The coalescent and infinite-site model of a small multigene family

The infinite-site model of a small multigene family with two duplicated genes is studied. The expectations of the amounts of nucleotide variation within and between two genes and linkage disequilibrium are obtained, and a coalescent-based method for simulating patterns of polymorphism in a small multigene family is developed. The pattern of DNA variation is much more complicated than that in a single-copy gene, which can be simulated by the standard coalescent. Using the coalescent simulation of duplicated genes, the applicability of statistical tests of neutrality to multigene families is considered.     

Properties of a neutral allele model with intragenic recombination

An infinite-site neutral allele model with crossing-over possible at any of an infinite number of sites is studied. A formula for the variance of the number of segregating sites in a sample of gametes is obtained. An approximate expression for the expected homozygosity is also derived. Simulation results are presented to indicate the accuracy of the approximations. The results concerning the number of segregating sites and the expected homozygosity indicate that a two-locus model and the infinite-site model behave similarly for 4Nu less than or equal to 2 and r less than or equal to 5u, where N is the population size, u is the neutral mutation rate, and r is the recombination rate. Simulations of a two-locus model and a four-locus model were also carried out to determine the effect of intragenic recombination on the homozygosity test of Watterson (Genetics 85, 789-814; 88, 405-417) and on the number of unique alleles in a sample. The results indicate that for 4Nu less than or equal to 2 and r less than or equal to 10u, the effect of recombination is quite small.     

The distribution of nucleotide site differences between two finite sequences

A simple method to obtain the distribution of site differences between two randomly chosen cistrons in a finite population is shown. It is assumed that the number of sites and the number of alleles at each site are finite and that no recombination occurs between sites. The mean and variance of the percent difference and the number of site differences between the two sequences are shown to be simple functions of two variables. The differences between a finite-site model an infinite-site model are discussed. The results are applied to the β-globin polymorphism in man.     

Statistical Properties of the Number of Recombination Events in the History of a Sample of DNA Sequences

Some statistical properties of samples of DNA sequences are studied under an infinite-site neutral model with recombination. The two quantities of interest are R, the number of recombination events in the history of a sample of sequences, and RM, the number of recombination events that can be parsimoniously inferred from a sample of sequences. Formulas are derived for the mean and variance of R. In contrast to R, RM can be determined from the sample. Since no formulas are known for the mean and variance of RM, they are estimated with Monte Carlo simulations. It is found that RM is often much less than R, therefore, the number of recombination events may be greatly under-estimated in a parsimonious reconstruction of the history of a sample. The statistic RM can be used to estimate the product of the recombination rate and the population size or, if the recombination rate is known, to estimate the population size. To illustrate this, DNA sequences from the Adh region of Drosophila melanogaster are used to estimate the effective population size of this species.     

Variance of genetic distance and correlation of heterozygosity between populations under the pressure of stepwise mutation

Using the stepwise mutation model of Ohta and Kimura (1973), formulas are developed for the correlation of heterozygosity and the variance of genetic distance between two finite populations. Studied in detail is the case where the sizes of the two descendant populations are equal to that of the ancestral population and the mutation rate is the same for all loci. Numerical computations are carried out by using the present formulas and those of Li and Nei (1975Genet. Res.25) for the infinite-allele model. The results are as follows: The correlation of heterozygosity decreases with time faster for the stepwise mutation model than for the infinite-allele model. However, the relationships between the correlation of heterozygosity and the normalized genetic identity for the two models are very similar, if the average heterozygosities of the two populations are around 0.20 or less. On the other hand, the variance of genetic distance for the stepwise mutation model may become considerably smaller than that for the infinite-allele model, if the average heterozygosities of the two populations are larger than 0.05. The ratio of the standard deviation to the mean is, however, very large for the stepwise mutation model as well as the infinite-allele model.     

Sau3A in situ digestion of human chromosome 3 pericentrometric heterochromatin. I. Differential digestion of alpha-satellite and satellite 1 DNA sequences.

