College of Chemistry, Sichuan University, Chengdu 610064, China.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China.
J Chem Phys. 2014 Mar 28;140(12):125102. doi: 10.1063/1.4869206.
A theoretical framework based on a generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and a power-law memory kernel is presented to describe the non-exponential kinetics of the unfolding of a single poly-ubiquitin molecule under a constant force [T.-L. Kuo, S. Garcia-Manyes, J. Li, I. Barel, H. Lu, B. J. Berne, M. Urbakh, J. Klafter, and J. M. Fernández, Proc. Natl. Acad. Sci. U.S.A. 107, 11336 (2010)]. Such a GLE-fGn strategy is made on the basis that the pulling coordinate variable x undergoes subdiffusion, usually resulting from conformational fluctuations, over a one-dimensional force-modified free-energy surface U(x, F). By using the Kramers' rate theory, we have obtained analytical formulae for the time-dependent rate coefficient k(t, F), the survival probability S(t, F) as well as the waiting time distribution function f(t, F) as functions of time t and force F. We find that our results can fit the experimental data of f(t, F) perfectly in the whole time range with a power-law exponent γ = 1/2, the characteristic of typical anomalous subdiffusion. In addition, the fitting of the survival probabilities for different forces facilitates us to reach rather reasonable estimations for intrinsic properties of the system, such as the free-energy barrier and the distance between the native conformation and the transition state conformation along the reaction coordinate, which are in good agreements with molecular dynamics simulations in the literatures. Although static disorder has been implicated in the original work of Kuo et al., our work suggests a sound and plausible alternative interpretation for the non-exponential kinetics in the stretching of poly-ubiquitin molecules, associated with dynamic disorder.
提出了一个基于具有分数高斯噪声（fGn）和幂律记忆核的广义朗之万方程（GLE）的理论框架，用于描述在恒定力下单个多聚泛素分子展开的非指数动力学[T.-L. Kuo，S. Garcia-Manyes，J. Li，I. Barel，H. Lu，B. J. Berne，M. Urbakh，J. Klafter 和 J. M. Fernández，Proc. Natl. Acad. Sci. U.S.A. 107, 11336（2010）]。这种 GLE-fGn 策略是基于以下假设：拉伸坐标变量 x 经历亚扩散，通常是由于构象波动，在一维力修饰的自由能表面 U(x, F)上。通过使用 Kramers 速率理论，我们已经获得了时间相关的速率系数 k(t, F)、生存概率 S(t, F)以及等待时间分布函数 f(t, F)作为时间 t 和力 F 的函数的解析公式。我们发现，我们的结果可以在整个时间范围内与实验数据完美拟合，幂律指数γ=1/2，这是典型异常亚扩散的特征。此外，不同力的生存概率拟合使我们能够对系统的固有特性（如自由能势垒和反应坐标上的天然构象和过渡态构象之间的距离）进行相当合理的估计，这些估计与文献中的分子动力学模拟结果一致。尽管在 Kuo 等人的原始工作中已经暗示了静态无序，但我们的工作为多聚泛素分子拉伸中非指数动力学提供了一种合理的替代解释，与动态无序有关。
