Based on three kinds of physiochemical properties of amino acids, twenty amino acids are divided into eight groups, and replaced at eight vertices of a cube. Then, we present a new way of generalized Chaos Game Representation (CGR) method to outline a dynamic 3D graphical representation called HPL curve. Furthermore, the mathematical descriptor is suggested to characterize the similarities/dissimilarities of two HPL curves. The usefulness of this approach can be illustrated by performing the comparison of sequences of ND6 proteins of eight species, as well as sequences of sixteen ND5 proteins. By the correlation analysis, ClustalW results were compared with our results and some other graphical representation results to demonstrate the effectiveness of our approach. © 2016 Wiley Periodicals, Inc.

A new graphical description of the primary structure of protein sequences is introduced. First, a three-dimensional space discrete point set of a protein sequence is created based on the three main physicochemical properties of the amino acids. Secondly, a continuous cubic B-spline curve interpolating the amino acid points is constructed to represent the shape of the protein sequence. Then the geometric properties (curvature and torsion) of the continuous curve are extracted for the purpose of analyzing the similarity between protein sequences. Finally, an improved Canberra distance comparison is introduced for the similarity analysis of protein sequences with different lengths. Experimental results show that our method is effective for the similarity comparison of protein sequences.