A model of the complex response of Staphylococcus aureus to methicillin

It is widely accepted that β-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that β-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called ‘Eagle-effect’. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.     

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.     

Reply to: “Comment on root orientation can affect detection accuracy of ground-penetrating radar”

Introduction

We showed that root orientation affected a parameter of ground penetrating radar (GPR), amplitude area (A) (Tanikawa et al. Plant Soil 373:317–327, 2013). The aims of this reply to Wu et al. (2014) are (i) to correct the two inaccuracies in Tanikawa et al. (2013) and (ii) to improve our method of estimating A(90°) using A(x) of root angle x.

Methods

Measured A values of Tanikawa et al. (2013) were analyzed with the modified equations.

Results

The first inaccuracy was the use of incorrect units for the coefficient b (the phase shift) in the sinusoidal waveform of A(x). The units should have been radians instead of degrees. The second inaccuracy was the mis-derivation of A(x) into A(x?+?90°). In the modified method, A(90°) was estimated by A(x) from two orthogonally intersecting transect lines and a transect line at a diagonal to them.

Conclusions

The two inaccuracies did not affect the previous main conclusions that the parameter T was suitable for estimating root diameter and that grid transects are likely to identify clear hyperbolas reflecting roots in radar profiles (Tanikawa et al. 2013). By the improved method, we could accurately estimate root diameter by scanning using three transect lines intersecting at angles of x, x?+?45°, and x?+?90°.     

Modelling the effects of climate change on the potential feeding activity of Thaumetopoea pityocampa (Den. & Schiff.) (Lep., Notodontidae) in France

Aim We investigated whether climate change has affected the potential feeding activity of a winter active larva, the pine processionary moth (PPM), Thaumetopoea pityocampa L., and whether it may explain its range expansion. Location The study area is France and, at a smaller scale, the Paris Basin. Methods We used a statistical model derived from Huchon and Démolin [1970 Revue Forestière Française (special issue: La lutte biologique en forêt), 220–234] to test whether their model, updated with climate change, could explain the observed range expansion. Since Battisti and colleagues have recently shown that climate could affect survival of the PPM through its effect on feeding activity, we also developed a mechanistic model based on larval feeding requirements (night air temperature above 0 °C and temperature inside the nest above 9 °C on the preceding day). We reconstructed the geographical distribution of feeding activity and we compared the resulting change with the PPM range expansion. Results The statistical model did not successfully predict the observed expansion but the mechanistic model showed considerable change in the feeding activity of the PPM. In the Paris Basin, the PPM border coincided with a zone unfavourable for feeding activity in the period 1992–96. Feeding conditions became more favourable in the period 2001–04, and the PPM succeeded in crossing this zone. Over larger temporal and spatial scales improved feeding conditions in the north‐western part of France were forecast by the mechanistic model. Main conclusions (1) The range distribution of the PPM in the Paris Basin is no longer limited by unfavourable feeding conditions. (2) The pattern of range expansion of the PPM is now governed mainly by its dispersal capabilities and host tree distribution. (3) At the country scale, this approach gives an approximate prediction of the potential distribution of the PPM, though the model may not be reliable in mountainous regions.     

Mating context and menstrual phase affect women's preferences for male voice pitch

Fundamental frequency (F₀) is the vocal acoustic parameter closest to what we perceive as pitch. Men speak at a lower F₀ than do women, even controlling for body size. Although the developmental and anatomical reasons for this sex difference are known, the evolutionary reasons are not. By examining fertility-related variation in women's preferences for men's voices, the present study tests the hypothesis that female choice for good genes influenced the evolution of male voice pitch (VP). Unlike previous correlational studies that did not consider the effects of menstrual phase and mating context on women's preferences for male VP, the present study includes these variables and utilizes experimental pitch (P) manipulations. Results indicate that low VP is preferred mainly in short-term mating contexts rather than in long-term, committed ones, and this mating context effect is greatest when women are in the fertile phase of their ovulatory cycles. Moreover, lower male F₀ correlated with higher self-reported mating success. These findings are consistent with the hypothesis that an association between low male VP and heritable fitness led to the evolution of the observed patterns in women's P preferences and men's mating success and that these patterns influenced the evolution of low VP in men. However, alternative explanations are considered.     

