A simple proof that certain quantities are independent of the geographical structure of population

This paper gives a proof that certain quantities are independent of the geographical structure of a population. The quantities are: (1) the fixation probability of a mutant; (2) the sum of the quantity x(1 ? x), where x is the mutant frequency, while the mutant is segregating; and (3) the quantity x(1 ? x) summed over the generations during which the gene frequency in the whole population assumes a specified value. The independence of geographical structure for the latter two quantities is not exact if there is selection, but is a close approximation.The model is a geographically structured version of Moran's haploid overlapping generation model. The population consists of colonies connected genetically by migration. Each individual has the same negative exponential lifetime distribution. When an individual dies, it is immediately replaced by an individual born in the same colony with a probability proportional to the frequency and fitness of the type giving birth. In a diploid population the quantity x(1 ? x) is proportional to the heterozygosity.     

Modeling population dynamics of yeast-like symbionts (Ascomycota: Pyrenomycetes: Clavicipitaceae) of the planthopper <Emphasis Type="Italic">Delphacodes kuscheli</Emphasis> (Hemiptera: Delphacidae)

Delphacodes kuscheli establish mutualistic relationship with yeast-like symbionts (YLS) that live in the fat body and are necessary for host survival and reproduction. We estimated for a host of age t, its body weight, W_(t), and the number of YLS per host, YLS_(t). The host body weight was calculated as: W_(t)?=?Lm/[1+ e ^(d–kt)], (Lm?=?the maximum observed weight, and d and k are constants), and the fat body was considered a fixed proportion of W_(t). We calculated the number of YLS per unit host body mass: α_(t)?=?YLS_(t)/W_(t). We also calculated the number of YLS per host, cYLS_(t), and analyzed the pattern of variation in both sexes adapting the expression of the logistic model: cYLS_(t)?=?KN_oe^rt/K+(e^rt -1)N_o, (N_o?=?initial number of YLS, r?=?intrinsic per capita rate of natural increase, and K?=?variable carrying capacity). In females the carrying capacity varied according to a constant proportion of the host’s weight: K_(t)?=?αW_(t). In males α_(t) was considered a decreasing function of the host age: K_(t)?=?α_(t)W_(t). The coefficients No, α, and r were subjected to parameterization. We found that the patterns of W_(t) and YLS_(t) of D. kuscheli were similar to other planthoppers. In females YLS increased up to the adult stage and then remained almost constant, varying similarly to individual weight. In males YLS increased up to the 5th instar nymph as the individual weight did, but the number of YLS decreased in the adult stage and the correlation was not so good. The calculated number of YLS per host matches reasonably well with the number estimated experimentally both in females and males. This is the first study that quantified and modeled the dynamics of YLS endosymbionts in a Neotropical planthopper pest. The models will be used in future studies for better understand the experimental reduction of YLS in young nymphal stages.     

A quantitative trait locus involved in maize yield is tightly associated to the r1 gene on the long arm of chromosome 10

We produced and studied for 3?years two synthetic populations of maize differing in their constitution only for the selected alleles present at the red color 1 (r1) locus (R-sc vs. r?Cr). r1 is a regulatory gene conferring anthocyanin pigmentation in different tissues: the R-sc allele confers pigmentation only in the aleurone seed layer, while the r?Cr allele confers pigmentation in several tissues such as root, silk and anther but the seed is colourless. The colourless population (r?Cr/r?Cr) was characterized by improved agronomic features, such as ear weight and plant height, compared with the R-sc/R-sc coloured population. This finding was confirmed by studying single F4 R/r families where the presence of the r?Cr allele conferred positive features, acting as a dominant trait. Quantitative trait locus (QTL) analysis performed using molecular markers on the long arm of chromosome 10 (bin 10.06), where the r1 gene maps, identified a QTL map position for plant height tightly associated to the r1 gene. Thus the r1 gene may represent a major QTL or it could be closely linked to another gene involved in the agronomic performance of the two populations studied.     

