# 分子对接与分子动力学计算模拟概论Progress in Molecular Docking and Molecular Dynamics Simulation

DOI: 10.12677/CC.2019.31001, PDF, HTML, XML, 下载: 1,152  浏览: 4,406

Abstract: With the rapid development of modern life science, computational biology has gradually become one of the core disciplines and methods of modern life science research. Computational biology predicts the three-dimensional structure and dynamic characteristics of proteins from protein sequence to study the relationship between the structure and function of biological macromolecules, the interaction between biological macromolecules and ligands, and promotes the development of protein engineering, protein design and computer-aided drug design.

1. 引言

2. 分子对接

2.1. 分子对接的一般原理

2.2. 分子对接的分类

Figure 1. Schematic diagram of ligand-receptor interaction

2.3. 分子对接的前期处理

Figure 2. Schematic diagram of processing small molecules

Figure 3. Schematic diagram of protein processing

2.4. 分子对接示意图

“蛋白–配体”间对接软件繁杂，主要软件包括Autodock，Vina，Dock等等。

“蛋白–蛋白”与“蛋白-核酸”分子间的对接，最常用的为Rosetta，Z-DOCK等(图5)。

2.5. 分子对接的应用

Figure 4. Analysis of docking results of protein-ligand molecules

Figure 5. Molecular docking analysis of protein-nucleic acid

3. 分子动力学模拟计算

3.1. 分子动力学模拟概述

3.2. 分子动力学模拟的基本原理

1) Verlet算法

Verlet提出的Verlet算法在分子动力学中运用最为广泛，也是最简单的。它运用原子在 $t$ 时刻的位置 $r\left(t\right)$ 和加速度 $a\left(t\right)$$t-\delta t$ 时刻的位置，计算出 $t+\delta t$ 时刻的位置。将粒子的位置以Taylor公式展开，即

$r\left(t+\delta t\right)=r\left(t\right)+\frac{\text{d}}{\text{d}t}r\left(t\right)\delta t+\frac{1}{2!}\frac{{\text{d}}^{2}}{\text{d}{t}^{2}}r\left(t\right){\left(\delta t\right)}^{2}+\cdots$

$r\left(t-\delta t\right)=r\left(t\right)-\frac{\text{d}}{\text{d}t}r\left(t\right)\delta t+\frac{1}{2!}\frac{{\text{d}}^{2}}{\text{d}{t}^{2}}r\left(t\right){\left(\delta t\right)}^{2}+\cdots$

$v\left(t\right)=\frac{\text{d}r}{\text{d}t}=\frac{1}{2\delta t}\left[r\left(t+\delta t\right)-r\left(t-\delta t\right)\right]$

$r\left(t+\delta t\right)=-r\left(t-\delta t\right)+2r\left(t\right)+\frac{{\text{d}}^{2}}{\text{d}{t}^{2}}r\left(t\right){\left(\delta t\right)}^{2}$

$\frac{{\text{d}}^{2}}{\text{d}{t}^{2}}r\left(t\right)=a\left(t\right)$ ，故依据上式可由 $t$$t-\delta t$ 的位置预测 $t+\delta t$ 时的位置。

Verlet算法执行简明，需要的内存小，但其缺点在于速度式中含有 $\frac{1}{\delta t}$ 项，而实际计算中通常选取很

2) 跳蛙法(leap-frog method)

$\left\{\begin{array}{l}{\stackrel{\to }{v}}_{i}\left(t+\frac{1}{2}\delta t\right)={\stackrel{\to }{v}}_{i}\left(t-\frac{1}{2}\delta t\right)+{\stackrel{\to }{a}}_{i}\left(t\right)\delta t\\ {\stackrel{\to }{r}}_{i}\left(t+\delta t\right)={\stackrel{\to }{r}}_{i}\left(t\right)+{\stackrel{\to }{v}}_{i}\left(t+\frac{1}{2}\delta t\right)\end{array}$

${\stackrel{\to }{v}}_{i}\left(t\right)=\frac{1}{2}\left[{\stackrel{\to }{v}}_{i}\left(t+\frac{1}{2}\delta t\right)+{\stackrel{\to }{v}}_{i}\left(t-\frac{1}{2}\delta t\right)\right]$

