Synchronous Sequential Computations with Biomolecular Reactions

We present a methodology for implementing synchronous sequential computation using molecular reactions. Such systems perform computations in terms of molecular concentrations, i.e., molecules per unit volume, whereas the traditional electronic systems perform computations in terms of voltages, i.e., energy per unit charge. Thus far, several researchers have already proposed molecular reactions to implement static logical and arithmetic functions such as addition, multiplication, exponentiation, square root, and logarithms. In this paper, we propose two mechanisms to implement a multi-phase clock using molecular reactions. In addition, we synthesize memory by transferring concentrations between molecular types in the alternating phases of the clock. We illustrate how our methodology can be used to construct finite impulse response (FIR) filter, an infinite impulse response (IIR) filter and a four-point, two-parallel fast Fourier transform (FFT). We also show how these molecular reactions can be translated into DNA strand displacement reactions and validate our designs through chemical kinetics simulations at the DNA reactions level. Our proposed methodology is conceptual but has potential in developing synthetic biological constructs for biochemical sensing and drug delivery.