Kinetic control of stationary flux ratios for a wide range of biochemical processes.
ABSTRACT: One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi-first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5'-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes.
Project description:Predicting the metabolic state of an organism after a gene knockout is a challenging task, because the regulatory system governs a series of transient metabolic changes that converge to a steady-state condition. Regulatory on/off minimization (ROOM) is a constraint-based algorithm for predicting the metabolic steady state after gene knockouts. It aims to minimize the number of significant flux changes (hence on/off) with respect to the wild type. ROOM is shown to accurately predict steady-state metabolic fluxes that maintain flux linearity, in agreement with experimental flux measurements, and to correctly identify short alternative pathways used for rerouting metabolic flux in response to gene knockouts. ROOM's growth rate and flux predictions are compared with previously suggested algorithms, minimization of metabolic adjustment, and flux balance analysis (FBA). We find that minimization of metabolic adjustment provides accurate predictions for the initial transient growth rates observed during the early postperturbation state, whereas ROOM and FBA more successfully predict final higher steady-state growth rates. Although FBA explicitly maximizes the growth rate, ROOM does not, and only implicitly favors flux distributions having high growth rates. This indicates that, even though the cell has not evolved to cope with specific mutations, regulatory mechanisms aiming to minimize flux changes after genetic perturbations may indeed work to this effect. Further work is needed to identify metrics that characterize the complete trajectory from the initial to the final metabolic steady states after genetic perturbations.
Project description:Fatty acid metabolism is an important feature of the pathogenicity of Mycobacterium tuberculosis during infection. Consumption of fatty acids requires regulation of carbon flux bifurcation between the oxidative TCA cycle and the glyoxylate shunt. In Escherichia coli, flux bifurcation is regulated by phosphorylation-mediated inhibition of isocitrate dehydrogenase (ICD), a paradigmatic example of post-translational mechanisms governing metabolic fluxes. Here, we demonstrate that, in contrast to E. coli, carbon flux bifurcation in mycobacteria is regulated not by phosphorylation but through metabolic cross-activation of ICD by glyoxylate, which is produced by the glyoxylate shunt enzyme isocitrate lyase (ICL). This regulatory circuit maintains stable partitioning of fluxes, thus ensuring a balance between anaplerosis, energy production, and precursor biosynthesis. The rheostat-like mechanism of metabolite-mediated control of flux partitioning demonstrates the importance of allosteric regulation during metabolic steady-state. The sensitivity of this regulatory mechanism to perturbations presents a potentially attractive target for chemotherapy.
Project description:The ever-increasing availability of transcriptomic and metabolomic data can be used to deeply analyze and make ever-expanding predictions about biological processes, as changes in the reaction fluxes through genome-wide pathways can now be tracked. Currently, constraint-based metabolic modeling approaches, such as flux balance analysis (FBA), can quantify metabolic fluxes and make steady-state flux predictions on a genome-wide scale using optimization principles. However, relating the differential gene expression or differential metabolite abundances in different physiological states to the differential flux profiles remains a challenge. Here we present a novel method, named REMI (Relative Expression and Metabolomic Integrations), that employs genome-scale metabolic models (GEMs) to translate differential gene expression and metabolite abundance data obtained through genetic or environmental perturbations into differential fluxes to analyze the altered physiology for any given pair of conditions. REMI allows for gene-expression, metabolite abundance, and thermodynamic data to be integrated into a single framework, then uses optimization principles to maximize the consistency between the differential gene-expression levels and metabolite abundance data and the estimated differential fluxes and thermodynamic constraints. We applied REMI to integrate into the Escherichia coli GEM publicly available sets of expression and metabolomic data obtained from two independent studies and under wide-ranging conditions. The differential flux distributions obtained from REMI corresponding to the various perturbations better agreed with the measured fluxomic data, and thus better reflected the different physiological states, than a traditional model. Compared to the similar alternative method that provides one solution from the solution space, REMI was able to enumerate several alternative flux profiles using a mixed-integer linear programming approach. Using this important advantage, we performed a high-frequency analysis of common genes and their associated reactions in the obtained alternative solutions and identified the most commonly regulated genes across any two given conditions. We illustrate that this new implementation provides more robust and biologically relevant results for a better understanding of the system physiology.
Project description:<h4>Background</h4>With the advent of genomic technology, the size of metabolic networks that are subject to analysis is growing. A common task when analyzing metabolic networks is to find all possible steady state regimes. There are several technical issues that have to be addressed when analyzing large metabolic networks including accumulation of numerical errors and presentation of the solution to the researcher. One way to resolve those technical issues is to analyze the network using symbolic methods. The aim of this paper is to develop a routine that symbolically finds the steady state solutions of large metabolic networks.<h4>Results</h4>A symbolic Gauss-Jordan elimination routine was developed for analyzing large metabolic networks. This routine was tested by finding the steady state solutions for a number of curated stoichiometric matrices with the largest having about 4000 reactions. The routine was able to find the solution with a computational time similar to the time used by a numerical singular value decomposition routine. As an advantage of symbolic solution, a set of independent fluxes can be suggested by the researcher leading to the formation of a desired flux basis describing the steady state solution of the network. These independent fluxes can be constrained using experimental data. We demonstrate the application of constraints by calculating a flux distribution for the central metabolic and amino acid biosynthesis pathways of yeast.<h4>Conclusions</h4>We were able to find symbolic solutions for the steady state flux distribution of large metabolic networks. The ability to choose a flux basis was found to be useful in the constraint process and provides a strong argument for using symbolic Gauss-Jordan elimination in place of singular value decomposition.
