A 3D graphical representation of protein sequences based on the Gray code

Based on the order of 6-bit binary Gray code, a cyclic order of 20 amino acids is introduced. A novel 3D graphical representation of protein sequences is proposed according to the CGR of DNA sequences. Furthermore, the mathematical descriptor is suggested to characterize the graphical representation curve. The efficiency of our approach can be illustrated by performing the comparison of similarities/dissimilarities among sequences of the ND5 proteins of nine different species. With the correlation and significance analysis, the comparisons of both our results and results of other graphical representation with the ClustalW's results can show the utility of our approach.

► The cyclic orders of the 20 amino acids are suggested based on the reflected binary code.
► A kind of 3D-graphical representation of a protein were proposed.
► Some numerical indices are introduced to characterize the 3D-graphical representations of protein.
► The similarities of the ND5 protein of nine species were compared to illustrate the utility of our methods.
► Using the correlation and significance analysis, our method and some other methods are compared.