Input-to-state stability of chemical reaction networks with application to molecular computation

In biological reaction systems, reaction rates may vary over time due to environmental fluctuations, regulation, or coupling with other reaction modules. Input-to-state stability (ISS) provides a useful tool for analyzing the robustness of time-varying chemical reaction networks (CRNs). Existing ISS results for CRNs typically rely on restrictive structural assumptions, such as zero deficiency, a single linkage class, or weak reversibility. This paper makes two main contributions. First, we establish ISS for a broader class of weakly reversible CRNs, allowing nonzero deficiency and multiple linkage classes. Second, we extend the analysis to certain CRNs that are not weakly reversible by using network transformation techniques (linear conjugacy and reconstruction). Together, these results enlarge the class of CRNs for which robustness under time-varying reaction-rate inputs can be certified. Since CRNs are a standard framework for biomolecular computation, our results further enable the stability analysis of parallel molecular computing systems, an important problem in biomolecular computation where multiple CRN-based computing modules operate simultaneously and perturb one another through time-varying effective reaction rates.