the time domain would facilitate a more accurate simulation for systems with multiple time-scales. Given typical rate constants, model reduction As illustrated by the idFBA results for the prototypic integrated system and particularly the representative yeast module, the methodology and analyses afforded by this framework can provide insight into fundamental characteristics of biological systems, including network components and interactions. Evaluating how whole-cell systems respond to different perturbations, including modifications to environmental cues as well as intracellular reactions, can offer insights into disease mechanisms and possible therapeutic avenues. For example, assessing how genetic perturbations of signaling proteins affect the transcriptional program and metabolism of a cell is essential to fully appreciating the end-stage phenotypic effects of the perturbations on the whole cell. Furthermore, evaluating how modifications to an existing transcriptional regulatory program  affect whole-cell behavior is essential in the design and engineering of metabolic systems. Such a complete picture of cellular response can drive accurate predictions of disease and drug discovery.Additionally, unlike kinetic-based models and other similar approaches, the idFBA framework requires significantly fewer parameters and can facilitate an approximation of the dynamics of large-scale systems quickly and efficiently, given a stoichiometric network reconstruction. As has been hypothesized in the literature recently, our idFBA results support the theory that the structure of a network, rather than the detailed kinetic values that describe it, can drive the dynamics of its phenotype In conclusion, a novel technique called integrated dynamic Flux Balance Analysis (idFBA) has been developed to analyze integrated systems, and specifically to account for the interactions between signaling, metabolic, and transcriptional regulatory networks across many time scales. This approach facilitates the study of systemic effects of extracellular cues on cellular behavior in a quantitative manner. Additionally, the success of idFBA on a prototypic integrated system as well as a representative integrated yeast module serves as a benchmark for future analyses of integrated biochemical systems.Text S1 - Prototypic Integrated System(0.06 MB PDF)Click here for additional data file.Text S2 - Representative Yeast Module(0.55 MB DOC)Click here for additional data file.


Halobacterium salinarum is a bioenergetically flexible,halophilic microorganism that can generate energy by respiration,photosynthesis, and the fermentation of arginine. In a previous study, using agenome-scale metabolic model, we have shown that the archaeon unexpectedlydegrades essential amino acids under aerobic conditions, a behavior that canlead to the termination of growth earlier than necessary. Here, we furtherintegratively investigate energy generation, nutrient utilization, and biomassproduction using an extended methodology that accounts for dynamically changingtransport patterns, including those that arise from interactions among thesupplied metabolites. Moreover, we widen the scope of our analysis to includephototrophic conditions to explore the interplay between different bioenergeticmodes. Surprisingly, we found that cells also degrade essential amino acids evenduring phototropy, when energy should already be abundant. We also found thatunder both conditions considerable amounts of nutrients that were taken up wereneither incorporated into the biomass nor used as respiratory substrates,implying the considerable production and accumulation of several metabolites inthe medium. Some of these are likely the products of forms of overflowmetabolism. In addition, our results also show that arginine fermentation,contrary to what is typically assumed, occurs simultaneously with respirationand photosynthesis and can contribute energy in levels that are comparable tothe primary bioenergetic modes, if not more. These findings portray a picturethat the organism takes an approach toward growth that favors the here and now,even at the cost of longer-term concerns. We believe that the seemingly“greedy” behavior exhibited actually consists of adaptationsby the organism to its natural environments, where nutrients are not onlyirregularly available but may altogether be absent for extended periods that mayspan several years. Such a setting probably predisposed the cells to grow asmuch as possible when the conditions become favorable. Halobacterium salinarum, is a model organism for thearchaeal domain of life. It is bioenergetically flexible in that it can performboth respiration and photosynthesis and in addition can also derive energy usingfermentation. Accordingly, it is a good model system for investigating theinterplay between different energy generating mechanisms. In this study, weinvestigate these relationships as well as how energy production is linked tothe other processes involved in growth, including the consumption of nutrientsand the production of cellular material. Because Halobacteriumsalinarum thrives in salt-saturated solutions, such as those that maybe found in salt lakes and solar salterns, our study yields insight on how thesecellular processes operate in environments that are lethal to most life onEarth.Living cells can produce usable energy through various means. For example,animals derive energy, through respiration, from nutrients that they consume,and plants from light using photosynthesis. The particular microorganism that westudy,  Halobacterium salinarum is a halophilic archaeon that thrives inextremely saline environments with salt concentrations reaching 4 M or higher. Theorganism is perhaps most well known for its retinal-protein bacteriorhodopsin (BR),which is a light-driven proton pump. BR is the only known nonchlorophyll structurethat allows photosynthesis H. salinarum's photosynthetic capabilitiesare its most well-studied aspects. For example, the 3D structure of BR has beenresolved, and its complete catalytic cycle elucidated at the molecular level. Essentially, FBA uses linear optimization to find a fluxdistribution that maximizes a particular objective function, e.g., growth rate orATP production Our aim in this study is two-fold. First, we set out to investigate the interplaybetween energy generation, nutrient utilization and biomass production underdifferent bioenergetic modes. Second, we also analyzed the relationships between thedifferent energy producing mechanisms of respiration, photosynthesis andfermentation themselves, which are typically examined individually. To achievethese, we used a genome-scale metabolic network that connects the different aspects.Our results include several findings that are contrary to assumptions which aretypically made; particularly with respect to the utilization of nutrients, and howthe bioenergetic modes operate. From a more methodological perspective, we alsosought out to extend the existing framework for hybrid genome-scale metabolic modelsto handle biological systems where nutrient utilization and growth rates vary withtime. Such changes in nutrient consumption, for example, can be the result of thedifferences between growth phases, or can arise from the interactions between