基于Level Set演化曲面的蛋白质分子场建模与特征分析研究
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摘要
蛋白质是生命活动的物质基础,蛋白质分子的运动与构象在生命活动中扮演着极为重要的角色,其中蛋白质分子的空间结构与功能的关系更是人们关注的焦点[1,2]。目前,许多来自生物、化学、计算机、数学、物理等领域的科学家正致力于研究和分析蛋白质复杂的空间三维结构,借助于信息科学、生物信息学、计算生物学、计算化学等手段,推演和预测蛋白质结构和功能关系。
考虑到现有的分子拓扑建模方法缺乏对分子的运动、分子势能场的有力刻画,难以描述生物分子的活性及动态功能,我们将生物大分子描述为包含多种作用力的原子系统,构建原子尺度上描述分子体系能量的势能场(即分子场),并对分子场进行几何、拓扑等方面的特征抽取与特征分析研究。本文介绍了我们在生物大分子的分子场建模与可视化、以及利用Level Set演化曲面探索分子场几何和拓扑等特征的研究工作,主要包括:
·从蛋白质分子三维空间结构出发,分别采用分子力学和量子力学理论,构建原子尺度上的蛋白质分子场。力图通过对蛋白质空间分子场的特征抽取来揭示蛋白质分子活性位点和功能区域;我们在空间分子场每个采样点上实施离散一阶、二阶局部微分计算,从而筛选出一系列数据场内的临界点;继而,计算数据场内各种型值的分子势能面,交互地探寻具有一定生物活性的“通道”区域;同时,探索运用多种点、面和体可视化技术,来寻找分子内部的宏观结构。
·从蛋白质分子场出发,构建其Level Set演化曲面。我们在已有的Chan-Vese模型基础上设计无需周期初始化的Level Set模型,与传统的Level Set方法相比,此模型在分子场上进行特征提取更加精确和有效;同时在每个迭代过程中,实时计算演化轮廓曲面的一些几何测度,并判断演化曲面是否收敛;进一步地,调整方程中各项参数,分析其对最终结果的影响程度;我们将Level Set曲面演化应用到HIV-1蛋白酶分子场和DPS蛋白质分子场上,探讨其生物学意义。
·对不同蛋白质分子场的Level Set曲面进行拓扑特征抽取及多属性比对,进一步揭示蛋白质分子场与分子生物活性之间的关系。一方面,构造体特征函数、抽取Level Set曲面的拓扑特征;另一方面,计算LevelSet曲面上的几何、生物多种属性,并通过比较这一系列属性的相似度,来判断Level Set曲面演化过程中分子场的变化,进而研究分子场能量分布的特点及变化趋势。
·基于共形几何理论,继续探索分子场Level Set曲面的几何、拓扑性质。首先,计算分子场Level Set曲面的高斯曲率、平均曲率,得到该曲面局部几何特征分布;然后,根据欧拉示性数公式计算分子场Level Set曲面的亏格数,描述该曲面的拓扑信息;再根据常数曲率度量对曲面进行分类,借鉴Gu等人的计算共形几何理论,对亏格为0、1、＞2的三种曲面分别实现共形参数化;最后,计算分子场Level Set曲面所有点的共形因子分布,揭示LevelSet曲面内蕴的几何特性。我们采用蛋白质分子场Level Set曲面的共形因子分析方法对不同分子场进行了比较。
实验表明,我们基于蛋白质分子场的Level Set演化曲面计算出来的特征与已有生物结论相一致,如DPS蛋白质与铁离子结合的空腔区域,HIV-1蛋白酶内部的水分子排除通道,HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化以及Globin同源蛋白进化过程中的异同等。生物学家认为这些结果可能对今后研究HIV-1蛋白酶的亲水、疏水性有重要的价值,并可作为“蛋白质-蛋白质”相互作用或“蛋白质-配体”相互作用中首要参考的活性位点。具有很好的研究意义。
Protein play a crucial role in life's processes. In recent years, there has been a growing interest in exploiting the relationship between molecular structure and biological activity. Many scientists from different research areas, e.g. biologist, chemist, computational scientist, mathematician or physicist, are trying to make some progresses from the view of either experiments or computational analysis. Now one of the main themes is using well-known protein structure to predict unknown protein molecular activity, based on the knowledge of computational science, biological informatics, computational biology, computational chemistry and so on.
