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 (e. g. , metabolism) 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 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.
Intracellular biochemical networks are comprised of signaling, metabolic, and regulatory processes. (Note that here we use “regulation” to refer specifically to transcriptional regulatory and protein synthesis networks, and “signaling” to describe intracellular reactions that drive responses to the extracellular environment.) 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 [1]–[4]. For example, signaling cascades are triggered by the presence of extracellular stimuli and often result in activation of transcription factors. These transcription factors function in regulatory networks, regulating the transcription of associated genes and the synthesis of various proteins used in signal transduction and metabolism. Cellular metabolism is responsible for the production of energy in the form of adenosine triphosphate (ATP) and the synthesis of amino acids among other biomass precursors, all of which are used elsewhere in the cell. Consequently, a key challenge in the post-genomic era is to consider the interconnectedness of biochemical networks and how extracellular cues affect highly integrated intracellular processes to elicit cellular responses such as growth or differentiation. Dynamic [5], [6] and structural analyses [7] have been employed to quantitatively analyze large-scale biochemical network modules. Typically, in dynamic analyses, a set of ordinary differential equations (ODEs) describing the mass (balance) of each species in the system is constructed. Despite its generality, the application of this type of mechanistic model at a genome-scale is largely considered impractical because it necessitates the consideration of many pathways for which detailed reactions and their kinetic parameters are not yet known. Structural analyses like flux balance analysis (FBA) can calculate phenotypic properties of a biological network like a steady-state flux (i. e. , reaction rate) distribution without detailed kinetic information. FBA requires a physiologically relevant objective function (e. g. , in the case of metabolism, maximizing the growth rate or maximizing ATP production), mass-balance constraints (i. e. , the stoichiometry of the reactions), and constraints on reaction directions and thermodynamics. Since the physicochemical constraints are readily defined (e. g. , from the annotated genome sequence and measured enzymatic capacities), FBA has been used effectively to study large-scale biochemical networks, particularly metabolic networks [8]. However, in general, the steady-state assumption of FBA prevents it from generating dynamic concentration profiles of intracellular species. An additional challenge to the modeling of 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 [9]. By contrast, receptor internalization [10] and regulatory events [11], [12], as well as end-stage phenotypic properties such as cellular growth or differentiation [13] can take several minutes to hours. These multiple time-scales pose computational challenges for the quantitative analysis of integrated systems. For instance, kinetic model-based strategies suffer from a scarcity of values for kinetic parameters as well as poor accuracy of known kinetic parameters [14]. In addition, models of integrated systems are inherently “stiff, ” i. e. , they must include “fast” and “slow” reaction dynamics simultaneously [15], and they are consequently difficult to simulate and extremely sensitive to modeling errors [16]. Indeed, it is challenging to apply FBA to models of integrated systems because of the steady-state assumption intrinsic to FBA and the “fast” and “slow” reaction dynamics that coexist intracellularly. Due to these complexities, previous models and analyses have focused primarily on network modules rather than integrated systems. These include kinetic, stoichiometric, and causality analyses of modular signaling systems [17]–[20], metabolism [21]–[25], and regulation [26], [27]. Some preliminary dynamic analyses of integrated systems have been completed. Integrated analyses of regulatory and metabolic networks revealed novel mechanisms in Saccharomyces cerevisiae and Escherichia coli [28]–[30]. Metabolic reactions were represented stoichiometrically, and regulatory reactions were captured by representing gene regulatory rules using a Boolean formalism. FBA was implemented assuming quasi-steady-state conditions, i. e. , the typical time constant of metabolic transients was relatively faster than the simulation time step for temporal integration of phenotypic variables (e. g. , biomass as a measure of cellular growth). Recently, a kinetic model accounting for signal transduction, metabolism, and regulation was constructed to describe the response of S. cerevisiae to osmotic shock [31]. This model connected specific outputs of one network (e. g. , signaling) with the inputs of another network (e. g. , metabolism) in a “sequential” fashion. The complete set of interactions among the biochemical networks, such as feedback and feed-forward of proteins expressed as a function of the regulatory network to signaling and metabolism, was not considered. Additionally, it required an exhaustive list of kinetic parameters (e. g. , rate constants) for the reactions, and time-courses of individual modules (or collections of reactions) were evaluated separately. As reconstructions of large-scale signaling and metabolic networks are emerging, there is a growing need for the development of a framework to study these networks from an integrated perspective [9]. 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 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.