thesupplied metabolites. We demonstrate that the extended methodology not only accountsfor such dynamics, but in several instances actually led to the identification ofthe underlying causes.H.salinarum has analogs of all five complexes associated withoxidative phosporylation found in mitochondria and E. coli(complexes I through V). However, there are significant differences from itsbetter-studied counterparts. For example, the subunits of complex I thatcomprise the NADH acceptor module (nuoEFG) could not be assigned, similar towhat has been observed for Sulfolobus solfataricusH. salinarum. Rather, NADH is oxidized by anon-homologous type II NADH dehydrogenase that also reduces quinones but isincapable of proton translocation H.salinarum pathway is also different in that menaquinone, ratherthan ubiquinone, is the likely mobile carrier used to shuttle electrons from thecomplex I analog to the complex III analog. A similar proposal has been made forthe closely related organism Natronomonas pharaonisMost of the reactions in the genome-scale metabolic network we use in this studyare taken directly from previous reconstructions E. coli are the composition of the complex IIIanalog and the mobile carrier which carries electrons to the terminal oxidase. The cytochrome c1 subunit(petC) of E. coli complex III, responsible fortransfering electrons to the mobile carrier of the organism, cytochrome c, doesnot seem to have a homolog in H. salinarum. In fact, geneswhich code for cytochrome c could also not be assigned. Accordingly, we believethat H. salinarum likely uses a different carrier. We proposethis to be halocyanin, which is a blue copper protein originally isolated fromN. pharaonisN.pharaonis, based on its localization as a membrane protein and itsmidpoint potential that is consistent with a mobile carrier's hcpB, is fused with the cbaD subunit ofcomplex IV in H. salinarumTwo other important differences of the proposed pathway from the systems inmitochondria and H. salinarum.Fortunately, while information on the individual components are unavailable,data on the aggregate process of respiration exists. This is very important formodeling because it determines the overall energy production capability of theorganism. O2 pulse experiments indicated an ATP to O2ratio of 1∶1. Measurements of initial proton uptake duringphosphorylation demonstrated a ratio of 10∶1 betweenH+ and ATP +, given that lightinhibits respiration with an observed stoichiometry of 24 photons perO2 molecule Very little is known regarding the stoichiometry of the proton translocatingprocesses in the respiratory chain of cf.Consumption and production rates were modeled using differential equations of theform of either Equation (2) or Equation (3) cf., with thH. salinarumduring aerobic growth, at least among the nutrients supplied. Unlike most of theother provided metabolites, the uptake patterns of these amino acids remainedconstant, and their consumption rates high, up until their depletion. Theexperimental nutrient utilization data and the corresponding model simulationsare shown in arginine deiminase . Citrulline is then converted to ornithine and carbamoyl-phosphate byornithine carbamoyltransferase .Ornithine is mainly transported outside through an arginine-ornithine antiporter(≈95%), a process that accounts for most of the arginine takenup. On the other hand, carbamoyl-phosphate, via the action of carbamatekinase , is degraded to NH3 andCO2 in a reaction that produces ATP from ADP. In summary, most ofthe supplied arginine is rapidly converted to ornithine through a process thatproduces ATP. As will be discussed later, this fermentation process accounts formost of the energy in the cells at the early stages of growth.In contrast to aspartate, leucine and isoleucine, the piecewise uptake equationform is clearly superior over the basic definition (Equation 2) for somemetabolites. Most notable of these are ornithine, alanine and proline, for whichresidual errors dropped by 98.6%, 92.4% and54.5%, respectively. Each of these amino acids, at some point,switches from production to consumption. For ornithine and proline, it isinteresting that the points at which their respective utilization patternschange are close to each other, and that both occur near the time when arginineis depleted. This makes sense as arginine is consumed rapidly by the cells, andboth ornithine and proline are downstream of its catabolic route. Flux-balancesimulation at a point before arginine depletion shows the situation depicted inHalobacterium salinarum during aerobic growth. Accordingly,cells had to switch their metabolism to utilize more of the substitute sourcesin order to sustain growth. Alternative explanations are provided assupplementary information  they can be secreted after conversion to anothermetabolite, for example following partial degradation. Given that the rates atwhich most of the supplied amino acids were consumed far exceeded therequirements for biomass incorporation as described in the first fate mentionedabove, then at least one of the other three possible fates must also be true forthe relevant amino acids. The results for individual metabolites are summarizedin Nutrients consumed by cells can have various fates: (1) they can be incorporatedinto the biomass with at most very minimal changes, such as in the case of aminoacids incorporated as protein residues or free metabolites; (2) they can beconverted to other biomass components, typically after partial degradation; (3)they can be oxidatively degraded to COH.salinarum. The heavy rates at which they are degraded can cause theorganism to prematurely terminate its own growth. One would typically assumethat it would be better for the cells to use essential nutrients sparingly,especially considering the fact that there are other non-essential sources ofenergy and carbon available. However, leucine and isoleucine, as discussedearlier, are even among the preferred metabolites of H.salinarum, i.e., nutrients for which the highest uptake rates wereobserved.Consistent with our previous observations All nutrients that are taken up by cells are either incorporated into the biomass(fates 1 and 2 mentioned above) or converted to metabolic by-products (fates 3and 4). By approximating the biomass composition using measurements,calculations and assumptions, and then correlating these information with theobserved population sizes, analysis and prediction of the latter set of fatesbecomes possible. We took most of the biomass composition values from ourprevious work 2 is an expected metabolic by-product of cells under aerobicconditions. Indeed, if it is assumed that all carbon atoms that are taken up anddo not appear in the biomass are completely degraded through respiration, thenCO2 should account for the bulk of the by-product pool. Wecalculated the  amount of oxygen that will be needed under such ascenario at various points during growth, using flux balance analysis where weset energy production as the objective function and assumed an unlimited oxygensupply. Note that stoichiometric relationships between the oxidation of carbonsubstrates and the consumption of oxygen are implicitly defined by the reactions(pathways) in the metabolic network. However, comparison of these calculatedresults with actual oxygen