Asynchronous discrete-time signal processing with molecular reactions

This paper presents a new methodology to synthesize molecular reactions for discrete-time signal processing (DSP) computations that produce time-varying quantities of molecules as a function of time-varying input quantities. DSP structures include delay elements which need to be synchronized by a clock signal. This paper demonstrates an approach to synthesize molecular reactions to implement DSP operations without requiring a clock signal. In the proposed approach, each delay and output variables are mapped to two types of molecules. The scheduling of the reactions is controlled by absence indicators, i.e., signals transfer according to the absence of other signals. All computations are scheduled in four phases. The input signal and values stored in all delay elements are consumed for computations in the first phase. Results of computations are stored in the first types of molecule corresponding to the delay elements and output variables. During the second phase, the value of the first molecular type is transferred to the second molecular type for the output variable. In the third phase, the values of first types of molecule are transferred to the second types of molecule associated with each delay element. The output molecules are collected in the fourth phase. The method is illustrated by synthesizing a simple FIR filter, an IIR filter, and an 8-point real-valued fast Fourier transform (FFT). The synthesized systems consist of bimolecular reactions and are translated to DNA-strand displacement reactions. The methodology is validated through mass-action simulations of DNA kinetics. The proposed approach may play a potential role in applications such as drug delivery and in monitoring spectral content of proteins.