Roseibacterium beibuensis sp. nov., a Novel Member of Roseobacter Clade Isolated from Beibu Gulf in the South China Sea

A novel aerobic, bacteriochlorophyll-containing bacteria strain JLT1202r^T was isolated from Beibu Gulf in the South China Sea. Cells were gram-negative, non-motile, and short-ovoid to rod-shaped with two narrower poles. Strain JLT1202r^T formed circular, opaque, wine-red colonies, and grew optimally at 3–4?% NaCl, pH 7.5–8.0 and 28–30?°C. The strain was catalase, oxidase, ONPG, gelatin, and Voges–Proskauer test positive. In vivo absorption spectrum of bacteriochlorophyll a presented two peaks at 800 and 877?nm. The predominant cellular fatty acid was C_18:1 ω7c and significant amounts of C_16:0, C_18:0, C_10:0 3-OH, C_16:0 2-OH, and 11-methyl C_18:1 ω7c were present. Strain JLT1202r^T contained Q-10 as the major respiratory quinone and the genomic DNA G+C content was 76.3?mol%. Phylogenetic analysis based on 16S rRNA gene sequences of various species with validly published names showed that strain JLT1202r^T fell within the genus Roseibacterium, family Rhodobacteraceae, sharing the highest similarity with Roseibacterium elongatum OCh 323^T (97.9?% similarity), followed by Dinoroseobacter shibae DFL 12^T (95.4?% similarity). The phylogenetic distance of pufM genes between strain JLT1202r^T and R. elongatum OCh 323^T was 9.4?%, suggesting that strain JLT1202r^T was distinct from the only strain of the genus Roseibacterium. Based on the variabilities of phylogenetic and phenotypic characteristics, strain JLT1202r^T stands for a novel species of the genus Roseibacterium and the name R. beibuensis sp. nov. is proposed with JLT1202r^T as the type strain (=JCM 18015^T?=?CGMCC 1.10994^T).     

Synthesis,characterization, and molecular structure of the quadruply bonded ditungsten(ll) complex,W2Cl4(dppm)2

The reaction of W₂Cl₄[P(n-Bu)₃]₄ with bis(diphenylphosphino)methane (dppm) affords the highly air-sensitive material, W₂Cl₄(dppm)₂, which has been characterized by IR and visible spectroscopy, and by X-ray crystallography. The compound crystallizes in the centrosymmetric space group C2/c with the following parameters: a = 17.298(3); b = 17.011- (2); c = 18.413(2) Å; β = 98.93(2); V = 5352(2) ų; Z = 4. The molecule is positioned about a C₂ axis which allows for a net torsion angle of 17.25° down the WW vector. This does not seem to significantly effect the WW bond distance (2.269(1) Å) relative to other quadruply bonded ditungsten species.     

Simulation of internal transport barriers by means of the canonical profile transport model

Models with critical gradients are widely used to describe energy balance in L-mode discharges. The so-called first critical gradient can be found from the canonical temperature profile. Here, it is suggested that discharge regimes with transport barriers can be described based on the idea of the second critical gradient. If, in a certain plasma region, the pressure gradient exceeds the second critical gradient, then the plasma bifurcates into a new state and a transport barrier forms in this region. This idea was implemented in a modified canonical profile transport model that makes it possible to describe the energy and particle balance in tokamak plasmas with arbitrary cross sections and aspect ratios. The magnitude of the second critical gradient was chosen by comparing the results calculated for several tokamak discharges with the experimental data. It is found that the second critical gradient is related to the magnetic shear s. The criterion of the transport barrier formation has the form (a ²/r)d/drln(p/p _c ) > z ₀ (r), where r is the radial coordinate, a is the plasma minor radius, p is the plasma pressure, p _c is the canonical pressure profile, and the dimensionless function z _O(r) = C _O + C ₁ s (with C _0i ～1, C _0e ～3, and C _1i,e ～2) describes the difference between the first and second critical gradients. Simulations show that this criterion is close to that obtained experimentally in JET. The model constructed here is used to simulate internal transport barriers in the JET, TFTR, DIII-D, and MAST tokamaks. The possible dependence of the second critical gradient on the plasma parameters is discussed.     