consumption measurements indicated thatrespiratory-linked degradation is not the fate of most carbon atoms that areconsumed but do not get incorporated into the biomass. In fact, the data showsthat cells use only about 20% of the oxygen that they would otherwiseneed to completely oxidize all the material. Thus, the formation andaccumulation of other by-products in significant quantities (in the mM range),probably including those that result from forms of overflow metabolism, likelyoccur in the preparations. In addition, the described situation already seems tohave been the case even before the oxygen supply became limiting at CO2/OD·ml·hr during growth. At about We observed a maximal respiratory rate of approximately 1 µmolO2O = ADP+P)into the network, and performed flux balance analysis with it defined as theobjective function. Under aerobic conditions, cells can derive energy (ATP) through respiration andsubstrate level phosphorylation. We calculated the maximum  energythat the system can produce as well as the fraction of this that can beattributed to respiration at various points, using the observed nutrientutilization. The values are reflected by the red and blue curves, respectively,in H.salinarum can be grown with neither oxygen nor light just asreadily, by supplying large amounts of arginine. After the amino acid isdepleted, respiration accounts for most of the produced energy. The additionalenergy that can be produced through the further non-respiratory-relateddegradation of other (non-arginine) nutrients is significantly smaller. Thisbeing the case, it is remarkable that non-respiratory-related processes accountfor approximately 80% of the nutrients that are consumed but notincorporated into the biomass. Again, we should note that the pertinentmetabolites include essential ones.Throughout growth, the theoretical maximum energy that the system can produce havebeen found to be repressed during phototrophy, presumably to repress thesecondary energy source We modeled the consumption and production of nutrients during phototrophy usingthe same procedure we employed for the aerobic case. Accordingly, the ormation . AnalogoNext to arginine, aspartate exhibited the highest uptake rate, and is the secondsupplied amino acid that was depleted at abolites , not eveUnlike in the aerobic case, the depletion of phenylalanine coincided with anumber of discernable qualitative changes in the uptake patterns of thenutrients. In addition to the ones stated above, consumption of the amino acidserine seems to have stopped at about the same time, even though growth, albeitalready in the late exponential phase, could still be observed. The reason forthis is unclear. Serine was already nearly exhausted at about 0.2 mM by then.Moreover, it is also at this point that alanine switched from production toconsumption. Serine and alanine are metabolically related to each other throughtheir degradative pathways, as the two can enter central metabolism throughpyruvate. In the aerobic case, not only were we unable to observe an arrest inserine uptake, but the switch of alanine from production to consumption actuallyconincided with the acceleration of serine consumption. While neither serine noralanine share the catabolic route of phenylalanine, it is possible thatphenylalanine played a more important role in the phototrophic case; that is,the observed behaviors may have been indirect effects of the aminoacid's depletion. In this respect, we should note that the earlybiosynthetic steps of aromatic amino acids are shared with the quinones, whichplay critical roles in respiration.H. salinarum. Nevertheless, in retrospect, thisbehavior is consistent with the emerging picture that the organism takes anapproach toward growth that is focused on the here and now, even at the cost oflonger-term concerns. Indeed, the essential amino acids leucine, lysine,isoleucine, methionine and valine are again among the amino acids that are takenup in amounts far more than required for biomass formation.Analogous to the aerobic case and somewhat unexpectedly, the rates at which mostof the supplied amino acids were taken up from the medium far exceeded the ratesat which they were incorporated into the biomass with minimal modifications(fate 1). These findings are summarized in 2 to O2 ratiowhich was calculated using the stoichiometry of the parts of the metabolicnetwork that are involved in the oxidation of the relevant aminoacids—shows that approximately 66% of the carbon wasneither incorporated nor respired. Considering the fact that the growth ratesobserved for phototrophy were nearly five-fold slower, it is remarkable that theratios of the nonincorporated, nonrespired carbon under both conditions are asclose to each other as they are. Indeed, aerobic cultures already reached 1.5 ODafter only slightly more than 80 hours, while, in stark contrast, phototrophiccultures took about 450 hours to reach similar levels. It would therefore seemthat a large part of the nutrients that were taken up but were neitherincorporated into the biomass nor used as respiratory substrates has more to dowith growth (biomass production) than with any form of maintenance. For thisreason, it is likely that some as of yet uncharacterized, non-maintenance growthprocesses are at least partially responsible for the low carbon incorporationrates.When phototrophic cultures reached 1.5 OD, only about 14% of thesupplied carbon that had been consumed could be attributed to the amino acidcontent of the biomass  that essential amino acids are degraded not only during respirationbut even under phototrophic (anaerobic) conditions, where energy should alreadybe abundant; (2) that fermentation of arginine, which is often considered asecondary, alternative energy source, occurs simultaneously with eitherrespiration or photosynthesis; (3) that considerable amounts of metabolites areproduced and accumulate in the medium under both conditions, as a result ofnutrients that are consumed but not incorporated into the biomass nor used asrespiratory substrates; and (4) in connection with the previous point, that thetotal carbon incorporation rate is extremely low even under phototrophic(anaerobic) conditions (approximately 20%), when one would typicallyexpect nutrient consumption to be in quantities that are only sufficient forbiomass production since energy is already derived from light. All of thesefindings are consistent with the seemingly “greedy” behaviordemonstrated by Halobacteriumsalinarum may be found, life is characterized by blooms that may notoccur for years after a previous episode. In the Dead Sea for example, no growthof the unicellular green alga, Dunaliella parva, which isresponsible for all of the primary productivity, is possible when the saltconcentration of the water column is invariably high. Blooms ofDunaliella in the Dead Sea occur only after significantdilution of the upper levels by the influx of freshwater. In turn, this allowsthe archaeal community to bloom at the expense of the organic material producedby the alga Halobacterium salinarum to grow as much as possible whenthe conditions become favorable. In connection to this, as for the times whentheir environments are not conducive to growth, the capacity of the halobacteriato survive in adverse conditions