Discrete-time signal processing with DNA

We present a methodology for implementing discrete-time signal processing operations, such as filtering, with molecular reactions. The reactions produce time-varying output quantities of molecules as a function of time-varying input quantities according to a functional specification. This computation is robust and independent of the reaction rates, provided that the rate constants fall within coarse categories. We describe two approaches: one entails synchronization with a clock signal, implemented through sustained chemical oscillations; the other is "self-timed" or asynchronous. We illustrate the methodology by synthesizing a simple moving-average filter, a biquad filter, and a Fast Fourier Transform (FFT). Abstract molecular reactions for these filters and transforms are translated into DNA strand displacement reactions. The computation is validated through mass-action simulations of the DNA kinetics. Although a proof of concept for the time being, molecular filters and transforms have potential applications in fields such as biochemical sensing and drug delivery.