MSPA-MCS: Topological Shape Description Applied to Protein-Protein Interfaces

摘要本研究致力于开发新的数学技术来捕捉复杂三维物体的几何特征。 一个关键的应用是蛋白质-蛋白质相互作用问题，建模和预测蛋白质相互作用位点的位置的问题。 这个问题是理解生物活动动力学的关键，也是结构生物学当前面临的主要挑战之一。这项研究将产生广泛的影响，因为开发的算法将应用于许多问题，涉及形状匹配和几何物体的描述。几何可能会发挥关键作用，在寻找一个解决方案的蛋白质-蛋白质相互作用的问题，沿着的物理功能，如静电和溶剂化。 目前的形状拟合问题的方法依赖于形状描述函数，该函数在界面上取值，用于匹配曲面片。当与蛋白质一起工作时，这种方法具有缺点，包括由表面位置的不确定性引起的不稳定性以及由局部运动和柔性引起的表面波动。本研究发展了一种新的方法的基础上的功能，有三维域支持的边界曲面的邻域。与这些功能相关联的水平集的拓扑分析将导致新的描述的表面特征，如凹陷和突起，是稳定的波动和不确定性的数据。 这项研究涉及发展一个严格的数学理论的表面描述符的基础上，这样的三维功能。

AbstractThis research focuses on developing new mathematical techniques to capture geometric features of complicated three-dimensional objects. A key application is the protein-protein interaction problem, the problem of modeling and predicting the locations of sites where pairs of proteins interact. This problem is the key to understanding the dynamics of biological activities, and is one of the major current challenges in structural biology. The research will have broad impact since the algorithms developed will have applications to the many problems that involve shape matching and description of geometric objects.Geometry will likely play a key role in finding a solution to the protein-protein interaction problem, along with physical functions like electrostatics and solvation. Current approaches to shape fitting problems rely on shape description functions that take values on an interface surface, which are used to match surface patches. Such approaches have drawbacks when working with proteins, including instability caused by uncertainty of the surface location and fluctuations of the surface caused by local motions and flexibility. This research develops a new approach based on functions that have 3-dimensional domains supported in a neighborhood of the boundary surfaces. Topological analysis of the level sets associated to such functions will lead to new descriptions of surface features such as depressions and protrusions that are stable under fluctuation and uncertainty in the data. The research involves the development of a rigorous mathematical theory of surface descriptors based on such 3-dimensional functions.