MATHEMATICAL STUDIES ON THE EVOLUTIONARY CHANGE OF DNA SEQUENCES

With the aim of understanding the mechanism of molecular evolution, mathematical problems on the evolutionary change of DNA sequences are studied. The problems studied and the results obtained are as follows: (1) Estimation of evolutionary distance between nucleotide sequences. Studying the pattern of nucleotide substitution for the case of unequal substitution rates, a new mathematical formula for estimating the average number of nucleotide substitutions per site between two homologous DNA sequences is developed. It is shown that this formula has a wider applicability than currently available formulae. A statistical method for estimating the number of nucleotide changes due to deletion and insertion is also developed. (2) Biases of the estimates of nucleotide substitutions obtained by the restriction enzyme method. The deviation of the estimate of nucleotide substitutions obtained by the restriction enzyme method from the true value is investigated theoretically. It is shown that the amount of the deviation depends on the nucleotides in the recognition sequence of the restriction enzyme used, unequal rates of substitution among different nucleotides, and nucleotide frequences, but the primary factor is the unequal rates of nucleotide substitution. When many different kinds of enzymes are used, however, the amount of average deviation is generally small. (3) Distribution of restriction fragment lengths. To see the effect of undetectable restriction fragments and fragment differences on the estimate of nucleotide differences, the theoretical distribution of fragment lengths is studied. This distribution depends on the type of restriction enzymes used as well as on the relative frequencies of four nucleotides. It is shown that undetectability of small fragments or fragment differences gives a serious underestimate of nucleotide substitutions when the length-difference method of estimation is used, but the extent of underestimation is small when the site-difference method is used. (4) Evolutionary relationships of DNA sequences in finite populations. A mathematical theory on the expected evolutionary relationships among DNA sequences (nucleons) randomly chosen from the same or different populations is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author). UMI ^

STUDIES ON THE PATTERNS OF NUCLEOTIDE AND AMINO ACID SUBSTITUTION (ELECTROPHORESIS, MUTATION RATE, SELECTION, BASE, COMPOSITION)

Theoretical and empirical studies were conducted on the pattern of nucleotide and amino acid substitution in evolution, taking into account the effects of mutation at the nucleotide level and purifying selection at the amino acid level. A theoretical model for predicting the evolutionary change in electrophoretic mobility of a protein was also developed by using information on the pattern of amino acid substitution. The specific problems studied and the main results obtained are as follows: (1) Estimation of the pattern of nucleotide substitution in DNA nuclear genomes. The pattern of point mutations and nucleotide substitutions among the four different nucleotides are inferred from the evolutionary changes of pseudogenes and functional genes, respectively. Both patterns are non-random, the rate of change varying considerably with nucleotide pair, and that in both cases transitions occur somewhat more frequently than transversions. In protein evolution, substitution occurs more often between amino acids with similar physico-chemical properties than between dissimilar amino acids. (2) Estimation of the pattern of nucleotide substitution in RNA genomes. The majority of mutations in retroviruses accumulate at the reverse transcription stage. Selection at the amino acid level is very weak, and almost non-existent between synonymous codons. The pattern of mutation is very different from that in DNA genomes. Nevertheless, the pattern of purifying selection at the amino acid level is similar to that in DNA genomes, although selection intensity is much weaker. (3) Evaluation of the determinants of molecular evolutionary rates in protein-coding genes. Based on rates of nucleotide substitution for mammalian genes, the rate of amino acid substitution of a protein is determined by its amino acid composition. The content of glycine is shown to correlate strongly and negatively with the rate of substitution. Empirical formulae, called indices of mutability, are developed in order to predict the rate of molecular evolution of a protein from data on its amino acid sequence. (4) Studies on the evolutionary patterns of electrophoretic mobility of proteins. A theoretical model was constructed that predicts the electric charge of a protein at any given pH and its isoelectric point from data on its primary and quaternary structures. Using this model, the evolutionary change in electrophoretic mobilities of different proteins and the expected amount of electrophoretically hidden genetic variation were studied. In the absence of selection for the pI value, proteins will on the average evolve toward a mildly basic pI. (Abstract shortened with permission of author.) ^