Quaternion Modeling And Analysis Of Protein Three-dimensional Structure

Since the 21 st century, the problem of protein structure modeling has become a hot research areas, the subject develop the protein structure analysis theory, and explain the association between function and structure of the protein. The subject has important practical significance and research prospects for protein three-dimensional structure prediction. In traditional methods, matrix often used as a mathematical means for structural analysis and similarity comparison of proteins, for example, the distance matrix, rotation matrix, etc. Because of the matrix contains more number of elements, calculation process become more complicated. Aiming at solving the problems of high computational complexity and unclear geometric significance,which is prevalent in traditional protein structure modeling methods. This paper adopts quaternions as a mathematical means and proposed 2 new methods in two aspects : α helix detection of protein structure,.and protein space structure comparison.According to the geometric characteristics of α helix, we use quaternion instead of rotation matrix to describe the relative rotation between the proteins’ adjacent Cα coordinates. The paper has proposed a new method for α helix detection based on quaternion. Based on PDBselect database to verify the proposed method, the detection accuracy for α helix reached 91.7%. The detection method has obvious advantages of high accuracy, low computational complexity and clear geometric meaning.The traditional methods of protein spatial structure comparison usually use the distance matrix to optimize the protein backbone registration, so that larger protein molecules need longer time and more computational complexity in the operation. In the paper, the spatial coordinates of the protein converted to symmetric positive definite matrices, which contains a large amount of geometry information of the protein’s skeleton structure, and based on quaternions to obtain the distance between symmetric positive definite matrices of two proteins, namely quaternion riemannian metric. Quaternion riemannian metric is taken as a measure of protein structure similarity index. The method uses quaternion instead of distance matrix, because quaternion contains only four parameters, save all the geometry information while significantly reduce the computational complexity. This paper designs 4 experiments from 4 different perspectives : different algorithms, different levels of protein structure data, the commonly used experimental data set and the typical data set. The experiments validate effectiveness and feasibility of the proposed method on a large amount of PDB data. The average matching accuracy of 700 protein double-structural instances in HOMSTRAD database reached 89%. The results show that the proposed method not only effectively reduces the computational complexity, but also has good statistical properties and matching accuracy.Quaternion as a mathematical tool in detection of α helix detection and protein structure comparison, not only has the advantages of simple operation, fast speed and computational advantages, but also has high detection accuracy and matching accuracy when compared with the traditional methods. The experiments has verified that quaternion modeling method of protein three-dimensional structure has significant advantages.