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 op- erations 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.