Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

RESEARCH ARTICLE Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm Wout Megchelenbrink1,2,3*, Sergio Rossell2,3,4, Martijn A. Huynen2,3, Richard A. Notebaart2,3☯*, Elena Marchiori1,3☯ 1 Institute for Computing and Information Sciences (ICIS), Radboud University, Nijmegen, the Netherlands, 2 Centre for Molecular and Biomolecular Informatics (CMBI), Radboud University Medical Centre, Nijmegen, the Netherlands, 3 Centre for Systems Biology and Bioenergetics (CSBB), Radboud University Medical Centre, Nijmegen, the Netherlands, 4 Netherlands Cancer Institute (NKI), Amsterdam, the Netherlands ☯ These authors contributed equally to this work. * (WM); (RAN) Abstract Motivation OPEN ACCESS Citation: Megchelenbrink W, Rossell S, Huynen MA, Notebaart RA, Marchiori E (2015) Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm. PLoS ONE 10(10): e0139665. doi:10.1371/journal.pone.0139665 Editor: Mukund Thattai, Tata Institute of Fundamental Research, INDIA Received: December 17, 2014 Accepted: September 16, 2015 Published: October 12, 2015 Copyright: © 2015 Megchelenbrink et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: Data is contained within the paper and/or Supporting Information files. Funding: This work was supported by CSBR (Centres for Systems Biology Research) from the Netherlands Organisation for Scientific Research (NWO) (CSBR09/ 013V). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Genome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions. Results Here, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux PLOS ONE | DOI:10.1371/journal.pone.0139665 October 12, 2015 1 / 16 Estimating Metabolic Flux Using a Maximum Network Flexibility Paradigm space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information. Availability MMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf. Introduction Advances in obtaining quantitative “omics” data have led to the availability of genome-scale metabolic network reconstructions for many organisms. Successful metabolic modelling examples range from predicting the impact of cell perturbation experiments in micro-organisms [1] and in silico yield optimization of valuable products such as bioethanol [2] to metabolic engineering for drug synthesis [3] and tumor vulnerability studies in cancer cells [4–8]. At the heart of these models lies the stoichiometric matrix (S), containing m metabolites and n reactions. Entry Si,j denotes the stoichiometric coefficient of metabolite i in reaction j. The allowable flux range vj for reaction j is bounded by the mass-balance equations (considered at steady-state) and flux capacity constraints d~ x ¼ S~ v¼0 dt ð1Þ vlbj  vj  vub j ; 8j 2 f1; 2; . . . ; ng ð2Þ where ~ x and ~ v are vectors denoting the metabolite concentrations and reaction rates respectively. In metabolic networks the reactions typically outnumber the metabolites, leaving the system of linear equations S underdetermined [9]. This means that there is no unique solution, but rather a convex space of (infinitely many) feasible flux distributions [10], known as the steady-state solution space. Knowledge of the actual flux distribution the organism utilizes is of great importance for many biological engineering purposes [9,11], making reduction of the solution space a central problem in metabolic modeling. Since the reaction stoichiometry in eq (1) is fixed, reduction of the solution space can only be achieved by tightening the feasible flux ranges in eq (2). Methods for reducing the feasible fluxes to those that are biologically most relevant can be divided into three main categories. i) Computational methods that select flux distributions based on optimization of a biologically sound objective, such as biomass or ATP yield. Flux Balance Analysis (FBA) [10,12] is arguably the most applied technique that has shown to be accurate in predicting maximum growth [13] and byproduct secretion rates [14] for micro-organisms. Often, the flux distribution obtained by FBA is not unique and multiple optima exist. Flux Variability Analysis (FVA) [15] can be viewed as an extension of FBA that, instead of finding a unique flux distribution, computes the minimum and maximum allowable flux through each reaction while optimizing an obje (...truncated)