A graphical representation of protein based on a novel iterated function system

• A function system was introduced to outline a graphical representation of protein.
• Some numerical indices are suggested to describe the 2D-graphical representation.
• The similarities of ND5 and ND6 proteins were compared to illustrate the method.
• Using the correlation analysis, our method and some other methods are compared.

In this article, a novel family of iterated function system (IFS) was introduced to outline a 2D graphical representation of protein sequences, which incorporates with various physicochemical properties of amino acids. Then a mathematical description was suggested to quantificationally compare the similarities and dissimilarities of protein sequences from their 2D curves. Based on this method, similarities/dissimilarities were compared among sequences of the ND5 proteins of nine different species, as well as sequences of eight ND6 proteins. The phylogenetic tree of the nine ND5 proteins was constructed according to Fuzzy cluster analysis. By correlation analysis, the ClustalW results were compared with our similarity/dissimilarity results and other graphical representation results to demonstrate the effectiveness of our approach.