Existing molecular models are mostly constructed by atom positions and connections between atoms. They don't contain the information of molecular mechanics or molecular force energy, and may limit the study of molecular structure-activity relationships. In this paper, we consider the protein as a whole system composed of different force interactions, which is called "Molecular Field". Then we use Level Set evolutional surfaces to extract and analyze the feature of molecular field, and show the results by several kinds of rendering techniques. Our main contributions include:
Molecular Field in a quantitative manner is constructed; Then by applying the first order and the second order local differential operators on individual node, a set of critical points which potentially depicts the active region of protein molecule are found; Also this chapter gives some results about computing a sequence of molecular potential energy in the data field and interactively exploring the potential "tunnel" region exhibiting biological sense. In addition, the point-based, surface and volume rendering techniques are exploited to find the macro-structure inside the data field.
Level Set model in Molecular Field is presented, which is based on Chan-Vese model but doesn't need to re-initialize Level Set function in period; By using the geometrical measure, the convergence of Level Set model is detected; And the influences of each parameters in the whole process are discussed; Finally this chapter shows results and discussion about the Level Set models on HIV-1 protease Molecular Field and DPS protein Molecular Fields.
Techniques of topological analysis and multi-attribute comparison of Level Set evolutional surfaces are presented. On one side, we propose a volume feature extraction function to detect the topological features imbedded in the Level Set surfaces; On the other side, we compute the geometrical and biological attributes on Level Set surface, and explore multiple attributes on the Level Set surface to study the progression of the Molecular Field.
Based conformal geometry theory, the further study of geometrical and topological feature on Level Set surface is presented. First, we compute the gaussian curvature and mean curvature of Level Set surface on Molecular Field, to explore the surface local geometrical feature distribution; Also, by using Euler-characteristic formular, the global surface topological feature is described by genus number; Then we classify surfaces by the constant curvature measure, and conformal map the Level Set surfaces on Molecular Field; Finally, we compute the conformal factor distribution on Level Set surface, which indicates the surface intrinsic feature. Then we compare different molecular field using their conformal factors.
Our approach provides an intuitive way to study molecular structure-activity relationships. Initial results on some typical protein molecules reveals their active region inside, such as the escape route of water molecules hidden in the HIV-1 protease, the internal cavity of the DPS protein for the iron atom's entry or deposition, the molecular activity change of HIV-1 protease in water during SMD process, and the Globin homology protein group similarity during evolution can be successfully found, which are in accordance with biological experiments.
考虑到现有的分子拓扑建模方法缺乏对分子的运动、分子势能场的有力刻画,难以描述生物分子的活性及动态功能,我们将生物大分子描述为包含多种作用力的原子系统,构建原子尺度上描述分子体系能量的势能场(即分子场),并对分子场进行几何、拓扑等方面的特征抽取与特征分析研究。本文介绍了我们在生物大分子的分子场建模与可视化、以及利用Level Set演化曲面探索分子场几何和拓扑等特征的研究工作,主要包括:
·从蛋白质分子三维空间结构出发,分别采用分子力学和量子力学理论,构建原子尺度上的蛋白质分子场。力图通过对蛋白质空间分子场的特征抽取来揭示蛋白质分子活性位点和功能区域;我们在空间分子场每个采样点上实施离散一阶、二阶局部微分计算,从而筛选出一系列数据场内的临界点;继而,计算数据场内各种型值的分子势能面,交互地探寻具有一定生物活性的“通道”区域;同时,探索运用多种点、面和体可视化技术,来寻找分子内部的宏观结构。
·从蛋白质分子场出发,构建其Level Set演化曲面。我们在已有的Chan-Vese模型基础上设计无需周期初始化的Level Set模型,与传统的Level Set方法相比,此模型在分子场上进行特征提取更加精确和有效;同时在每个迭代过程中,实时计算演化轮廓曲面的一些几何测度,并判断演化曲面是否收敛;进一步地,调整方程中各项参数,分析其对最终结果的影响程度;我们将Level Set曲面演化应用到HIV-1蛋白酶分子场和DPS蛋白质分子场上,探讨其生物学意义。
·对不同蛋白质分子场的Level Set曲面进行拓扑特征抽取及多属性比对,进一步揭示蛋白质分子场与分子生物活性之间的关系。一方面,构造体特征函数、抽取Level Set曲面的拓扑特征;另一方面,计算LevelSet曲面上的几何、生物多种属性,并通过比较这一系列属性的相似度,来判断Level Set曲面演化过程中分子场的变化,进而研究分子场能量分布的特点及变化趋势。
·基于共形几何理论,继续探索分子场Level Set曲面的几何、拓扑性质。首先,计算分子场Level Set曲面的高斯曲率、平均曲率,得到该曲面局部几何特征分布;然后,根据欧拉示性数公式计算分子场Level Set曲面的亏格数,描述该曲面的拓扑信息;再根据常数曲率度量对曲面进行分类,借鉴Gu等人的计算共形几何理论,对亏格为0、1、＞2的三种曲面分别实现共形参数化;最后,计算分子场Level Set曲面所有点的共形因子分布,揭示LevelSet曲面内蕴的几何特性。我们采用蛋白质分子场Level Set曲面的共形因子分析方法对不同分子场进行了比较。