Frequency dependence of the frog skin impedance

At frequencies between 20 Hz and 1 kHz the impedance locus of the isolated frog skin is circular; below 20 Hz the resistive component of the impedance is frequently greater than would be expected from extrapolation of the high-frequency locus. At frequencies greater than twice the highest frequency at which there are deviations from the circular locus the variation of impedance Z with angular frequency ω is closely described by the equation Z = r₁ + r₀/[1+(jωτ)^1-α], where j is √?1, r¹ and r⁰ are resistance, τ is a time constant and α a constant in the range 0.02–0.14.     

On indicator dilution and perfusion heterogeneity: A stochastic model

Unidirectional extraction of a substrate S in the capillaries following the arterial injection of a bolus containing S and a reference tracer R is assumed to follow first-order kinetics. If C_R and C_S denote normalized venous effluent concentrations of R and S, respectively, let L(t)=ln[C_R(t)⧸C_S(t)]. We derive a formula which expresses the experimental L(t) data in terms of the mean μ(t) and variance of the transit times of those capillaries which are contributing indicators at each sample time t. We examine the information thus contained in the L data about capillary and noncapillary transit times under several kinematic assumptions. We show that if the capillary and noncapillary transit times are stochastically independent with frequency functions h_c(t) and h_av(t), respectively, then the shapes of the graphs of L(t) and μ(t) depend on the variances and skewnesses of h_c(t) and h_av(t). Specifically, let r₂ be the ratio of the variance of h_c(t) to the variance of h_av(t), and let r₃ be the ratio of skewnesses in the same order. Then the graph of μ(t) is concave downward if r₂⧸r₃ > 1, concave upward if r₂⧸r₃< 1, and linear if r₂⧸r₃ = 1. If the fraction of S extracted is not too large, L(t) has nearly the same shape as μ(t), and therefore, L(t) contains information about h_c(t) and h_av(t).     

Identification of DPY19L3 as the C-mannosyltransferase of R-spondin1 in human cells

R-spondin1 (Rspo1) is a secreted protein that enhances Wnt signaling, which has crucial functions in embryonic development and several cancers. C-mannosylation is a rare type of glycosylation and might regulate secretion, protein–protein interactions, and enzymatic activity. Although human Rspo1 contains 2 predicted C-mannosylation sites, C-mannosylation of Rspo1 has not been reported, nor have its functional effects on this protein. In this study, we demonstrate by mass spectrometry that Rspo1 is C-mannosylated at W¹⁵³ and W¹⁵⁶. Using Lec15.2 cells, which lack dolichol-phosphate-mannose synthesis activity, and mutant Rspo1-expressing cells that replace W¹⁵³ and W¹⁵⁶ by alanine residues, we observed that C-mannosylation of Rspo1 is required for its secretion. Further, the enhancement of canonical Wnt signaling by Rspo1 is regulated by C-mannosylation. Recently DPY19 was reported to be a C-mannosyltransferase in Caenorhabditis elegans, but no C-mannosyltransferases have been identified in any other organism. In gain- and loss-of-function experiments, human DPY19L3 selectively modified Rspo1 at W¹⁵⁶ but not W¹⁵³ based on mass spectrometry. Moreover, knockdown of DPY19L3 inhibited the secretion of Rspo1. In conclusion, we identified DPY19L3 as the C-mannosyltransferase of Rspo1 at W¹⁵⁶ and found that DPY19L3-mediated C-mannosylation of Rspo1 at W¹⁵⁶ is required for its secretion.     

Isolation and characterization of sex chromosome rearrangements generating male muscle dystrophy and female abnormal oogenesis in the silkworm, Bombyx mori

