Mathematical Approach to Protein Sequence Comparison Based on Physiochemical Properties

[Image: see text] The difficult aspect of developing new protein sequence comparison techniques is coming up with a method that can quickly and effectively handle huge data sets of various lengths in a timely manner. In this work, we first obtain two numerical representations of protein sequences separately based on one physical property and one chemical property of amino acids. The lengths of all the sequences under comparison are made equal by appending the required number of zeroes. Then, fast Fourier transform is applied to this numerical time series to obtain the corresponding spectrum. Next, the spectrum values are reduced by the standard inter coefficient difference method. Finally, the corresponding normalized values of the reduced spectrum are selected as the descriptors for protein sequence comparison. Using these descriptors, the distance matrices are obtained using Euclidian distance. They are subsequently used to draw the phylogenetic trees using the UPGMA algorithm. Phylogenetic trees are first constructed for 9 ND4, 9 ND5, and 9 ND6 proteins using the polarity value as the chemical property and the molecular weight as the physical property. They are compared, and it is seen that polarity is a better choice than molecular weight in protein sequence comparison. Next, using the polarity property, phylogenetic trees are obtained for 12 baculovirus and 24 transferrin proteins. The results are compared with those obtained earlier on the identical sequences by other methods. Three assessment criteria are considered for comparison of the results—quality based on rationalized perception, quantitative measures based on symmetric distance, and computational speed. In all the cases, the results are found to be more satisfactory.