Metabolic control analysis of biochemical pathways based on a thermokinetic description of reaction rates.
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ABSTRACT:
SUBMITTER: Nielsen J
PROVIDER: S-EPMC1218046 | biostudies-other | 1997 Jan
REPOSITORIES: biostudies-other
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Project description:We previously developed the biochemical reaction simulator WinBEST-KIT. In recent years, research interest has shifted from analysis of individual biochemical reactions to analysis of metabolic pathways as systems. These large-scale and complicated metabolic pathways can be considered as characteristic multi-layered structures, which, for convenience, are separated from whole biological systems according to their specific roles. These pathways include reactants having the same name but with unique stoichiometric coefficients arranged across many different places and connected between arbitrary layers. Accordingly, in this study, we have developed a new version of WinBEST-KIT that allows users (1) to utilize shortcut symbols that can be arranged with multiple reactants having the same name but with unique stoichiometric coefficients, thereby providing a layout that is similar to metabolic pathways depicted in biochemical textbooks; (2) to create layers that divide large-scale and complicated metabolic pathways according to their specific roles; (3) to connect the layers by using shortcut symbols; and (4) to analyze the interactions between these layers. These new and existing features allow users to create and analyze such multi-layered metabolic pathways efficiently. Furthermore, WinBEST-KIT supports SBML, making it possible for users to utilize these new and existing features to create and publish SBML models.
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Project description:The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of interleukin-12 (IL-12) signaling in naïve CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo-equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.
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Project description:Our knowledge of metabolism can be represented as a network comprising several thousands of nodes (compounds and reactions). Several groups applied graph theory to analyse the topological properties of this network and to infer metabolic pathways by path finding. This is, however, not straightforward, with a major problem caused by traversing irrelevant shortcuts through highly connected nodes, which correspond to pool metabolites and co-factors (e.g. H2O, NADP and H+). In this study, we present a web server implementing two simple approaches, which circumvent this problem, thereby improving the relevance of the inferred pathways. In the simplest approach, the shortest path is computed, while filtering out the selection of highly connected compounds. In the second approach, the shortest path is computed on the weighted metabolic graph where each compound is assigned a weight equal to its connectivity in the network. This approach significantly increases the accuracy of the inferred pathways, enabling the correct inference of relatively long pathways (e.g. with as many as eight intermediate reactions). Available options include the calculation of the k-shortest paths between two specified seed nodes (either compounds or reactions). Multiple requests can be submitted in a queue. Results are returned by email, in textual as well as graphical formats (available in http://www.scmbb.ulb.ac.be/pathfinding/).
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Project description:I have used electrical analogues for calculating the Flux Control Coefficients of metabolic pathways. An analogue circuit consists of resistances that are connected in series (or parallel) with a voltage (or current) source. In constructing the analogues, each of the enzymes in the pathway is associated with a resistance whose magnitude depends on the Elasticity Coefficients of the enzymes. These circuits can be designed in a heuristic fashion directly from the configuration of the pathway, without the necessity of writing down the governing equations with the use of Summation and Connectivity Theorems. The Flux Control Coefficients of the enzymes are represented by voltages across (or currents through) the resistances and are determined by an application of Ohm's Law. Results are given for (a) a simple linear pathway without feedback or feedforward regulation, and (b) a linear pathway with feedback inhibition. The analogue circuits are also convenient for assessing the relative importance of the various enzymes in flux control, and for simplifying the structure of a given pathway.
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Project description:BackgroundStochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space.ResultsWe develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise". The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate, which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal, revealing hidden parameter dependencies and sensitivities in reaction networks.ConclusionsAs a gradient-free method, the proposed sensitivity analysis provides a significant advantage when dealing with complex stochastic systems with a large number of parameters. In addition, the knowledge of the structure of the FIM can allow to efficiently address questions on parameter identifiability, estimation and robustness. The proposed method is tested and validated on three biochemical systems, namely: (a) a protein production/degradation model where explicit solutions are available, permitting a careful assessment of the method, (b) the p53 reaction network where quasi-steady stochastic oscillations of the concentrations are observed, and for which continuum approximations (e.g. mean field, stochastic Langevin, etc.) break down due to persistent oscillations between high and low populations, and (c) an Epidermal Growth Factor Receptor model which is an example of a high-dimensional stochastic reaction network with more than 200 reactions and a corresponding number of parameters.
