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In this thesis, we present four results concerning the computing capabilities of chemical reaction networks (CRNs) under deterministic mass action semantics: (1) we introduce a modular method for computing concentration signals using CRN extension operators; (2) we present a thorough analysis of two CRN signal restoration algorithms that prevent certain concentration signals from degrading over time; (3) we introduce a new model called input/output chemical reaction networks (I/O CRNs) which generalizes the CRN model to allow receiving input signals over time; and (4) we investigate what I/O CRNs can compute robustly and prove that I/O CRNs are capable of robustly simulating any nondeterministic finite automaton (NFA). CRN extension operators are operations that can be applied to a CRN to add extra functionality without affecting its original behavior. We show that common operators such as addition, multiplication, integration, and many others can be characterized as CRN extension operators. By iteratively applying these extensions, complex concentration signals can be modularly constructed from simple CRNs. To explore the full generality of these extensions, we introduce a notion of weakly CRN-computable signals and show that any CRN that can weakly compute a signal can be extended to exactly compute it. The two signal restoration algorithms that we investigate are related to the approximate majority algorithm for population protocols originally developed by Angluin, Aspnes, and Eisenstat. Under deterministic semantics, these algorithms are commonly used to prevent discrete memory from deteriorating over time. We investigate the behavior of these algorithms in the presence of adversarial reactions and show that under modest 2 CRNs under deterministic mass action semantics are also referred to as “mass action CRNs” or “CRNs with mass action kinetics.”

Modular and Robust Computation with Deterministic Chemical Reaction Networks