Mathematical Modeling in Bioinformatics: Application of an Alignment-Free Method Combined with Principal Component Analysis

Abstract

In this paper, an alignment-free bioinformatics technique, termed the 20D-Dynamic Representation of Protein Sequences, is utilized to investigate the similarity/dissimilarity between Baculovirus and Echinococcus multilocularis genome sequences. In this method, amino acid sequences are depicted as 20D-dynamic graphs, comprising sets of “material points” in a 20-dimensional space. The spatial distribution of these material points is indicative of the sequence characteristics and is quantitatively described by sequence descriptors akin to those employed in dynamics, such as coordinates of the center of mass of the 20D-dynamic graph and the tensor of the moment of inertia of the graph (defined as a symmetric matrix). Each descriptor unveils distinct features of similarity and is employed to establish similarity relations among the examined sequences, manifested either as a symmetric distance matrix (“similarity matrix”), a classification map, or a phylogenetic tree. The classification maps are introduced as a new way of visualizing the similarity relations obtained using the 20D-Dynamic Representation of Protein Sequences. Some classification maps are obtained using the Principal Component Analysis (PCA) for the center of mass coordinates and normalized moments of inertia of 20D-dynamic graphs as input data. Although the method operates in a multidimensional space, we also apply some visualization techniques, including the projection of 20D-dynamic graphs onto a 2D plane. Studies on model sequences indicate that the method is of high quality, both graphically and numerically. Despite the high similarity observed among the sequences of E. multilocularis, subtle discrepancies can be discerned on the 2D graphs. Employing this approach has led to the discovery of numerous new similarity relations compared to our prior study conducted at the DNA level, using the 4D-Dynamic Representation of DNA/RNA Sequences, another alignment-free bioinformatics method also introduced by us.