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 ^

Sustained attention in children with two etiologies of early hydrocephalus.

Several studies have shown that children with spina bifida meningomyelocele (SBM) and hydrocephalus have attention problems on parent ratings and difficulties in stimulus orienting associated with a posterior brain attention system. Less is known about response control and inhibition associated with an anterior brain attention system. Using the Gordon Vigilance Task (Gordon, 1983), we studied error rate, reaction time, and performance over time for sustained attention, a key anterior attention function, in 101 children with SBM, 17 with aqueductal stenosis (AS; another condition involving congenital hydrocephalus), and 40 typically developing controls (NC). In SBM, we investigated the relation between cognitive attention and parent ratings of inattention and hyperactivity and explored the impact of medical variables. Children with SBM did not differ from AS or NC groups on measures of sustained attention, but they committed more errors and responded more slowly. Approximately one-third of the SBM group had attention symptoms, although parent attention ratings were not associated with task performance. Hydrocephalus does not account for the attention profile of children with SBM, which also reflects the distinctive brain dysmorphologies associated with this condition.