The Essential Role of Thermodynamics in metabolic network modeling: physical insights and computational challenges

Quantitative studies of cell metabolism are often based on large chemical reaction network models. A steady state approach is suited to analyze phenomena on the timescale of cell growth and circumvents the problem of incomplete experimental knowledge on kinetic laws and parameters, but it shall be supported by a correct implementation of thermodynamic constraints. In this article we review the latter aspect highlighting its computational challenges and physical insights. The simple introduction of Gibbs inequalities avoids the presence of unfeasible loops allowing for correct timescale analysis but leads to possibly non-convex feasible flux spaces, whose exploration needs efficient algorithms. We shorty review on the implementation of thermodynamics through variational principles in constraints based models of metabolic networks.