A comparative study on structural proteins of viruses that belong to the identical family

Recent studies have focused on the similarity between SARS Cov-2 and various viruses from the Coronaviridae family (such as MERS Cov,  SARS Cov and Bat Cov RaTG13) to uncover the mystery of SARS Cov-2. Specifically, some studies identified that the SARS Cov-2 is closely related to Bat Cov RaTG13 (a SARS-related coronavirus found in bats) rather than the other viruses in that family. These studies are mainly focusing on the biological techniques to show the similarity between the SARS Cov-2 and other viruses. Examining proteins is not easy for common researchers unless for biologists. To rectify this flaw, we have to convert the protein to one of the known formats, which are easy to understand. Consequently, this study uses viral structural proteins to analyse the relationship between SARS Cov-2 and the rest of the coronavirus with the help of mathematical and statistical parameters and explores the various graph representations of MERS Cov,  SARS Cov,  Bat Cov RaTG13 and SARS Cov-2 structural proteins, such as zig-zag curve, Protein Contact Map ( $$ ) and Chaos Game Representation ( $$ ). Though these graph interpretations are visually similar, a slight variation between the graphs reflects their structural and functional differences. Thus, we use an elegant parameter known as the fractal dimension to observe their minor changes. According to the nature of the graph, we employ different types of fractal dimensions, namely mass dimension and box dimension. Furthermore, we perform the similarity tests with normalized cross-correlation and cosine similarity to assess the comparability of the $$ and $$ graphs. The acquired $$ values are near the sequence identity between SARS Cov-2 and MERS Cov,  SARS Cov,  Bat Cov RaTG13.