In situ digestion with the restriction endonuclease (RE) Sau3A (Sau3A REISD) uncovers a polymorphism for the pericentromeric heterochromatin of human chromosome 3, which can be positively stained (3+) or not (3-), and has proven useful to differentiate donor and recipient cells after sex-matched bone marrow transplantation and to analyze the so-called hemopoietic chimerism. The aim of the present investigation was to obtain insight into the molecular basis of such polymorphism to optimize its use for chimerism quantification using methodological approaches other than REISD. To this end, fluorescence in situ hybridization (FISH) assays using probes for the satellite DNA sequences that mainly constitute chromosome 3 pericentromeric heterochromatin (alpha-satellite and satellite 1 DNA) were performed on control and Sau3A-digested chromosomes. The results obtained suggest that chromosome 3 alpha-satellite DNA is digested in all individuals studied, irrespective of the karyotype obtained by Sau3A REISD (3++, 3+-, 3--), and thus it does not seem to be involved in the polymorphism uncovered by Sau3A on this chromosome. Satellite 1 DNA is not digested in any case, and shows a polymorphism for its domain size, which correlates with the polymorphism uncovered by Sau3A in such a way that 3+ chromosomes show a large domain (3L) and 3- chromosomes show a small domain (3S). It seems, therefore, that the cause of the polymorphism uncovered by Sau3A on the pericentromeric region of chromosome 3 is a difference in the size of the satellite 1 DNA domain. Small satellite 1 DNA domains fall under the resolution level of REISD technique and are identified as 3-.     

An evolutionary model for maximum likelihood alignment of DNA sequences

Summary Most algorithms for the alignment of biological sequences are not derived from an evolutionary model. Consequently, these alignment algorithms lack a strong statistical basis. A maximum likelihood method for the alignment of two DNA sequences is presented. This method is based upon a statistical model of DNA sequence evolution for which we have obtained explicit transition probabilities. The evolutionary model can also be used as the basis of procedures that estimate the evolutionary parameters relevant to a pair of unaligned DNA sequences. A parameter-estimation approach which takes into account all possible alignments between two sequences is introduced; the danger of estimating evolutionary parameters from a single alignment is discussed.     

A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

Relationship between Migration and DNA Polymorphism in a Local Population

The expected amount of DNA polymorphism, measured in terms of the number of nucleotide differences between the two DNA sequences randomly sampled from subpopulations, was studied by using the stepping-stone model and the finite island model, under the assumption that the migration rate is not the same among different subpopulations. The results obtained indicate that the expected amount of DNA polymorphism in the subpopulation with lower migration rate is smaller than that of higher migration rate. This suggests that marginal populations tend to have lower level of DNA polymorphism than central populations if the migration rate in the marginal populations is lower than that of the central populations.     

Estimating the total number of alleles using a sample coverage method.

Previously reported methods for estimating the number of different alleles at a single locus in a population have not described a useful general result. Using the number of alleles observed in a sample gives an underestimate for the true number of alleles. The similar problem of estimating the number of species in a population was first investigated in 1943. In this article we use the sample coverage method proposed by Chao and Lee in 1992 to estimate the number of alleles in a population when there are unequal allele frequencies. Simulation studies under the recurrent mutation model show that, for reasonable sample sizes, a significantly better estimate of the true number can be obtained than that using only the observed alleles. Results under the stepwise mutation model and infinite-allele model are presented. Possible applications include improving the characterization of the prior distribution for the allele frequencies, adjusting the estimates of genetic diversity, and estimating the range of microsatellite alleles.     

Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: justification and implications

This paper examines a quasi-equilibrium theory of rare alleles for subdivided populations that follow an island-model version of the Wright-Fisher model of evolution. All mutations are assumed to create new alleles. We present four results: (1) conditions for the theory to apply are formally established using properties of the moments of the binomial distribution; (2) approximations currently in the literature can be replaced with exact results that are in better agreement with our simulations; (3) a modified maximum likelihood estimator of migration rate exhibits the same good performance on island-model data or on data simulated from the multinomial mixed with the Dirichlet distribution, and (4) a connection between the rare-allele method and the Ewens Sampling Formula for the infinite-allele mutation model is made. This introduces a new and simpler proof for the expected number of alleles implied by the Ewens Sampling Formula.     

Theories for analyzing polymorphism data in duplicated genes

A simple model for the evolutionary process of a pair of duplicated genes under concerted evolution is developed. The model considers mutation, recombination and gene conversion between two genes in a finite population. Based on diffusion theory, the expected amount of DNA variation within and between two genes are obtained. To investigate the pattern of DNA polymorphism, a coalescent tool to simulate patterns of polymorphism is developed. The theoretical results are well in agreement with polymorphism data in duplicated genes. The effect of selection on the pattern of polymorphism is also considered.     

Estimation of the Amount of DNA Polymorphism When the Neutral Mutation Rate Varies among Sites

Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (π), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, θ is often used as a measure of the amount of DNA polymorphism, where θ = 4Nμ, N is the effective population size and μ is the neutral mutation rate per site per generation. It is known that θ estimated from π, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating θ under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.     

