Current address: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada
Current address: Department of Chemical and Biomolecular Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois, United States of America
Conceived and designed the experiments: JL EG JP. Performed the experiments: JL EG JE. Analyzed the data: JL EG JP. Contributed reagents/materials/analysis tools: JL EG JE JP. Wrote the paper: JL EG JP.
The authors have declared that no competing interests exist.
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
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.
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
Dynamic
An additional challenge to the modeling of
Some preliminary dynamic analyses of integrated systems have been completed. Integrated analyses of regulatory and metabolic networks revealed novel mechanisms in
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
The prototypic integrated system, comprised of integrated signaling, metabolism, and regulation, is illustrated. Solid boundary lines indicate the three functional network modules: signal transduction (upper left), metabolism (upper right), and transcriptional regulation (bottom). Dashed lines between the modules represent interactions spanning multiple modules, arising from compounds that simultaneously participate in reactions of different functional modules. The components and reactions within these networks are based on published network reconstructions of actual biological systems. Primary roles of network components are shaded by color: blue for signaling, red for metabolism, and green for regulation. Detailed reactions are presented in
Network components with overlapping functions across the three functional network modules of signal transduction, metabolism, and transcriptional regulation are illustrated. Primary roles of the network components are shaded by color: blue for signaling, red for metabolism, and green for regulation. (See
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
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 (see
Most of the metabolic reactions in the model are “fast” and achieve steady states in several seconds. The growth of biomass is on the order of hours. The typical order of magnitude of metabolite concentrations is milli-molar (mM)
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
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
Protein | Protein | ||||
10 | 20 | 15 | 15 | ||
10 | 25 | 20 | 10 | ||
13 | 18 | 18 | 13 | ||
R1 | 20 | 40 | S1 | 30 | 30 |
T1 | 25 | 35 | IS1 | 35 | 35 |
R2 | 25 | 45 | S2 | 30 | 40 |
T2 | 25 | 55 | IS2 | 35 | 45 |
R3 | 15 | 55 | S3 | 15 | 25 |
T3 | 20 | 20 | IS3 | 10 | 30 |
The variables
The prototypic transcriptional regulatory network presented here is comprised of 18 genes (see
Expression of a gene | Regulation |
If (T1p) | |
If (T2p) | |
If (T3p) | |
If ((T1p) AND (T2p)) | |
If ((T1p) AND (T2p) AND (T3p)) | |
If ((T1p) AND (T3p)) |
A total of six genes are regulated by three transcription factors in the prototypic regulatory system. The Boolean regulatory rules for these six genes over these three transcription factors are presented.
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
Input | Output | Time scale | |
LigandsEnergyProteins | Activated transcription factors | Fast & Slow | |
CarbonProteins | EnergyAmino acidsBiomassProteins | Fast & Slow | |
Activated transcription factorsAmino acids | Slow |
The degree of interconnectivity across signaling, metabolism, and regulation in the prototypic integrated system is summarized (see
To assess the applicability of idFBA to actual biological systems, a representative integrated module in
A representative integrated module in
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 (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
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
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
After the network is reconstructed, fluxes are calculated by deriving a dynamic mass balance for all the components within the system
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
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 (e.g., cellular growth or differentiation) 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 (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.
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
One of the pathways of the prototypic signaling network is illustrated. Here, solid black lines represent reactions that have non-zero fluxes, while dotted red lines represent reactions that have zero fluxes when the production of the activated transcription factor T1p is maximized as the pathway objective.
To address this challenge, we model the objective of a signaling network by introducing a binary parameter, represented as the matrix
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
The key steps in the idFBA framework are summarized. Specifically, the time window is discretized into small steps, Δ
Discretize the time window into small steps, Δ
Initialize a
For each reaction in the system
Solve Equation 5 for the optimized flux vector,
Given the optimized flux vector for
Update
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).
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 (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
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.
The sample time, Δ
The 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
Temporal parameters (namely τ
The binary variable
If the flux of a phosphorylated component was not zero (i.e., if the component was considered to be in an “active state”), elements of
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
The optimized fluxes for the production of activated transcription factors (
As we describe subsequently (see “
To evaluate the utility of the idFBA framework, the phenotypic characteristics of the prototypic integrated system were evaluated under a variety of different conditions. First, the dependence of cellular growth on different combinations of input ligands L1, L2, and L3 was assessed.