for extended periods has been well establishedIn the salt lakes and solar salterns where 2by-products/metabolites accumulate in the medium in significant amounts underboth aerobic and photorophic conditions, likely including partially degradedforms of the supplied nutrients. Unfortunately, attempts to identify thesecreted molecules are complicated by the (necessary) extremely high saltconcentrations (4 M) in the growth media. We intend to focus on theidentification of these metabolites and on the elucidation of thereasons/dynamics behind their accumulation in a succeeding study.One of the predictions of our model is that non-COSpecific sets of nutrients dominate material uptake at various points duringgrowth. For example, at the early stages, highest uptake rates were observed foraspartate and leucine, and, to a lesser extent, glutamate and serine. Note thatarginine uptake was the highest, but most of its carbon skeleton was secreted asornithine. With this information in hand, we would like to perform flux analysisusing labeled substrates For the consumption or production of each nutrient Preliminary inspection of the data revealed that the transport patterns of someof the metabolites change during growth. For example, ornithine, at some point,switches from being produced and accumulated in the medium to being steadilyconsumed by cells. Accordingly, we used a simple extension of Equation (2) thatallows for two modes:fminsearch function of MATLAB.Systematically defined sets of initial parameter values were used in solving theinverse problems (parameter estimation). To minimize the possibility ofoverfitting, the more sophisticated form of Equation (3) was used in the finalmodel, in favor over the simpler equation form, only if it resulted insignificant improvement, that is, the residual error, a measure of the(dis-)agreement between the model and data, is substantially lower. In thisrespect, it is reasuring that although Equation (3) is clearly better for somemetabolites, such as alanine and ornithine, it hardly makes any improvement forothers, such as leucine and isoleucine, which seem to be staples of the cells cells were grown inchemically-defined medium, with composition defined in Strain ormation . SimilarFigure S1et al., 2008), with the population size. Thistotal incorporation value is represented by the red broken curve. To allowfor a comparison between material uptake and incorporation, we use the bluecurve to indicate the total amount of carbon that has disappeared from themedium, calculated using the supplied nutrients and ornithine . Att = 140 h, only about19% of the total carbon that has been consumed can be accountedfor by the biomass. A similar graph for the phototrophic case is provided inTotal carbon consumption and biomass incorporation of aerobically growncells. The green circles indicate the amount of carbon in the biomass thatis due to amino acids (primarily protein). To account for the fact thatamino acids (proteins) are not the only components of the biomass, weapproximated the total carbon incorporation (inclusive of the amino acids)by scaling (multiplying) the biomass reaction definition, which is describedin the section titled “Aerobic Growth” and characterizedin Click here for additional data file.Figure S2Amino acid composition of biomass during aerobic growth. Theamount of each individual amino acid in the biomass was quantified atdifferent optical densities. The measurements include those that areintegrated into proteins (residues) and those that are free inside thecells. The red line in each graph indicates the best linear fit for theparticular molecule. Average deviation from the line in all cases is below12.5%. Due to experimental limitations, we were not able toobtain values for cysteine and tryptophan, and the values for aspartate andglutamate are already inclusive of asparagine and glutamine, respectively.(0.04 MB EPS)Click here for additional data file.Figure S3t = 30 h. The smallerpeaks and troughs of the red curve are due to the discontinuities of thepiecewise models used for the uptake of several metabolites.Theoretical  and actual oxygen consumptionrates. The red broken curve indicates the amount of oxygen that wouldhave been needed if all nutrients that were taken up but did not getincorporated into the biomass were used for respiration. The blue brokencurve shows the actual oxygen utilization rate. The large discrepancybetween the two curves suggest that overflow metabolism is prevalent. Theoxygen supply starts to become limiting at about(0.01 MB EPS)Click here for additional data file.Figure S4t {similar, tilde operator } 15), fermentation ofthe amino acid generates most of the energy in the system, even more thanrespiration.System energy in ATP equivalent. The red curve shows the maximumamount of energy, computed using FBA, that the system can produce at variouspoints during growth. The blue curve indicates the amount of energy that isproduced through respiration. Interestingly, prior to the depletion ofarginine ((0.01 MB EPS)Click here for additional data file.Figure S5Growth curves. (Left) Cells grown aerobically in the dark. Adoubling time of approximately 11 hours was observed. (Right) Cells grownanaerobically in light. The culture exhibited a much slower growth rate,with a doubling time of about 50 hours. Both cultures are the result ofthree rounds of adaptation by repeated inoculation to the respectivecondition.(0.02 MB EPS)Click here for additional data file.Figure S6ti,b parameter value, which representsa point near where the qualitative change occurs, is indicated with aninverted green triangle. This figure is similar to Nutrient consumption and production data from cells grown anaerobicallyin light. Experimental data are indicated using diamonds(average) with error bars provided. Model simulations are illustrated usingred broken curves. The transport patterns of several metabolitesqualitatively change during growth. For such metabolites, the piecewiseEquation (3) was used to model utilization, and the corresponding(0.15 MB EPS)Click here for additional data file.Figure S7Summary of nutrient uptake and incorporation rates under phototrophic(anaerobic) conditions. The blue curves indicate the total amountof each amino acid that has been consumed/produced. The red curves show thetotal amount of that particular amino acid that has been incoporated intothe biomass, whether integrated into proteins or as free metabolites, ascalculated from the population size and the growth (biomass) function.Similar to the aerobic case, and somewhat unexpectedly, most of the suppliedamino acids exhibited uptake rates that far exceeded the rates at which theywere incorporated. This implies that the amino acids, in addition to biomassincorporation, are also catabolized significantly.(0.24 MB EPS)Click here for additional data file.Figure S8et al., 2008), with thepopulation size. This total incorporation value is represented by the redbroken curve. To allow for a comparison between material uptake andincorporation, we use the blue curve to indicate the total amount of carbonthat has disappeared from the medium, calculated using the suppliednutrients and ornithine . Att = 650 h, only{similar, tilde operator }20% of the total carbon that has beenconsumed can be found in the biomass.Total carbon consumption and biomass incorporation of phototrophicallygrown cells. The green circles indicate the amount of carbon inthe biomass that is due to amino acids (primarily protein). To account forthe fact that amino acids (proteins) are not the only components of thebiomass, we approximated the total carbon incorporation (inclusive of theamino acids) by scaling (multiplying) the biomass reaction definition, whichis described in the section titled “Aerobic Growth” andcharacterized in Click here for additional data file.Table S1Composition of chemically-defined medium.(0.02 MB PDF)Click here for additional data file.Text S1Analysis of boundary parameters.(0.11 MB PDF)Click here for additional data file.Text S2Oxygen measurements.(0.05 MB PDF)Click here for additional data file.


