Feature Extraction Of Protein Molecular Surface And Molecular Fields

Proteins are essential elements of life. The detection of the active sites of proteins are crucial to the prediction of protein-protein interactions, the recognition of proteins and drug design. It is the goal of the biologists and the scientists from related fields to develop efficient and robust algorithms to predict the active sites of the proteins automatically. In recent years, many scientists from different research areas, e.g. biology, chemistry, computer science, mathematics and physics, are trying to solve this problem base on the geometrical structure of proteins or from other viewpoints.The active sites of a protein depends not only with its 3D geometrical structure, but also with all kinds of the force fields and the potentials of all of its atoms. Besides that, the protein can only perform its function when it is active. By utilizing geometry, graph theory, topology and information theory, we try to analyze the active sites of a protein and predict its local structural changes from three different points of view. They are the geometrical features of the molecular surface point of view, the features of the static protein fields point of view and the features of the dynamical protein fields point of view. Our works are as follows:We propose a novel method to predict the docking between proteins base on graph theory. We first identify the cavities of the molecular surface which are usually the active sites of a protein base on theαshapes. Then we bind the two proteins together by partial matching the cavities with the local shape of another protein. The partial shape matching problem is converted to that of detecting the maximum clique in graph theory. By solving it, we are able to compute the best rigid transformation for docking.We present an efficient algorithm to detect the critical values of the protein fields. First we design an algorithm to compute the Betti number of a triangular mesh, where the Betti number is a topological invariant of the mesh. Then by analyzing the isosurfaces of the protein field with our algorithm, we can detect the critical isovalues which are correspond to the topological changes of the protein field.We suggest an approach to predict the key time step of the dynamical process of proteins. First we calculate the dynamical protein field of the dynamical process. Then we extract the spherical harmonic descriptors of each protein field. By comparing these descriptors, we can detect which time step is more important in the entire process.We develop a novel approach to analyze the local structural changes of the protein in its dynamical process. We first calculate the dynamical multi-attribute protein fields. Then we divide each protein field into blocks and define the importance of each block to be their entropies. By analyzing the time varying importance curve of each block, we can decide if it belongs to the local structural change areas and when the change happens.We apply our methods to several typical proteins and protein-protein interaction systems. It shows that our results are identical to the experiment results. The biologists regard our methods to be crucial to several important areas, e.g. the protein-protein interaction prediction and the protein recognition.