基于Level Set方法的分子场特征分析
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摘要
在这篇文章中,我们构造了一种Level Set模型对生物大分子的分子场进行特征提取和分析。对于3维大分子的分子场上的体数据,我们定义了一个新颖的跟踪几何活动轮廓线的变分方程,这个方程包含两部分:外部能量和内部能量。外部能量用来控制活动轮廓线的移动,而内部能量则作为Level Set函数的惩罚项,以避免该模型在迭代过程中周期性地重新初始化。我们不断改变方程中相关的参数,分析在整个演化过程中这些参数对最后结果的影响。与传统的LevelSet方法相比,我们的方法在分子场上进行特征提取更加精确和有效。
采用上述模型,我们对静态和动态的分子场数据进行分析。对于静态分子场,选取能量跃变区域来揭示分子场特征,同时构造体特征函数来分析LevelSet曲面的拓扑特征区域和整体分子场的能量分布特点。对于动态分子场,我们考察同一蛋白质分子在不同运动状态下的数据,例如观察HIV-1蛋白酶间接受水分子作用改变构象、形成中间通道的整个过程。与此同时,对不同的运动状态,计算分子场多属性Level Set曲面,根据属性的相似程度,寻找分子运动过程中Level Set曲面显著变化的关键时刻。通过上述特征分析方法,结合多种面以及体可视化绘制技术,本文成功地揭示了蛋白质分子场的重要特征。
初步实验表明,本文的方法计算出来的特征与已有生物学结论一致,如HIV-1蛋白酶内部的水分子排除通道,DPS蛋白质与铁离子结合的空腔区域,以及HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化等。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,具有非常巨大的研究意义。
In this paper, we exploit a Level Set method to extract and analyze the feature of macromolecular field. For the 3D volume data of the field, we propose a novel variational formulation for geometric active contour, which is composed of an external energy to drive the active contours' motion, and an internal energy which penalizes the Level Set function adaptively to avoid periodically re-initializing. We adjust the parameters of each component and investigate their influence in the whole process. According to the comparison with the traditional frameworks, our approach is shown to be more accurate and efficient on the feature extraction.
Based on the Level Set method constructed in the first part, we give a further analysis for the static and dynamic molecular field data. For the static molecular field, we choose the region where the energy has the quantum leap and analyze the molecular field. Then, we construct the volume feature function to extract the topological region and get the energy distribution of the whole molecular field. For the dynamic molecular field, we consider the same protein in the different states, like observing the process in changing the conformation and forming the middle tunnel. At the mean time, we calculate the multi-attributes of these states and try to find the crucial time during the movement of the molecular. According to the surface and volume rendering techniques, we reveal the significant feature of the macromolecular field.
Preliminary results show that, we successfully find 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 and deposition and biological activity of HIV-1 protease when processing SMD simulation in the aqueous solution. Both of these results are in accordance with the experimental results given by chemists and biologists. Biologists believe that these results may be useful to study the hydrophilic and hydrophobic of HIV-1 protease in the future, and these active cites can be considered as the most important regions in the protein-protein interaction and protein-ligand interaction.
采用上述模型,我们对静态和动态的分子场数据进行分析。对于静态分子场,选取能量跃变区域来揭示分子场特征,同时构造体特征函数来分析LevelSet曲面的拓扑特征区域和整体分子场的能量分布特点。对于动态分子场,我们考察同一蛋白质分子在不同运动状态下的数据,例如观察HIV-1蛋白酶间接受水分子作用改变构象、形成中间通道的整个过程。与此同时,对不同的运动状态,计算分子场多属性Level Set曲面,根据属性的相似程度,寻找分子运动过程中Level Set曲面显著变化的关键时刻。通过上述特征分析方法,结合多种面以及体可视化绘制技术,本文成功地揭示了蛋白质分子场的重要特征。
初步实验表明,本文的方法计算出来的特征与已有生物学结论一致,如HIV-1蛋白酶内部的水分子排除通道,DPS蛋白质与铁离子结合的空腔区域,以及HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化等。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,具有非常巨大的研究意义。
In this paper, we exploit a Level Set method to extract and analyze the feature of macromolecular field. For the 3D volume data of the field, we propose a novel variational formulation for geometric active contour, which is composed of an external energy to drive the active contours' motion, and an internal energy which penalizes the Level Set function adaptively to avoid periodically re-initializing. We adjust the parameters of each component and investigate their influence in the whole process. According to the comparison with the traditional frameworks, our approach is shown to be more accurate and efficient on the feature extraction.
