Concentration-Based Polynomial Calculations on Nicked DNA

In this paper, we introduce a novel scheme for computing polynomial functions on a substrate of nicked DNA. We first discuss a fractional encoding of data, based on the concentration of nicked double DNA strands. Then we show how to perform multiplication on this representation. Next we describe the read-out process, effected by releasing single strands. We show how to perform simple mathematical operations such as addition and subtraction, as well as how to scale constant values using probabilistic switches. We also describe two complex operations: calculating a vector dot product and computing a general polynomial function. We conclude by discussing potential applications of our scheme, practical challenges, and future research directions.