Fixed Points and Attractors of Reactantless and Inhibitorless Reaction Systems

Abstract

Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems related to the existence of fixed points and attractors in two constrained classes of reaction systems, in which either reactants or inhibitors are disallowed. These problems have biological relevance and have been extensively studied in the unconstrained case; however, they remain unexplored in the context of reactantless or inhibitorless systems. Interestingly, we demonstrate that although the absence of reactants or inhibitors simplifies the system's dynamics, it does not always lead to a reduction in the complexity of the considered problems.

32 pages. The previous version contained major mistakes. The wrong results are the former Corollaries 9, 10, 15, 17, 23, 25, 25, 32 and 36, Proposition 31 and Remark 30 (all following from a single mistake). We have now corrected all these results