IRREGULARITY OF DISTRIBUTION OF AMINO-ACID SUBSTITUTIONS ALONG AMINO-ACID-SEQUENCES OF HOMOLOGOUS PROTEINS

A group of aligned sequences of homologous proteins is divided into two groups comprising m and n closest sequences. Each position is then characterized by a point variability which is equal to a number of noncoincidences through all the possible intergroup mutual comparisons divided by m . n. The values of point variability averaged for ten consecutive positions are plotted versus the segment number to obtain an intergroup profile of local variability. The area S of a figure enclosed between the profile curve and straight line at the level of the mean value of the local variability is compared with an averaged noise area S(c) for 1000 families of artificial homologous proteins which are obtained by permutations of columns of amino acid residues of the initial family. If S exceeds S(c) by more than two standard deviations sigma(c) then the variability profile manifests peaks and valleys which correspond to meaningfully conserved and variable sequences. To identify these segments, it is necessary to cut off an area ''surplus'', deltaS = S -(S(c) + 2 sigma(c)), by two horizontal lines, each of them detaching an area of deltaS/2. The difference (S - S(c)), expressed in units of standard deviation, is suggested as a measure of overall irregularity of substitutions along the homologous protein sequences OI = (S - S(c))/sigma(c). The proposed method was applied to identify authentic variable and conserved segments in six families of homologous proteins: phospholipases A2, cytochromes b, alpha-subunits of Na,K-ATPases, L- and M-subunits of photoreaction center of photobacteria, and rhodopsins. For model families of homologous proteins, obtained by k-fold repetition of natural proteins, the value of overall irregularity was shown to be proportional to square-root k. Comparison of the extent of irregularity of substitutions in amino acid sequences of homologous proteins of various length L can be made by referring the values of overall irregularity of substitution in each family to the length of an average protein domain comprising 250 residues.