Application of 2D graphic representation of protein sequence based on Huffman tree method

Abstract

Based on Huffman tree method, we propose a new 2D graphic representation of protein sequence. This representation can completely avoid loss of information in the transfer of data from a protein sequence to its graphic representation. The method consists of two parts. One is about the 0–1 codes of 20 amino acids by Huffman tree with amino acid frequency. The amino acid frequency is defined as the statistical number of an amino acid in the analyzed protein sequences. The other is about the 2D graphic representation of protein sequence based on the 0–1 codes. Then the applications of the method on ten ND5 genes and seven Escherichia coli strains are presented in detail. The results show that the proposed model may provide us with some new sights to understand the evolution patterns determined from protein sequences and complete genomes.

Introduction

The rapid growth of biological sequence such as DNA and protein has created many challenges for bioscientists. Facing the explosive growth of DNA and protein sequences, experimental, mathematical and graphic approaches have been employed to study the structure, function, evolution and attribution [1] of these sequences.

Graphic techniques have emerged as a powerful tool for the analysis and visualization of long biology sequences. The advantage of graphic representations of biology sequences is that they provide a simple way of viewing, sorting, and comparing various gene structures, helping in recognizing major differences among similar DNA and protein sequences. Graphical method for visualizing DNA sequence is early proposed by Hamori in 1983 [2]. Afterwards, Hamori [3] and Jeffrey [4] considered two other graphical representation methods of DNA sequences. The original plot of a DNA sequence as a random walk on a 2D grid using the four cardinal directions to represent the four bases A (adenine), G (guanine), T (thymine) and C (cytosine) was done by Gates [5], Nandy [6] and Leong and Morgenthaler [7]. In recent ten years, some authors such as Bielinska-Waz [8], [9], Randić [10], [11], [12], [13], Jaklic [14], Novic [15] and Qi [16], [17], [18], also presented their graphical representations. These graphical methods visualizing DNA sequences provide useful insights into local and global characteristics along a sequence, which are not easily observed from DNA sequences. In recent two references, Randić et al. [19] and Ghosh and Nandy [20], authors gave more detailed introduction about graphical methods visualizing DNA sequences. Readers can find more detailed accounts of various graphical representation of DNA.

Compared with the graphical representation of DNA, the first graphical representation of proteins was published in 2004 [21]. It assumes a unique correspondence between one selected collections of 20 nucleotide triplets and the 20 amino acids, which they represent. The Virtual Genetic Code converts a protein sequence into a hypothetical DNA sequence, and allows one to use available graphical representations of DNA to generate a graphical representation for proteins [19]. Then some novel graphical approaches were developed for graphical representation of proteins that allow a direct representation of proteins [22], [23]. In addition, to reflect the difference among 20 natural amino acids, some graphic representations of proteins consider more physicochemical properties. For example, Chou et al. [24] proposed a 2D representation method, ‘wenxiang diagram’, to characterize the disposition of hydrophobic and hydrophilic residue. Wen and Zhang [25] proposes a 2D graphic representation based on the pKa values of different amino acids. Wu et al. [26] build up a web-server for creating graphic representation of protein sequences by two different physicochemical properties of their constituent amino acids.

In the present study, we propose a new 2D graphic representation of protein sequence based on the 0–1 codes of 20 amino acids from Huffman tree. The 0–1 codes of 20 amino acids based on Huffman tree can provide an approach with a compression to represent protein sequences by binary unit. Further, the use of 0–1 codes can still reflect the overall frequency characteristic within the considered protein sequences. The proposed method can graphically represent the sequence with no degeneracy and loss of information. The rest of the paper is organized as follows. Section 2 presents the 2D graphic representation of protein sequence based on Huffman tree method. Section 3 mainly discusses the application in genome comparison of seven Escherichia coli strains. Section 4 gives the conclusion of this paper.