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 Figures 1 and 2). Specifically, we generated representative reactions with stoichiometric relationships and estimated their associated rate constants from literature. Here we briefly describe the reactions that are considered in each network and their typical time scales. Detailed information on these reactions and associated kinetic parameters is provided in Text S1. To assess the applicability of idFBA to actual biological systems, a representative integrated module in S. 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 [34]. The signaling, metabolic, and regulatory activities included in this module are illustrated in Figure 3. Specifically, we reconstructed a portion of the high-osmolarity glycerol response (HOG) pathway, one of four major mitogen-activated protein (MAP) kinase cascades 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 [35]. For example, yeast cells deficient in this pathway cannot proliferate on media containing high levels of osmotically active molecules [34]–[36]. Extensive genetic analysis has previously been performed, leading to experimental identification of many activating and inhibiting components of the HOG signaling pathway [37]. In general, yeast cells use the HOG pathway to accumulate glycerol under hyperosmotic conditions, to balance the osmotic pressure with the extracellular environment. Osmotic stress signals are communicated via the HOG signaling pathway, leading to the activation of Hot1 and other transcription factors. These transcription factors subsequently promote the expression of glycolytic enzymes, such as Stl1, Gpd1, and Gpp2, thereby catalyzing metabolic reactions leading to increased glycerol production. 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 (signaling) 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 (signal transduction and metabolism), and the synthesis of metabolic enzymes Stl1, Gpd1, and Gpp2 for reactions involved in the conversion of glucose to glycerol (transcriptional regulation and metabolism). Other reactions in the HOG pathway as previously experimentally characterized (e. g. , inhibition of Hog1 by phosphatases Ptp2, Ptp3, and Ptc1, thereby allowing the cell to keep the HOG pathway in check and maintain osmotic balance) 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 [31], and the two approaches were contrasted for validation purposes. Rate constants describing the kinetics of the system were culled from available experimental data, notably [31]. For complete details of the reconstructed yeast HOG pathway, including listings of reactions, rate constants, and kinetic equations, see Text S2. 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 [8], [38], [39]. These constraints are physico-chemical (i. e. , physical laws like conservation of mass and energy); topological (i. e. , spatial restrictions on metabolites within cellular compartments); and environmental (i. e. , nutrient availability, pH, and temperature, all of which vary over time and space) [8], [20], [38]. Because FBA yields fluxes rather than concentrations, limited kinetic information is required for its implementation. 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 [40]. This biochemical network reconstruction can be represented in matrix form, 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. After the network is reconstructed, fluxes are calculated by deriving a dynamic mass balance for all the components within the system [7], [38]. Specifically, at steady state, the change in the amount of a component 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. (3) Here, 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 [24], [41]. 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 [42]. It is defined as a linear equation (Equation 4), where c is the vector that defines the coefficients, or weights, for each of the fluxes in v [41]. (4) This general representation of Z, 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 [24], [43], energy [44], and byproduct production [45]. 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 v that optimizes Z while lying in the bounded solution space defined by a set of physio-chemical, topological, and environmental constraints. (5) Note that 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 vlb = 0. Though the steady-state assumption of FBA precludes the calculation of dynamic concentrations of the network components, dynamic profiles of cellular phenotypes (e. g. , cellular growth or differentiation) have been successfully predicted with a quasi-steady-state assumption [24], [25], [29]. This assumption involves discretizing the time domain into intervals, and (1) solving the LP problem contained within FBA at the beginning of each interval, and (2) based on the resultant flux data, solving a system of ODEs for concentrations over time within each interval. 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 [28], [29]. In these cases, the regulatory constraints were described as Boolean operators and imposed in a time-delayed manner. However, these examples are limited to metabolic and regulatory processes and do not consider changes in the mass balance (e. g. , protein synthesis) arising from the interactions between metabolic and regulatory processes and signaling systems. Consequently, quantitative, dynamic analyses of integrated cellular systems have not been explored in detail, limiting the characterization of whole-cell function. 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 [32]. The stoichiometric reconstruction and FBA are particularly applicable to large-scale networks, for which a lack of kinetic data (e. g. , rate constants) makes kinetic-based approaches impractical. Indeed, stoichiometric reconstruction and FBA have been applied successfully to large-scale metabolic and signaling networks, elucidating characteristics of these networks [8], [9]. 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 (e. g. , the production of biomass), objectives of signaling and regulatory systems are not well-defined. Second, integrated networks are comprised of reactions with mixed time scales (e. g. , signaling reactions are generally much faster than regulatory reactions), 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. 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 [46]. In other words, the rate of change of the concentration Ci of the ith compound within a system may be described as in Equation 11 below [46]. Here Sij is the stoichiometric coefficient, vj is the rate of the jth reaction, and n is the total number of reactions in the network. Reactions that produce or consume the ith compound have non-zero stoichiometric coefficients and are therefore included in the ith differential equation. (11) The reaction rates for the network, v, are functions of component concentrations, such as the concentrations of enzymes (e. g. , kinases and phosphatases within a signaling network), 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 [47], [48]. Our ODE models of the prototypic integrated system and representative integrated yeast module were constructed from the underlying reaction network, with rate constants (i. e. , kinetic parameters) obtained from literature. The systems of ODEs were continuously solved over the time window of interest (equivalent to that of the corresponding idFBA implementations). Details of these models, including the kinetic equations, kinetic constants, and ordinary differential equations, are presented in Text S1 and S2. 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 [49].
