A Polynomialization Algorithm for Elementary Functions and ODEs, and their Compilation into Chemical Reaction Networks

In this short paper extracted from [7], we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in polynomial differential equations (PODE). This algorithm is used as a front-end transformation in a pipeline to compile any elementary mathematical function, either of time or of some input variable, into a finite Chemical Reaction Network (CRN) which computes it. We illustrate the performance of our compiler on a benchmark of elementary functions which serve as formal specification of CRN design problems in synthetic biology, and as comparison basis with natural CRNs exhibiting similar behaviours.