In deletion-mapping of W-specific RAPD (W-RAPD) markers and putative female determinant gene (Fem), we used X-ray irradiation to break the translocation-carrying W chromosome (W ^Ze ). We succeeded in obtaining a fragment of the W ^Ze chromosome designated as Ze ^W, having 3 of 12 W-RAPD markers (W-Bonsai, W-Yukemuri-S, W-Yukemuri-L). Inheritance of the Ze ^W fragment by males indicates that it does not include the Fem gene. On the basis of these results, we determined the relative positions of W-Yukemuri-S and W-Yukemuri-L, and we narrowed down the region where Fem gene is located. In addition to the Ze ^W fragment, the Z chromosome was also broken into a large fragment (Z₁) having the + ^sch (1-21.5) and a small fragment (Z₂) having the + ^od (1-49.6). Moreover, a new chromosomal fragment (Ze ^WZ₂) was generated by a fusion event between the Ze ^W and the Z₂ fragments. We analyzed the genetic behavior of the Z₁ fragment and the Ze ^WZ₂ fragment during male (Z/Z₁ Ze ^WZ₂) and female (Z₁ Ze ^WZ₂/W) meiosis using phenotypic markers. It was observed that the Z₁ fragment and the Z or the W chromosomes separate without fail. On the other hand, non-disjunction between the Ze ^WZ₂ fragment and the Z chromosome and also between the Ze ^WZ₂ fragment and the W chromosome occurred. Furthermore, the females (2A: Z/Ze ^WZ₂/W) and males (2A: Z/Z₁) resulting from non-disjunction between the Ze ^WZ₂ fragment and the W chromosome had phenotypic defects: namely, females exhibited abnormal oogenesis and males were flapless due to abnormal indirect flight muscle structure. These results suggest that Z₂ region of the Z chromosome contains dose-sensitive gene(s), which are involved in oogenesis and indirect flight muscle development.     

Association of neighboring β-strands of outer membrane protein A in lipid bilayers revealed by site-directed fluorescence quenching

We present a detailed study on the formation of neighboring β-strands during the folding of a monomeric integral membrane protein of the β-barrel type. β-Strand and β-barrel formations were investigated for the eight-stranded transmembrane domain of outer membrane protein A (OmpA) with single-tryptophan (W), single-cysteine (C) OmpA mutants. Based on the OmpA structure, W and C were introduced in two neighboring β-strands oriented toward the hydrocarbon core of the membrane. Replaced residue pairs were closer to either the periplasmic turns (named cis-side) or the outer loops (named trans-side) of the strand. W_nC_m OmpA mutants containing W at position n and C at position m along the polypeptide chain were labeled at the C by a nitroxyl spin label, which is a short-range fluorescence quencher. To monitor the association of neighboring β-strands, we determined the proximity between fluorescent W and labeled C in OmpA folding experiments by intramolecular fluorescence quenching. Formation of native β-strand contacts in folding experiments required the lipid membrane. Residues in the trans-side of strands β₁, β₂, and β₃, represented by mutants W₁₅C₃₅ (β₁β₂, trans) and W₅₇C₃₅ (β₃β₂, trans), reached close proximity prior to residues in the N(β₁)- and C(β₈)-terminal strands as examined for mutants W₁₅C₁₆₂ (β₁β₈, trans) and W₇C₁₇₀ (β₁β₈, cis). Tryptophan and cysteine converged slightly faster in W₁₅C₁₆₂ (β₁β₈, trans) than in W₇C₁₇₀ (β₁β₈, cis). The last folding step was observed for residues at the cis-ends of strands β₁ and β₂ for the mutant W₇C₄₃ (β₁β₂, cis). The data also demonstrate that the neighboring β-strands associate upon insertion into the hydrophobic core of the lipid bilayer.     

Survival Chances of Mutants Starting With One Individual

A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. First case: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N mutants W_n^M(N) after the multiplication phase M of the n-th generation (with probability δ of an error in the replication, where all possible errors are fatal errors) and W_n^S(N) after the following selection phase S (with probability β that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction W_∞^S(0) are obtained. Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N_p primary mutants and N_m of the new form W_n^M(N_p, N_m) after the multiplication phase M of the n-th generation (probability ε of an error in the replication of the primary mutant giving the new form) and W_n^S(N_p, N_m) after the following selection phase S (probabilities β_p and β_m that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained.     

