Distribution of nucleotide differences between two randomly chosen cistrons in a subdivided population: The finite island model

Using the island model of finite size, the distributions as well as the means and variances of d_w and d_b are obtained, where d_w is the number of nucleotide differences between two cistrons randomly chosen from the same colony and d_b is the corresponding number between two cistrons randomly chosen from different colonies. The rate for the means to approach equilibrium is independent of mutation while that for the variances is somewhat retarded by mutation. At the steady state, the mean of d_w is independent of population subdivision and migration rate, as long as there is migration. It has been shown that the actual genic variation in a colony may be much larger than that revealed by the heterozygosity in the colony.     

Distribution of nucleotide differences between two randomly chosen cistrons in a population of variable size

The distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population is studied here when the population size changes from generation to generation. When genetic variability is measured by heterozygosity (i.e., the probability that two cistrons are different), by the probability that two cistrons differ at two or more nucleotide sites, or by mean number of site differences between cistrons, it is seen that in a population going through a small bottleneck all of these measures decline rapidly but, as soon as population size becomes large, they start to increase owing to new mutations. The amount of reduction in these measures depends not only on the size of bottleneck but also on the rate of population growth. The implications of this study explaining the observed variations in the rates of amino acid substitutions during the evolutionary process are also discussed.     

Genetic variability maintained by mutation and overdominant selection in finite populations

Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (ν) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.     

Effects of the shape of distribution of mutant effect in nearly neutral mutation models

Models of the theory of nearly neutral mutation incorporate a continuous distribution of mutation effects in contrast to the theory of purely neutral mutation which allows no mutations with intermediate effects. Previous studies of one such model, namely the house-of-cards mutation model, assumed normal distribution of mutation effect. Here I study the house-of-cards mutation model in random-mating finite populations using the weak-mutation approximation, paying attention to the effects of the distribution of mutant effects. The average selection coefficient, substitution rate and average heterozygosity in the equilibrium and transient states were studied mainly by computer simulation. The main findings are: (i) Very rapid decrease of the substitution rate and very slow approach to equilibrium as selection becomes stronger are characteristics of assuming normal distribution of mutant effect. If the right tail of the mutation distribution decays more rapidly than that of the normal distribution, the decrease of substitution rate becomes slower and equilibrium is achieved more quickly. (ii) The dispersion index becomes smaller or larger than 1 depending on the time and the intensity of selection, (iii) LetN be the population size. When selection is strong the ratio of 4N times the substitution rate to the average heterozygosity, which is expected to be 1 under neutrality, is larger than 1 in earlier generations but becomes less than 1 in later generations. These findings show the importance of the distribution of mutant effect and time in determination of the behaviour of various statistics frequently used in the study of molecular evolution.     

Properties of the Mg2+-induced low-affinity nucleotide binding site of (Na++ K+)-activated ATPase

(1) The Mg²⁺-induced low-affinity nucleotide binding by (Na⁺ + K⁺)-ATPase has been further investigated. Both heat treatment (50–65°C) and treatment with N-ethylmaleimide reduce the binding capacity irreversibly without altering the K_d value. The rate constant of inactivation is about one-third of that for the high-affinity site and for the (Na⁺ + K⁺)-ATPase activity. (2) Thermodynamic parameters (ΔH° and ΔS°) for the apparent affinity in the ATPase reaction (K_m ATP) and for the true affinity in the binding of AdoPP[NH]P (K_d and K_i) differ greatly in sign and magnitude, indicating that one or more reaction steps following binding significantly contribute to the K_m value, which thus is smaller than the K_d value. (3) Ouabain does not affect the capacity of low-affinity nucleotide binding, but only increases the K_d value to an extent depending on the nucleotide used. GTP and CTP appear to be most sensitive, ATP and ADP intermediately sensitive and AdoPP[NH]P and least sensitive to ouabain. Ouabain reduces the high-affinity nucleotide binding capacity without affecting the K_d value. (4) The nucleotide specificity of low-affinity binding site is the same for binding (competition with AdoPP[NH]P) and for the ATPase activity (competition with ATP): AdoPP[NH]P > ATP > ADP > AMP. (5) The low-affinity nucleotide binding capacity is preserved in the ouabain-stabilized phosphorylated state, and the K_d value is not increased more than by ouabain alone. (6) It is inferred that the low-affinity site is Iocated on the enzyme, more specifically its α-subunit, and not on the surrounding phospholipids. It is situated outside the phosphorylation centre. The possible functional role of the low-affinity binding is discussed.     

