Chou Chun Tung
School of Computer Science and Engineering, University of New South Wales, Sydney, NSW, Australia.
Synth Biol (Oxf). 2017 Apr 28;2(1):ysx002. doi: 10.1093/synbio/ysx002. eCollection 2017 Jan.
Living cells constantly process information from their living environment. It has recently been shown that a number of cell signaling mechanisms (e.g. G protein-coupled receptor and epidermal growth factor) can be interpreted as computing the logarithm of the ligand concentration. This suggests that logarithm is a fundamental computation primitive in cells. There is also an increasing interest in the synthetic biology community to implement analog computation and computing the logarithm is one such example. The aim of this article is to study how the computation of logarithm can be realized using chemical reaction networks (CRNs). CRNs cannot compute logarithm exactly. A standard method is to use power series or rational function approximation to compute logarithm approximately. Although CRNs can realize these polynomial or rational function computations in a straightforward manner, the issue is that in order to be able to compute logarithm accurately over a large input range, it is necessary to use high-order approximation that results in CRNs with a large number of reactions. This article proposes a novel method to compute logarithm accurately in CRNs while keeping the number of reactions in CRNs low. The proposed method can create CRNs that can compute logarithm to different levels of accuracy by adjusting two design parameters. In this article, we present the chemical reactions required to realize the CRNs for computing logarithm. The key contribution of this article is a novel method to create CRNs that can compute logarithm accurately over a wide input range using only a small number of chemical reactions.
活细胞不断处理来自其生存环境的信息。最近有研究表明，许多细胞信号传导机制（如G蛋白偶联受体和表皮生长因子）可以解释为对配体浓度的对数进行计算。这表明对数是细胞中的一种基本计算原语。合成生物学界对实现模拟计算的兴趣也与日俱增，计算对数就是其中一个例子。本文的目的是研究如何利用化学反应网络（CRN）来实现对数计算。CRN无法精确计算对数。一种标准方法是使用幂级数或有理函数逼近法来近似计算对数。虽然CRN可以直接实现这些多项式或有理函数计算，但问题在于，为了能够在较大的输入范围内精确计算对数，有必要使用高阶逼近法，这会导致CRN包含大量反应。本文提出了一种新颖的方法，能够在CRN中精确计算对数，同时保持CRN中的反应数量较少。所提出的方法可以通过调整两个设计参数来创建能够以不同精度水平计算对数的CRN。在本文中，我们展示了实现用于计算对数的CRN所需的化学反应。本文的关键贡献在于提出了一种新颖的方法，能够仅使用少量化学反应创建在宽输入范围内精确计算对数的CRN。