Oligomerization of the Cu(II) and Ni(II) tetraazaannulene complexes: A pulse radiolysis study of the associated reaction mechanism

The oligomerization of [Cu^II(H_x(tmdnTAA))]^x+ (x = 0, 1, 2 and (tmdnTAA))²⁻ is 2,4,9,11-tetramethyl-dinaphto[14]-2,4,6,9,11,13-hexaeneN₄) was initiated in homogeneous solution via the reaction of this Cu(II) complex with pulse radiolytically generated radicals. The reaction produces Cu(III) intermediates which are rapidly converted to Cu(II) ligand-radical species. In contrast to the mechanism proposed for the electrochemical oligomerization, where the local concentration of radicals is probably high, the reaction kinetics in homogeneous solution is propagated by a process where the Cu(II) ligand-radical precursors react with [Cu^II(H_x(tmdnTAA))]^x+.     

Morphological characteristics and chromosome behaviour in F1, F2 and BC1 progenies between Chrysanthemum × morifolium and Ajania pacifica

The garden chrysanthemum (Chrysanthemum × morifolium) variety ??Aoyunhuoju?? (2n = 6x = 54) was crossed as female with Ajania pacifica (2n = 10x = 90) to produce intergeneric F1 hybrids, which were used both as the source of F₂ generation and as the parent for a first back-cross with ??Aoyunhuoju??. The morphology of all of the F₁ hybrids and hybrid derivatives was intermediate with respect to the two parents, although the BC₁ progenies resembled ??Aoyunhuoju?? more closely than any of the F₁ and F₂ progenies did. In the F₁ generation, the density of silvery hairs on the lower leaf surface and along the margin of the leaf was lower than in A. pacifica, while that in the BC1 generation, this trait was less prominent than in the F₁. The somatic chromosome number of the F₁, F₂ (with an exception of F₂-6 of a mainly 63) and BC1 generations was 2n = 8x = 72, 2n = 8x = 72 and 2n = 7x = 63 respectively, as expected. The hybrids and their derivatives retained a variable degree of fertility. There was a low frequency of meiotic chromosome pairing failure in all three hybrid generations, with most of the chromosomes involved as bivalents. Some BC₁ individuals show potential for commercialization thanks both to their flower shape and the inheritance of the silvery leaf trait from A. pacifica.     

A Semiparametric Estimator of the Crossing Point in the Two‐Sample Linear Shift Function: Application to Crossing Lifetime Distributions

Let X and Y be two random variables with continuous distribution functions F and G. Consider two independent observations X₁, … , X_m from F and Y₁, … , Y_n from G. Moreover, suppose there exists a unique x* such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x* or vice versa. A semiparametric model with a linear shift function (Doksum, 1974) that is equivalent to a location‐scale model (Hsieh, 1995) will be assumed and an empirical process approach (Hsieh, 1995) is used to estimate the parameters of the shift function. Then, the estimated shift function is set to zero, and the solution is defined to be an estimate of the crossing‐point x*. An approximate confidence band of the linear shift function at the crossing‐point x* is also presented, which is inverted to yield an approximate confidence interval for the crossing‐point. Finally, the lifetime of guinea pigs in days observed in a treatment‐control experiment in Bjerkedal (1960) is used to demonstrate our procedure for estimating the crossing‐point. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Data-based optimization of protein production processes

While data-based modeling is possible in various ways, data-based optimization has not been previously described. Here we present such an optimization technique. It is based on dynamic programming principles and uses data directly from exploratory experiments where the influence of the adjustable variables u were tested at various values. Instead of formulating the performance index J as a function of time t within a cultivation process it is formulated as a function of the biomass x. The advantage of this representation is that in most biochemical production processes J(x) only depends of the vector u of the adjustable variables. This given, mathematical programming techniques allow determining the desired optimal paths u _opt (x) from the x-derivatives of J(x). The resulting u _opt (x) can easily be transformed back to the u(t) profiles that can then be used in an improved fermentation run. The optimization technique can easily be explained graphically. With numerical experiments the feasibility of the method is demonstrated. Then, two optimization runs for recombinant protein formations in E. coli are discussed and experimental validation results are presented.     

