4D Graphical representation research of DNA sequences

Graphical representation of DNA sequences is a key component in studying biological problems. In order to gain new insights in DNA sequences, this paper combined the digitized methods of single-base, base pairs and coding in triplet bases with the times of base appearing, and then a novel 4D graphical representation method of DNA sequences was put forward. It was a one-to-one correspondence of the arbitrary DNA sequence and 4D graphical representation, that avoided causing non-unique 4D graphical representation and overlapping lines. The method could reflect the biological information features of DNA sequence more comprehensively and effectively without any losses. Based on the 4D graphical representation, we used the geometric center of 4D graphical representation as eigenvalue of DNA sequences analyses, which kept the original features of the data, and then established the Euclidean distances and included angles between vectors' terminal point for similarity analyses of the first extron of the beta-globulin gene among 11 species. Finally, we established the graph of systematic hierarchical cluster analysis of 11 species to observe more easily the relationship between species. A positive outcome was reached, and the results were in accord with biological taxonomy, which also supported the rationality and effectiveness of the novel 4D graphical representation.