Research Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8902, Japan; email:
Quantitative Biology Center (QBiC), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan; email:
Annu Rev Biophys. 2018 May 20;47:273-290. doi: 10.1146/annurev-biophys-070317-033155.
We present a macroscopic theory to characterize the plasticity, robustness, and evolvability of biological responses and their fluctuations. First, linear approximation in intracellular reaction dynamics is used to demonstrate proportional changes in the expression of all cellular components in response to a given environmental stress, with the proportion coefficient determined by the change in growth rate as a consequence of the steady growth of cells. We further demonstrate that this relationship is supported through adaptation experiments of bacteria, perhaps too well as this proportionality is held even across cultures of different types of conditions. On the basis of simulations of cell models, we further show that this global proportionality is a consequence of evolution in which expression changes in response to environmental or genetic perturbations are constrained along a unique one-dimensional curve, which is a result of evolutionary robustness. It then follows that the expression changes induced by environmental changes are proportionally reduced across different components of a cell by evolution, which is akin to the Le Chatelier thermodynamics principle. Finally, with the aid of a fluctuation-response relationship, this proportionality is shown to hold between fluctuations caused by genetic changes and those caused by noise. Overall, these results and support from the theoretical and experimental literature suggest a formulation of cellular systems akin to thermodynamics, in which a macroscopic potential is given by the growth rate (or fitness) represented as a function of environmental and evolutionary changes.
我们提出了一种宏观理论来描述生物响应及其波动的可塑性、鲁棒性和可进化性。首先，我们利用细胞内反应动力学的线性近似，证明了在给定环境压力下，所有细胞成分的表达都会按比例发生变化，比例系数由细胞稳定生长所导致的增长率变化决定。我们进一步通过细菌的适应实验证明了这一关系，这种比例关系似乎太完美了，因为即使在不同类型条件的培养物中，这种比例关系仍然存在。基于细胞模型的模拟，我们进一步表明，这种全局比例性是进化的结果，其中响应环境或遗传扰动的表达变化沿着唯一的一维曲线受到约束，这是进化鲁棒性的结果。因此，进化使细胞不同组成部分受到环境变化诱导的表达变化按比例减少，这类似于勒夏特列热力学原理。最后，借助波动-响应关系，我们证明了遗传变化引起的波动与噪声引起的波动之间存在这种比例关系。总的来说，这些结果以及理论和实验文献的支持表明，细胞系统的表述类似于热力学，其中宏观势由生长率（或适应度）表示，生长率作为环境和进化变化的函数。
