A main goal in DNA computing is to build DNA circuits to compute designated functions using a minimal number of DNA strands. Here, we propose a novel architecture to build compact DNA strand displacement circuits to compute a broad scope of functions in an analog fashion. A circuit by this architecture is composed of three autocatalytic amplifiers, and the amplifiers interact to perform computation. We show DNA circuits to compute functions sqrt(x), ln(x) and exp(x) for x in tunable ranges with simulation results. A key innovation in our architecture, inspired by Napier’s use of logarithm transforms to compute square roots on a slide rule, is to make use of autocatalytic amplifiers to do logarithmic and exponential transforms in concentration and time. In particular, we convert from the input that is encoded by the initial concentration of the input DNA strand, to time, and then back again to the output encoded by the concentration of the output DNA strand at equilibrium. This combined use of strand-concentration and time encoding of computational values may have impact on other forms of molecular computation.

中文翻译：

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使用自动催化放大器进行模拟计算的紧凑型DNA链置换电路的设计和分析

DNA计算的主要目标是建立DNA电路，以使用最少数量的DNA链来计算指定功能。在这里，我们提出了一种新颖的架构来构建紧凑的DNA链置换电路，以模拟方式计算广泛的功能。这种架构的电路由三个自动催化放大器组成，这些放大器相互作用以执行计算。我们表明DNA电路来计算功能SQRT（X），LN（X）和EXP（X）为X在可调范围内并具有仿真结果。受纳皮尔（Napier）使用对数变换在计算尺上计算平方根的启发，我们架构的一项关键创新是利用自动催化放大器对浓度和时间进行对数和指数变换。特别地，我们从输入DNA链的初始浓度编码的输入转换为时间，然后再返回到平衡时输出DNA链的浓度编码的输出。链浓度和计算值的时间编码的这种结合使用可能对其他形式的分子计算产生影响。