The stepwise mutation model: an experimental evaluation utilizing hemoglobin variants

The stepwise mutation model of Ohta and Kimura (1973) was proposed to explain patterns of genetic variability revealed by means of electrophoresis. The assumption that electrophoretic mobility was principally determined by unit changes in net molecular charge has been criticized by Johnson (1974, 1977). This assumption has been tested directly using hemoglobin. Twenty-seven human hemoglobin variants with known amino acid substitutions, and 26 nonhuman hemoglobins with known sequences were studied by starch gel electrophoresis. Of these hemoglobins, 60 to 70% had electrophoretic mobilities that could be predicted solely on the basis of net charge calculated from the amino acid composition alone, ignoring tertiary structure. Only four hemoglobins showed a mobility that was clearly different from an expected mobility calculated using only the net charge of the molecule. For the remaining 30% of hemoglobins studied, mobility was determined by a combination of net charge and other unidentified components, probably reflecting changes in ionization of some amino acid residues as a result of small alterations in tertiary structure due to the amino acid substitution in the variant. For the nonhuman hemoglobins, the deviation of a sample from its expected mobility increased with increasing amino acid divergence from human hemoglobin A.-It is concluded that the net electrostatic charge of a molecule is the principal determinant of electrophoretic mobility under the conditions studied. However, because of the significant deviation from strict stepwise mobility detected for 30 to 40% of the variants studied, it is further concluded that the infinite-allele model of Kimura and Crow (1964) or a "mixed model" such as that proposed by Li (1976) may be more appropriate than the stepwise mutation model for the analysis of much of the available electrophoretic data from natural populations.     

Re-usable DNA template for the polymerase chain reaction.

DNA covalently bound to an uncharged nylon membrane was used for consecutive amplifications of several different genes by PCR. Successful PCR amplifications were obtained for membrane-bound genomic and plasmid DNA. Membrane-bound genomic DNA templates were re-used at least 15 times for PCR with specific amplification of the desired gene each time. PCR amplifications of specific sequences of p53, p16, CYP1A1, CYP2D6, GSTM1 and GSTM3 were performed independently on the same strips of uncharged nylon membrane containing genomic DNA. PCR products were subjected to restriction fragment length polymorphism analysis, single-strand conformational polymorphism analysis and/or dideoxy sequencing to confirm PCR-amplified gene sequences. We found that PCR fragments obtained by amplification from bound genomic DNA as template were identical in sequence to those of PCR products obtained from free genomic DNA in solution. PCR was performed using as little as 5 ng genomic or 4 fg plasmid DNA bound to membrane. These results suggest that DNA covalently bound to membrane can be re-used for sample-specific PCR amplifications, providing a potentially unlimited source of DNA for PCR.     

Nucleic acid from saliva and salivary cells for noninvasive genotyping of Crohn's disease patients

CARD15 genes carrying the 3020insC frameshift polymorphism encode a truncated CARD15 protein that is unresponsive to bacterial muramyl dipeptide, and are strongly associated with increased susceptibility to Crohn's disease (CD). In this study we established that CARD15 gene sequences encompassing the major 3020insC polymorphism could be readily amplified from the DNA found in saliva. In addition, CARD15 RNA sequences can be readily derived from the cellular component of saliva, which is primarily comprised of buccal epithelial cells. Our results demonstrate that saliva is a readily accessible source of DNA and RNA for genotyping CD patients for variants of the CARD15 gene, representing an alternative source of nucleic acid to that obtained from venous blood.     

A semi-symmetric two-locus model

The two-locus symmetric viability model characterized by its invariance with respect to the exchange of alleles at each locus, is a well-studied model of classical two-locus theory. The symmetric model introduced by Lewontin and Kojima is among the few multi-locus models with epistatic interactions between loci for which a polymorphism with linkage equilibrium can be stable and this happens when recombination is sufficiently large. We show that an analogous property holds true for a different model, in which symmetry need exist at only one locus. The properties of this new semi-symmetric model are compared with those of the classical symmetric model. For tight linkage, two classes of polymorphisms are possible, depending on the magnitude of additive epistasis. The recombination rate above which linkage equilibrium becomes stable is derived analytically. As in the symmetric model, intervals of recombination in which no polymorphism is stable are possible, and stable polymorphisms can coexist with stable fixations.     

Characterization of the Bellevalia sarmatica (Georgi) woronow populations from Volgograd oblast using molecular genetic identification

DNA samples obtained from the populations of the Red Data Book species Bellevalia sarmatica (Georgi) Worovow from Volgograd oblast were examined using RAPD and AFLP analyses. DNA marking revealed considerable differences in the levels of interpopulation and intraspecific polymorphism of the Bellevalia. Furthermore, RAPD analysis, despite of lower levels of interpopulation polymorphism identified, made it possible to obtain clearer data on population subdivision upon statistical treatment of the results. The results of this study can be used in developing conservation strategies for maintenance of the species abundance and genetic diversity, as well as in elaborating the criteria for construction genetic collections.