A structured-population model of Proteus mirabilis swarm-colony development

In this paper we present continuous age- and space-structured models and numerical computations of Proteus mirabilis swarm-colony development. We base the mathematical representation of the cell-cycle dynamics of Proteus mirabilis on those developed by Esipov and Shapiro, which are the best understood aspects of the system, and we make minimum assumptions about less-understood mechanisms, such as precise forms of the spatial diffusion. The models in this paper have explicit age-structure and, when solved numerically, display both the temporal and spatial regularity seen in experiments, whereas the Esipov and Shapiro model, when solved accurately, shows only the temporal regularity. The composite hyperbolic-parabolic partial differential equations used to model Proteus mirabilis swarm-colony development are relevant to other biological systems where the spatial dynamics depend on local physiological structure. We use computational methods designed for such systems, with known convergence properties, to obtain the numerical results presented in this paper.     

Chemotactic collapse for the Keller-Segel model

 This work is concerned with the system (S) {u _t =Δu − χ∇ (u∇v) for x∈Ω, t>0Γ v _t =Δv+(u−1) for x∈Ω, t>0 where Γ, χ are positive constants and Ω is a bounded and smooth open set in ℝ². On the boundary ∂Ω, we impose no-flux conditions: (N) ∂u∂n =∂v∂n =0 for x∈∂ Ω, t>0 Problem (S), (N) is a classical model to describe chemotaxis corresponding to a species of concentration u(x, t) which tends to aggregate towards high concentrations of a chemical that the species releases. When completed with suitable initial values at t=0 for u(x, t), v(x, t), the problem under consideration is known to be well posed, locally in time. By means of matched asymptotic expansions techniques, we show here that there exist radial solutions exhibiting chemotactic collapse. By this we mean that u(r, t) →Aδ(y) as t→T for some T<∞, where A is the total concentration of the species. Received 9 March 1995; received in revised form 25 December 1995     

Probing the role of structural features of mouse PrP in yeast by expression as Sup35-PrP fusions

The yeast Saccharomyces cerevisiae is a tractable model organism in which both to explore the molecular mechanisms underlying the generation of disease-associated protein misfolding and to map the cellular responses to potentially toxic misfolded proteins. Specific targets have included proteins which in certain disease states form amyloids and lead to neurodegeneration. Such studies are greatly facilitated by the extensive ‘toolbox’ available to the yeast researcher that provides a range of cell engineering options. Consequently, a number of assays at the cell and molecular level have been set up to report on specific protein misfolding events associated with endogenous or heterologous proteins. One major target is the mammalian prion protein PrP because we know little about what specific sequence and/or structural feature(s) of PrP are important for its conversion to the infectious prion form, PrP^Sc. Here, using a study of the expression in yeast of fusion proteins comprising the yeast prion protein Sup35 fused to various regions of mouse PrP protein, we show how PrP sequences can direct the formation of non-transmissible amyloids and focus in particular on the role of the mouse octarepeat region. Through this study we illustrate the benefits and limitations of yeast-based models for protein misfolding disorders.     

Spreading speeds as slowest wave speeds for cooperative systems

It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models have the same property, we are unaware of any proof to support this belief. The present work establishes this result for a class of multi-species model of a kind studied by Lui [Biological growth and spread modeled by systems of recursions. I: Mathematical theory, Math. Biosci. 93 (1989) 269] and generalized by the authors [Weinberger et al., Analysis of the linear conjecture for spread in cooperative models, J. Math. Biol. 45 (2002) 183; Lewis et al., Spreading speeds and the linear conjecture for two-species competition models, J. Math. Biol. 45 (2002) 219]. Lui showed the existence of a single spreading speed c(*) for all species. For the systems in the two aforementioned studies by the authors, which include related continuous-time models such as reaction-diffusion systems, as well as some standard competition models, it sometimes happens that different species spread at different rates, so that there are a slowest speed c(*) and a fastest speed c(f)(*). It is shown here that, for a large class of such multi-species systems, the slowest spreading speed c(*) is always characterized as the slowest speed of a class of traveling wave solutions.     

