Application of Markov chains to linked genes with interference. I. No selection.

The case of a population that reproduces wholly by selfing and has three loci with two alleles each is considered. Expressions are obtained for the mean number of times that a process passes through a transient state and for the mean number of generations needed to reach an absorbing state; expressions for other interesting parameters are also obtained. Both the probability of recombination and the coincidence (C) have been considered as variables. The objective of the study was to find expressions that allow (i) direct computation of the entries of the inverse matrices with the aim of avoiding problems of ill-conditioning that could appear in the stochastic matrices involved and (ii) analysis of the psi i(C,s,q) functions of the coincidence C and gene distances s,q. In this part of the work, selective values for the genotypes and expressions for the asymmetry of the distributions are not included. Finally, values are assigned to each of the psi i, psi i(C0,q0,s0).     

Dominance and overdominance of mildly deleterious induced mutations for fitness traits in Caenorhabditis elegans

We estimated the average dominance coefficient of mildly deleterious mutations (h, the proportion by which mutations in the heterozygous state reduce fitness components relative to those in the homozygous state) in the nematode Caenorhabditis elegans. From 56 worm lines that carry mutations induced by the point mutagen ethyl methanesulfonate (EMS), we selected 19 lines that are relatively high in fitness and estimated the viabilities, productivities, and relative fitnesses of heterozygotes and homozygotes compared to the ancestral wild type. There was very little effect of homozygous or heterozygous mutations on egg-to-adult viability. For productivity and relative fitness, we found that the average dominance coefficient, h, was approximately 0.1, suggesting that mildly deleterious mutations are on average partially recessive. These estimates were not significantly different from zero (complete recessivity) but were significantly different from 0.5 (additivity). In addition, there was a significant amount of variation in h among lines, and analysis of average dominance coefficients of individual lines suggested that several lines showed overdominance for fitness. Further investigation of two of these lines partially confirmed this finding.     

Penetration of host cell lines by bacteria. Characteristics of the process of intracellular bacterial infection

A model which describes the characteristics of the penetration of the cells by bacteria is presented. Since the process of invasion is preceded necessarily by the step in which the bacteria adhere to the cells, the proposed model is based on the expressions previously derived for the process of adhesion, which allow us to determine the number of attached bacteria under different conditions. Thus, the model considers that invasion occurs irreversibly from attached bacteria to specific receptors located on the cell surface with a rate coefficient=k _i so that the invasive capacity in a given bacterium-host cell system is mainly determined by the value of this coefficient. Once internalized, the bacteria can follow three different time courses, namely: 1) intracellular growth is hindered so that the bacteria remain in stationary phase, 2) there is a lag phase during which the bacteria stay in stationary phase before they are able to grow exponentially with a rate coefficient=k _c , and 3) the bacteria exhibit a growth exponertial phase as they enter the cells. In turn, the time course followed by extracellular bacteria also has a decisive influence on the process of invasion and, in this regard, unbound bacteria are considered either in stationary or in exponential phase. Expressions for these different situations have been derived, and from them, procedures to determine the levels of bacterial infection and for quantitative invasive data analysis are presented.     

Pulse velocities in initially stressed cylindrical rubber tubes

Expressions are obtained for the pulse velocities in cylindrical tubes of rubber-like materials which are under a state of initial stress. The development is based on the theory of finite elastic deformations and a Mooney materials is considered for illustrative purposes. Numerical results are given in terms of dimensionless parameters which involve the stretch ratio and lumen volume ratio. For the thoracic aorta, a value for the pulse velocity is obtained which is lower than the experimental value.     

Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations

The influence of small population size (N) on the genetic variance within and between randomly bred unselected lines, with selfing permitted, is investigated for a model of a quantitative trait determined by linked genes that show dominance within loci but are additive over loci. Formulae for within-line variance include terms in linkage disequilibrum, which occurs by chance in the lines and these are evaluated in terms of N, map length and gene number.—The expected variance within lines is increased by this disequilibrium, quite substantially if there are many loci, with most of the increase being between or within full-sib families and almost no change expected between half-sib families or in the covariance of offspring and parent. If all loci are unlinked, there is no increase in variance within full-sib families. The variance between lines is little affected by disequilibrum generated by chance.—Expressions for the variance between individuals in heterozygosity over the whole genome are special cases of those for the variance due to linked dominated genes, and formulae are given and evaluated. The coefficient of variation of heterozygosity is at least (see PDF) and can be much higher for species with few chromosomes.     

Energetics of enzyme catalysis. I. Isotopic experiments, enzyme interconversion, and oversaturation

An enzyme-catalyzed interconversion of one substrate, S, and one product P, by an enzyme that exists in two forms E1 and E2 where E1 binds S and E2 binds P, is considered S + E1 in equilibrium E1S in equilibrium E2P in equilibrium E2 + P. Under reversible conditions (where the concentrations of S and P are not far removed from their equilibrium values) it is shown that, in addition to the usual unsaturated and saturated behaviour there exists a third regime at high substrate concentration: the oversaturated region. In this region, the rate-limiting transition state is the interconversion of the unliganded forms of the enzyme: E1 and E2. Expressions for six different experiments involving deuterium, tritium and 14C labels are presented. By considering the results from these experiments, the nature and importance of the enzyme interconversion steps can be elucidated.     

