Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN, 55455, USA.
Sci Rep. 2018 May 29;8(1):8312. doi: 10.1038/s41598-018-26709-6.
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.
本文讨论了在一般的分子反应中，特别是在 DNA 链置换反应中，实现指数、三角函数、sigmoid 函数和感知器函数等数学函数的方法。这些函数的分子构建基于输入和输出值的一种新表示形式：分数编码，其中值由两种分子类型的相对浓度表示，分别表示为类型 1 和类型 0。这种表示形式受到数字电子设计中一种称为随机逻辑的技术的启发，其中值由随机生成的 0 和 1 流中 1 的概率表示。电子领域的研究表明，使用这种随机方法可以用非常简单的电路计算各种复杂的函数。本文演示了如何将随机电子设计转化为分子电路。它提出了比迄今为止任何一种都复杂得多的数学函数的分子实现。所有设计都使用 DNA 链置换反应的化学动力学的质量作用模拟进行验证。
