Programming and training rate-independent chemical reaction networks.
Proc Natl Acad Sci U S A 2022;
119:e2111552119. [PMID:
35679345 PMCID:
PMC9214506 DOI:
10.1073/pnas.2111552119]
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Abstract
To program complex behavior in environments incompatible with electronic controllers such as within bioreactors or engineered cells, we turn to chemical information processors. While chemical reactions can perform computation in the stoichiometric exchange of reactants for products (how many molecules of which reactants result in how many molecules of which products), the control of reaction rates is usually thought to allow more complex computation. Motivated by the fact that correct stoichiometry is easier to ensure than reaction rates, we provide a method for programming and training chemical computation by stoichiometry. We show that such computation can be straightforwardly programmed in a manner analogous to sequential programming, and demonstrate the execution of neural networks capable of complex machine learning tasks.
Embedding computation in biochemical environments incompatible with traditional electronics is expected to have a wide-ranging impact in synthetic biology, medicine, nanofabrication, and other fields. Natural biochemical systems are typically modeled by chemical reaction networks (CRNs) which can also be used as a specification language for synthetic chemical computation. In this paper, we identify a syntactically checkable class of CRNs called noncompetitive (NC) whose equilibria are absolutely robust to reaction rates and kinetic rate law, because their behavior is captured solely by their stoichiometric structure. In spite of the inherently parallel nature of chemistry, the robustness property allows for programming as if each reaction applies sequentially. We also present a technique to program NC-CRNs using well-founded deep learning methods, showing a translation procedure from rectified linear unit (ReLU) neural networks to NC-CRNs. In the case of binary weight ReLU networks, our translation procedure is surprisingly tight in the sense that a single bimolecular reaction corresponds to a single ReLU node and vice versa. This compactness argues that neural networks may be a fitting paradigm for programming rate-independent chemical computation. As proof of principle, we demonstrate our scheme with numerical simulations of CRNs translated from neural networks trained on traditional machine learning datasets, as well as tasks better aligned with potential biological applications including virus detection and spatial pattern formation.
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