Long-range interactions between macromolecules in ordered media

The results of theoretical calculations of interactions between macromolecules dissolved in ordered media such as liquid crystals and biological membranes (lipid bilayers) are reviewed. Expressions for the potentials of interactions between macromolecules of different shape incorporated into nematic liquid crystals, thin films, and lipid mono- and bilayers were derived. In addition to exact expressions, simple evaluating formulae are given. The two-dimensional "gas" of macromolecules swimming on the membrane was considered, and the expression of state for this "gas" was derived. It was shown that in the "gas", phase transitions accompanied by the formation of two-dimensional clusters may occur. The estimates of critical density at which these transitions occur are given.     

On the Theory of Partially Inbreeding Finite Populations. I. Partial Selfing

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is Ne = N'/(1 + FIS), where FIS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is found to be 2(N'/N)(FISS1 + (1 - FIS)S2), where S1 and S2 are the selective advantages of AA and AA in comparison with AA. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions Ne = N/(1 + 3FIS).     

Quantitative genetics of autogamous F2

General quantitative genetic properties are derived for the F2 originating from self-fertilisation of hybrid (F1) individuals. These results extend and generalize previous restricted knowledge about this F2. New equations are found for all genotype frequencies, allele frequencies, inbreeding coefficient, genic (additive-genetic) and dominance variances, broadsense and narrowsense heritabilities, and selection potential. The bulk mean is generally lower, and the genotypic variance is generally higher, than those of the F1 and the allogamous F2. Genic and dominance variances for the selfed F2 are very different to the classical counterparts. Their relationships with inbreeding have been investigated, and they are more elaborate than previously considered. The level of inbreeding is constant irrespective of parental combinations, which is different to the inbreeding of an allogamous F2. Selection potential is generally high, and selection advance generally exceeds bulk inbreeding depression. If selection is assisted by dispersion, the autogamous F2 may obtain greater genetic advance than its allogamous counterpart for the same selection pressure. Under conditions of spatially separated F2, swarms, natural selection may be enhanced by selfing.     

On dominance relations and the structure of animal societies: I. Effect of inherent characteristics

Societies are considered in which a non-transitive dominance relation exists between every pair of members, such as the peck-right in a flock of hens. A one-dimensional measure of the structure of such a society,h, is defined, withh=0 for equality andh=1 for the hierarchy. It is assumed that each member of the society is characterized by an ability vector whose components depend on individual characteristics such as size, concentration of sex hormone, etc., but not on social factors such as social rank. The distribution of abilities among members of the society is assumed to be given by a distribution function which is the same for all members, and the probability that one member dominates another is given by a function of the ability vectors of the two. On these assumptions formulas for the expected (mean) value and variance ofh are determined in terms of the distribution and dominance probability functions. Some special cases are calculated, especially that for normany distributed abilities and dominance probability given by the normal probability integral. Several conclusions are derived. If all members are of equal ability, so that dominance probability is 1/2, then any sizable society is much more likely to be near the equality than the hierarchy; and, as the size of the society increases, the probability that it will be near the hierarchy becomes vanishingly small. If the dominance probability is a weighted sum of several independent components, which make up the ability vector, then the society is less likely to be close to the hierarchy as the number of these components increases. The hierarchy is the prevalent structure only if unreasonably small differences in ability are decisive for dominance. From this it appears that the social factors, or psychological factors such as the previous history of dominance, which are not included in the present treatment, may be of great importance in explaining the observed prevalence of structures very close to the hierarchy in flocks of domestic hens.     

Analysis of some nonrandom mating models

In this paper a few asymmetric models are presented taking account of the effects of assortative mating on an autosomal trait controlled by a single locus possibly with multiple alleles. The models are developed by specifying the intensities for preference mating for various phenotypes. The analysis is confined to the case in which preference is exercised by the individuals of one sex only. It is assumed that males possess unlimited fertility.The dynamics of the population and its equilibrium distribution are discussed. The gene frequency usually changes with time and equilibrium distribution in most cases depends only on the assortment parameters. Expressions are obtained giving the additive and dominance components of variance, and covariances for relatives for populations in equilibrium for some of the models.     

