Boolean constraint satisfaction problems for reaction networks

We define and study a class of (random) Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions. The constraints we consider encode, respectively, for hard mass-balance conditions (where the consumption and production fluxes of each chemical species are matched) and for soft mass-balance conditions (where a net production of compounds is in principle allowed). We solve these constraint satisfaction problems under the Bethe approximation and derive the corresponding belief propagation equations, which involve eight different messages. The statistical properties of ensembles of random problems are studied via the population dynamics methods. By varying a chemical potential attached to the activity of reactions, we find first-order transitions and strong hysteresis, suggesting a non-trivial structure in the space of feasible solutions. © 2013 IOP Publishing Ltd and SISSA Medialab srl.