Boolean constraint satisfaction problems for reaction networks

TL;DR

This paper models chemical reaction networks as Boolean constraint satisfaction problems, analyzing their solution space and phase transitions using statistical physics methods, revealing complex solution structures.

Contribution

It introduces a novel Boolean CSP framework for reaction networks and applies Bethe approximation and population dynamics to study their properties.

Findings

First order phase transitions observed in solution space

Strong hysteresis indicates complex solution structure

Bethe approximation effectively models the problem's statistical properties

Abstract

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, that involve 8 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.