Department of Electrical and Computer Engineering, University of Minnesota Twin-Cities, Minneapolis, MN, United States of America.
PLoS One. 2023 May 8;18(5):e0281574. doi: 10.1371/journal.pone.0281574. eCollection 2023.
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".
本文提出了一种基于数字设计理论的计算分子反应中数学函数的新策略。它演示了如何基于指定由随机逻辑计算的模拟函数的真值表来设计化学反应网络。随机逻辑理论需要使用零和一的随机流来表示概率值。一方面，随机逻辑中随机变量的表示与分子系统中变量作为分子浓度的表示之间存在联系。随机逻辑的研究表明，许多感兴趣的数学函数可以用由逻辑门构建的简单电路来计算。本文提出了一种将随机逻辑电路计算的数学函数转换为化学反应网络的通用且高效的方法。模拟表明，在对数阶约束内，反应网络执行的计算对于反应速率的变化是准确和稳健的。给出了用于图像处理和信号处理以及机器学习等应用的计算函数的反应网络：反正切、指数、贝塞尔和 sinc。提出了一种使用特定实验底盘的实现：使用称为 DNA“concatemers”的 DNA 链置换单元。
