Gopi Soundhararajan, Singh Animesh, Suresh Swaathiratna, Paul Suvadip, Ranu Sayan, Naganathan Athi N
Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India.
Phys Chem Chem Phys. 2017 Aug 9;19(31):20891-20903. doi: 10.1039/c7cp03011h.
How many structurally different microscopic routes are accessible to a protein molecule while folding? This has been a challenging question to address experimentally as single-molecule studies are constrained by the limited number of observed folding events while ensemble measurements, by definition, report only an average and not the distribution of the quantity under study. Atomistic simulations, on the other hand, are restricted by sampling and the inability to reproduce thermodynamic observables directly. We overcome these bottlenecks in the current work and provide a quantitative description of folding pathway heterogeneity by developing a comprehensive, scalable and yet experimentally consistent approach combining concepts from statistical mechanics, physical kinetics and graph theory. We quantify the folding pathway heterogeneity of five single-domain proteins under two thermodynamic conditions from an analysis of 100 000 folding events generated from a statistical mechanical model incorporating the detailed energetics from more than a million conformational states. The resulting microstate energetics predicts the results of protein engineering experiments, the thermodynamic stabilities of secondary-structure segments from NMR studies, and the end-to-end distance estimates from single-molecule force spectroscopy measurements. We find that a minimum of ∼3-200 microscopic routes, with a diverse ensemble of transition-path structures, are required to account for the total folding flux across the five proteins and the thermodynamic conditions. The partitioning of flux amongst the numerous pathways is shown to be subtly dependent on the experimental conditions that modulate protein stability, topological complexity and the structural resolution at which the folding events are observed. Our predictive methodology thus reveals the presence of rich ensembles of folding mechanisms that are generally invisible in experiments, reconciles the contradictory observations from experiments and simulations and provides an experimentally consistent avenue to quantify folding heterogeneity.
蛋白质分子在折叠时可通过多少种结构不同的微观路径？这一直是一个具有挑战性的问题，难以通过实验解决，因为单分子研究受到观察到的折叠事件数量有限的限制，而总体测量根据定义仅报告平均值，而非所研究数量的分布。另一方面，原子模拟受到采样的限制，并且无法直接重现热力学可观测量。在当前工作中，我们克服了这些瓶颈，通过开发一种综合、可扩展且与实验一致的方法，结合统计力学、物理动力学和图论的概念，对折叠途径的异质性进行了定量描述。我们从一个包含超过一百万个构象状态详细能量学的统计力学模型生成的100000次折叠事件分析中，量化了两种热力学条件下五个单结构域蛋白质的折叠途径异质性。由此产生的微态能量学预测了蛋白质工程实验的结果、核磁共振研究中二级结构片段的热力学稳定性以及单分子力谱测量中的端到端距离估计。我们发现，至少需要约3 - 200条微观路径以及各种不同的过渡路径结构集合，才能解释这五种蛋白质在不同热力学条件下的总折叠通量。结果表明，众多路径之间的通量分配微妙地取决于调节蛋白质稳定性、拓扑复杂性以及观察折叠事件的结构分辨率的实验条件。因此，我们的预测方法揭示了丰富的折叠机制集合的存在，这些机制在实验中通常是不可见的，调和了实验和模拟中相互矛盾的观察结果，并提供了一条与实验一致的途径来量化折叠异质性。
