Dual Quaternion Modeling And Comparison Of The Local Protein Secondary Structure

The problem of protein secondary structure comparison and modeling is one of the central problem in bioinformatics. Any thinking and discussion about protein function needs to center on the protein structure. In the traditional method, protein elements’ three-dimensional coordinate information is used to describe and compare protein structure. However, due to the excessive protein element number, it is unbalanced to extract geometry information. This paper adopts dual quaternion proposing two new methods in protein secondary structure modeling and protein space structure comparison.We will use dual quaternion in protein secondary structure modeling. The algorithm takes the current peptide plane as the fitting peptide plane and the next peptide plane as the matching plane. Taking the Rotation and Translation of the protein’s local secondary structure unified in the dual quaternion to construct the least square fitting equation of two planes. Though the series dual quaternion realize the fitting of the secondary structure and on this basis, geometrical feature amount information of protein secondary structure will be extracted. The protein α spiral is detected by setting three eigenvalues threshold. Based on the detection alpha helix of 100 kinds of protein which derives from the SCOP database. The detection accuracy reaches 91.3%, which verifies the application of dual quaternion in the local of protein secondary structure description and modeling is of simplicity and high efficiency.In current methods of structure comparison, many of them use the percent which produced by the number of residues of the same structure cores and their RMSD(Root Mean Square Deviation)to measure the significance of structure similarity. A method of dual quaternion distance for protein structure comparison is proposed in this paper because of the complicated computation. The geometric parameters of the protein backbone and 3-D coordinate data are applied to constitute a symmetric positive definite matrix. Convert Symmetric positive definite matrix into dual quaternion form and use dual quaternion distance to measure the similarity between two proteins localized secondary structure. In order to verify the feasibility and effectiveness of our method, three different groups of experiments with different protein data and algorithms have been proposed. Compared with the traditional methods, our comparison results are more accurate. Especially the result to the 10 groups proteins which are more difficult to identify, the matching precision was almost improved by 1.6%. All results show that our method based on dual quaternion is more easily and accurately to express the structure differences of different proteins.