标题： 蛋白质进化中的波动性和预测的极限 显示英文标题

标题： Fluctuations and the limit of predictability in protein evolution

摘要： 蛋白质进化涉及在广泛的时空尺度上发生的突变。 类似于统计物理中的无序系统，这种动态异质性表明不同位点和时间发生的突变之间存在强相关性。 为了量化这些相关性，我们研究了在蛋白质进化中各种涨落源的作用，这些涨落通过数据驱动的能量景观作为蛋白质适应度的代理来进行模拟。 通过应用在无序物理系统背景下开发的时空相关函数，我们将起始条件引起的涨落（即进化过程起源的祖先序列）与沿独立进化路径的随机突变驱动的涨落区分开来。 我们的分析显示，在多种蛋白质家族中，较短时间尺度上的涨落主要来源于祖先序列。 这使我们能够确定一个祖先序列信息持续存在的时间尺度，从而实现其重建。 我们将这种持续性与上位相互作用的强度联系起来：具有更强上位特征的祖先序列会在更长时间内影响进化轨迹。 然而，在更长时间尺度上，祖先的影响会减弱，因为上位约束的位点会集体进化。 为了验证这一观点，我们应用了一个标准的祖先序列重建算法，并确认时间依赖的恢复误差受到祖先自身特性的影响。 总体而言，我们的结果揭示了祖先序列的特性——特别是它们的上位约束——会影响初始的进化动力学以及标准祖先序列重建算法的性能。 显示英文摘要

摘要： Protein evolution involves mutations occurring across a wide range of time scales. In analogy with disordered systems in statistical physics, this dynamical heterogeneity suggests strong correlations between mutations happening at distinct sites and times. To quantify these correlations, we examine the role of various fluctuation sources in protein evolution, simulated using a data-driven energy landscape as a proxy for protein fitness. By applying spatio-temporal correlation functions developed in the context of disordered physical systems, we disentangle fluctuations originating from the initial condition, i.e. the ancestral sequence from which the evolutionary process originated, from those driven by stochastic mutations along independent evolutionary paths. Our analysis shows that, in diverse protein families, fluctuations from the ancestral sequence predominate at shorter time scales. This allows us to identify a time scale over which ancestral sequence information persists, enabling its reconstruction. We link this persistence to the strength of epistatic interactions: ancestral sequences with stronger epistatic signatures impact evolutionary trajectories over extended periods. At longer time scales, however, ancestral influence fades as epistatically constrained sites evolve collectively. To confirm this idea, we apply a standard ancestral sequence reconstruction algorithm and verify that the time-dependent recovery error is influenced by the properties of the ancestor itself. Overall, our results reveal that the properties of ancestral sequences - particularly their epistatic constraints - influence the initial evolutionary dynamics and the performance of standard ancestral sequence reconstruction algorithms.