Barriers to diffusion in dendrites and estimation of calcium spread following synaptic inputs

The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as D_cyto/D_water = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm).     

Beyond Bt resistance of pests in the context of population dynamical complexity

Complexity in ecological systems often prevents long-term predictions about changes in population size and properties of the population dynamics. Mathematical modeling of such complex system behaviors can provide a rough idea of scenarios of the population dynamics. We use the reaction–diffusion model [Medvinsky, A.B., Morozov, A.Y., Velkov, V.V., Li, B.-L., Sokolov, M.S., Malchow, H., 2004. Modeling the invasion of recessive Bt-resistant insects: an impact on transgenic plants. J. Theor. Biol. 231, 121–127] to study the impact of pests resistant to toxins produced by genetically modified plants on the dynamics of the plant–insect system. Using genetically modified crops is an effective pest management tool for world-wide growers. However, there is a concern that pests may develop resistance to Bt toxins, which are a product of Bacillus thuringiensis genes introduced into genetically modified Bt plants. We show by computer simulations that the Bt plant–Bt-resistant insect dynamics resulting from the invasion of the Bt-resistant pests leads to variety of complex changes in the plant–insect biomass, which underlie the dependence of the Bt plant biomass on the duration of the insect reproduction period. We demonstrate that the plant and insect biomass can undergo both regular and irregular oscillations. We show that the character of such oscillations essentially depends on local insect fluxes resulting from inhomogeneous spatial distributions of the insects. In order to characterize the insect diffusion fluxes we introduce a new parameter, the diffusion number Dn. We show that the dependence between a value of Dn and regularity/irregularity of the plant–insect biomass oscillations is governed by a region in the model parameter space. In one of the regions the growth of the value of the diffusion number correlates with the transformation of regular oscillations into irregular ones, while in the neighboring region of the model parameter space the dependence between the character of the plant–insect oscillations and the value of the diffusion number Dn is more complex. The oscillations are irregular if the values of Dn are between 0.05 and 0.25. On either side of this interval the plant–insect oscillations are regular. The complex character of the response of the Bt crop–pest system to the invasion of Bt-resistant insects can lead to significant complications in attempts to regulate the system dynamics.     

Pollination biology and breeding system in five nocturnal species of <Emphasis Type="Italic">Oenothera</Emphasis> (Onagraceae): reproductive assurance and opportunities for outcrossing

The capacity to produce seed, both by selfing and outcrossing, or mixed mating strategies, is considered a mechanism for overcoming unpredictable pollinator availability. In the present study, we investigate breeding system, insect visitations and the role of insect visitors in the pollination of five species of Oenothera subsect. Oenothera. Field experiments showed that autonomous selfing occurs at bud stage, prior to the opening of the flower. Control flowers showed similar seed set to hand-pollinated flowers, whereas emasculated flowers and those subject to open pollination set fewer seed. These results are consistent with the hypothesis that the investigated Oenothera exhibit a great capacity for autonomous selfing and that selfing is selected in order to provide reproductive assurance. Although flowers were visited mostly by nocturnal lepidopterans, these insects did not precipitate pollination and are thus considered nectar thieves. Conversely, analysis of pollen loads and behavior during foraging by diurnal insect visitors revealed that honeybees and bumblebees are the probable pollinators. We conclude that production of flowers capable of autonomous selfing at bud stage, followed by anthesis and opportunities for outcrossing, probably improves the invasive potential of these Oenothera in Europe, together with a rapid increase in their populations, even when pollinators are scarce.     

A mathematical model of mucilage expansion in myxospermous seeds of Capsella bursa-pastoris (shepherd's purse)

Background and Aims

Myxospermy is a term which describes the ability of a seed to produce mucilage upon hydration. The mucilage is mainly comprised of plant cell-wall polysaccharides which are deposited during development of those cells that comprise the seed coat (testa). Myxospermy is more prevalent among those plant species adapted to surviving on arid sandy soils, though its significance in determining the ecological fitness of plants is unclear. In this study, the first mathematical model of myxospermous seed mucilage expansion is presented based on seeds of the model plant species Capsella bursa-pastoris (shepherd''s purse).

Methods

The structures underpinning the expansion process were described using light, electron and time-lapse confocal micrographs. The data and experimental observations were used to create a mathematical model of myxospermous seed mucilage expansion based on diffusion equations.

Key Results

The mucilage expansion was rapid, taking 5 s, during which the cell mucilage volume increased 75-fold. At the level of the seed, this represented a 6-fold increase in seed volume and a 2·5-fold increase in seed surface area. These increases were shown to be a function of water uptake (16 g water g⁻¹ mucilage dry weight), and relaxation of the polymers which comprised the mucilage. In addition, the osmotic pressure of the seed mucilage, estimated by assessing the mucilage expansion of seeds hydrated in solutions of varying osmotic pressure, was –0·54 MPa (equivalent to 0·11 m or 6·6 g L⁻¹ NaCl).