Controlling the prion propensity of glutamine/asparagine-rich proteins

ABSTRACT

The yeast Saccharomyces cerevisiae can harbor a number of distinct prions. Most of the yeast prion proteins contain a glutamine/asparagine (Q/N) rich region that drives prion formation. Prion-like domains, defined as regions with high compositional similarity to yeast prion domains, are common in eukaryotic proteomes, and mutations in various human proteins containing prion-like domains have been linked to degenerative diseases, including amyotrophic lateral sclerosis. Here, we discuss a recent study in which we utilized two strategies to generate prion activity in non-prion Q/N-rich domains. First, we made targeted mutations in four non-prion Q/N-rich domains, replacing predicted prion-inhibiting amino acids with prion-promoting amino acids. All four mutants formed foci when expressed in yeast, and two acquired bona fide prion activity. Prion activity could be generated with as few as two mutations, suggesting that many non-prion Q/N-rich proteins may be just a small number of mutations from acquiring aggregation or prion activity. Second, we created tandem repeats of short prion-prone segments, and observed length-dependent prion activity. These studies demonstrate the considerable progress that has been made in understanding the sequence basis for aggregation of prion and prion-like domains, and suggest possible mechanisms by which new prion domains could evolve.     

An age-and-cyclin-structured cell population model for healthy and tumoral tissues

We present a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments. The proliferative phase represents the complete cell cycle (G ₁−S−G ₂−M) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of Cyclin D/(CDK4 or 6) complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in two cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated and its analytic predictions are confirmed numerically.     

Functional Analysis of the Thioredoxin Domain in Porphyromonas gingivalis HBP35

Periodontitis is one of the most common oral diseases in humans. This caused by infection by the oral bacterium Porphyromonas gingivalis. Our strategy to prevent this infection is to establish a passive immunization system in which endogenous antibodies can be applied directly to neutralize virulent factors associated with this bacterium. We focused our attention on the P. gingivalis 35 kDa surface protein, or HBP35, since this protein is involved not only in the coaggregation with oral miroflora but also in hemin binding. In addition, nucleotide sequencing of the gene, hbp35, coding for this protein revealed the presence of a catalytic center for thioredoxin, and we further attempted to characterized the protein by amino acid substitution. A total of four Cys residues were substituted for Ser residues by combining the simple method for site-directed mutagenesis and the heterodimer system, an approach designed to construct chimeric plasmids readily. Native and mutagenized hbp35 were introduced into the Eschericha coli dsbA mutant strain, JCB 572, defective in both alkaline phosphatase and motile activities due to inefficient disulfide bond formation. Transformant harboring the native hbp35 could complement the dsbA mutation, suggesting a role of disulfide bond formation of this protein in P. gingivalis cells. Possible roles of the Cys residues in complementation are discussed.     

Parameter estimation techniques for interaction and redistribution models: a predator-prey example

Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.     

Priority of color over scent during flower visitation by adult <Emphasis Type="Italic">Vanessa indica</Emphasis> butterflies

Most flower visitors innately prefer a particular color and scent, and use them as cues for flower recognition and selection. However, in most cases, since color and scent serve as a combined signal, not only does the preference for an individual cue, but also the preference hierarchy among different cues, influence their flower visitation. In the present study, we attempted to reveal (1) the chromatic and (2) the olfactory cues that stimulate flower visiting, and (3) the preference hierarchy between these cues, using the naïve adult butterfly Vanessa indica. When we offered 12 different-colored (six chromatic and six achromatic) paper flower models, V. indica showed a color preference for yellow and blue. When we examined the proboscis extension reflex (PER) of V. indica towards 16 individual compounds identified in the floral scents from two nectar plants belonging to the family Compositae, Taraxacum officinale and Cirsium japonicum, six compounds were found to have relatively high PER-eliciting activities, including benzaldehyde, acetophenone, and (E+Z)-nerolidol. When we combined color and scent cues in two-choice bioassays, where butterflies were offered flower models that were purple (a relatively unattractive color), the models scented with these active compounds were significantly more attractive than the odorless controls. In addition, synthetic blends mimicking the floral scents of T. officinale and C. japonicum (at doses equivalent to that of ten flowers) enhanced the number of visits to the scented models. However, the effect of odorizing was not conspicuous in parallel bioassays when yellow flower models were used, and the butterflies also significantly preferred odorless yellow models to scented purple models. These results demonstrate that V. indica depends primarily on color and secondarily on scent during flower visitation.     