Letter: Notes on "heat loss from a Newtonian animal"

Parker, Baker &; Smith (1972) have demonstrated mathematically that given the evolution of sexual reproduction, disruptive selection for the production of either many small gametes or a few large gametes may occur, resulting in a stable polymorphism of “sperm” and “egg” producers. Their model for the evolution of anisogamy requires only that zygote fitness (F) increase steeply with increases in zygote volume (V) (for Foc∝ V^x, x must be greater than 1·5) and that a sufficiently broad range of zygote productivity-size variants exist in the population (the higher the value of x, the broader the range needed). They suggest that anisogamy is almost universal in multicellular organisms but relatively rare in unicellular organisms because only for the former is an investment in extra gametic reserves at the expense of the number of gametes produced likely to be worthwhile in terms of increasing the survival probability of the zygote. In this note a graphical analysis and evidence from the anisogamous Protista will be presented concerning this hypothesis.     

Frequency and Fitness Consequences of Bacteriophage Φ6 Host Range Mutations

Viruses readily mutate and gain the ability to infect novel hosts, but few data are available regarding the number of possible host range-expanding mutations allowing infection of any given novel host, and the fitness consequences of these mutations on original and novel hosts. To gain insight into the process of host range expansion, we isolated and sequenced 69 independent mutants of the dsRNA bacteriophage Φ6 able to infect the novel host, Pseudomonas pseudoalcaligenes. In total, we found at least 17 unique suites of mutations among these 69 mutants. We assayed fitness for 13 of 17 mutant genotypes on P. pseudoalcaligenes and the standard laboratory host, P. phaseolicola. Mutants exhibited significantly lower fitnesses on P. pseudoalcaligenes compared to P. phaseolicola. Furthermore, 12 of the 13 assayed mutants showed reduced fitness on P. phaseolicola compared to wildtype Φ6, confirming the prevalence of antagonistic pleiotropy during host range expansion. Further experiments revealed that the mechanistic basis of these fitness differences was likely variation in host attachment ability. In addition, using computational protein modeling, we show that host-range expanding mutations occurred in hotspots on the surface of the phage''s host attachment protein opposite a putative hydrophobic anchoring domain.     

LOCAL ADAPTATION,PHENOTYPIC DIFFERENTIATION,AND HYBRID FITNESS IN DIVERGED NATURAL POPULATIONS OF ARABIDOPSIS LYRATA

Selection for local adaptation results in genetic differentiation in ecologically important traits. In a perennial, outcrossing model plant Arabidopsis lyrata, several differentiated phenotypic traits contribute to local adaptation, as demonstrated by fitness advantage of the local population at each site in reciprocal transplant experiments. Here we compared fitness components, hierarchical total fitness and differentiation in putatively ecologically important traits of plants from two diverged parental populations from different continents in the native climate conditions of the populations in Norway and in North Carolina (NC, U.S.A.). Survival and number of fruits per inflorescence indicated local advantage at both sites and aster life‐history models provided additional evidence for local adaptation also at the level of hierarchical total fitness. Populations were also differentiated in flowering start date and floral display. We also included reciprocal experimental F₁ and F₂ hybrids to examine the genetic basis of adaptation. Surprisingly, the F₂ hybrids showed heterosis at the study site in Norway, likely because of a combination of beneficial dominance effects from different traits. At the NC site, hybrid fitness was mostly intermediate relative to the parental populations. Local cytoplasmic origin was associated with higher fitness, indicating that cytoplasmic genomes also may contribute to the evolution of local adaptation.     

