Fixed Points and Attractors of Reactantless and Inhibitorless Reaction Systems

TL;DR

This paper explores the computational complexity of fixed points and attractors in simplified reaction systems lacking either reactants or inhibitors, revealing that such simplifications do not always reduce problem complexity.

Contribution

It provides the first complexity analysis of fixed points and attractors in reactantless and inhibitorless reaction systems, highlighting unexpected complexity results.

Findings

Complexity remains high despite system simplifications

Certain problems are computationally hard even in constrained systems

Biological relevance of fixed points and attractors is emphasized

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.