Besetzungsmodelle

Starting with the classical occupancy with boxes, balls and probabilities for occupying boxes, we employ new models: a ball, which met a box, occupies this box with a probability depending on the size of box content, and - using several kinds of balls - by the composition of the content too. For that purpose several models are constructed with distinctive forms of the conditions. Dealing with these models - they are special MARKO vian chains - we pay attention mainly to the so called first passage time T_z for defined events Z; in particular for certain events Z we have to prove that T_z is a random variable, and have to set up the appropriate probability generating function.     

The distribution of <Emphasis Type="Italic">F</Emphasis><Subscript><Emphasis Type="Italic">st</Emphasis></Subscript> and other genetic statistics for a class of population structure models

We examine genetic statistics used in the study of structured populations. In a 1999 paper, Wakeley observed that the coalescent process associated with the finite island model can be decomposed into a scattering phase and a collecting phase. This decomposition becomes exact in the large population limit with the coalescent at the end of the scattering phase converging to the Ewens sampling formula and the coalescent during the collecting phase converging to the Kingman coalescent. In this paper we introduce a class of limiting models, which we refer to as G/KC models, that generalize Wakeley’s decomposition. G in G/KC represents a completely general limit for the scattering phase, while KC represents a Kingman coalescent limit for the collecting phase. We show that both the island and two-dimensional stepping stone models converge to G/KC models in the large population limit. We then derive the distribution of the statistic F _st for all G/KC models under a large sample limit for the cases of strong or weak mutation, thereby deriving the large population, large sample limiting distribution of F _st for the island and two-dimensional stepping stone models as a special case of a general formula. Our methods allow us to take the large population and large sample limits simultaneously. In the context of large population, large sample limits, we show that the variance of F _st in the presence of weak mutation collapses as O(\frac1logd){O(\frac{1}{\log d})} where d is the number of demes sampled. Further, we show that this O(\frac1logd){O(\frac{1}{\log d})} is caused by a heavy tail in the distribution of F _st . Our analysis of F _st can be extended to an entire class of genetic statistics, and we use our approach to examine homozygosity measures. Our analysis uses coalescent based methods.     

Evaluating niche changes during invasion with seasonal models in Capsella bursa-pastoris

Premise

Researchers often use ecological niche models to predict where species might establish and persist under future or novel climate conditions. However, these predictive methods assume species have stable niches across time and space. Furthermore, ignoring the time of occurrence data can obscure important information about species reproduction and ultimately fitness. Here, we assess compare ecological niche models generated from full-year averages to seasonal models.

Methods

In this study, we generate full-year and monthly ecological niche models for Capsella bursa-pastoris in Europe and North America to see if we can detect changes in the seasonal niche of the species after long-distance dispersal.

Results

We find full-year ecological niche models have low transferability across continents and there are continental differences in the climate conditions that influence the distribution of C. bursa-pastoris. Monthly models have greater predictive accuracy than full-year models in cooler seasons, but no monthly models can predict North American summer occurrences very well.

Conclusions

The relative predictive ability of European monthly models compared to North American monthly models suggests a change in the seasonal timing between the native range to the non-native range. These results highlight the utility of ecological niche models at finer temporal scales in predicting species distributions and unmasking subtle patterns of evolution.     

Process-based species delimitation leads to identification of more biologically relevant species*