Identifying essential genes in bacteria supports to identify potential drug targets and an understanding of minimal requirements for a synthetic cell. However, experimentally assaying the essentiality of their coding genes is resource intensive and not feasible for all bacterial organisms, in particular if they are infective.Salmonella typhimurium. We compared our predictions to the viability of experimental knock-outs of S. typhimurium and identified 35 enzymes, which are highly relevant to be considered as potential drug targets. Specifically, we detected promising drug targets in the non-mevalonate pathway.We developed a machine learning technique to identify essential genes using the experimental data of genome-wide knock-out screens from one bacterial organism to infer essential genes of another related bacterial organism. We used a broad variety of topological features, sequence characteristics and co-expression properties potentially associated with essentiality, such as flux deviations, centrality, codon frequencies of the sequences, co-regulation and phyletic retention. An organism-wise cross-validation on bacterial species yielded reliable results with good accuracies (area under the receiver-operator-curve of 75% - 81%). Finally, it was applied to drug target predictions for Using elaborated features characterizing network topology, sequence information and microarray data enables to predict essential genes from a bacterial reference organism to a related query organism without any knowledge about the essentiality of genes of the query organism. In general, such a method is beneficial for inferring drug targets when experimental data about genome-wide knockout screens is not available for the investigated organism. By definition, essential proteins of a cellular organism are necessary to live and replicate, and are therefore attractive targets for antimicrobial treatments. However, experimentally assaying the essentiality of their coding genes is error prone when done in high throughput. Additionally, experimental screens are resource intensive and not feasible for all organisms, as typically, for each gene a knock-out strain needs to be constructed. Besides this, pathogenic bacterial organisms are hazardous to cultivate and therefore need higher laboratorial efforts. The metabolism of a cell is substantial for maintaining life and growth, and hence metabolic enzymes have been successfully targeted by antibiotics inhibiting essential processes in bacterial genomes .in silico. Flux balance analyses (FBA) is widely used to assess the essentiality of genes [P. falciparum [S. cerevisiae to the less studied yeast strain S. mikatae [E. coli and S. cerevisiae [Several computational techniques have been developed to identify essential genes of genes . Howeverof genes . Descripof genes -6. The tof genes . In a prlciparum -12. It wlciparum . Also se mikatae . Additiorevisiae ,15. AlthEscherichia coli [Escherichia coli [Pseudomonas aeruginosa [E. coli and P. aeruginosa, i.e. we trained with E. coli and validated with P. aeruginosa (and vice versa) to obtain the quality of the performance of this approach. We then applied the trained and validated classifiers to the pathogenic bacterium Salmonella typhimurium. We compared our results with the literature and experimental data of a large knock-out study for S. typhimurium [S. typhimurium, 23 out of which have been described previously as drug targets in other micro-organisms. We suggest these and the remaining twelve as potential new drug targets for the organism we studied (S. typhimurium).In a previous study, we developed and applied an integrative machine learning method that combined these topology based methods to validate an experimental knock-out screen of hia coli . We now hia coli ,18 and Pruginosa ,20 to trruginosa , and genhimurium . FurtherE. coli. For this, we trained classifiers (machines) with the experimental data of two genome-wide knock-out screens of Pseudomonas aeruginosa . We trained several (100) classifiers with all essential genes and an equal amount of randomly selected non-essential genes (stratification of the training data). The trained machines were then applied to predict essential genes for the query organism (E. coli). The output of all machines was summed up and used as a voting score that represented the propensity of a gene to be lethal for the cell. In turn, the same scheme was applied to predict essential genes for P. aeruginosa with classifiers which were now trained with two datasets from E. coli  of 0.80 and 0.79 when compared to the experimental datasets paeL and paeJ, respectively. In turn, for E. coli we yielded an AUC of 0.81 and 0.75 when compared to ecoB and ecoG, respectively. We wanted to obtain a reliable list of potential drug targets. For this, predictions for essential genes needed a low number of false positives. Hence, we set a high stringency and calculated the precision  with a high selection criterion (more than 195 out of 200 votes). We yielded a precision of 67%  and 100%  when predicting essential genes for P. aeruginosa. In turn, we yielded a precision of 61%  and 65%  for E. coli. We yielded the best classifier results when using all features, in comparison to the classification performance when using individual sets of features  and the corresponding feature values. Figure in silico) mutant could not produce one or more downstream products, RUP was zero whereas the percentage of unreachable products was increased in comparison to the situation in which all products could be produced. The higher the percentage of unreachable products of the mutant, the less products of the knocked out enzyme could be covered by alternative pathways. The number of substrates and products of the reactions of the knocked out gene  were positively correlated to gene essentiality  showing that essential enzymes metabolize more different compounds. Interestingly, the number of neighboring reactions (NNR) and the number of neighbors of neighboring reactions (NNNR) showed a weak negative correlation to essentiality . This is reasonable as a reaction with a high number of neighboring reactions may have more metabolites as products that can be produced by alternative enzymes. The clustering coefficients (CCV) showed the same tendency  also pointing to advantageous alternative pathways.The efficiency of flux deviations was estimated by the features RUP and PUP which gave an estimate if all products of the knocked-out