Department of Chemistry, Chung-Ang University, Seoul 156-756, Republic of Korea.
Proc Natl Acad Sci U S A. 2009 Dec 1;106(48):20288-93. doi: 10.1073/pnas.0905764106. Epub 2009 Nov 13.
Single-molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench by using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, tau(F), depends asymmetrically on deltaf(S) = f (S) - f (m) and deltaf (Q) = f (m) - f (Q) where f (S) (f (Q)) is the stretch (quench) force and f (m) is the transition midforce of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, R(t), occurs in three stages: A rapid initial decrease in the extension is followed by a plateau and finally, an abrupt reduction in R(t) occurs as the native state is approached. The duration of the plateau increases as lambda = tau (Q)/tau (F) decreases (where tau (Q) is the time in which the force is reduced from f (S) to f (Q)). Variations in the mechanisms of force-quench relaxation as lambda is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in R(t). The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding.
单分子力谱方法可用于从折叠景观的任意区域生成生物聚合物的折叠轨迹。我们通过模拟 RNA 发夹和基于 de Gennes 模型的同聚物折叠理论来展示 RNA 和蛋白质在力猝灭时折叠动力学的复杂性和通用特征。折叠时间 τ（F）不对称地依赖于 δf（S）=f（S）-f（m）和 δf（Q）=f（m）-f（Q），其中 f（S）（f（Q））是拉伸（猝灭）力，f（m）是 RNA 发夹的过渡中间力。与实验一致，分子延伸的弛豫动力学在三个阶段发生：延伸的快速初始下降后是一个平台，最后，当接近天然状态时，R（t）突然减少。平台的持续时间随着 λ=τ（Q）/τ（F）的减小而增加（其中 τ（Q）是力从 f（S）减小到 f（Q）的时间）。当 λ改变时，力猝灭弛豫机制的变化反映在实验可测量的时间相关熵中，该熵直接从折叠轨迹中计算得出。在张力下 de Gennes 模型的解析解再现了 R（t）中的多阶段动力学。预测聚合物的初始崩溃阶段也应该是一个通用特征，这一预测通过在不良溶剂中猝灭完全拉伸状态下的力时，模拟半柔性（柔性）同聚物的环（球）形成动力学得到验证。我们的发现为蛋白质折叠的多个不同实验观察提供了统一的解释。