Diploidy and repair of radiation damage in Saccharomyces mutants

Diploid wild-type cells of Saccharomyces and cells homozygous for one of the single genes r^s₁, r^s₂ of the two alleles of the r^s₃ gene (rad 2 gene) were tested for their response to ionizing irradiation in the presence and absence of oxygen. Both immediate and delayed plating (agar-holding) techniques were used.An identical oxygen enhancement ratio (OER) of 2.5 was observed in r^s₁r^s₁, r^s₂r^s₂ cells and the wild type. In r^s_3?1r^s_3?1 and r^s_3?2r^s_3?2 cells the OER was reduced. Their sensitivity to ionizing irradiation in oxic conditions was the same as that of the wild type.r^s₂r^s₂ cells showed an increase in relative sensitivity by a factor of 4 in both conditions of irradiation. The relative sensitivity of r^s₁r^s₁ cells was increased by a factor of 2.5 in hypoxic conditions and the sensitivity in hypoxia was identical to that of wild type cells in oxic conditions. In contrast to haploid r^s₁ cells the oxygen effect was fully expressed in diploid r^s₁r^s₁ cells.The results on diploid strains are discussed in terms of three independent genetically determined repair systems in Saccharomyces. The expression of these systems is influenced by ploidy.     

Genic Variation in Male Haploids under Deterministic Selection

Genic variation in male haploids and male diploids was compared assuming constant fitnesses (derived from computer-generated random numbers) and infinite population size. Several models were studied, differing by the fitness correlation between the sexes (r_s) and genotypes (r_g), and by the intensity of selection as measured by the coefficient of variation (CV) of the fitness distribution. Genic variation was quantified using the proportion of polymorphic loci, P, the gene diversity at polymorphic loci, H_p, and the gene diversity over all loci, H_a. The two genetic systems were compared via variation ratios: variation in male haploidy/variation in male diploidy.—P and H_a were markedly lower for male-haploids than for male diploids, the variation ratios declining with increasing r_s, r_g and CV, but the two genetic systems were similar for H_p. Except for male diploids with r_s = 1, the two sexes had different equilibrium gene frequencies but the sample sizes required to detect such differences reliably were larger than usually possible in surveys of natural populations.—Data from natural populations fit the above trends qualitatively, but the variation ratios are much lower than those from our analyses, except that for H_p, which is higher when Drosophila is excluded. Also, the frequency distribution of most common alleles from electrophoretic data has a deficiency of intermediate frequencies compared to that from the computer-generated sets of fitnesses, possibly reflecting either the influence of stochastic processes shifting frequencies away from equilibrium or the involvement of alleles under selection-mutation balance.——While electrophoretic data suggest that Drosophila has unusually high levels of genic variation, unusually low levels of genic variation in male haploids compared with male diploids are not strongly indicated. However, if further data confirm male haploids as having low levels of genic variation, likely explanations are that the bulk of electrophoretically detected variation involves fixed-fitness balancing selection, selection-mutation balance involving slightly deleterious recessive alleles, new favorable male haploid alleles moving more rapidly to fixation than under male diploidy and thus carrying linked loci to fixation faster, or some combination of these possible factors.     

Natural selection and fitness entropy in a density-regulated population

The entropy H(p_o,p*) of a population with the initial allele frequency p_o given the equilibrium polymorphic frequency p* has been proposed as a measure of natural selection. In the present paper, we have extended this concept to include a particular aspect of density-dependent selection. We compared size trajectory of a population initially at genetic equilibrium, N(t), with the size trajectories of populations not initially at p*,N(t), but which do eventually converge to a common equilibrium allele frequency and equilibrium density, N*. The following experimentally testable hyopthesis was established. The total area defined by the difference between the trajectories of N(t) and N(t) as they converge to N* is directly proportional to the fitness entropy when population size is transformed using the density-dependent fitness value. Two properties of this relationship were noted. First, it is independent of the magnitude of natural selection and, secondly, it does not depend upon the initial population density as long as the equilibrium and nonequilibrium populations have the same initial numbers. This hypothesis was evaluated with experimental data on the flour beetle Tribolium castaneum.     

Photorespiration in Green Plants During Photosynthesis Estimated by Use of Isotopic CO(2)

Photosynthetic re-absorption of photorespired CO₂ causes underestimation in measured photorespiration and turnover rate of the substrate for photorespiration. Actual values of photorespiration exceed the measured by a factor greater than 1 + R′_w/r_p + [C_L]_x/(r_p·L_x). (R′_w and r_p are the partial resistances to CO₂ uptake between atmosphere, mesophyll evaporating surface, and photosynthetic sink, respectively; L_x is the measured flux of photorespired CO₂ and [C_L]_x is the ambient conc of photorespired CO₂). In 8 species, 1 + R′_w/r_p alone amounted to a correction ranging between 148% and 233%.     

