噪声环境下鲁棒性演化的物理力学研究
A statistical-mechanical study of evolution of robustness in noisy environment
摘要：
在生物系统中，表达动力学，可以提供适合的表型模式，相对于一个特定的功能已经通过突变进化。这已经在蛋白质的进化中观察到，以实现通过其形成靶结构的折叠动力学。我们通过引入相互作用的自旋，其中的配置的自旋和它们的相互作用$\bm{J}$代表的表型和基因型，分别介绍了一个物理力学模型来研究这个进化过程。表型动力学由具有温度$T_{S}$的随机过程在具有$\bm{J}$的哈密顿量下给出。$\bm{J}$的演化也是随温度$T_{J}$随机的，并且遵循引入到$\bm{J}$中的突变和基于针对给定的一组目标自旋的配置定义的适应度的选择。低于某一温度$T_{S}^{c2}$，实现目标图案的相互作用$\bm{J}$演变，而在$T_{S}^{c1}<T_{S}^{c2}$处观察到另一相变。在低温$T_{S}<T_{S}^{c1}$下，哈密顿量表现出类似自旋玻璃的相，其中朝向目标模式的动力学需要长的时间步长，并且适应度通常由于到$\bm{J}$的单个突变而急剧降低。在中温区，形成靶图案的动力学快速进行，并且对$\bm{J}$的突变具有鲁棒性。在这个区域的相互作用没有挫折周围的目标模式，并在漏斗型动力学的结果。我们提出，漏斗型动力学的普遍存在，观察到的蛋白质折叠，是进化的结果受到超过一定水平的热噪声，这也导致突变的健壮性的健身。
英文摘要：
In biological systems, expression dynamics that can provide fitted phenotype patterns with respect to a specific function have evolved through mutations. This has been observed in the evolution of proteins for realizing folding dynamics through which a target structure is shaped. We study this evolutionary process by introducing a statistical-mechanical model of interacting spins, where a configuration of spins and their interactions $\bm{J}$ represent a phenotype and genotype, respectively. The phenotype dynamics are given by a stochastic process with temperature $T_{S}$ under a Hamiltonian with $\bm{J}$. The evolution of $\bm{J}$ is also stochastic with temperature $T_{J}$ and follows mutations introduced into $\bm{J}$ and selection based on a fitness defined for a configuration of a given set of target spins. Below a certain temperature $T_{S}^{c2}$, the interactions $\bm{J}$ that achieve the target pattern evolve, whereas another phase transition is observed at $T_{S}^{c1}<T_{S}^{c2}$. At low temperatures $T_{S}<T_{S}^{c1}$, the Hamiltonian exhibits a spin-glass like phase, where the dynamics toward the target pattern require long time steps, and the fitness often decreases drastically as a result of a single mutation to $\bm{J}$. In the intermediate-temperature region, the dynamics to shape the target pattern proceed rapidly and are robust to mutations of $\bm{J}$. The interactions in this region have no frustration around the target pattern and results in funnel-type dynamics. We propose that the ubiquity of funnel-type dynamics, as observed in protein folding, is a consequence of evolution subjected to thermal noise beyond a certain level; this also leads to mutational robustness of the fitness.
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