Lacunarity analysis of protein sequences reveal fractal like behavior of amino acid distributions

Abstract

This paper reports the use of lacunarity analysis of protein sequences as a new method to analyze the distribution of amino acids in a protein sequence. One of the key results is that distribution of hydrophobic amino acids in a protein sequence exhibit fractal like behavior. It is found that lacunarity plots of distribution of hydrophobic amino acids follow similar patterns for a given protein sequence as well as for amino acid sequences that are extracted from the given protein sequence as prefixes with length reduced by half from the original sequence length. Another interesting result is that using the lacunarity values of chaos game representations of amino acid sequences, we can prove the non-random nature of protein sequences. Lacunarity values also help us to classify a set of true and random protein sequences. These two findings affirm lacunarity analysis as a novel and promising bio-sequence analysis method. © 2011 Springer-Verlag.