3) Beeman法

Beeman法是除Verlet跳蛙法外，另一种较为常见的方法。其积分公式如下

$\left\{\begin{array}{l}{\stackrel{\to }{r}}_{i}\left(t+\delta t\right)={\stackrel{\to }{r}}_{i}\left(t\right)+{\stackrel{\to }{v}}_{i}\left(t\right)\delta t+\frac{1}{6}\left[4{\stackrel{\to }{a}}_{i}\left(t\right)-{\stackrel{\to }{a}}_{i}\left(t-\delta t\right)\right]\delta {t}^{2}\\ {\stackrel{\to }{v}}_{i}\left(t+\delta t\right)={\stackrel{\to }{v}}_{i}\left(t\right)+\frac{1}{6}\left[2{\stackrel{\to }{a}}_{i}\left(t+\delta t\right)+5{\stackrel{\to }{a}}_{i}\left(t\right)-{\stackrel{\to }{a}}_{i}\left(t-\delta t\right)\right]\delta t\end{array}$

4) 校正预测法(predictor-corrector method)

Gear提出了基于预测–校正积分方法的校正预测法。因为经典运动粒子的轨迹为连续的，故于时间 $t+\delta t$ 时的位置、速度等可由时间 $t$ 的Taylor展开式预测得

$\left\{\begin{array}{l}{\stackrel{\to }{r}}^{p}\left(t+\delta t\right)=\stackrel{\to }{r}\left(t\right)+\stackrel{\to }{v}\left(t\right)\delta t+\frac{1}{2}\stackrel{\to }{a}\left(t\right)\delta {t}^{2}+\frac{1}{6}\stackrel{\to }{b}\left(t\right)\delta {t}^{3}+\cdots \\ {\stackrel{\to }{v}}^{p}\left(t+\delta t\right)=\stackrel{\to }{v}\left(t\right)+\stackrel{\to }{a}\left(t\right)\delta t+\frac{1}{2}\stackrel{\to }{b}\left(t\right)\delta {t}^{2}+\cdots \\ {\stackrel{\to }{a}}^{p}\left(t+\delta t\right)=\stackrel{\to }{a}\left(t\right)+\stackrel{\to }{b}\left(t\right)\delta t+\cdots \\ {\stackrel{\to }{b}}^{p}\left(t+\delta t\right)=\stackrel{\to }{b}\left(t\right)+\cdots \end{array}$

$\Delta \stackrel{\to }{a}\left(t+\delta t\right)={\stackrel{\to }{c}}^{c}\left(t+\delta t\right)-{\stackrel{\to }{a}}^{p}\left(t+\delta t\right)$

$\left\{\begin{array}{l}{\stackrel{\to }{r}}^{c}\left(t+\delta t\right)={\stackrel{\to }{r}}^{p}\left(\left(t+\delta t\right)+{c}_{0}\Delta \stackrel{\to }{a}\left(t+\delta t\right)\\ {\stackrel{\to }{v}}^{c}\left(t+\delta t\right)={\stackrel{\to }{v}}^{p}\left(t+\delta t\right)+{c}_{1}\Delta \stackrel{\to }{a}\left(t+\delta t\right)\\ {\stackrel{\to }{a}}^{c}\left(t+\delta t\right)={\stackrel{\to }{a}}^{p}\left(t+\delta t\right)+{c}_{2}\Delta \stackrel{\to }{a}\left(t+\delta t\right)\\ {\stackrel{\to }{b}}^{c}\left(t+\delta t\right)={\stackrel{\to }{b}}^{p}\left(t+\delta t\right)+{c}_{3}\Delta \stackrel{\to }{a}\left(t+\delta t\right)\end{array}$

3.3. 分子动力学模拟中的重要概念

1) 周期性边界条件：只模拟实际物质中很小一部分，使模拟体系成为无限的具有相同性质的分子体系的，该部分在三维空间中周期性的存在，代表整个体系。

2) 势函数：势函数是描述原子(分子)间相互作用的函数。原子间的相互作用控制着原子间的相互作用行为，从根本上决定材料的所有性质，这种作用具体由势函数来描述，在分子动力学模拟中，势函数的选取对模拟的结果起着决定性的作用。

3) 系综：在一定的宏观条件下，大量性质和结构完全相同的、处于各种运动状态的、各自独立的系统的集合。系综是用统计方法描述热力学系统的统计规律性时引入的一个基本概念。

4) 积分步长：分子动力学计算的基本思想是赋予分子体系初始运动状态之后利用分子的自然运动在相空间中抽取样本进行统计计算，积分步长就是抽样的间隔。选取合适的积分步长的原则是积分步长小于系统中最快运动周期的十分之一。在节省时间的同时也保证计算的精确性。

3.4. 分子动力学模拟的应用

4. 结语

NOTES

*通讯作者。

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