Computing mathematical functions with chemical reactions via stochastic logic

Abstract

This paper presents a novel strategy for computing mathematical functions with molecular reactions, based on theory from the realm of digital design. It demonstrates how to design chemical reaction networks based on truth tables that specify analog functions, computed by stochastic logic. The theory of stochastic logic entails the use of random streams of zeros and ones to represent probabilistic values. A link is made between the representation of random variables with stochastic logic on the one hand, and the representation of variables in molecular systems as the concentration of molecular species, on the other. Research in stochastic logic has demonstrated that many mathematical functions of interest can be computed with simple circuits built with logic gates. This paper presents a general and efficient methodology for translating mathematical functions computed by stochastic logic circuits into chemical reaction networks. Simulations show that the computation performed by the reaction networks is accurate and robust to variations in the reaction rates, within a log-order constraint. Reaction networks are given that compute functions for applications such as image and signal processing, as well as machine learning: arctan, exponential, Bessel, and sinc. An implementation is proposed with a specific experimental chassis: DNA strand displacement with units called DNA “concatemers”.

Neural network execution using nicked DNA and microfluidics

“…However, a practical DNA storage system, particularly one that is inherently programmable, has the potential to change this scenario. Such storage opens up the possibility of 'in-memory' computing, which involves performing computation directly on the data stored in DNA [2,16,17]. This computation is not performed on the sequence of nucleotides, but rather by making topological modifications to the DNA strands: introducing breaks in the phosphodiester backbone known as 'nicks' and gaps in the backbone referred to as 'toeholds'.…”

“…Recent research has demonstrated the capability of using DNA molecules to store not just genetic information but also encoded digital information [ 1 ]. Inspired by this breakthrough computer scientists have been researching way to compute with DNA molecules resulting in designs capable of performing logical operations as well as complex arithmetic such as vector-matrix operations [ 2 – 4 ]. Due to the ultra-compact form factor and unprecedented characteristics of the DNA molecule favoring its future use as big-data storage medium, we envision a computing platform using DNA molecules that are capable of computation in-situ without the need for domain conversion of information from DNA to electronics.…”

“…This can either be done by encoding binary values, where the presence of the specific strand represents a 1 and its absence a 0 [ 30 ], or by employing a non-integer value encoding based on the concentration, referred to as a direct representation [ 36 ]. Recent research has explored the use of a fractional representation [ 2 , 35 , 37 ]. The central idea is to use the concentrations of two species of strand, X 0 and X 1 , to represent a value x with the relationship: where x ∈ [0, 1].…”

“…Recent research has demonstrated the capability of using DNA molecules to store not just genetic information but also encoded digital information [1]. Inspired by this breakthrough computer scientists have been researching way to compute with DNA molecules resulting in designs capable of performing logical operations as well as complex arithmetic such as vector-matrix operations [2][3][4]. Due to the ultra-compact form factor and unprecedented characteristics of…”