实验表明,我们基于蛋白质分子场的Level Set演化曲面计算出来的特征与已有生物结论相一致,如DPS蛋白质与铁离子结合的空腔区域,HIV-1蛋白酶内部的水分子排除通道,HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化以及Globin同源蛋白进化过程中的异同等。生物学家认为这些结果可能对今后研究HIV-1蛋白酶的亲水、疏水性有重要的价值,并可作为“蛋白质-蛋白质”相互作用或“蛋白质-配体”相互作用中首要参考的活性位点。具有很好的研究意义。
Protein play a crucial role in life's processes. In recent years, there has been a growing interest in exploiting the relationship between molecular structure and biological activity. Many scientists from different research areas, e.g. biologist, chemist, computational scientist, mathematician or physicist, are trying to make some progresses from the view of either experiments or computational analysis. Now one of the main themes is using well-known protein structure to predict unknown protein molecular activity, based on the knowledge of computational science, biological informatics, computational biology, computational chemistry and so on.
Existing molecular models are mostly constructed by atom positions and connections between atoms. They don't contain the information of molecular mechanics or molecular force energy, and may limit the study of molecular structure-activity relationships. In this paper, we consider the protein as a whole system composed of different force interactions, which is called "Molecular Field". Then we use Level Set evolutional surfaces to extract and analyze the feature of molecular field, and show the results by several kinds of rendering techniques. Our main contributions include:
Molecular Field in a quantitative manner is constructed; Then by applying the first order and the second order local differential operators on individual node, a set of critical points which potentially depicts the active region of protein molecule are found; Also this chapter gives some results about computing a sequence of molecular potential energy in the data field and interactively exploring the potential "tunnel" region exhibiting biological sense. In addition, the point-based, surface and volume rendering techniques are exploited to find the macro-structure inside the data field.
Level Set model in Molecular Field is presented, which is based on Chan-Vese model but doesn't need to re-initialize Level Set function in period; By using the geometrical measure, the convergence of Level Set model is detected; And the influences of each parameters in the whole process are discussed; Finally this chapter shows results and discussion about the Level Set models on HIV-1 protease Molecular Field and DPS protein Molecular Fields.
Techniques of topological analysis and multi-attribute comparison of Level Set evolutional surfaces are presented. On one side, we propose a volume feature extraction function to detect the topological features imbedded in the Level Set surfaces; On the other side, we compute the geometrical and biological attributes on Level Set surface, and explore multiple attributes on the Level Set surface to study the progression of the Molecular Field.
Based conformal geometry theory, the further study of geometrical and topological feature on Level Set surface is presented. First, we compute the gaussian curvature and mean curvature of Level Set surface on Molecular Field, to explore the surface local geometrical feature distribution; Also, by using Euler-characteristic formular, the global surface topological feature is described by genus number; Then we classify surfaces by the constant curvature measure, and conformal map the Level Set surfaces on Molecular Field; Finally, we compute the conformal factor distribution on Level Set surface, which indicates the surface intrinsic feature. Then we compare different molecular field using their conformal factors.
Our approach provides an intuitive way to study molecular structure-activity relationships. Initial results on some typical protein molecules reveals their active region inside, such as the escape route of water molecules hidden in the HIV-1 protease, the internal cavity of the DPS protein for the iron atom's entry or deposition, the molecular activity change of HIV-1 protease in water during SMD process, and the Globin homology protein group similarity during evolution can be successfully found, which are in accordance with biological experiments.
引文
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