  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 ($10^6$) of flux configurations generated randomly and
compatibly with the prior information available on reaction reversibility.
