Appendix to DNA Reservoir Computing: A Novel Molecular Computing Approach

In this appendix, we justify the reduction of the nonlinear ODE system describing three coupled deoxyribozyme oscillators. We show that the kinetic simulation of the deoxyribozime chemistry agrees with the result of the laboratory experiment. We make simplifying assumption that help us reduce a system of nine ODEs into three linear ODEs that is more amenable to mathematical analysis. We show that the reduced ODEs preserves the essentially properties of the original nonlinear ODEs and we use it to perform stability analysis on the system’s dynamics. A Kinetics and Oscillation in a Network of Deoxyribozyme Logic Gates The fundamental units of our deoxyribozyme design are input, gate, substrate, and product. We denote the concentrations of these species by symbols [Ii], [Gi], [Si], [Pi], where the subscript i is used as index to show compatible interacting reactants whenever we have more than one of each type of species in our reactions. The gate molecules become active in the presence of input molecules and cleave the substrate molecules [3]. As a result, substrate molecules turn into product molecules. The reaction of gates and substrates and hence production of products can be described by d[P] dt = β [S][G], where β = 5× 10 −7 nM−1 s−1 is the reaction rate constant measured experimentally [1]. Figure 1a depicts the simulation of the actual experiment where 250 nM of gate molecules and 2500 nM of substrate molecules interact to produce products in the presence of different concentrations of input molecules (given in nM). For [I] > [G], we observe that there is nonlinear growth in product concentration with a rate that is nearly independent of [I]. This simulation result agrees closely with the lab experiment reported in [1]. The effect of input molecules on gate molecules is very rapid, compared with the other reactions in the system. Since the only purpose of this reaction is to make the gates active we ignore this activation altogether and throughout this paper whenever we write [G] we mean gate molecules that have been activated.