Hypermutable Non-Synonymous Sites Are under Stronger Negative Selection

Mutation rate varies greatly between nucleotide sites of the human genome and depends both on the global genomic location and the local sequence context of a site. In particular, CpG context elevates the mutation rate by an order of magnitude. Mutations also vary widely in their effect on the molecular function, phenotype, and fitness. Independence of the probability of occurrence of a new mutation''s effect has been a fundamental premise in genetics. However, highly mutable contexts may be preserved by negative selection at important sites but destroyed by mutation at sites under no selection. Thus, there may be a positive correlation between the rate of mutations at a nucleotide site and the magnitude of their effect on fitness. We studied the impact of CpG context on the rate of human–chimpanzee divergence and on intrahuman nucleotide diversity at non-synonymous coding sites. We compared nucleotides that occupy identical positions within codons of identical amino acids and only differ by being within versus outside CpG context. Nucleotides within CpG context are under a stronger negative selection, as revealed by their lower, proportionally to the mutation rate, rate of evolution and nucleotide diversity. In particular, the probability of fixation of a non-synonymous transition at a CpG site is two times lower than at a CpG site. Thus, sites with different mutation rates are not necessarily selectively equivalent. This suggests that the mutation rate may complement sequence conservation as a characteristic predictive of functional importance of nucleotide sites.     

Global mutations and local mutations have very different effects on evolution, illustrated by mixed strategies of asymmetric binary games

We study the evolutionary effect of rare mutations causing global changes in traits. We consider asymmetric binary games between two players. The first player takes two alternative options with probability x and 1−x; and the second player takes options with probability y and 1−y. Due to natural selection and recurrent mutation, the population evolves to have broad distributions of x and y. We analyze three cases showing qualitatively different dynamics, exemplified by (1) vigilance-intrusion game, (2) asymmetric hawk-dove game and (3) cleaner-client game. We found that the evolutionary outcome is strongly dependent upon the distribution of mutants’ traits, more than the mutation rates. For example in the vigilance-intrusion game, the evolutionary dynamics show a perpetual stable oscillation if mutants are always close to the parent (local-mutation mode), whilst the population converges to a stable equilibrium distribution if mutants can be quite different from the parent (global-mutation mode), even for extremely low mutation rate. When common local mutations and rare global mutations occur simultaneously, the evolutionary outcome is controlled by the latter.     

The Trouble with Sliding Windows and the Selective Pressure in BRCA1

Sliding-window analysis has widely been used to uncover synonymous (silent, d_S) and nonsynonymous (replacement, d_N) rate variation along the protein sequence and to detect regions of a protein under selective constraint (indicated by d_N<d_S) or positive selection (indicated by d_N>d_S). The approach compares two or more protein-coding genes and plots estimates dˆ _S and dˆ _N from each sliding window along the sequence. Here we demonstrate that the approach produces artifactual trends of synonymous and nonsynonymous rate variation, with greater variation in dˆ _S than in dˆ _N. Such trends are generated even if the true d_S and d_N are constant along the whole protein and different codons are evolving independently. Many published tests of negative and positive selection using sliding windows that we have examined appear to be invalid because they fail to correct for multiple testing. Instead, likelihood ratio tests provide a more rigorous framework for detecting signals of natural selection affecting protein evolution. We demonstrate that a previous finding that a particular region of the BRCA1 gene experienced a synonymous rate reduction driven by purifying selection is likely an artifact of the sliding window analysis. We evaluate various sliding-window analyses in molecular evolution, population genetics, and comparative genomics, and argue that the approach is not generally valid if it is not known a priori that a trend exists and if no correction for multiple testing is applied.     

The evolutionary landscape of the Mycobacterium tuberculosis genome

Mycobacterium tuberculosis is one of the most deadly human pathogens. The major mechanism for the adaptations of M. tuberculosis is nucleotide substitution. Previous studies have relied on the nonsynonymous-to-synonymous substitution rate (d_N/d_S) ratio as a measurement of selective constraint based on the assumed selective neutrality of synonymous substitutions. However, this assumption has been shown to be untrue in many cases. In this study, we used the substitution rate in intergenic regions (d_i) of the M. tuberculosis genome as the neutral reference, and conducted a genome-wide profiling for d_i, d_S, and the rate of insertions/deletions (indel rate) as compared with the genome of M. canettii using a 50 kb sliding window. We demonstrate significant variations in all of the three evolutionary measurements across the M. tuberculosis genome, even for regions in close vicinity. Furthermore, we identified a total of 233 genes with their d_S deviating significantly from d_i within the same window. Interestingly, d_S also varies significantly in some of the windows, indicating drastic changes in mutation rate and/or selection pressure within relatively short distances in the M. tuberculosis genome. Importantly, our results indicate that selection on synonymous substitutions is common in the M. tuberculosis genome. Therefore, the d_N/d_S ratio test must be applied carefully for measuring selection pressure on M. tuberculosis genes.     

Codon usage patterns and adaptive evolution of marine unicellular cyanobacteria Synechococcus and Prochlorococcus

Marine unicellular cyanobacteria, represented by Synechococcus and Prochlorococcus, dominate the total phytoplankton biomass and production in oligotrophic ocean. In this study, we employed comparative genomics approaches to extensively investigate synonymous codon usage bias and evolutionary rates in a large number of closely related species of marine unicellular cyanobacteria. Although these two groups of marine cyanobacteria have a close phylogenetic relationship, we find that they are highly divergent not only in codon usage patterns but also in the driving forces behind the diversification. It is revealed that in Prochlorococcus, mutation and genome compositional constraints are the main forces contributing to codon usage bias, whereas in Synechococcus, translational selection. In addition, nucleotide substitution rate analysis indicates that they are not evolving at a constant rate after the divergence and that the average d_N/d_S values of core genes in Synechococcus are significantly higher than those in Prochlorococcus. Our evolutionary genomic analysis provides the first insight into codon usage, evolutionary genetic mechanisms and environmental adaptation of Synechococcus and Prochlorococcus after divergence.     

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.     

ADENINE NUCLEOTIDE-INDUCED CONTRACTION OF THE INNER MITOCHONDRIAL MEMBRANE : II. Effect of Bongkrekic Acid

In bovine heart mitochondria bongkrekic acid at concentrations as low as about 4 nmol/mg protein (a) completely inhibits phosphorylation of exogenous adenosine diphosphate (ADP) and dephosphorylation of exogenous adenosine triphosphate (ATP), (b) completely reverses atractyloside inhibition of inner membrane contraction induced by exogenous adenine nucleotides, and (c) decreases the amount of adenine nucleotide required to elicit maximal exogenous adenine nucleotide-induced inner membrane contraction to a level which appears to correspond closely with the concentration of contractile, exogenous adenine nucleotide binding sites Bongkrekic acid at concentrations greater than 4 nmol/mg protein induces inner membrane contraction which seems to depend on the presence of endogenous ADP and/or ATP. The findings appear to be consistent with the interpretations (a) that the inner mitochondrial membrane contains two types of contractile, adenine nucleotide binding sites, (b) that the two sites differ markedly with regard to adenine nucleotide affinity, (c) that the high affinity site is identical with the adenine nucleotide exchange carrier, (d) that the low affinity site is accessible exclusively to endogenous adenine nucleotides and is largely unoccupied in the absence of bongkrekic acid, and (e) that bongkrekic acid increases the affinity of both sites in proportion to the amount of the antibiotic bound to the inner membrane.     

Probing the mechanisms of two exonuclease domain mutators of DNA polymerase ϵ

We report the properties of two mutations in the exonuclease domain of the Saccharomyces cerevisiae DNA polymerase ϵ. One, pol2-Y473F, increases the mutation rate by about 20-fold, similar to the catalytically dead pol2-D290A/E290A mutant. The other, pol2-N378K, is a stronger mutator. Both retain the ability to excise a nucleotide from double-stranded DNA, but with impaired activity. pol2-Y473F degrades DNA poorly, while pol2-N378K degrades single-stranded DNA at an elevated rate relative to double-stranded DNA. These data suggest that pol2-Y473F reduces the capacity of the enzyme to perform catalysis in the exonuclease active site, while pol2-N378K impairs partitioning to the exonuclease active site. Relative to wild-type Pol ϵ, both variants decrease the dNTP concentration required to elicit a switch between proofreading and polymerization by more than an order of magnitude. While neither mutation appears to alter the sequence specificity of polymerization, the N378K mutation stimulates polymerase activity, increasing the probability of incorporation and extension of a mismatch. Considered together, these data indicate that impairing the primer strand transfer pathway required for proofreading increases the probability of common mutations by Pol ϵ, elucidating the association of homologous mutations in human DNA polymerase ϵ with cancer.     

The preparation of UDP-N-acetylgalactosamine from UDP-N-acetylglucosamine employing UDP-N-acetylglucosamine-4-epimerase

A rapid, simple, and inexpensive method has been developed for preparing UDP-N-acetylgalactosamine in amounts sufficient for several thousand assays of enzymes that employ this nucleotide sugar as substrate. The UDP-N-acetylglucosamine-4-epimerase in extracts of porcine submaxillary glands was used to convert UDP-N-acetylglucosamine to an equilibrium mixture of UDP-N-acetylglucosamine and UDP-N-acetylgalactosamine (molar ratio, 77:23). The two nucleotide sugars were separated from components in the extract by ion-exchange chromatography and then separated from one another by affinity chromatography on a column of Griffonia simplicifolia lectin I bound to agarose. The UDP-N-acetylgalactosamine was obtained in pure form by ion-exchange chromatography in an overall yield of 91% from the equilibrium mixture. The separation of the two nucleotide sugars by affinity chromatography also provides a rapid assay for the UDPGlcNAc-4-epimerase, which is more accurate and less time consuming than earlier published assays.     

Hidden Genetic Variability within Electromorphs in Finite Populations

The amount of hidden genetic variability within electromorphs in finite populations is studied by using the infinite site model and stepwise mutation model simultaneously. A formula is developed for the bivariate probability generating function for the number of codon differences and the number of electromorph state differences between two randomly chosen cistrons. Using this formula, the distribution as well as the mean and variance of the number of codon differences between two identical or nonidentical electromorphs are studied. The distribution of the number of codon differences between two randomly chosen identical electromorphs is similar to the geometric distribution but more leptokurtic. Studies are also made on the number of codon differences between two electromorphs chosen at random one from each of two populations which have been separated for an arbitrary number of generations. It is shown that the amount of hidden genetic variability is very large if the product of effective population size and mutation rate is large.     

How often are polymorphic restriction sites due to a single mutation?

An approximate expression is obtained for the probability that a restriction site, which is polymorphic in a random sample, is a site at which two or more mutations have occurred in the descent to the sample from the most recent common ancestor of the sample. The analysis is based on the assumption that the population from which the sample is obtained is at equilibrium under a selectively neutral Wright-Fisher model. Monte Carlo simulations show that the approximation is quite accurate. For commonly observed levels of genetic variation in humans and in natural populations of Drosophila, it is found that multiple mutations would occur at 5 to 10 percent of polymorphic restriction sites assuming that six-cutter enzymes are used on samples of size 50 to 100. Simulations are also used to investigate the bias and mean square error of four estimators of 4Nu, where N is the population size and u is the neutral mutation rate per nucleotide site. Two of the estimators are biased by approximately 20 percent when levels of variation are similar to those which have been observed in natural populations of Drosophila.     

Is the between-population variance negligible in the total variance of heterozygosity? Case of a finite number of loci subject to the infinite-allele model in finite monoecious populations

The decomposition of the variance of the average heterozygosity into variances between and within populations is studied in the general case of a finite number of loci. These loci are assumed randomly distributed over chromosome pairs having a non-interference recombination scheme, and independently subject to mutation according to the infinite-allele model. The equilibrium behavior of that decomposition is discussed in the monoecious mating case with regard to each parameter of the model: mutation rate per gene per generation (u), population size (N), number of loci (n), map length of chomosome pairs (L). It is shown that the proportion Q of the between-population variability in the total variance of the average heterozygosity is decreasing as either the mean heterozygosity (θ = 4Nu/(1 + 4Nu)) or the mean number of mutations per gamete per generation (v = nu) is increasing. Moreover, even if Q is always smaller than for this model, it is not negligible unless θ is close to one or v is much larger than one for L long enough.     

The Spontaneous Mutation Rate in the Fission Yeast Schizosaccharomyces pombe

The rate at which new mutations arise in the genome is a key factor in the evolution and adaptation of species. Here we describe the rate and spectrum of spontaneous mutations for the fission yeast Schizosaccharomyces pombe, a key model organism with many similarities to higher eukaryotes. We undertook an ∼1700-generation mutation accumulation (MA) experiment with a haploid S. pombe, generating 422 single-base substitutions and 119 insertion-deletion mutations (indels) across the 96 replicates. This equates to a base-substitution mutation rate of 2.00 × 10⁻¹⁰ mutations per site per generation, similar to that reported for the distantly related budding yeast Saccharomyces cerevisiae. However, these two yeast species differ dramatically in their spectrum of base substitutions, the types of indels (S. pombe is more prone to insertions), and the pattern of selection required to counteract a strong AT-biased mutation rate. Overall, our results indicate that GC-biased gene conversion does not play a major role in shaping the nucleotide composition of the S. pombe genome and suggest that the mechanisms of DNA maintenance may have diverged significantly between fission and budding yeasts. Unexpectedly, CpG sites appear to be excessively liable to mutation in both species despite the likely absence of DNA methylation.     

Synthesis,biological evaluation and docking study of a new series of di-substituted benzoxazole derivatives as selective COX-2 inhibitors and anti-inflammatory agents

A new series of substituted-N-(3,4-dimethoxyphenyl)-benzoxazole derivatives 13a–13p was synthesized and evaluated in vitro for their COX (I and II) inhibitory activity, in vivo anti-inflammatory and ulcerogenic potential. Compounds 13d, 13h, 13k, 13l and 13n exhibited significant COX-2 inhibitory activity and selectivity towards COX-2 over COX-1. These selected compounds were screened for their in vivo anti-inflammatory activity by carrageenan induced rat paw edema method. Among these compounds, 13d was the most promising analogs of the series with percent inhibition of 84.09 and IC₅₀ value of 0.04?µM and 1.02?µM (COX-2 and COX-1) respectively. Furthermore, ulcerogenic study was performed and tested compounds (13d, 13h, 13k, 13l) demonstrated a significant gastric tolerance than ibuprofen. Molecular docking study was also performed with resolved crystal structure of COX-2 to understand the binding mechanisms of newly synthesized inhibitors in the active site of COX-2 enzyme and the results were found to be concordant with the biological evaluation studies of the compounds. These newly synthesized inhibitors also showed acceptable pharmacokinetic profile in the in silico ADME/T analyses.     

Analysis of steady-state Förster resonance energy transfer data by avoiding pitfalls: Interaction of JAK2 tyrosine kinase with N-methylanthraniloyl nucleotides

Förster resonance energy transfer (FRET) between the fluorescent ATP analogue 2′/3′-(N-methyl-anthraniloyl)-adenosine-5′-triphosphate (MANT–ATP) and enzymes is widely used to determine affinities for ATP–protein binding. However, in analysis of FRET fluorescence data, several important parameters are often ignored, resulting in poor accuracy of the calculated dissociation constant (K_d). In this study, we systematically analyze factors that interfere with K_d determination and describe methods for correction of primary and secondary inner filter effects that extend the use of the FRET method to higher MANT nucleotide concentrations. The interactions of the fluorescent nucleotide analogues MANT–ATP, MANT–ADP [2′/3′-O-(N-methylanthraniloyl) adenosine diphosphate], and MANT–AMP [2′/3′-O-(N-methylanthraniloyl) adenosine monophosphate] with the JAK2 tyrosine kinase domain are characterized. Taking all interfering factors into consideration, we found that JAK2 binds MANT–ATP tightly with a K_d of 15 to 25 nM and excluded the presence of a second binding site. The affinity for MANT–ADP is also tight with a K_d of 50 to 80 nM, whereas MANT–AMP does not bind. Titrations of JAK2 JH1 with nonhydrolyzable ATP analogue MANT–ATP-γ-S [2′/3′-O-(N-methylanthraniloyl) adenosine-5′-(thio)- triphosphate] yielded a K_d of 30 to 50 nM. The methods demonstrated here are applicable to other enzyme–fluorophore combinations and are expected to help improve the analysis of steady-state FRET data in MANT nucleotide binding studies and to obtain more accurate results for the affinities of nucleotide binding proteins.