Description | Reactions | Excluded reactions | τdel (min) | τdur (min) |
Degradation of phosphorylated compounds | — | — | 40 | |
Degradation of transcription factors | — | — | 40 | |
Production and degradation of additional proteins | — | 40 | 40 | |
Internalization of ligand receptor complexes | 40 | 6 | ||
Inhibitory reactions | 40 | 6 |
The superscript
We first simulated the case in which the concentration of all three ligands was 2.0 µM. The results are shown in
In (A), the concentration of carbon and amount of biomass within the cellular system over a simulation time of 10 h is illustrated. The decreasing lines represent the concentration of carbon (as indicated by the left
We subsequently simulated the case in which the ligands were temporarily unavailable for cellular uptake during the evaluated time-course (see
We also tested the effects of individual ligands or groups of ligands on cell growth by evaluating the phenotypic characteristics for the input cases described in Equation 15. For example, we considered the effect of ligand L1 by itself by restricting the availability of ligands L2 and L3 beyond t = 2 h. Similarly, we further assessed the effect of ligand L1 by restricting its availability while maintaining the concentrations of ligands L2 and L3 beyond t = 2 h.
As illustrated in
The concentration of carbon and amount of biomass within the cellular system over a simulation time of 10 h is illustrated. The decreasing lines represent the concentration of carbon (as indicated by the left
Changes to the regulatory program were evaluated as well. A new set of Boolean regulatory rules was implemented, as shown in
Expression of a gene | Regulation |
IS1 | If (T1p) |
IS2 | If (T2p) |
IS3 | If (T3p) |
EF | If NOT ((T1p) AND (T2p)) |
EINT | If ((T1p) AND (T2p) AND (T3p)) |
To evaluate how the idFBA framework performs under different sets of regulatory rules, a new set of Boolean rules for the transcriptional regulatory network was defined. These rules are summarized here.
The idFBA framework, as applied to the prototypic integrated system, was compared to a kinetic model that represented the reactions as ordinary differential equations. For the kinetic model, representative kinetic parameters were obtained from literature, as detailed in
To further assess the practicality of the idFBA framework at a large scale, we systematically evaluated how robust the framework was with respect to each of several parameters for the prototypic integrated system. Specifically, we considered the maximum carbon uptake rate,
We evaluated the sensitivity of the idFBA-based implementation of the prototypic integrated system to specific parameter values. (A–E) illustrate the sensitivity of the amount of biomass synthesized and amount of carbon consumed to the maximum carbon uptake rate, the degradation time of the transcription factors, the time delay due to transcription and translation, the degradation time of the proteins, and the time delay due to receptor-ligand internalization as well as lysosomal effects, respectively. Note that each graph includes plots for the original parameter value as well as 10%, 50%, and 90% variation in both directions (up and down), as described in the legend.
In general, robustness analyses facilitate an understanding of which parameters are most critical in determining overall system behavior. Parameters for which the system is particularly sensitive should be accurately inputted into the idFBA framework. Experimental protocols for measuring parameter values are improving. For example, substrate uptake rate can be determined by monitoring the depletion of the substrate source in filtered media samples over time using enzymatic assays or liquid chromatography.
Additionally, robustness analyses can systematically establish
The implementation of the idFBA framework on the
The sample time, Δ
The maximum carbon uptake rate,
To obtain optimal flux distributions in metabolism and signaling (facilitating the evaluation of “active” and “inactive” species), rates for the uptake of carbon and signal transduction of osmotic stress were chosen based on known experimental values
Temporal parameters (namely τ
The 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 (for the purposes of this reconstruction and analysis, glycerol) 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 (
To evaluate the representative integrated yeast module using the idFBA framework, the phenotypic characteristics of the system were investigated under two conditions, i.e., the presence and absence of osmotic stress due to the cell-environment interaction. The idFBA results are shown in
The idFBA and kinetic-based model dynamics of glucose, glycerol, the activated transcription factor Hot1, and cytosolic ATP are contrasted over a simulation time of 10 h. Here, the blue solid line corresponds to the idFBA framework and the red dashed line corresponds to the detailed kinetic-based model. (A) and (B) correspond to situations of osmotic stress and no osmotic stress, respectively.
Additionally, as illustrated in
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
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 (
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
The idFBA framework optimizes the system at the current time step,
The main assumption of a multi-horizon formulation is that the flux distribution at
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 (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
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
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.
(0.06 MB PDF)
(0.55 MB DOC)
We thank Markus W. Covert for helpful discussions about implementing FBA. In addition, we acknowledge Matthew A. Oberhardt and Arvind K. Chavali for general feedback and advice.