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arXiv · 1306.2480

Boolean constraint satisfaction problems for reaction networks

Alessandro Seganti·Andrea De Martino·Federico Ricci-Tersenghi
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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.

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Alessandro Seganti, Andrea De Martino, Federico Ricci-Tersenghi. 2014-10-13. Boolean constraint satisfaction problems for reaction networks. https://doi.org/10.1088/1742-5468%2F2013%2F09%2Fp09009

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