Chemical reaction network designs for asynchronous logic circuits

Chemical reaction networks (CRNs) are a versatile language for describing the dynamical behaviour of chemical kinetics, capable of modelling a variety of digital and analogue processes. While CRN designs for synchronous sequential logic circuits have been proposed and their implementation in DNA demonstrated, a physical realisation of these devices is difficult because of their reliance on a clock. Asynchronous sequential logic, on the other hand, does not require a clock, and instead relies on handshaking protocols to ensure the temporal ordering of different phases of the computation. This paper provides novel CRN designs for the construction of asynchronous logic, arithmetic and control flow elements based on a bi-molecular reaction motif with catalytic reactions and uniform reaction rates. We model and validate the designs for the deterministic and stochastic semantics using Microsoft's GEC tool and the probabilistic model checker PRISM, demonstrating their ability to emulate the function of asynchronous components under low molecular count.