Conclusions

The results showed that the mucilage may be characterized as hydrogel and seed-mucilage expansion may be modelled using the diffusion equation described. The potential of myxospermous seeds to affect the ecological services provided by soil is discussed briefly.     

Spatial patterns and travelling waves in population genetics.

We consider a reaction-diffusion equation to model a multi-allelic, single locus problem. The population can migrate in a homogeneous region and the diffusion rates depend upon the genotype. It is shown that if there is an equilibrium point with all alleles present and if this polymorphism is stable for the classical reaction system then it is also stable for the reaction-diffusion equation. Also a simplified model is used to investigate which allele will spread in the two-allele case. Alleles which are associated with large fitness and small dispersion do best.     

Chemical constituents of the seeds of Ammopiptanthus (Leguminosae) and their systematic and ecological significance

Eleven flavonoids including a new flavone glycoside, 7,3′-dihydroxy-4′-methoxyflavone-7-O-β-glucopyranoside, and a quinolizidine alkaloid, lupanine, were isolated from the seeds of two Ammopiptanthus (Leguminosae) species, Ammopiptanthus mongolicus and Ammopiptanthus nanus. 7,3′-Dihydroxy-4′-methoxyflavone and lupanine were the major constituents in the seeds of both species. The patterns of seed flavonoids presented a clear systematic relationship between the two species. The simple seed alkaloid composition was presumed to be responsible for the weak defense capability of the seeds to insect pests in both species.     

Formation of the insect head involves lateral contribution of the intercalary segment, which depends on Tc-labial function

The insect head is composed of several segments. During embryonic development, the segments fuse to form a rigid head capsule where obvious segmental boundaries are lacking. Hence, the assignment of regions of the insect head to specific segments is hampered, especially with respect to dorsal (vertex) and lateral (gena) parts. We show that upon Tribolium labial (Tc-lab) knock down, the intercalary segment is deleted but not transformed. Furthermore, we find that the intercalary segment contributes to lateral parts of the head cuticle in Tribolium. Based on several additional mutant and RNAi phenotypes that interfere with gnathal segment development, we show that these segments do not contribute to the dorsal head capsule apart from the dorsal ridge. Opposing the classical view but in line with findings in the vinegar fly Drosophila melanogaster and the milkweed bug Oncopeltus fasciatus, we propose a “bend and zipper” model for insect head capsule formation.     

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0<x<L(t), where L(t) is the length of the growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).     

mRNA diffusion explains protein gradients in Drosophila early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of Drosophila. In this model, we consider that bicoid mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11-14 of the developing embryo of Drosophila. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of bicoid mRNA is in the range , in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of bicoid mRNA in Drosophila [Spirov et al. (2009). Development 136, 605-614].     

Multi-scale methods predict invasion speeds in variable landscapes

Spread rates of invasive plant species depend heavily on variable seed/seedling survivorships over various habitat types as well as on variability in seed dispersal induced by rapid transport of propagules in open areas and slow transport in vegetated areas. The ability to capture spatial variability in seed survivorship and dispersal is crucial to accurately predict the rate of spread of plants in real world landscapes. However, current analytic methods for predicting spread rates are not suited for arbitrary, spatially heterogeneous systems. Here, we analyze invasion rates of the invasive plant Phragmites australis (common reed) over variable wetland landscapes. Phragmites is one of the most pervasive perennial grasses, outcompeting native vegetation, providing poor wildlife habitat, and proving difficult to eradicate across its invasive range in North America. Phragmites spreads sexually via seeds and asexually via underground (rhizomes) and aboveground (stolons) stems. We construct a structured integrodifference equation model of the Phragmites life cycle capturing variable seed survivorship in a seed bank, sexual and asexual recruitment into a juvenile age class, and differential competition among all classes with adults. The demographic model is coupled with a homogenized ecological diffusion/settling seed dispersal model that allows for seed deposition that varies with habitat type. The dispersal kernel we develop does not require local normalization and can be implemented efficiently using standard computational techniques. The model generates a traveling wave of isolated patches, establishing only in suitable habitats. We use the method of multiple scales to predict invasion speed as a solvability condition at large scales and test the predictions numerically. Accurate predictions are generated for a wide range of landscape parameters, indicating that invasion speeds can be understood in landscapes of arbitrary structure using this approach.     