Most approaches to species delimitation to date have considered divergence-only models. Although these models are appropriate for allopatric speciation, their failure to incorporate many of the population-level processes that drive speciation, such as gene flow (e.g., in sympatric speciation), places an unnecessary limit on our collective understanding of the processes that produce biodiversity. To consider these processes while inferring species boundaries, we introduce the R-package delimitR and apply it to identify species boundaries in the reticulate taildropper slug (Prophysaon andersoni). Results suggest that secondary contact is an important mechanism driving speciation in this system. By considering process, we both avoid erroneous inferences that can be made when population-level processes such as secondary contact drive speciation but only divergence is considered, and gain insight into the process of speciation in terrestrial slugs. Further, we apply delimitR to three published empirical datasets and find results corroborating previous findings. Finally, we evaluate the performance of delimitR using simulation studies, and find that error rates are near zero when comparing models that include lineage divergence and gene flow for three populations with a modest number of Single Nucleotide Polymorphisms (SNPs; 1500) and moderate divergence times (<100,000 generations). When we apply delimitR to a complex model set (i.e., including divergence, gene flow, and population size changes), error rates are moderate (∼0.15; 10,000 SNPs), and, when present, misclassifications occur among highly similar models.     

Evaluation in tobacco of the organ specificity and strength of therolD promoter,domain A of the 35S promoter and the 35S2 promoter

In order to study the expression in plants of therolD promoter ofAgrobacterium rhizogenes, we have constructed chimaeric genes placing the coding region of thegusA (uidA) marker gene under control of tworolD promoter fragments of different length. Similar results were obtained with both genes. Expression studies were carried out in transformed R₁ progeny plants. In mature transformed tobacco plants, therolD-gus genes were expressed strongly in roots, and to much lower levels in stems and leaves. This pattern of expression was transmitted to progeny, though the ratio of the level of expression in roots relative to that in leaves was much lower in young seedlings. The degree of root specificity inrolD-gus transformants was less than that of a gene constructed with domain A of the CaMV 35S promoter,domA-gus, but the level of root expression was much higher than with the latter gene. However, the level of expression of therolD-gus genes was less than that of agus gene with a 35S promoter with doubled domain B, 35S²-gus. TherolD-gus genes had a distinctive pattern of expression in roots, compared to that of the two other genes, with the strongest GUS activity observed in the root elongation zone and in vascular tissue, and much less in the root apex.     

The Secondary Structure of Mammalian Mitochondrial 16S rRNA Molecules: Refinements Based on a Comparative Phylogenetic Approach

Eighty six complete 16S ribosomal RNA (rRNA) gene sequences representing every mammalian order (one monotreme, 33 marsupials, 52 placentals) were employed to establish a core secondary structure model for mammalian 16S rRNA. Starting with the Gutell et al. (1993) and De Rijk et al. (1999) models, we used the criteria of potential base-pairing and positional covariance to make refinements in these models for mammalian 16S rRNA molecules. Our results suggest a mammalian secondary structure model with deletions as well as additions to the Gutell et al. (1993) and De Rijk et al. (1999) models for cow. We recognize 53 stems, 41 of which show at least some positional covariance within Mammalia. In addition, we recognize four tertiary interactions. Stems and loops have distinctly different properties, including base composition and relative substitution rates. Accounting for these differences results in improved models of sequence evolution.     

Invertebrate models of lysosomal storage disease: what have we learned so far?

The lysosomal storage diseases (LSDs) collectively account for death in 1 in 8,000 children. Although some forms are treatable, they are essentially incurable and usually are lethal in the first decade of life. The most intractable forms of LSD are those with neuronal involvement. In an effort to identify the pathological signaling driving pathology in the LSDs, invertebrate models have been developed. In this review, we outline our current understanding of LSDs and recent findings using invertebrate models. We outline strategies and pitfalls for the development of such models. Available models of LSD in Drosophila and Caenorhabditis elegans are uncovering roles for LSD-related proteins with previously unknown function using both gain-of-function and loss-of-function strategies. These models of LSD in Drosophila and C. elegans have identified potential pathogenic signaling cascades that are proving critical to our understanding of these lethal diseases.     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

Ordinal response regression models in ecology

Abstract. Although ordinal data are not rare in ecology, ecological studies have, until now, seriously neglected the use of specific ordinal regression models. Here, we present three models – the Proportional Odds, the Continuation Ratio and the Stereotype models – that can be successfully applied to ordinal data. Their differences and respective fields of application are discussed. Finally, as an example of application, PO models are used to predict spatial abundance of plant species in a Geographical Information System. It shows that ordinal models give as good a result as binary logistic models for predicting presence‐absence, but are additionally able to predict abundance satisfactorily.