Dual quaternion applications to bioinformatics for kinematical analysis of Protein Backbone

Bioinformatics has opened up interesting and challenging area for interdisciplinary research. One of the main component of research in bioinformatics and structural Biology is to model the protein folding phenomenon. Proteins are highly flexible objects, that are capable of organizing themselves into specific three dimensional structures through conformational changes called protein folding. We need a measure to express how much a molecule changes, going from one conformation to another or how two conformations differ from each other. The paper presents a method for optimal alignment of a Protein Backbone with respect to another. Two protein structures 1YRF and 1VII from the Protein Data Bank (PDB entry) of the villin headpiece subdomain are considered for analysis. Kabsch Method for optimal orientation is used which consists of finding the optimal translation and rotation. The technique used minimizes the inter-molecular distance measure (Root Mean Square Deviation) RMSD. Dual quaternion is used to find the translation and the rotation is performed with optimal Quaternion for exact orientation.