Effect of insect cadaver desiccation and soil water potential during rehydration on entomopathogenic nematode (Rhabditida: Steinernematidae and Heterorhabditidae) production and virulence

We examined the influence of insect cadaver desiccation on the virulence and production of entomopathogenic nematodes (EPNs), common natural enemies of many soil-dwelling insects. EPNs are often used in biological control, and we investigated the feasibility of applying EPNs within desiccated insect cadavers. Desiccation studies were conducted using the factitious host, Galleria mellonella (Lepidoptera: Pyralidae, wax moth larvae) and three EPN species (Heterorhabditis bacteriophora ‘HB1’, Steinernema carpocapsae ‘All’, and Steinernema riobrave). Weights of individual insect cadavers were tracked daily during the desiccation process, and cohorts were placed into emergence traps when average mass losses reached 50%, 60%, and 70% levels. We tracked the proportion of insect cadavers producing infective juveniles (IJs), the number and virulence of IJs produced from desiccated insect cadavers, and the influence of soil water potentials on IJ production of desiccated insect cadavers. We observed apparent differences in the desiccation rate of the insect cadavers among the three species, as well as apparent differences among the three species in both the proportion of insect cadavers producing IJs and IJ production per insect cadaver. Exposure of desiccated insect cadavers to water potentials greater than −2.75 kPa stimulated IJ emergence. Among the nematode species examined, H. bacteriophora exhibited lower proportions of desiccated insect cadavers producing IJs than the other two species. Desiccation significantly reduced the number of IJs produced from insect cadavers. At the 60% mass loss level, however, desiccated insect cadavers from each of the three species successfully produced IJs when exposed to moist sand, suggesting that insect cadaver desiccation may be a useful approach for biological control of soil insect pests.     

Functional interpretation of APN receptor from M.sexta using a molecular model

Insect pests are the major cause of damage to commercially important agricultural crops. The continuous application of synthetic pesticides resulted in severe insect resistance by plants. This causes irreversible damage to the environment. Bacillus thuringiensis (Bt) emerged as a valuable biological alternative in pest control. However, insect resistance against Bt has been reported in many cases. Insects develop resistance to insecticides through mechanisms that reduce the binding of toxins to gut receptors. Nonetheless, the molecular mechanism of insect resistance is not fully understood. Therefore, it is important to study the mechanism of toxin resistance by analyzing amino‐peptidase‐N (APN) receptor of the insect M. sexta. A homology model of APN was constructed using Insight II molecular modeling software and the model was further evaluated using the PROCHECK program. Oligosaccharides participating in post translational modification were constructed and docked onto specific APN functional sites. Post analyses of the APN model provide insights on the functional properties of APN towards the understanding of receptor and toxin interactions. We also discuss the predicted binding sites for ligands, metals and Bt toxins in M. sexta APN receptor. These data help in the development of a roadmap for the design and synthesis of novel insect resistant Cry toxins.     

Cotton Root Protection from Plant-Parasitic Nematodes by Abamectin-Treated Seed

Abamectin is nematicidal to Meloidogyne incognita and Rotylenchulus reniformis, but the duration and length of cotton taproot protection from nematode infection by abamectin-treated seed is unknown. Based on the position of initial root-gall formation along the developing taproot from 21 to 35 d after planting, infection by M. incognita was reduced by abamectin seed treatment. Penetration of developing taproots by both nematode species was suppressed at taproot length of 5 cm by abamectin-treated seed, but root penetration increased rapidly with taproot development. Based on an assay of nematode mobility to measure abamectin toxicity, the mortality of M. incognita associated with a 2-d-old emerging cotton radicle was lower than mortality associated with the seed coat, indicating that more abamectin was on the seed coat than on the radicle. Thus, the limited protection of early stage root development suggested that only a small portion of abamectin applied to the seed was transferred to the developing root system.     

An alternative insect pathogenic strategy in an Aspergillus flavus auxotroph

In order to study fungal pathogen evolution, we used a model system whereby the opportunistic fungus Aspergillus flavus was serially propagated through the insect (Galleria mellonella) larvae, yielding a cysteine/methionine auxotroph of A. flavus with properties of an obligate insect pathogen. The auxotroph exhibited insect host restriction but did not show any difference in virulence when compared with the wild-type (Scully LR, Bidochka MJ, 2006. Microbiology 152, 223-232). Here, we report that on 1 % insect cuticle medium and synthetic Galleria medium, the auxotroph displayed increased extracellular protease production, a virulence factor necessary for insect pathogenesis. In the wild-type strain, protease production was deregulated during carbon (glucose), nitrogen (nitrate), or sulphate deprivation. If all three were present, protease production was vastly reduced. However, in the cysteine/methionine auxotroph, protease production was deregulated in complete medium. We suggest that the deficiency in sulphate assimilation in the auxotroph resulted in deregulation of protease production. The auxotroph exhibited delayed germination and slower hyphal growth when compared to the wild-type but there were no differences in virulence or cuticle penetration, suggesting a shift in pathogenic strategy that compensated decreased growth with increased virulence factor (extracellular protease) production. We concluded that the biosynthetic deficiency that mediated insect host restriction also increased protease production in the slow-growing auxotroph, resulting in an alternate, more host-specific pathogenic strategy. However, we argue that transmission is not necessarily correlated with virulence as competition bioassays in insect larvae showed that the wild-type generally out-competed the auxotroph by producing the majority of the conidia on the sporulating cadavers. This is one of the few examples that highlight the effect of genome decay on nutrition acquisition, virulence, and transmission in fungal pathogen evolution.     