Fitness of natural willow hybrids in a pioneer mosaic hybrid zone

Hybrid fitness is an important parameter to predict the evolutionary consequences of a hybridization event and to characterize hybrid zones. We studied fitness parameters of F₁ and later‐generation hybrids between the lowland species Salix purpurea and the alpine S. helvetica that have recently emerged during colonization of an alpine glacier forefield. Fruit production (number of capsules per catkin and fruit set) did not differ between hybrids and parents, but the number of seeds per capsule of F₁ hybrids was slightly lower than that of later‐generation hybrids and of the parents. Germination rates and seedling growth were tested on three substrates (pH 4.5, 7.0, and 8.0). Germination rates of seeds collected from F₁ hybrids were lower on acid and neutral substrates, but equal at pH 8.0 compared to all other groups, while the seeds from later‐generation hybrids performed as well as the parents on all three substrates. In seedling growth, the colonizer S. purpurea performed better than all other taxa on all three substrates, while hybrids resembled the subalpine species S. helvetica. Results suggest that endogenous selection acts against F₁ hybrids, but favors fitter genotypes in later‐generation hybrids. Exogenous selection via soil pH appears to be weak during seedling establishment. The pioneer vegetation on the glacier forefield may offer sufficient niche space for hybrid seedlings. Owing to the relatively high fitness of the hybrids and the scattered distribution of hybrids and parental individuals on the glacier forefield, this hybrid zone can be assigned to a mosaic model, probably facilitating gene flow and introgression between the parental species. As establishment of the hybrid zone appears to be linked to a colonization process, we propose to call it a pioneer mosaic hybrid zone.     

Estimating Population-Level Coancestry Coefficients by an Admixture F Model

In this article, we develop an admixture F model (AFM) for the estimation of population-level coancestry coefficients from neutral molecular markers. In contrast to the previously published F model, the AFM enables disentangling small population size and lack of migration as causes of genetic differentiation behind a given level of F_ST. We develop a Bayesian estimation scheme for fitting the AFM to multiallelic data acquired from a number of local populations. We demonstrate the performance of the AFM, using simulated data sets and real data on ninespine sticklebacks (Pungitius pungitius) and common shrews (Sorex araneus). The results show that the parameterization of the AFM conveys more information about the evolutionary history than a simple summary parameter such as F_ST. The methods are implemented in the R package RAFM.     

Rangewide population differentiation and population substructure in <Emphasis Type="Italic">Quercus rubra</Emphasis> L.

Genetic diversity and differentiation in Quercus rubra remains undescribed for most of the native range. Using 10 highly informative gSSR markers, we genotyped 23 populations (980 trees), from across the native range, at local and rangewide spatial scales. We used a hierarchical Bayesian method to generate population-specific F _st estimates. The posterior probabilities of 3 spatial and 19 climate factors revealed that latitude and precipitation in the warmest quarter were the only plausible models for population-specific F _st estimates. Population-specific F _st estimates increased as a linear function of population latitude (R ² = 0.745, p < 0.0001), the expected effect of postglacial range expansion. Measures of shared ancestry (pairwise local differentiation) among populations sampled at fine spatial scales within locations also increased with the latitude of the location (R ² = 0.495, p = 0.014), suggesting an influence on differentiation that could not be attributed to postglacial range expansion. As precipitation in the warmest quarter drives radial growth rate in this species, we propose that growth rate influences generation time, which determines the time required to re-establish migration-drift equilibrium among local regenerating stands. Population substructure analysis detected four groups, only one of which was geographically coherent. Most other populations were moderately admixed. Sampling designs that include both fine and coarse spatial scales can begin to disentangle the effect of past range expansions from the effect of recent disturbances. Accounting for population substructure in this species will require additional studies involving functional genes, interspecific interactions, and species distribution modeling.     

ANTIBIOTIC RESISTANCE AND STRESS IN THE LIGHT OF FISHER'S MODEL

The role of mutations in evolution depends upon the distribution of their effects on fitness. This distribution is likely to depend on the environment. Indeed genotype‐by‐environment interactions are key for the process of local adaptation and ecological specialization. An important trait in bacterial evolution is antibiotic resistance, which presents a clear case of change in the direction of selection between environments with and without antibiotics. Here, we study the distribution of fitness effects of mutations, conferring antibiotic resistance to Escherichia coli, in benign and stressful environments without drugs. We interpret the distributions in the light of a fitness landscape model that assumes a single fitness peak. We find that mutation effects (s) are well described by a shifted gamma distribution, with a shift parameter that reflects the distance to the fitness peak and varies across environments. Consistent with the theoretical predictions of Fisher's geometrical model, with a Gaussian relationship between phenotype and fitness, we find that the main effect of stress is to increase the variance in s. Our findings are in agreement with the results of a recent meta‐analysis, which suggest that a simple fitness landscape model may capture the variation of mutation effects across species and environments.     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.