Based on the Level Set method constructed in the first part, we give a further analysis for the static and dynamic molecular field data. For the static molecular field, we choose the region where the energy has the quantum leap and analyze the molecular field. Then, we construct the volume feature function to extract the topological region and get the energy distribution of the whole molecular field. For the dynamic molecular field, we consider the same protein in the different states, like observing the process in changing the conformation and forming the middle tunnel. At the mean time, we calculate the multi-attributes of these states and try to find the crucial time during the movement of the molecular. According to the surface and volume rendering techniques, we reveal the significant feature of the macromolecular field.
Preliminary results show that, we successfully find 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 and deposition and biological activity of HIV-1 protease when processing SMD simulation in the aqueous solution. Both of these results are in accordance with the experimental results given by chemists and biologists. Biologists believe that these results may be useful to study the hydrophilic and hydrophobic of HIV-1 protease in the future, and these active cites can be considered as the most important regions in the protein-protein interaction and protein-ligand interaction.
引文
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[16]S.Takahashi,G.M.Nielson,Y.Takeshima,and I.Fujishiro.Topological volume skeletonization using adaptive tetrahedralization.In Proceedings of Geometric Modeling and Processing,pages 227-236,2004.
[17]S.Takahashi,Y.Takeshima,and I.Fujishiro.Topological volume skeletonization and its application to transfer function design.Graphical Models,66(1):24-49,2004.
[18]Z.Wood,H.Hoppe,M.Desbrun,and P.Schroder.Removing excess topology from isosur-faces.A CM Transactions on Graphics,23(2):190-208,2004.
[19]H.Carr,J.Snoeyink,and U.Axen.Computing contour trees in all dimensions.In Symposium on Discrete Algorithms,pages 918-926,2000.
[20]S.Smale.On gradient dynamical systems.Ann.of Math.,74:199-206,1961.
[21]S.Smale.Generalized poincare's conjecture in dimensions greater than four.The Annals of Mathematics,Second Series,74(2):391-406,1961.
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[23]P.T.Bremer,H.Edelsbrunner,B.Hamann,and V.Pascucci.A topological hierarchy for functions on triangulated surfaces.IEEE Transactions on Visualization and Computer Graphics,10(4):385-396,2004.
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[27]A.Gyulassy,V.Natarajan,V.Pascucci,and B.Hamann.Efficient computation of morsesmale complexes for three-dimensional scalar functions.IEEE Transactions on Visualization and Computer Graphics,13(6):1440-1447,2007.
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[29]V.Natarajan and H.Edelsbrunner.Simplification of three-dimensional density maps.IEEE Transactions on Visualization and Computer Graphics,10(5):587-597,2004.
[30]M.Garland and Y.Zhou.Quadric-based simplification in any dimension.ACM Transactions on Graphics,24(2):209-239,2005.
[31]S.J.Osher and R.Fedkiw.Level set methods and dynamic implicit surfaces.Applied Mathematical Science.Springer,page 153,2002.
[32]J.A.Sethian.Fast Marching Methods and Level Set Methods:Evolving Interfaces in Computational Geometry,Fluid Mechanics.Cambridge University Press:Cambridge,UK,1999.
[33]T.Cootes,A.Hill,C.J.Taylor,and J.Haslam.The use of active shape models for locating structures in medical images.Information Processing in Medical Imaging(IPMI'93) number 687 in Lecture Notes in Computer Science,pages 33-47,1993.
[34]C.Bajaj,Z.Y.Yu,and M.Auer.Volumetric filtering,feature extraction,and visualization of volumetric tomographic molecular imaging.Journal of Structural Biology,2003.
[35]X.C.Tai and T.F.Chan.A survey on multiple level set methods with applications for identifying piecewise constant functions.International Journal of Numerical Analysis and Modelling,1(1):25-48,2004.
[36]R.Whitaker,D.Breen,K.Museth,and N.Soni.Segmentation of biological volume datasets using a level-set.Volume Graphics,pages 249-263,2001.
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