Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. proof uses previous functions defined polynomial ordinary differential equations (PODE), dual-rail encoding variables difference concentration between two species, and back-end quadratization transformation to restrict elementary reactants. In this paper, we present polynomialization algorithm quadratic time complexity transform system in PODE. This is used as front-end compile mathematical function, either or some input into CRN. We illustrate performance our compiler on benchmark relevant design problems synthetic biology specified functions. particular, abstract obtained compilation Hill order 5 compared natural structure MAPK signalling networks.