Dynamics of protein evolution.

Protein sequences of the SWISS-PROT data bank were analysed by fractal techniques and harmonic analysis. In both cases, the results show the presence of self-affinity, a kind of self-similarity, in the sequences. Self-Similarity is a sign of fractality and fractality is a consequence of a chaotic dynamical process. The evolution of the protein sequences is modelled as a dynamical system. The abundance of the fractal form in biology and creation of fractal forms as a result of "chaos" is already established. It may be noted that the word "chaos" here implies that most predictable processes can also become unpredictable under certain conditions, and that the most unpredictable processes are not as unpredictable as they are expected to be. In evolutionary dynamics, this allows scope for mutations and variations in otherwise predictable situations, potentially leading to increased diversity.

Proteins as special subsets of polypeptides.

A large protein sequence database with over 31,000 sequences and 10 million residues has been analysed. The pair probabilities have been converted to entropies using Boltzmann's law of statistical thermodynamics. A scoring weight corresponding to "mixing entropy" of the amino acid pairs has been developed from which the entropies of the protein sequences have been calculated. The entropy values of natural sequences are lower than their random counterparts of same length and similar amino acid composition. Based on the results it has been proposed that natural sequences are a special set of polypeptides with additional qualification of biological functionality that can be quantified using the entropy concept as worked out in this paper.

Correlation analysis of frequency distributions of residues in proteins.

Autocorrelation and spectrum analyses of amino acid residues along protein chains in a large data base has been performed. Results reveal the presence of general long range correlations. Similar analyses of simulated (random) peptides do not exhibit any such long range correlations. Based on the results of nur analysis, an attempt has been made to model the distribution of residues in protein sequences on a fractional Brownian motion and individual sequences as multi-fractals. For this purpose, the characteristics of an fractional Brownian motion namely, the scaling parameter H. the spectral exponent β and the fractal dimension D, have been described.

Periodicities in protein sequences.

The correlation between various amino acid residues (either same or different), along the polypeptide chain have been studied using a large data base. A table of preference values for pairs having strong correlations has been constructed, which can be used to study any sequence and by calculating the weight of these sequences based on these preference values, a rough distinction between a “natural” and a “random” sequence can be made, One can further comment on the evolutionary status of proteins based on these weights.

Protein sequences as random fractals.

The analysis of primary sequences from a protein sequence data base suggests that the sequences can be considered as examples of constrained random fractals. Fractal dimensions of the positional distributions of the 20 residues along the chain have been calculated. These fractal dimensions can be used as indices of intrinsic preferences of various residues.