On BIOCHAM Symbolic Computation Pipeline for Compiling Mathematical Functions into Biochemistry

François Fages, Mathieu Hemery, Sylvain Soliman (2025).

ACM Communications in Computer Algebra, 58 (2):15-22.

[polynomialization ; quadratization ; stabilization ; online computation ; algebraic functions ; elementary functions ; Turing-completeness ; program synthesis ; chemical computation ; Analog computation]

Chemical Reaction Networks (CRNs) are a standard formalism used in chemistry and biology to model complex molecular interaction systems. In the perspective of systems biology, they are a central tool to analyze the high-level functions of the cell in terms of their low-level molecular interactions. In the perspective of synthetic biology, they constitute a target programming language to implement in chemistry new functions either in vitro, in artificial vesicles, or in living cells. In this paper, we describe the CRN synthesis tool part of our CRN modeling and analysis software BIOCHAM (Biochemi-cal Abstract Machine). This compiler transforms any elementary (resp. algebraic) real function into a formal finite CRN to compute it (resp. with absolute functional robustness), through a pipeline of symbolic computation steps, among which quadratization optimization plays a key role to restrict to elementary reactions with atmost two reactants and a minimum number of molecular species.