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Project description:Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.
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Project description:Information transmission in cells occurs through complex networks of proteins and genes and is relayed through cascades of biochemical modifications, which are typically studied through ordinary differential equations. However, it is becoming increasingly clear that spatial factors can strongly influence chemical information transmission in cells. In this article, we systematically disentangle the effects of space in signaling cascades. This is done by examining the effects of localization/compartmentalization and diffusion of enzymes and substrates in multiple variants of chemical modification cascades. This includes situations where the modified form of species at one stage 1) acts as an enzyme for the next stage; 2) acts as a substrate for the next stage; and 3) is involved in phosphotransfer. Our analysis reveals the multiple effects of space in signal transduction cascades. Although in some cases space plays a modulatory effect (itself of interest), in other cases, spatial regulation and control can profoundly affect the nature of information processing as a result of the subtle interplay between the patterns of localization of species, diffusion, and the nature of the modification cascades. Our results provide a platform for disentangling the role of space and spatial control in multiple cellular contexts and a basis for engineering spatial control in signaling cascades through localization/compartmentalization.
| S-EPMC4472220 | biostudies-other
Project description:BackgroundSensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species.ResultsWe present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for analytically approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge.ConclusionsEstimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.
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Project description:Optogenetic tools provide a level of spatial and temporal resolution needed to shed new light on dynamic intercellular processes. In this chapter we outline specific protocols for applying these tools to cell motility (optogenetic cofilin), apoptosis [optogenetic Bcl-like protein 4 (Bax)], and protein kinase-mediated signaling pathways [optogenetic cAMP-dependent protein kinase (PKA)]. The activity of these optogenetic species is regulated by the light-mediated dimerization of a cryptochrome/Cib protein pair, which controls the intracellular positioning of the protein of interest. The light induced recruitment of cofilin to the cytoskeleton is utilized for directed migration studies and filopodial dynamics. Light-triggered migration of Bax to the outer mitochondrial membrane induces cellular collapse and eventual apoptosis. Finally, the light-mediated movement of PKA to specific intracellular compartments offers the means to assess the consequences of PKA activity in a site-specific fashion via phosphoproteomic analysis.
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Project description:BackgroundEstimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.ResultsWe introduce a Bayesian analysis approach for computing thermodynamically consistent estimates of the rate constants of a closed biochemical reaction system with known stoichiometry given experimental data. Our method employs an appropriately designed prior probability density function that effectively integrates fundamental biophysical and thermodynamic knowledge into the inference problem. Moreover, it takes into account experimental strategies for collecting informative observations of molecular concentrations through perturbations. The proposed method employs a maximization-expectation-maximization algorithm that provides thermodynamically feasible estimates of the rate constant values and computes appropriate measures of estimation accuracy. We demonstrate various aspects of the proposed method on synthetic data obtained by simulating a subset of a well-known model of the EGF/ERK signaling pathway, and examine its robustness under conditions that violate key assumptions. Software, coded in MATLAB®, which implements all Bayesian analysis techniques discussed in this paper, is available free of charge at http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html.ConclusionsOur approach provides an attractive statistical methodology for estimating thermodynamically feasible values for the rate constants of a biochemical reaction system from noisy time series observations of molecular concentrations obtained through perturbations. The proposed technique is theoretically sound and computationally feasible, but restricted to quantitative data obtained from closed biochemical reaction systems. This necessitates development of similar techniques for estimating the rate constants of open biochemical reaction systems, which are more realistic models of cellular function.
| S-EPMC3248051 | biostudies-literature