Inferences about the distribution of dominance drawn from yeast gene knockout data

Data from several thousand knockout mutations in yeast (Saccharomyces cerevisiae) were used to estimate the distribution of dominance coefficients. We propose a new unbiased likelihood approach to measuring dominance coefficients. On average, deleterious mutations are partially recessive, with a mean dominance coefficient ~0.2. Alleles with large homozygous effects are more likely to be more recessive than are alleles of weaker effect. Our approach allows us to quantify, for the first time, the substantial variance and skew in the distribution of dominance coefficients. This heterogeneity is so great that many population genetic processes analyses based on the mean dominance coefficient alone will be in substantial error. These results are applied to the debate about various mechanisms for the evolution of dominance, and we conclude that they are most consistent with models that depend on indirect selection on homeostatic gene expression or on the ability to perform well under periods of high demand for a protein.     

Some thoughts about genetics, differentiation, and malignancy.

This article deals with three related questions: (1) whether malignancy is determined by genetic or epigenetic mechanisms; (2) whether epigenetic mechanisms, as conventionally defined, actually exist; (3) what criteria are appropriate for defining dominance or recessiveness of the malignant state in cell fusion experiments.     

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.     

Genomic prediction of hybrid crops allows disentangling dominance and epistasis

We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted “residual genetic” line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme—e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes.     

Genetic analysis of polyauxotrophy and early mitotic progeny of Saccharomyces cerevisiae zygotes. II. Spore-forming segregants in the mitotic and meiotic progeny of polyauxotrophic clones

This article continues the investigation of polyauxotrophic (PA) clones formed in early mitotic progeny of zygotes. Cloning and segregation analysis of PA progeny suggest an unusual state of diploid genome in these strains, which is expressed as elimination of the dominance effect of the wild allele and as suppression or conversion of either of two loci of mating type. In PA progeny, except for recombinant haploids, sporulating diploids and unstable clones were detected. The tetrad analysis of the diploids points to homozygotization for individual markers. Over-replication of diploid set of chromosomes, prior to meiosis, and replacement of the haploid nucleus (the product of meiosis) for the diploid nucleus may explain the appearance of sporulating segregants in the diploid meiotic progeny. Unstable segregants may be considered as heterokaryons with complex interaction of nuclei.     

Analysis of cytoplasmic and maternal effects. II. Genetic models for triploid endosperms

Genetic models for quantitative traits of triploid endosperms are proposed for the analysis of direct gene effects, cytoplasmic effects, and maternal gene effects. The maternal effect is partitioned into maternal additive and dominance components. In the full genetic model, the direct effect is partitioned into direct additive and dominance components and high-order dominance component, which are the cumulative effects of three-allele interactions. If the high-order dominance effects are of no importance, a reduced genetic model can be used. Monte Carlo simulations were conducted in this study for demonstrating unbiasedness of estimated variance and covariance components from the MINQUE (0/1) procedure, which is a minimum norm quadratic unbiased estimation (MINQUE) method setting 0 for all the prior covariances and 1 for all the prior variances. Robustness of estimating variance and covariance components for the genetic models was tested by simulations. Both full and reduced genetic models are shown to be robust for estimating variance and covariance components under several situations of no specific effects. Efficiency of predicting random genetic effects for the genetic models by the MINQUE (0/1) procedure was compared with the best linear unbiased prediction (BLUP). A worked example is given to illustrate the use of the reduced genetic model for kernel growth characteristics in corn (Zea mays L.).     

Kinetic cooperativity in the concerted model for allosteric enzymes.

The cooperativity of enzyme-substrate interactions is investigated in the concerted allosteric model of Monod, Wyman and Changeux. The general case of K-V systems is considered, in which the two protomer conformational states R and T postulated in the theory differ in catalytic and binding properties. An expression for the Hill coefficient nH defined with respect to the asymptotic velocity V infinity to is analyzed in conditions which exclude substrate inhibition. Kinetic cooperativity is always positive (nH greater than 1) in the case of a dimer enzyme, and in the case of an inactive T state. Slight kinetic negative cooperativity (nH less than 1) occurs under restrictive conditions for larger numbers of protomers when the substrate binds significantly to the less active state of the enzyme, but the phenomenon remains negligible for trimers and tetramers. These conclusions differ from those obtained [A. Goldbeter, J. Mol.Biol.90 (1974) 185] with the Hill coefficient based on the absolute maximum velocity, which may exceed the experimental value V infinity to in K-V systems. The results extend those of Paulus and DeRiel [J. Mol. Biol. 97 (1975) 667] and support the view that in most cases, negative cooperativity is not compatible with a mechanism based on a concerted and conservative allosteric transition. The Hill coefficients for binding and catalysis are compared in K-V systems.     

On simultaneous determinations of the permeability of a membrane and of the diffusion coefficient in an adjacent medium

This paper deals with diffusion into a medium of finite thickness through a flat structure which can be considered either as a slice of tissue or as a membrane. Formulae are given to determine the diffusion coefficients in both the flat structure and the adjacent medium from the knowledge of the amount of substance penetrating the medium. The meaning of the formula: (permeability coefficient) = (diffusion coefficient)/(membrane thickness) and the experimentally observed variability of the permeability coefficient in the non-steady state are interpreted on the basis of the mathematical theory of diffusion.