This paper introduces memristors realized by molecular and DNA reactions. Molecular memristors process one input molecule, generate two output molecules, and are realized using two molecular reactions with two different rate constants. The DNA memristors are realized using five DNA strand displacement (DSD) reactions with two effective rate constants. The hysteresis behavior is preserved in the proposed memristors, and this behavior can be altered by changing the ratios of the rate constants. The state of the memristor can be computed from the concentrations of the two output molecules using bipolar fractional coding. We describe how the proposed memristors can be used to learn the spatial and temporal properties of data via the reservoir computing (RC) model. An RC system can be divided into two parts: reservoir and readout layer. The first part transfers the information from the input space to a high-dimensional spatiotemporal feature space represented by the state of reservoirs. The connectivity structure of the reservoir will remain fixed through the dynamical evaluations. The readout layer effectively maps the projected features to the target output. A dynamical memristor array is used to implement an RC system that exploits the internal dynamical processes of the memristors. The readout layer implements a matrix-vector multiplication using molecular reactions, also based on bipolar fractional coding. All molecular reactions are mapped to DSD reactions. The RC system based on the DNA reservoir and the DNA readout layer is used to solve a handwritten digit recognition task and a second-order time series prediction task. The performance of the DNA RC system is comparable to that of an electronic memristor RC system for both tasks.
Keywords: DNA memristors; DNA readout layer; DNA reservoir computing; digit classification; fractional coding; time series prediction.