Section: New Results

Compiling mathematical functions and programs in CRNs

Participants : Auriane Cozic, Elisabeth Degrand, François Fages, Mathieu Hemery, Wei-Chih Huang, Lena Le Quellec, Sylvain Soliman.

In a previous paper, we have proven that any computable function over the reals in the sense of computable analysis (i.e. computable with finite yet arbitrary precision by a Turing machine) is computable by a continuous CRN over a finite set of molecular species. In this approach, the real-valued molecular concentrations are the information carriers and computation can be purely analog. We have derived from the proof of this result a compiler of real functions (of either time or input concentrations) specified by polynomial initial value problems (PIVP) in elementary CRNs. This compiler makes it possible to automate the design of abstract CRNs for implementing arbitrary computable functions over the reals presented by PIVPs, in particular arithmetic, trigonometric, sigmoid and logical functions. The compilation of sequentiality, program control flows and mixed analog-digital imperative programs lead us however to consider more efficient implementations of Heavyside functions with simple CRNs that have no simple mathematical expression as input/output functions. Our goal is to develop a compiler of high-level mixed analog-digital programs in efficient abstract CRNs amenable to practical implementation with real enzymes in DNA-free vesicles, as illustrated in Section 7.8.