Metabolic network reductions

Abstract

Genome-scale metabolic networks are exceptionally huge and even efficient algorithms can take a while to run because of the sheer size of the problem instances. To address this problem, metabolic network reductions can substantially reduce the overwhelming size of the problem instances at hand. We begin by formulating some reasonable axioms defining what it means for a metabolic network reduction to be "canonical" which conceptually enforces reversibility without loss of any information on the feasible flux distributions. Then, we start to search for an efficient way to deduce some of the attributes of the original network from the reduced one in order to improve the performance. As the next step, we will demonstrate how to reduce a metabolic network repeatedly until no more reductions are possible. In the end, we sum up by pointing out some of the biological implications of this study apart from the computational aspects discussed earlier.Keywords: systems biology; metabolic network analysis; canonical metabolic network reduction; quantitative flux coupling analysis; QFCA. Author summaryMetabolic networks appear at first sight to be nothing more than an enormous body of reactions. The dynamics of each reaction obey the same fundamental laws and a metabolic network as a whole is the melange of its reactions. The oversight in this kind of reductionist thinking is that although the behavior of a metabolic network is determined by the states of its reactions in theory, nevertheless it cannot be inferred directly from them in practice. Apart from the infeasibility of this viewpoint, metabolic pathways are what explain the biological functions of the organism and thus also what we are frequently concerned about at the system level.Canonical metabolic network reductions decrease the number of reactions substantially despite leaving the metabolic pathways intact. In other words, the reduced metabolic networks are smaller in size while retaining the same metabolic pathways. The possibility of such operations is rooted in the fact that the total degrees of freedom of a metabolic network in the steady-state conditions are significantly lower than the number of its reactions because of some emergent redundancies. Strangely enough, these redundancies turn out to be very well-studied in the literature.

A structural property for reduction of biochemical networks

“…Since the removal of complexes in this way results in expressing one flux as a sum of others, the reduced network is unique and does not depend on the order of removing the balanced complexes. A similar idea has been used in the unbiased efficient reduction of stoichiometric models (Tefagh and Boyd, 2019), however, based on the coupling of reactions around balanced species and without the rewiring of reactions.…”

“…These approaches can be categorized based on different criteria: (i) whether they only employ the structure of the network (i.e. stoichiometry of biochemical reactions) (Clarke, 1992;Jonnalagadda and Srinivasan, 2014;Sambamoorthy and Raman, 2020;Singh and Lercher, 2020;Tefagh and Boyd, 2019) or also consider the kinetics of reaction fluxes (Danø et al, 2006;Feliu et al, 2019;Wiuf, 2013, 2012;Radulescu et al, 2008;Rao et al, 2014;Roussel and Fraser, 2001;Sáez et al, 2017;Schmidt et al, 2008; . CC-BY-NC-ND 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.…”

“…CC-BY-NC-ND 4.0 International license made available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprint this version posted March 19, 2021. ; https://doi.org/10.1101/2021.03.17.435785 doi: bioRxiv preprint Sunnåker et al, 2011), (ii) whether they approximate or provide one-to-one correspondence of the steady-state properties between the original and reduced network (Erdrich et al, 2015;Feliu and Wiuf, 2013;Röhl and Bockmayr, 2017;Tefagh and Boyd, 2019), and (iii) whether the reduction process is fully automated, i.e. unbiased, or semi-automated (i.e.…”

“…Other approaches in this group start with user-defined subsystems that are subsequently connected (and further refined) to obtain a minimal model that can fulfil a prespecified function (Baroukh et al, 2014). In contrast, using ideas from reaction coupling (Burgard et al, 2004), a recent unbiased approach provides an efficient reduction of stoichiometric models by reaction removal, while ensuring one-to-one correspondence between the elementary flux modes of the original and reduced model (Tefagh and Boyd, 2019). Since these approaches do not consider kinetics of reaction flux, they remain silent about the effects that the reduction has on the concentrations of the remaining metabolites.…”

“…These approaches can be categorized based on different criteria: (i) whether they only employ the structure of the network (i.e. stoichiometry of biochemical reactions) (Clarke, 1992; Jonnalagadda and Srinivasan, 2014; Sambamoorthy and Raman, 2020; Singh and Lercher, 2020; Tefagh and Boyd, 2019) or also consider the kinetics of reaction fluxes (Danø et al, 2006; Feliu et al, 2019; Feliu and Wiuf, 2013, 2012; Radulescu et al, 2008; Rao et al, 2014; Roussel and Fraser, 2001; Sáez et al, 2017; Schmidt et al, 2008; Sunnåker et al, 2011), (ii) whether they approximate or provide one-to-one correspondence of the steady-state properties between the original and reduced network (Erdrich et al, 2015; Feliu and Wiuf, 2013; Röhl and Bockmayr, 2017; Tefagh and Boyd, 2019), and (iii) whether the reduction process is fully automated, i.e. unbiased, or semi-automated (i.e.…”