The cell: A chemical analog calculator

A cell processes the information of the chemical signals it receives from its environment by performing noise filtering, signal amplification and often analog-digital conversion functions to produce all-or-nothing responses. This chapter shows how the Turing-completeness proof of continuous chemical reaction networks (CRNs) over a finite number of molecular species proposes the bases of such a reconciliation, without artificial construction, with capabilities for both analysis of natural chemical programs in living cells and synthesis of artificial chemical programs in non-living vesicles. CRNs are a basic formalism in chemistry and biology for describing complex systems of molecular interactions. The Church-Turing thesis states that there is only one notion of effective computation over discrete data structures, and by extension over arbitrary-precision real numbers.