reaction could be produced without the reaction (RUP) and how large the percentage of non-producible products (PUP) was. RUP was a Boolean feature to observe if the mutant could produce all products of the knocked-out reaction. RUP = 1 was set if all downstream products could be produced by the mutant while RUP was set to zero if at least one downstream product could not be produced. The number of reachable products (RUP) was highly negative correlated and the percentage of unreachable products (PUP) highly positive correlated to the essentiality of a gene  as shown in Figure We estimated the feasibility of possible flux deviations by a set of features describing alternative pathways. The number of alternative pathways (ND), the average path length of the deviations (APL) and the length of the shortest alternative path (LSP) described the feasibility of alternative pathways. As expected, all of them were negatively correlated to essentiality , i.e. knocked out enzymes for which alternative pathways existed were less likely to cause a lethal phenotype if knocked out. Choke-points (CP) are uniquely consumed or produced compounds in the metabolism and showed a positive correlation with essentiality (P = 2.8E-04) as choke-points are often difficult to be replaced by the rest of the metabolism. Load-scores (LS) give an estimate of how often a reaction is involved in metabolic processes. They were also positively correlated to essentiality (P = 9.4E-04). Betweenness centrality (BW) and eccentricity (EC) were strongly positive correlated to essentiality  showing that enzymes have a higher influence on vitality if placed in the center of the network. Closeness centrality (CN) also showed a positive correlation (P = 0.0020). Interestingly, the eigenvector centrality (EV) showed a negative correlation (P = 0.0013). Betweenness, closeness and eccentricity centrality are global centrality measures considering the whole network while the eigenvector centrality is a measure for local centrality and is computed from its neighbors. Note that typically a node with a high value of eigenvector centrality is a hub (node with high connectivity) with other hubs connected to it. Hence, flux deviations may be more likely for local hubs that have hubs in their vicinity making the node replaceable whereas global central nodes seemed to be generally substantial for maintaining the metabolic flow in the network. Therefore the eigenvector centrality may describe the network topology more in the sense as the clustering coefficient, specifically in respect to the likelihood of alternative pathways.-5 (H5) worked best showing that also non-perfectly matching sequences may take over functions of the knocked out gene. The number of genes having similar expression (NGSE) exhibited also a negative correlation to essentiality (P = 1.7E-04) which may be due to co-expression of genes with analogous function. For the feature phyletic retention (PR), the number of prokaryotes having orthologs of the knocked out gene showed a positive correlation to essentiality (P = 2.1E-16) supporting the findings of a previous study that conserved genes in evolution hint for their essentiality [As expected, the number of homologous genes  showed a negative correlation to essentiality . Interestingly, an E-value cut-off of 10ntiality .rd codon position facilitates stable genetic inheritance into off-springs and cellular replicates. Interestingly, we observed a larger difference of T3s in E. coli when compared to P. aeruginosa. It was found that a large average of G and C content at the third codon position is common for all genes in P. aeruginosa [E. coli compared to P. aeruginosa , we used decision trees for an alternative approach to determine the most discriminating features for gene essentiality. Decision trees were trained with the datasets ecoB, ecoG, paeL and paeJ. It is known that the first decision of a decision tree is performed with the best discriminating feature . TherefoS. typhimurium and obtained votes from four hundred machines for each gene of S. typhimurium to be essential. To obtain a reasonable threshold for the number of votes predicting a gene to be essential, we compared the number of essentially predicted genes with the numbers of the training sets for E. coli and P. aeruginosa. For E. coli 104 and 147 genes were essential corresponding to the datasets ecoB and ecoG, respectively, and for P. aeruginosa, 92 and 150 . Therefore, we set a threshold of 350 votes (of 400 machines) to classify a gene as essential for S. typhimurium and obtained a comparable amount of 128 predicted essential genes. The complete list of genes being predicted as essential is given in the supplement  and were recognized by our classifiers. We then searched in the literature to find drug treatments of these enzymes for other micro-organisms. The results are listed in the following. Two asterisks (**) mark a gene for which enzyme we found clear evidence to be a drug target for a micro-organism. One asterisk (*) was set for a gene when we found reasonable evidence for its enzyme to serve as a drug target for a micro-organism. Hence, enzymes with one asterisk may serve for finding new drug targets and enzymes with two asterisks for transferring drug targets from other bacterial diseases to the disease we studied (S. typhimurium). Table We applied our trained machines from all four datasets  to predict essential genes for himurium . They deStaphylococcus aureus [** murE: UDP-N-acetylmuramoylalanyl-D-glutamate-2,6-diaminopimelate ligase is an essential enzyme and a well-known target against bacterial cell walls of s aureus .* murG: N-acetylglucosaminyl transferase is a potential antibiotic targeting the biosynthesis of bacterial peptidoglycans. However, it is difficult to design inhibitors for this enzyme. Identifying inhibitors is under current research ,30.Escherichia coli, Proteus mirabilis and Klebsiella pneumoniae [** murC: UDP-N-acetylmuramate-L-alanine ligase catalyzes an essential step in the pathway for synthesizing peptidoglycan precursors. Recently, new inhibitors of the MurC enzyme have been successfully tested for eumoniae .Mycobacterium tuberculosis [* pyrH: The gene for uridylate kinase is essential in rculosis .Streptococcus pneumoniae [** uppS: Undecaprenyl pyrophosphate synthase (UPPS) is a novel antibacterial target of eumoniae .