Programming and Training Rate-Independent Chemical Reaction Networks

TL;DR

This paper introduces a class of chemical reaction networks called non-competitive (NC) CRNs that are robust to reaction rates, and presents a method to program them using neural networks, enabling rate-independent biochemical computation.

Contribution

The paper defines non-competitive CRNs, proves their rate-independence, and provides a translation from neural networks to these CRNs for robust biochemical computation.

Findings

NC-CRNs are rate-independent and robust to reaction rate variations.

A tight translation exists between ReLU neural networks and NC-CRNs.

Numerical simulations demonstrate practical applications in biological tasks.

Abstract

Embedding computation in biochemical environments incompatible with traditional electronics is expected to have wide-ranging impact in synthetic biology, medicine, nanofabrication and other fields. Natural biochemical systems are typically modeled by chemical reaction networks (CRNs), and CRNs can be used as a specification language for synthetic chemical computation. In this paper, we identify a class of CRNs called non-competitive (NC) whose equilibria are absolutely robust to reaction rates and kinetic rate law, because their behavior is captured solely by their stoichiometric structure. Unlike prior work on rate-independent CRNs, checking non-competition and using it as a design criterion is easy and promises robust output. 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 (IRIS and MNIST), as well as tasks better aligned with potential biological applications including virus detection and spatial pattern formation.