A Scalable Algorithm to Explore the Gibbs Energy Landscape of Genome-Scale Metabolic Networks

Abstract

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample ( ) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.

Metabolic Resource Allocation in Individual Microbes Determines Ecosystem Interactions and Spatial Dynamics

“…Alternative uses of stoichiometric constrains (e.g. sampling of the feasible space (Bordel et al, 2010)), integration with high-throughput data (Becker and Palsson, 2008; Collins et al, 2012) and economy-inspired theory (Fleming, 2011; De Martino et al, 2012; Reznik et al, 2013; Schuetz et al, 2012) are among the new directions being sought in order to overcome some of these limitations.…”

A proof for loop-law constraints in stoichiometric metabolic networks

“…Such cycles of reactions violate a “loop law” that is analogous to Kirchhoff’s second law for electrical circuits, as discussed previously by Beard et al [4]. Many approaches have successfully constrained these loops using known flux directionality [5], energy-balance equations [4], and known [6-11] or predicted [12] thermodynamic parameters. Loops have also been indirectly removed by minimizing network flux [6,13-15], or by coupling flux to enzyme synthesis costs [16].…”

An analytic approximation of the feasible space of metabolic networks

“…In these situations, in principle, the convergence time of the algorithm should be established independently for each new value of the parameter. Another limitation of this class of sampling strategies is the difficulty of imposing other constraints15 such as the experimentally measured distribution profiles of specific subset of fluxes (typically biomass and/or in-take/out-take of the network), a particularly timely issue given the recent breakthrough of metabolic measurements in single cell16, although recent attempts in this direction exist1718.…”