Project description:It is shown by analysis of a numerical example that kinetic barrier diagrams [Südi (1991) Biochem. J. 276; 265-268] are also useful for displaying the phenomenological resistance of an enzymic turnover to net chemical fluxes observed under steady-state conditions. Most importantly, a new additivity rule is revealed by net flux profiles, which refers to limiting ('ideal') conditions. The rule states that the net fluxes that one obtains under initial steady-state conditions are strictly identical with the overall flux in the corresponding equilibrium system. This finding amounts to defining the relation between unidirectional fluxes and net fluxes, and explains why the total 'one-way flux resistance' to the overall reaction at chemical equilibrium on the one hand, and the 'net flux resistance' to both initial steady-state reactions on the other hand, have to be equal. The conclusions are claimed to be generally valid for consecutive chemical reactions.
Project description:Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli's glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.
Project description:Deciphering the mechanisms of regulation of metabolic networks subjected to perturbations, including disease states and drug-induced stress, relies on tracing metabolic fluxes. One of the most informative data to predict metabolic fluxes are 13C based metabolomics, which provide information about how carbons are redistributed along central carbon metabolism. Such data can be integrated using 13C Metabolic Flux Analysis (13C MFA) to provide quantitative metabolic maps of flux distributions. However, 13C MFA might be unable to reduce the solution space towards a unique solution either in large metabolic networks or when small sets of measurements are integrated. Here we present parsimonious 13C MFA (p13CMFA), an approach that runs a secondary optimization in the 13C MFA solution space to identify the solution that minimizes the total reaction flux. Furthermore, flux minimization can be weighted by gene expression measurements allowing seamless integration of gene expression data with 13C data. As proof of concept, we demonstrate how p13CMFA can be used to estimate intracellular flux distributions from 13C measurements and transcriptomics data. We have implemented p13CMFA in Iso2Flux, our in-house developed isotopic steady-state 13C MFA software. The source code is freely available on GitHub (https://github.com/cfoguet/iso2flux/releases/tag/0.7.2).
Project description:Kinetic models of metabolic networks offer the promise of quantitative phenotype prediction. The mechanistic characterization of enzyme catalyzed reactions allows for tracing the effect of perturbations in metabolite concentrations and reaction fluxes in response to genetic and environmental perturbation that are beyond the scope of stoichiometric models. In this study, we develop a two-step computational pipeline for the rapid parameterization of kinetic models of metabolic networks using a curated metabolic model and available 13C-labeling distributions under multiple genetic and environmental perturbations. The first step involves the elucidation of all intracellular fluxes in a core model of E. coli containing 74 reactions and 61 metabolites using 13C-Metabolic Flux Analysis (13C-MFA). Here, fluxes corresponding to the mid-exponential growth phase are elucidated for seven single gene deletion mutants from upper glycolysis, pentose phosphate pathway and the Entner-Doudoroff pathway. The computed flux ranges are then used to parameterize the same (i.e., k-ecoli74) core kinetic model for E. coli with 55 substrate-level regulations using the newly developed K-FIT parameterization algorithm. The K-FIT algorithm employs a combination of equation decomposition and iterative solution techniques to evaluate steady-state fluxes in response to genetic perturbations. k-ecoli74 predicted 86% of flux values for strains used during fitting within a single standard deviation of 13C-MFA estimated values. By performing both tasks using the same network, errors associated with lack of congruity between the two networks are avoided, allowing for seamless integration of data with model building. Product yield predictions and comparison with previously developed kinetic models indicate shifts in flux ranges and the presence or absence of mutant strains delivering flux towards pathways of interest from training data significantly impact predictive capabilities. Using this workflow, the impact of completeness of fluxomic datasets and the importance of specific genetic perturbations on uncertainties in kinetic parameter estimation are evaluated.
Project description:Metabolic control analysis is adapted as a method for describing and analysing the control by organs in the body over the fluxes and concentrations of substances carried in the blood. This physiological control analysis can most usefully be applied to substances with fluxes into and out of organs that are uniquely dependent only on their plasma concentrations. The organ flux of a substance is defined as the steady-state net flux of a substance into a particular organ. The organ flux control coefficients quantify the extent to which a particular organ controls the flux of a substance into the same or another particular organ. Organ concentration control coefficients quantify the extent to which an organ controls the steady-state concentration of a substance in the blood. The control coefficients are additive and obey summation, connectivity and branching theorems. Thus the control coefficients can be determined experimentally by measuring the sensitivities (elasticities) of organ fluxes to the plasma concentration of the substance. As an example of the application of these concepts, the control of ketone-body metabolism in vivo is analysed using data from the literature.
Project description:MOTIVATION:Metabolic flux balance analysis (FBA) is a standard tool in analyzing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place model assumptions on fluxes due to the convenience of formulating the problem as a linear programing model, while many methods do not consider the inherent uncertainty in flux estimates. RESULTS:We introduce a novel paradigm of Bayesian metabolic flux analysis that models the reactions of the whole genome-scale cellular system in probabilistic terms, and can infer the full flux vector distribution of genome-scale metabolic systems based on exchange and intracellular (e.g. 13C) flux measurements, steady-state assumptions, and objective function assumptions. The Bayesian model couples all fluxes jointly together in a simple truncated multivariate posterior distribution, which reveals informative flux couplings. Our model is a plug-in replacement to conventional metabolic balance methods, such as FBA. Our experiments indicate that we can characterize the genome-scale flux covariances, reveal flux couplings, and determine more intracellular unobserved fluxes in Clostridium acetobutylicum from 13C data than flux variability analysis. AVAILABILITY AND IMPLEMENTATION:The COBRA compatible software is available at github.com/markusheinonen/bamfa. SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.