铁皮石斛种子的室内共生萌发

由于人为的采挖和原生境的破坏,使得铁皮石斛野生资源已濒临灭绝。因此,保护铁皮石斛野生资源及其生境,加快其野生资源的繁殖显得非常重要。以铁皮石斛种子(TTC染色显示种子生活力为77.65%)为材料,与分离自2种野生兰科植物根部的4株共生真菌 (C20来自铁皮石斛,L12,L24b 和 L28来自美花石斛)在燕麦培养基上进行共生萌发。经过18周的共生培养,4株真菌均不同程度地促进了铁皮石斛种子的萌发,其中菌株L24b (Epulorhiza)和L28 (Epulorhiza)显著提高了种子的萌发率,分别比对照高出26.51%和12.20%,但未形成幼苗,只是处于原生分生组织阶段(阶段3);菌株C20(Epulorhiza)和L12 (Alternaria) 虽没有显著提高种子的萌发率,但对原球茎的发育和幼苗的生长有明显的促进作用;而对照的种子仍然处于膨大转绿期,即萌发阶段(阶段2)。同时发现,TTC染色显示的铁皮石斛种子生活力要高于种子共生萌发的萌发率(除了菌株L24b)。研究结果表明:种子生活力染色检测的活力值只代表种子所具有的潜在的萌发能力,而不能代表实际的萌发率。在异地条件下,铁皮石斛与共生真菌间没有严格的专一性,可以与瘤菌根菌属、链格孢属真菌形成共生关系。菌株C20和L12能促进萌发后的种子进一步分化成幼苗。这两个菌株为铁皮石斛的人工优质栽培和野外种群的建立提供了可能。     

A spatial model of the development of pest resistance to a transgenic insecticidal crop: European corn borer on Bt maize

A mathematical model was constructed to describe the evolution of resistance to the Bacillus thuringiensis toxin (Bt) in an insect pest (European corn borer) population on a transgenic crop (Bt corn). The model comprises a set of partial differential equations of the reaction-diffusion type; local interactions of three competing pest genotypes formed by alleles of Bt resistance and susceptibility are described as in the Kostitzin model, and the spread of insects is modeled as diffusion. The model was used to evaluate the influence of pest characteristics on the efficacy of the high-dose/refuge strategy aiming to prevent or delay the spread of Bt resistance in pest populations. It was shown, by contrast, that a model based on Fisher-Haldane-Wright equations and formally incorporating a diffusion term cannot adequately describe the evolution of Bt resistance in a spatially inhomogeneous pest population. Further development of the proposed demo-genetic model is discussed.     

The finite element implementation of a K.P.P. equation for the simulation of tsetse control measures in the vicinity of a game reserve

An equation, strongly reminiscent of Fisher’s equation, is used to model the response of tsetse populations to proposed control measures in the vicinity of a game reserve. The model assumes movement is by diffusion and that growth is logistic. This logistic growth is dependent on an historical population, in contrast to Fisher’s equation which bases it on the present population. The model therefore takes into account the fact that new additions to the adult fly population are, in actual fact, the descendents of a population which existed one puparial duration ago, furthermore, that this puparial duration is temperature dependent. Artificially imposed mortality is modelled as a proportion at a constant rate. Fisher’s equation is also solved as a formality.The temporary imposition of a 2 % day⁻¹ mortality everywhere outside the reserve for a period of 2 years will have no lasting effect on the influence of the reserve on either the Glossina austeni or the G. brevipalpis populations, although it certainly will eradicate tsetse from poor habitat, outside the reserve. A 5 km-wide barrier with a minimum mortality of 4 % day⁻¹, throughout, will succeed in isolating a worst-case, G. austeni population and its associated trypanosomiasis from the surrounding areas. A more optimistic estimate of its mobility suggests a mortality of 2 % day⁻¹ will suffice. For a given target-related mortality, more mobile species are found to be more vulnerable to eradication than more sedentary species, while the opposite is true for containment.