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

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. Author Summary: The operation of biological systems is constrained under all circumstances by the laws of physics. Thermodynamics, in particular, dictates preferential directions in which biochemical reactions should flow at stationarity. When applied to cellular reaction systems (like metabolic networks), it favors the emergence of some (thermodynamically feasible) ways to organize the flow of matter while prohibiting others. The development of detailed predictive models for the biochemical activity of a cell relies on the possibility to integrate the laws of thermodynamics in genome-scale reconstructions of cellular metabolic networks. In this work we have devised an efficient relaxation algorithm to implement thermodynamic constraints in genome-scale models. Besides allowing to check for thermodynamic feasibility of reaction flow configurations, it is also capable of providing information on other relevant physico-chemical quantities. We have applied it to two cellular metabolic networks of different complexity, namely that of human red blood cells and that of the bacterium Escherichia coli. In the former case, we have obtained predictions for the intracellular chemical state (in terms of metabolite concentrations and reaction free energies) consistent with empirical knowledge; in the latter, we have effectively corrected thermodynamically infeasible flux configurations.