Markov-Chain Monte-Carlo Sampling of Metabolite Concentrations to Identify Thermodynamically Feasible Reaction Directionalities for Flux Balance Analysis

Flux balance analysis (FBA) is a widely used tool for both the understanding and design of cell metabolism. Without any kinetic
data, qualitative as well as quantitative predictions of metabolic flux activity to achieve optimal growth can be made. It is also
computationally inexpensive as only linear problems need to be solved. Among its shortcomings, however, is the lack of a rigorous
enforcement of the thermodynamical feasibility of reactions; this is due to the fact that FBA’s steady­state assumption evades the
consideration of metabolite concentrations, which impact changes in Gibbs' free energies. Existing approaches to ensure
thermodynamic feasibility are based on computationally expensive mixed­integer linear programming.

Here, we propose a Markov­-Chain Monte-­Carlo (MCMC) approach to identify metabolite concentrations that ensure
thermodynamic feasibility. We sample metabolite concentration vectors, and use these to determine reaction directionalities that
violate thermodynamic constraints. We then identify a biomass-­producing FBA solution with minimal total flux F through these
infeasible reactions. Solutions with lower F are deemed more likely, and hence the sampled concentrations are expected to
converge towards thermodynamically feasible solutions.

We compare several Markov Chain designs and evaluate the gains through high-performance computing implementations.