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 [29], which do not account for the effects of extracellular signaling cues on cellular phenotype. 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 (e. g. , biomass production) 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” (e. g. , receptor internalization and protein degradation). These reactions were specified as “active” to denote their participation in the reaction network by imposing simple constraints (v = 0) on their counterparts, as described in “Conceptual Methods and Framework. ” Comparison with the detailed kinetic model validates the idFBA approach. Specifically, approximating the temporal progression of “slow” reactions in signaling, metabolic, and regulatory networks as steady-state constraints with time-delay and duration parameters provides acceptable predictions of the dynamic trends of a cell' s phenotypic behavior. The primary motivation for comparing idFBA with a detailed kinetic model was to determine whether idFBA would yield comparable temporal behavior in spite of the inherent approximation it contained. Optimization-based approaches have provided accurate quantitative predictions of cellular growth [24]. However, signaling networks have not previously been modeled at a scale comparable to that of metabolic and regulatory networks [9]. Databases are increasingly available for signaling networks and efforts are ongoing to reconstruct larger, genome-scale signaling systems [32]. As this information becomes available, the idFBA framework can be applied to cellular systems and be coupled with experimental assays to generate quantitative hypotheses and assist in an iterative model-building process for deriving emergent properties of these systems. The idFBA framework optimizes the system at the current time step, tcurrent, according to the linear programming formulation of FBA (Equation 17). (17) Altering this framework to impose a multi-horizon formulation may facilitate the evaluation of different objective functions because the formulation naturally accounts for long-term effects of the calculated flux distribution at the current time step [25]. The multi-horizon formulation is shown in Equation 18, where wj is the weight associated with the objective after Tj sample times. (18) The main assumption of a multi-horizon formulation is that the flux distribution at tcurrent 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 [64], it may shed light on whether signal transduction at the current time step is optimally driven by a long-term objective. Currently, multi-stage optimization problems have been solved only for metabolic systems [25]. 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 [54]. This method identifies objectives from experimental fluxes by defining a putative stoichiometric objective reaction, adding this reaction to the existing set of stoichiometric constraints, and maximizing it via linear programming. This new approach is capable of inferring the objective functions of metabolic networks, as well as metabolic and regulatory networks for which the objective is not well-characterized experimentally. Therefore, utilizing BOSS to identify objectives for the signaling, regulatory, and metabolic networks would facilitate the identification of an in silico flux distribution for the integrated system, a key step in the idFBA framework. The fact that different reactions occur on different time scales (e. g. , signaling reactions are usually fast whereas regulatory reactions are usually slow) 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 [15] and Monte Carlo sampling [65] techniques may help characterize representative time-scales of a given system as well. 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 (e. g. , altering the Boolean rules governing transcription of one or more genes) 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 [66]. 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.
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 (e. g. , the numbers of rate constants involved). 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.
cell biology/cell signaling
computational biology/transcriptional regulation
mathematics
computational biology/metabolic networks
computational biology/signaling networks
computational biology/molecular dynamics
computational biology/systems biology
Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks