Evolution at a multiallelic locus under migration and uniform selection

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape. The drift and diffusion coefficients may depend on position, but the selection coefficients do not. It is established that if p is a uniform equilibrium point under pure selection, then p is a migration-selection equilibrium, and that generically the introduction of migration does not change the stability of p. It is also proved that if p is a uniform, globally asymptotically stable, internal equilibrium point under pure selection, then the gene frequencies converge to p when both migration and selection are present. Thus, in this case, after a sufficiently long time, there is no genetic indication of the spatial distribution of the population.     

DNA multiallelic systems reveal gene/longevity associations not detected by diallelic systems. The APOB locus

To identify possible genetic factors affecting human longevity we compared allele pools at two candidate loci for longevity between a sample of 143 centenarians (S) and a control sample of 158 individuals (C). The candidate loci were APOB and TPO, which code for apolipoprotein B and thyroid peroxidase, respectively. Both restriction fragment length (RFL) (XbaI₂₄₈₈ and EcoRI₄₁₅₄) and variable number of tandem repeat (VNTR) (3′APOB-VNTR) polymorphisms were analysed at the APOB locus; the TPO-VNTR polymorphism (intron 10) was analysed at the TPO locus. The main result of the investigation was that there is an association between the APOB locus and longevity that is revealed only when multiallelic polymorphisms are considered. In particular: (i) the frequency of 3′APOB-VNTR alleles with fewer than 35 repeats is significantly lower in cases than in controls; (ii) the linkage disequilibrium between the XbaI-RFLP and the EcoRI-RFLP is significantly different from 0 in cases but not in controls; (iii) the EcoRI-RFLP and XbaI-RFLP allele frequencies do not discriminate between cases and controls. The differences observed between case and control allele pools are specific to the APOB locus, since no significant difference was observed at the TPO locus. Received: 27 November 1995 / Revised: 24 July 1996     

Viability-fecundity selection at a single multiallelic locus in random mating populations: Protectedness of an allele

To simplify comprehension of the effect of combined viability and fecundity selection on the genetic structure, emphasis is put on the definition of those population parameters, such as average fitness of genotypes or alleles, which provide insight into the principles which govern the system's dynamics. With the help of these parameters, it is possible to point out the resemblance of the model presented here to the known models of pure viability selection. Protectedness of alleles is considered in two steps: (1) treatment of the possibility that alleles become extinct in finite time, and (2) provided sudden extinction cannot occur, derivation of conditions for the initial increase of a new allele. The range of relevance of these results is demonstrated by applying them to the most frequently used factorizations of fecundity into the male and female contributions, namely the multiplicative and the additive.     

公平规范与自然资源保护——基于进化博弈的理论模型

传统理论认为社区对公共自然资源的管理必然导致"公共地悲剧".但新近研究证明个人行为往往受到社会规范的影响并遵循公平互惠等"非理性"原则,进而指出社群有可能自发实现对公共资源有效的合作保护.基于这一思路,综合运用进化博弈论与行为经济学理论构建数学模型模拟了社区居民参与对自然资源的家庭承包管护的策略演化动态,并分析公平规范在该过程中能够发挥的潜在作用.结果表明在经济补偿相对管护所需劳动成本较为有限的情况下,"理性"的参与者无法长期维持高水平的保护合作;相比之下,如果公平规范对当地居民有较强的约束力,则可以实现更高的保护合作水平,其最终均衡由群体中对公平有较高要求的参与者比例决定.这一结果从理论上预测了利用公平规范推动社区参与自然资源保护合作并提高生态补偿效率的可行性.     

The biallelica mating type locus ofUstilago maydis: remnants of an additional pheromone gene indicate evolution from a multiallelic ancestor

Thea mating type locus ofUstilago maydis contains the structural genes for a pheromone-based cell recognition system that governs fusion of haploid cells. The locus exists in two alleles, termeda1 anda2. We have completed the analysis of the nucleotide sequences unique toa1 anda2. Within these dissimilar regions we find two short patches of DNA sequence similarity. Interestingly, one of these segments corresponds to the transcribed region of thea1 pheromone precursor. As a result of multiple nucleotide exchanges this sequence does not code for a functional product. The existence of a second pheromone gene in thea2 allele suggests that the present locus had a multiallelic ancestor. In addition, we describe the presence of two additional genes in thea2 allele. We have investigated the role of these genes during mating and pathogenic development and speculate that they might affect mitochondrial inheritance.     

Spermine-nucleic acid interactions: a theoretical study

The interaction of spermine with nucleic acids is simulated theoretically using refined semi-empirical energy formulae and an advanced minimization procedure. Various nucleic acids are considered: model homopolymeric DNA's, a dodecamer (CGCGAATTCGCG) of type B-DNA, as well as a transfer RNA, tRNA^Phe. The dominant role of electrostatic potential in determining the preferential binding sites of spermine is demonstrated in each of these cases and the role of counterions, nucleic acid structure, and base-pair sequence is analyzed.     

Some electrophysiological consequences of electrogenic sodium and potassium transport in cardiac muscle: a theoretical study

A previous paper described a kinetic model for electrogenic sodium-potassium transport in cardiac muscle, combining a thermodynamically-constrained transport model with simple passive permeabilities for sodium and potassium to generate a cardiac action potential (Chapman, Kootsey & Johnson, 1979). The present paper explores the extent to which this simplest of active-passive transport models can account (without further modification) for the electrophysiological behavior of cardiac muscle. The long term (several minutes) changes in the duration of the action potential observed following a change in stimulation rate are predicted by the model through a shift in the steady-state current-voltage relationship caused by small changes in inside ion concentrations. The diastolic hyperpolarization observed following an increase in rate is also predicted, including the linear relationship between the maximum diastolic depolarization and the rate of stimulation. Varying the outside potassium concentration in the model produces changes in the rest potential and current-voltage relationship similar to published data. Deviations from ideal potassium electrode behavior occur at both high and low concentrations because of effects on the pump. The model not only predicts the observed shift of the current-voltage curve in the depolarizing direction with increasing [K⁺]₀, but also the crossing of the curve in normal [K ⁺]₀ without having to assume a variation in g_K. Anoxia was introduced into the model by changing the concentrations of ATP and ADP, thereby enabling the model to account for the rapid diastolic depolarization observed in myocardial ischemia.     

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

Quantitative study of natural antioxidant systems for cellular nitrofurantoin toxicity

The toxicity of nitrofurantoin was studied on human WI-38 fibroblasts: this chemical was lethal when added at concentrations higher than 5·10⁻⁵ M in the culture medium. The protection afforded by anitoxidants was then tested: α-tocopherol gave at 10⁻⁴ M a light protection in contrast to ascorbic acid which even became toxic at high concentrations. We also tested catalase, superoxide dismutase and glutathione peroxidase introduced intracellularly by the microinjection technique. On a molecular basis, glutathione peroxidase was 23-times more efficient than catalase and 3000-times more than superoxide dismutase. The results also showed that a similar range of enzyme concentrations was found for the protection against high oxygen pressure. This suggests that, in the case of both oxygen and nitrofurantoin toxicity, the peroxide derivatives are the most toxic intermediates of the free radical attacks.     

Quantitative study of natural antioxidant systems for cellular nitrofurantoin toxicity

The toxicity of nitrofurantoin was studied on human WI-38 fibroblasts: this chemical was lethal when added at concentrations higher than 5.10(-5) M in the culture medium. The protection afforded by antioxidants was then tested: alpha-tocopherol gave at 10(-4) M a light protection in contrast to ascorbic acid which even became toxic at high concentrations. We also tested catalase, superoxide dismutase and glutathione peroxidase introduced intracellularly by the microinjection technique. On a molecular basis, glutathione peroxidase was 23-times more efficient than catalase and 3000-times more than superoxide dismutase. The results also showed that a similar range of enzyme concentrations was found for the protection against high oxygen pressure. This suggests that, in the case of both oxygen and nitrofurantoin toxicity, the peroxide derivatives are the most toxic intermediates of the free radical attacks.     

The biallelica mating type locus ofUstilago maydis: remnants of an additional pheromone gene indicate evolution from a multiallelic ancestor

Thea mating type locus ofUstilago maydis contains the structural genes for a pheromone-based cell recognition system that governs fusion of haploid cells. The locus exists in two alleles, termeda1 anda2. We have completed the analysis of the nucleotide sequences unique toa1 anda2. Within these dissimilar regions we find two short patches of DNA sequence similarity. Interestingly, one of these segments corresponds to the transcribed region of thea1 pheromone precursor. As a result of multiple nucleotide exchanges this sequence does not code for a functional product. The existence of a second pheromone gene in thea2 allele suggests that the present locus had a multiallelic ancestor. In addition, we describe the presence of two additional genes in thea2 allele. We have investigated the role of these genes during mating and pathogenic development and speculate that they might affect mitochondrial inheritance.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.