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 […]
Mon, Jul 1, 2024
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 over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE […]
Wed, Sep 1, 2021
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 […]
Wed, Sep 1, 2021
Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a Turing-complete model of analog computattion, in the sense that any computable function over the reals can be computed by a finite number of molecular species with a continuous CRN which approximates the result of that function in one of its components in arbitrary precision. The proof of that result is based on a previous result of Bournez et al […]
Tue, Sep 1, 2020