FUNDNA Software for Computing Mathematical Functions by DNA

Abstract

Abstract Chemical reaction networks (CRNs) are commonly used as a design and modeling language for molecular computing. Thanks to the advancement of biotechnology, the implementation of more complex molecular computing circuits becomes feasible that makes generating efficient CRNs for these circuits difficult. This paper presents the development of a software tool, called FUNDNA, that automates the design of CRNs for computing mathematical functions. The generated CRNs can be mapped to DNA reactions using existing software tools. FUNDNA receives target mathematical functions from its user, approximates them by McLaurin series, and rearranges the series such that they can be transferred to a cascade of molecular AND/NAND (M-AND/M-NAND) units. To transfer the rearranged series into M-AND/M-NAND units, the software forms a connected graph of inputs, output, and the units using terms in the series. Each unit is then replaced by four reactions to generate the desired computing CRN. The computation is based on fractional encoding, where pairs of molecules are used to represent input and output variables. While individual units compute multiplication of their inputs the whole cascade performs the desired computation. We validated the software tool for 14 different functions. We mapped the generated CRNs into DNA reactions and the simulation results for different functions show that the tool can achieve computing CRNs with mean square error less than \(3.52\times {10}^{-4}\).