热噪声下演化的漏斗景观和突变鲁棒性
Funnel landscape and mutational robustness as a result of evolution under thermal noise
摘要：
在生物系统中，通过基因突变来形成适合功能的表型的表达动力学已经进化，如在蛋白质中漏斗景观的进化中所观察到的。我们研究了这个进化过程中的相互作用的自旋，其中拟合的表型是由一组给定的配置表示的“目标自旋”和自旋之间的相互作用矩阵J是基因型进化的几代人的螺旋机械模型。动力学的表达是由随机过程给出的，其中温度T_S是为了降低给定J集合的能量。J的演化也是随机的，随着J的突变和基于目标自旋的配置给出的适应度的选择，温度T_J。当温度T_S^{c2}低于一定值时，出现高度适应的J，而在T_S^{c1}<T_S^{c2}时，出现另一个以阻挫为特征的相变。当温度低于T_S^{c1}时，哈密顿量表现出类似自旋玻璃的阶段，此时动力学需要很长的时间步长来产生拟合的表型，并且适应度往往会因单次突变而急剧下降。相比之下，在T_S^{c1}和T_S^{c2}之间的中间温度阶段，进化的基因型在目标自旋周围没有挫折（我们称之为“局部马蒂斯状态”），给出了漏斗状的快速表达动力学，并且对突变具有鲁棒性。这些结果意味着，在超过一定水平的热噪声下的进化导致漏斗动力学和突变鲁棒性。我们将用热力学-力学方法解释其机理。
英文摘要：
In biological systems, expression dynamics to shape a fitted phenotype for function has evolved through mutations to genes, as observed in the evolution of funnel landscape in protein. We study this evolutionary process with a statistical-mechanical model of interacting spins, where the fitted phenotype is represented by a configuration of a given set of "target spins" and interaction matrix J among spins is genotype evolving over generations. The expression dynamics is given by stochastic process with temperature T_S to decrease energy for a given set of J. The evolution of J is also stochastic with temperature T_J, following mutation in J and selection based on a fitness given by configurations of the target spins. Below a certain temperature T_S^{c2}, the highly adapted J evolves, whereasanother phase transition characterised by frustration occurs at T_S^{c1}<T_S^{c2}. At temperature lower than T_S^{c1}, the Hamiltonian exhibits a spin-glass like phase, where the dynamics requires long time steps to produce the fitted phenotype, and the fitness often decreases drastically by single mutation. In contrast, in the intermediate temperature phase between T_S^{c1} and T_S^{c2}, the evolved genotypes, that have no frustration around the target spins (we call "local Mattis state"), give a funnel-like rapid expression dynamics and are robust to mutation. These results imply that evolution under thermal noise beyond a certain level leads to funnel dynamics and mutational robustness. We will explain its mechanism with the statistical-mechanical method.
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