Adaptation of Mycobacteria to Growth Conditions: A Theoretical Analysis of Changes in Gene Expression Revealed by Microarrays

Background

Microarray analysis is a powerful technique for investigating changes in gene expression. Currently, results (r-values) are interpreted empirically as either unchanged or up- or down-regulated. We now present a mathematical framework, which relates r-values to the macromolecular properties of population-average cells. The theory is illustrated by the analysis of published data for two species; namely, Mycobacterium bovis BCG Pasteur and Mycobacterium smegmatis mc² 155. Each species was grown in a chemostat at two different growth rates. Application of the theory reveals the growth rate dependent changes in the mycobacterial proteomes.

Principal Findings

The r-value r _(i) of any ORF (ORF_(i)) encoding protein p _(i) was shown to be equal to the ratio of the concentrations of p _(i) and so directly proportional to the ratio of the numbers of copies of p _(i) per population-average cells of the two cultures. The proportionality constant can be obtained from the ratios DNA: RNA: protein. Several subgroups of ORFs were identified because they shared a particular r-value. Histograms of the number of ORFs versus the expression ratio were simulated by combining the particular r-values of several subgroups of ORFs. The largest subgroup was ORF_(j) (r _(j)  = 1.00± SD) which was estimated to comprise respectively 59% and 49% of ORFs of M. bovis BCG Pasteur and M. smegmatis mc² 155. The standard deviations reflect the properties of the cDNA preparations investigated.

Significance

The analysis provided a quantitative view of growth rate dependent changes in the proteomes of the mycobacteria studied. The majority of the ORFs were found to be constitutively expressed. In contrast, the protein compositions of the outer permeability barriers and cytoplasmic membranes were found to be dependent on growth rate; thus illustrating the response of bacteria to their environment. The theoretical approach applies to any cultivatable bacterium under a wide range of growth conditions.     

Distribution of Gene Frequency as a Test of the Theory of the Selective Neutrality of Polymorphisms

The variation in gene frequency among populations or between generations within a population is a result of breeding structure and selection. But breeding structure should affect all loci and alleles in the same way. If there is significant heterogeneity between loci in their apparent inbreeding coefficients F=s_p²/p(1-p), this heterogeneity may be taken as evidence for selection. We have given the statistical properties of F and shown how tests of heterogeneity can be made. Using data from human populations we have shown highly significant heterogeneity in F values for human polymorphic genes over the world, thus demonstrating that a significant fraction of human polymorphisms owe their current gene frequencies to the action of natural selection. We have also applied the method to temporal variation within a population for data on Dacus oleae and have found no significant evidence of selection.     

A bisexual multitype branching process with applications in population genetics

A bisexual multiple branching process is studied. Consider a population with respect to three genotypes in both the female and male populations and let $$X(n) = \left\langle {X_1 (n), X_2 (n), X_3 (n)} \right\rangle and Y(n) = \left\langle {Y_1 (n), Y_2 (n), Y_3 (n)} \right\rangle$$ be random vectors giving the number of females and males (respectively) of each genotype in generationn. The mating of females and males is accommodated in the model withZ _ij (n) representing the number of females of theith genotype mated with a male of thejth genotype in generationn. The mating system is such that a female may be mated to only one male but a male may be mated with more than one female. By arranging the nine random variablesZ _ij (n),i, j=1, 2, 3, in a 1×9, vectorZ(n) it is shown that under certain conditions there is a positive constant ? such that when ?>1 the vectorsZ _n /ρⁿ,X _n /ρⁿ andY _n /ρⁿ converge almost surely asn→∞ to random vectors with fixed directions. The paper is divided into four sections. In section 1 the model is described in detail and its potential applications to population genetics are discussed. In section 2, the generating function of the transition probabilities of theZ-process are derived. Section3 is devoted to the study of the limiting behavior of the first and second moments of theZ-process, and in section4 the results of section3 are utilized to study the behavior of the random vectorsZ(n),X(n) andY(n) asn→∞.