P System Models of Bistable, Enzyme Driven Chemical Reaction Networks

Abstract

In certain classes of chemical reaction networks (CRN), there may be two stable states. The challenge is to find a model of the CRN such that the stability properties can be predicted. In this paper we consider the problem of building a P-system designed to simulate the CRN in an attempt to determine if the CRN is stable or bistable. We found that for the networks in [2] none of the bistable CRN would have a bistable P-system by stoichiometry alone. The reaction kinetics must be included in the P-system model; the implementation of which has been considered an open problem. In this paper we conclude that a P-system for a CRN in mreactants and nproducts has at most 2(m2+ mn) membranes and 6(m2+ mn) rules. This suggests that P-system models of a chemical reaction network, including both stoichiometry and reaction kinetics can be built.