** accA: Acetyl-CoA carboxylase is a drug target for anti-obesity and antibiotic drugs ,35.Brucella abortus [* hemH: Ferrochelatase is essential for multiplication and intracellular survival of  abortus .Haemophilus influenzae [E.coli [* kdsB: Analogs of 3-deoxy-D-manno-octulosonate (KDO) were designed to inhibit CTP:CMP-KDO cytidylyltransferase (CMP-KDO synthetase) . It is afluenzae  and E.co [E.coli .Mycobacterium bovis BCG [* fabD: Acyl carrier protein S-malonyltransferase is a potential target of ovis BCG .E. coli, B. subtilis, and S. aureus [** fabG: 3-ketoacyl-(acyl-carrier-protein) reductase is a well-known drug target of . aureus .E. coli [Escherichia coli K12 which were defective in phosphatidylserine synthetase, were isolated as temperature-sensitive, conditional lethals [* pssA: Phosphatidylserine synthetase is required for motility and chemotaxis in E. coli . Further lethals .E. coli, it is essential for cell growth and accounts for conditional lethality associated with mutations in KDO biosynthesis [* kdtA: 3-deoxy-D-manno-octulosonic-acid transferase is the enzyme of kdtA. In ynthesis .E. coli and Mycobacterium tuberculosis [** dfp: Pantothenate kinase is uptream of phosphopantothenoylcysteine decarboxylase in the biosynthesis of pantothenate and CoA. It is a well-known target for antimicrobial drugs against rculosis .B. subtilis [Stapphylococcus aureus [* rep: ATP-dependent DNA helicase Rep. Its deletion was found to be lethal in subtilis  and Staps aureus .E. coli [* rpoB: DNA-directed RNA polymerase is a promising target for the discovery of new antimicrobial agents against E. coli .S. typhimurium [S. typhimurium. Note that the arrows in the figure do not represent information about the irreversibility of these reactions but rather show the direction of the overall flux. This rather linear pathway starts at 1-deoxy-D-xylulose-5-phosphate-synthase (EC 2.2.1.7) which corresponding gene dxs has been identified to be essential also by the experimental knock-out study of Knuth and co-workers [S. typhimurium and found five genes to be essential  [S. typhimurium. We searched in the literature and indicated our findings by one and two asterisks as described above. For two genes we found clear evidences (two asterisks) and for six genes reasonable evidences (one asterisks) to code for drug targets  with all pathways from KEGG  and founhimurium ,53. Figu-workers . The nexG, ispH) . We propE. coli) and were employed to predict essential genes of the other organism (e.g. P. aeruginosa). These predictions did not depend on essentiality information of the query organism for which the predictions were made, but solely on features that were calculated from the metabolic network and genomic and transcriptomic information of the query organism. Such data is abundantly available for many pathogenic bacteria. We applied this method to predict essential genes of Salmonella typhimurium as the query organism of interest and proposed 35 potential drug targets. 27 targets resulted from the intersection between our predictions and an experimental study [S. typhimurium, we also inferred this by our machine learning approach. We discovered interesting correlations of our features to the essentiality of a gene. Various features describing the network topology served the machine to select reactions that showed no possible pathways for flux deviations, as e.g. in the linear non-mevalonate pathway. An intelligent combination of these features may be seen as an alternative approach to the established methods of flux balance analyses (FBA) and elementary flux modes (EFM) if detailed growth and nutrient information is lacking .E. coli, P. aeruginosa and S. typhimurium. Inferring essentiality information for an organism from another organism may be facilitated by investigating a closely related organism as we did with S. typhimurium being rather closely related to E. coli. To apply this method to other micro-organisms, the metabolism may need to be well described, and the method may need adaptation for less studied organisms or which show special metabolic capabilities. For applying this method to eukaryotic genomes, the compartments in the cell at which a reaction occurs may need to be considered. It will be very challenging to apply our method for inferring multiple drug targets using experimental double knock-out screens as e.g. of the synthetic lethal project of eSGA [Our method served well to estimate genes and their corresponding enzymes in the bacterial organisms of  of eSGA . For thiE. coli, P. aeruginosa, and S. typhimurium were reconstructed using the database of KEGG [The metabolic networks of  of KEGG . UnspeciE. coli and two of P. aeruginosa. Additionally we used data from a knock-out study of S. typhimurium which was also performed in LB rich medium. All datasets were taken from the NMPDR database [E. coli, we used the KEIO collection of Baba and co-workers [E. coli was from Gerdes and co-workers [P. aeruginosa we used the data of Liberati et al. [P. aeruginosa was taken from the study by of Jacobs et al. [S. typhimurium was from Knuth and co-workers [S. typhimurium clones was grown under permissive conditions. Upon switching to non-permissive temperature, discrimination between lethal and non-lethal insertions following homologous recombination allowed the trapping of genes with essential functions. With this method, genes were detected that were indispensable for growth. However, non-essential genes could not be determined. For the metabolism, 53 genes were found to be essential and for the remaining 711 the essentiality could not be determined by this method [To train and validate our predictions, we used published datasets from genome wide experimental knock-out screens. All were performed in LB rich medium. Two datasets were of database . For E. -workers  which we-workers  which wei et al.  denoted s et al. . We deno-workers  and bases method .Features were obtained from network topology properties and genomic and transcriptomic information. Table For the following features, we used the metabolic network in the representation of a bipartite graph consisting of two different alternating nodes, i.e. metabolites and reactions. As reported recently ,16, we ii. All metabolites acting as input nodes (substrates) and output nodes (products) of the knocked out reaction were selected. The set of substrates S defined the input nodes and the set of products P defined the output nodes. To get a broader list of available substrates we integrated other substrates into S. We included the substrates of the upstream reactions and the products of the downstream reactions into the sets S and P, respectively. Substrates of reactions that had at least one of the substrates S as a substrate were included into S. Further, substrates of reactions that had a metabolite out of P as a substrate were also included into S.ii. Reactions were selected which used only available compounds as substrates.iii. These selected reactions and their products were incorporated into the list of discovered reactions and products. The products were set as newly available metabolites in the network.iv. Steps ii and iii were repeated until no further reactions could be identified.v. The output nodes that could be produced were counted (reachable products P).After finishing the process, we used the number of defined output nodes that could be produced within the mutated network for two features, i.e. a quality feature defining if all products could be produced , and the percentage of products that could not be produced . We again run a breadth first search on the network to estimate possible deviations. Starting from S, the breadth first search explored the network for finding the direct products of the knocked out reaction. When the algorithm visited these products, it stored the corresponding pathway and continued its search to find further alternative paths until the network was entirely explored or a maximal path length of 10 reactions was reached. The organism may have many pathways to produce the products making the system more robust. Thus, we counted the number of possible alternative paths yielding feature ND . We took the average