Study On Protein Sequences Based On Fractal Theories

Information analysis of protein sequences is not only important contents to proteomics, but also a part of work in human genomic project. This paper aims to study the information of protein sequences on the sequence level and is mainly based on fractal theories to analyze the sequences’ fractal properties.Firstly, the programs of four encoding method, including quadrature encoding, five-digital encoding, profile encoding and Phy-Che-normalized encoding, of protein sequences are designed by Dev C++, and the programs by Matlab to calculating the box dimensions of coding curves are realized. The dimensional results show that quadrature encoding method is better than the other three methods to describe the special complexity of protein sequences.Then, the coding curves of28protein sequences,which belongs to the four structural types of protein’s secondary structure, are stimulated in fractal interpolation way by Matlab to be fractal interpolation curves, their local dimensions and global dimensions are computed and the conclusion are: the fractal dimensions of protein’s secondary structure are between1to2, the global dimensions of the four structural types from large to small are α>α/βα+β>β, which are similarity to the comparison of local dimensions1.5022>1.3501>1.3287>1.1659, what mentioned above matches the structural properties of what we discuss, and it proves the methods in this paper are feasible and easier than the ways that previous scholars studying by in the same problems.At last, multi-fractal analysis of protein sequences are tried and the conclusion is that protein sequences are very multi-fractal. By the pictures oflnε～lnχ (ε),ln～lnDq and α～f(α), a horizontal comparison is made with structural type a’s three protein sequences, whose dimensions are closed, and their Multi-fractal features are visually different; a vertical comparison as well as is conducted with four protein sequences respectively belonging to the four structural types to get the difference of their space structural complexity, and the results are similar to chapter four.This paper supports simple workable idea and methods also vast programs to study protein sequences in theory.