Exact solutions for kinetic models of macromolecular dynamics
Exact solutions for kinetic models of macromolecular dynamics
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DOI：
10.1021/jp076153r
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发表时间：
2008-05-15
影响因子：
3.3
通讯作者：
Bustamante, Carlos
中科院分区：
文献类型：
--
作者：
Chemla, Yann R.;Moffitt, Jeffrey R.;Bustamante, Carlos
动态的生物过程，如酶催化，分子运动易位，蛋白质和核酸构象动力学本质上是随机过程。然而，当在非同步系综上研究这样的过程时，固有的波动丢失了，并且只能测量过程的平均速率。随着单分子操作和检测方法的最新发展，现在可以跟踪单个分子的进展，不仅测量平均速率，还测量该速率的波动。这些涨落可以提供大量关于控制系统动力学行为的潜在动力学循环的细节。然而，从实验中提取这些信息需要能够计算任意复杂的理论动力学方案的一般性质。我们在这里提出了一个一般的技术，确定精确的平均速度和波动的措施的解析解。我们采用了一种形式主义的基础上的主方程，并显示如何在给定的时间的分子马达的位置的概率密度可以精确地解决在傅里叶-拉普拉斯空间。有了这个解析解，我们可以计算平均速度和波动相关的参数，如随机性参数（扩散常数和速度的无量纲比）和停留时间分布，它们完全表征了系统的波动，这两个参数都是单分子测量中常用的动力学参数。此外，我们表明，这种形式主义允许计算这些参数的更广泛的一类一般动力学模型比以前的方法证明。
Dynamic biological processes such as enzyme catalysis, molecular motor translocation, and protein and nucleic acid conformational dynamics are inherently stochastic processes. However, when such processes are studied on a nonsynchronized ensemble, the inherent fluctuations are lost, and only the average rate of the process can be measured. With the recent development of methods of single-molecule manipulation and detection, it is now possible to follow the progress of an individual molecule, measuring not just the average rate but the fluctuations in this rate as well. These fluctuations can provide a great deal of detail about the underlying kinetic cycle that governs the dynamical behavior of the system. However, extracting this information from experiments requires the ability to calculate the general properties of arbitrarily complex theoretical kinetic schemes. We present here a general technique that determines the exact analytical solution for the mean velocity and for measures of the fluctuations. We adopt a formalism based on the master equation and show how the probability density for the position of a molecular motor at a given time can be solved exactly in Fourier-Laplace space. With this analytic solution, we can then calculate the mean velocity and fluctuation-related parameters, such as the randomness parameter (a dimensionless ratio of the diffusion constant and the velocity) and the dwell time distributions, which fully characterize the fluctuations of the system, both commonly used kinetic parameters in single-molecule measurements. Furthermore, we show that this formalism allows calculation of these parameters for a much wider class of general kinetic models than demonstrated with previous methods.