path length  and the shortest path length  of the deviations as features for the classifier. The deviation features were used to find alternative pathways to produce products of the knocked out reaction by its substrates S. In the metabolic network, these substrates can also be consumed by other reactions yielding their products etc. Therefore, we kept track of alternative paths in the network for the potential of the organism to survive when a reaction was blocked.The number of substrates and products of the knocked out reaction were counted . We defined features for the number of Neighboring reactions (NNR) and the number of Neighbors of Neighboring reactions (NNNR). We calculated the clustering coefficient (CCV) as described in ,58 of thA reaction that uniquely consumes or produces a certain metabolite in the metabolic network is considered a choke point. Such a reaction shows high potential for essentiality ,5. We usThe damage was defined to determine potentially effected metabolites and reactions downstream of the knocked out reaction. We used the definition of damaged compounds and reactions from Lemke and co-workers  yieldingV, E) be a simple undirected graph with n vertices (reactions). Betweenness measures the frequency of a reaction (node) to be in the shortest path of all pairs of reactions [Cb(v) for a reaction v is given byFor these features, we used the network-representation of a reaction-pair network. We computed the centrality features by using the R package 'igraph'  consistieactions . The betdij is the number of shortest paths from reaction i to reaction j, and dij(v) is the number of shortest paths from i to j that pass through reaction v. The sum is composed of all pairs  of reactions of the network. Closeness centrality approximates how many edges are required to access every other reaction from a given reaction [Cc(v) for a reaction v is given byin which reaction . It is dn is the number of reactions in the network. Eccentricity is the longest distance from the given reaction to any other reaction [Ce(v) for a vertex v is given byin which reaction . The eccxi denote the score of a reaction i. Let Aij be the adjacency matrix of the network. Thus Aij = 1 if there is an edge between reactions i and j, and Aij = 0 otherwise. For reaction i, the centrality score is proportional to the average of the centralities of i's network neighbors:Eigenvector centrality is based on the assumption that the utility of a reaction is determined by the utility of the neighboring reactions . It scorNeighbor(i) is the set of neighboring reactions of reaction i, n is the total number of reactions and λ is a constant. This leads directly to the well-known eigenvector equation, Ax = λx. Normally, there are different eigenvalues λ for which an eigenvector solution exists. According to the Perron-Frobenius theorem only the eigenvector of the largest eigenvalue is the eigenvector centrality [in which ntrality .E. coli, P. aeruginosa, S. typhimurium). We used different E-value cutoffs, i.e. 10-3, 10-5, 10-7, 10-10, 10-20, and 10-30 to obtain the features H3, H5, H7, H10, H20 and H30, respectively. Sequences of all open reading frames were taken from the NCBI database .We calculated the number of homologous genes that might have taken over the function of the knocked out gene. Homologous genes were searched using BLAST  against E. coli, we used gene expression data from a study in which the regulation during oxygen deprivation was investigated [P. aeruginosa from a study observing the response to agmatine and putrescine treatment [S. typhimurium we used data of cells treated with nutrient limitation at different time points [We collected gene expression data for all three investigated organisms from public resources. The datasets were selected in respect to have a rather unspecific regulation, i.e. from treatments affecting not a small band but a broad range of metabolic pathways. For stigated , for P. reatment  and fromreatment . For S. e points  and datae points . The date points . Genes we points . TherefoE. coli, P. aeruginosa, and S. typhimurium) as described in Gustafson et al. [E. coli, P. aeruginosa, and S. typhimurium using bi-directional best BLAST hits .We selected 177 prokaryotic organisms  yielding the features T3s, C3s, A3s, G3s for thymine, cytosine, adenine and guanine, respectively. Additionally, the number of codons coding for all encoded amino acids  were counted. All codon counts were normalized by division of the total number of codons (Nc). Nc was also used as a feature.http://www.r-project.org. A radial basis function was used as the kernel. Parameter optimization was performed on the training data for the regularization term and the kernel width. The regularization term defined the costs for false classifications and was optimized using the values 2n with n = -4, -2, 0, 2, 4. The same range was taken for the kernel width. This optimization was realized by training with a grid search over all combinations of these parameters. The sizes of the two classes differed considerably in our data sets . For a broad spectrum of different sensitivities and specificities, we applied a voting scheme. We trained 100 Support Vector Machines (SVMs) with all essential genes and an equal amount of randomly selected non-essential genes. With this, we stratified the training data. For the classification of a query gene, the output of all machines was summed up and used as a voting score for the gene to be essential for the cell.We used Support Vector Machines from the R package 'e1071' to classify essential and non-essential genes of metabolism http://www.r-project.org to classify essential and non-essential genes of the metabolism. Gini impurity [The first decision in decision trees applies the best discriminating feature . Therefoimpurity  was usedFor assessing the performance of the classifier, the predictions were compared to the gold standard from the experimental screens. A prediction was either true positive , false positive , true negative  or false negative . We calculated the standard measures accuracy = (tp+tn)/(tp+tn+fp+fn), sensitivity = tp/(tp+fn), and specificity = tn/(tn+fp). A receiver operator characteristics (ROC-curve) was used to measure the performance for a classifier system with various thresholds. In the ROC-curve the sensitivity is plotted against 1 - specificity and the area under the curve (AUC) yields a performance estimate across the entire range of thresholds. P-values for Pearson's correlation coefficients for the features were calculated as described in .KP and RK put up the general concept and design of the study. KP carried out the data analysis. KP and RK drafted the manuscript. All authors read and approved the final manuscript.ROC curves for the essential gene predictions with subsets of features.Click here for fileCorrelation coefficients of the features to gene essentiality.Click here for fileHistograms for the frequency of T3s in essential genes and non-essential genes.Click here for fileS. typhimurium with our computational predictions and the experimental results of Knuth et al. (2004).All examined metabolic genes of Click here for fileS. typhimurium and their literature evidences.Predicted essential genes and potential drug targets for Click here for file