Recurrent neural chemical reaction networks that approximate arbitrary dynamics

Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. The construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields of synthetic biology and molecular nanotechnology. In this paper, we address this problem by putting forward a molecular version of a recurrent artificial neural network, which we call a "recurrent neural chemical reaction network" (RNCRN). The RNCRN uses a modular architecture-a network of chemical neurons-to approximate arbitrary dynamics. We first prove that, with sufficiently many chemical neurons and suitably fast reactions, the RNCRN can be systematically trained to achieve any dynamics. RNCRNs with a relatively small number of chemical neurons and a moderate range of reaction rates are then trained to display a variety of biologically important dynamical features. We also demonstrate that such RNCRNs are experimentally implementable with DNA-strand-displacement technologies. A record of this paper's transparent peer review process is included in the supplemental information.