Computing Mathematical Functions using DNA via Fractional Coding

Scientific Reports
Sayed Ahmad SalehiKeshab K Parhi

Abstract

This paper discusses the implementation of mathematical functions such as exponentials, trigonometric functions, the sigmoid function and the perceptron function with molecular reactions in general, and DNA strand displacement reactions in particular. The molecular constructs for these functions are predicated on a novel representation for input and output values: a fractional encoding, in which values are represented by the relative concentrations of two molecular types, denoted as type-1 and type-0. This representation is inspired by a technique from digital electronic design, termed stochastic logic, in which values are represented by the probability of 1's in a stream of randomly generated 0's and 1's. Research in the electronic realm has shown that a variety of complex functions can be computed with remarkably simple circuitry with this stochastic approach. This paper demonstrates how stochastic electronic designs can be translated to molecular circuits. It presents molecular implementations of mathematical functions that are considerably more complex than any shown to date. All designs are validated using mass-action simulations of the chemical kinetics of DNA strand displacement reactions.

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Citations

Apr 14, 2019·Chemistry : a European Journal·Vadde RamuAlexander Schiller
May 28, 2020·Nanoscale·Congzhou ChenXiaolong Shi
Apr 13, 2019·Molecules : a Journal of Synthetic Chemistry and Natural Product Chemistry·Christina BaekByoung-Tak Zhang
May 24, 2019·ACS Nano·Xin Song, John Reif
Nov 24, 2021·Nanoscale·Muhammad Tayyab RazaSung Ha Park
Jan 27, 2022·ACS Synthetic Biology·Xingyi Liu, Keshab K Parhi

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Software Mentioned

Perceptron C
Mult
NMult

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