Effects of long-range taxis and population pressure on the range expansion of invasive species in heterogeneous environments

We consider a new model for biological invasions in periodic patchy environments, in which long-range taxis and population pressure are incorporated in the framework of reaction-diffusion-advection equations. We assume that long-range taxis is induced by a weighted integral of stimuli within a certain sensing range. Population pressure is incorporated in the diffusion coefficient that linearly increases with population density. We first analyze the model in the absence of population pressure and demonstrate how the sensing length of long-range taxis influences the range expansion pattern of invasive species and its rate of spread. The effects of population pressure are examined for both homogeneous and periodic patchy environments. For the homogeneous environment, an exact and explicit traveling wave solution and the spreading speed are obtained. For the periodic patchy environment, we find numerically that a population starting from any localized distribution evolves to a traveling periodic wave if the null solution of the RDA equation is locally unstable, and that the traveling wave speed significantly increases with increasing population pressure. Furthermore, the population pressure and taxis intensity synergistically enhance the spreading speed when they are increased together.     

Traveling wave solutions in a plant population model with a seed bank

We propose an integro-difference equation model to predict the spatial spread of a plant population with a seed bank. The formulation of the model consists of a nonmonotone convolution integral operator describing the recruitment and seed dispersal and a linear contraction operator addressing the effect of the seed bank. The recursion operator of the model is noncompact, which poses a challenge to establishing the existence of traveling wave solutions. We show that the model has a spreading speed, and prove that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions by using an asymptotic fixed point theorem. Our numerical simulations show that the seed bank has the stabilizing effect on the spatial patterns of traveling wave solutions.     

Entry of herpes simplex virus 1 in BJ cells that constitutively express viral glycoprotein D is by endocytosis and results in degradation of the virus.

The BJ cell line which constitutively expresses herpes simplex virus 1 glycoprotein D is resistant to infection with herpes simplex viruses. Analysis of clonal lines indicated that resistance to superinfecting virus correlates with the expression of glycoprotein D. Resistance was not due to a failure of attachment to cells, since the superinfecting virus absorbed to the BJ cells. Electron microscopic studies showed that the virions are juxtaposed to coated pits and are then taken up into endocytic vesicles. The virus particles contained in the vesicles were in various stages of degradation. Viral DNA that reached the nucleus was present in fewer copies per BJ cell than that in the parental BHKtk- cells infected at the same multiplicity. Moreover, unlike the viral DNA in BHKtk- cells which was amplified, that in BJ cells decreased in copy number. The results suggest that the glycoprotein D expressed in the BJ cell line interfered with fusion of the virion envelope with the plasma membrane but not with the adsorption of the virus to cells and that the viral proteins that mediate adsorption to and fusion of membranes appear to be distinct.     

Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models

How growth, mortality, and dispersal in a species affect the species' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.     

Spreading speeds and traveling waves in competitive recursion systems

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.     

Cell-free transmission of human adenovirus by passive mass transfer in cell culture simulated in a computer model

Viruses spread between cells, tissues, and organisms by cell-free and cell-cell transmissions. Both mechanisms enhance disease development, but it is difficult to distinguish between them. Here, we analyzed the transmission mode of human adenovirus (HAdV) in monolayers of epithelial cells by wet laboratory experimentation and a computer simulation. Using live-cell fluorescence microscopy and replication-competent HAdV2 expressing green fluorescent protein, we found that the spread of infection invariably occurred after cell lysis. It was affected by convection and blocked by neutralizing antibodies but was independent of second-round infections. If cells were overlaid with agarose, convection was blocked and round plaques developed around lytic infected cells. Infected cells that did not lyse did not give rise to plaques, highlighting the importance of cell-free transmission. Key parameters for cell-free virus transmission were the time from infection to lysis, the dose of free viruses determining infection probability, and the diffusion of single HAdV particles in aqueous medium. With these parameters, we developed an in silico model using multiscale hybrid dynamics, cellular automata, and particle strength exchange. This so-called white box model is based on experimentally determined parameters and reproduces viral infection spreading as a function of the local concentration of free viruses. These analyses imply that the extent of lytic infections can be determined by either direct plaque assays or can be predicted by calculations of virus diffusion constants and modeling.     

In vivo egress of an alphaherpesvirus from axons

Many alphaherpesviruses establish a latent infection in the peripheral nervous systems of their hosts. This life cycle requires the virus to move long distances in axons toward the neuron's cell body during infection and away from the cell body during reactivation. While the events underlying entry of the virion into neurons during infection are understood in principle, no such consensus exists regarding viral egress from neurons after reactivation. In this study, we challenged two different models of viral egress from neurons by using pseudorabies virus (PRV) infection of the rat retina: does PRV egress solely from axon terminals, or can the virus egress from axon shafts as well as axon terminals? We took advantage of PRV gD mutants that are not infectious as extracellular particles but are capable of spreading by cell-cell contact. We observed that both wild-type virus and a PRV gD null mutant are capable of spreading from axons to closely apposed nonneuronal cells within the rat optic nerve after intravitreal infection. However, infection does not spread from these infected nonneuronal cells. We suggest that viral egress can occur sporadically along the length of infected axons and is not confined solely to axon terminals. Moreover, it is likely that extracellular particles are not involved in nonneuronal cell infections. Taking these together with previous data, we suggest a model of viral egress from neurons that unifies previous apparently contradictory data.     

Enhancement of the Influenza A Hemagglutinin (HA)-Mediated Cell-Cell Fusion and Virus Entry by the Viral Neuraminidase (NA)

Background

The major role of the neuraminidase (NA) protein of influenza A virus is related to its sialidase activity, which disrupts the interaction between the envelope hemagglutin (HA) protein and the sialic acid receptors expressed at the surface of infected cells. This enzymatic activity is known to promote the release and spread of progeny viral particles following their production by infected cells, but a potential role of NA in earlier steps of the viral life cycle has never been clearly demonstrated. In this study we have examined the impact of NA expression on influenza HA-mediated viral membrane fusion and virion infectivity.

Methodology/Principal Findings

The role of NA in the early stages of influenza virus replication was examined using a cell-cell fusion assay that mimics HA-mediated membrane fusion, and a virion infectivity assay using HIV-based pseudoparticles expressing influenza HA and/or NA proteins. In the cell-cell fusion assay, which bypasses the endocytocytosis step that is characteristic of influenza virus entry, we found that in proper HA maturation conditions, NA clearly enhanced fusion in a dose-dependent manner. Similarly, expression of NA at the surface of pseudoparticles significantly enhanced virion infectivity. Further experiments using exogeneous soluble NA revealed that the most likely mechanism for enhancement of fusion and infectivity by NA was related to desialylation of virion-expressed HA.

Conclusion/Significance

The NA protein of influenza A virus is not only required for virion release and spread but also plays a critical role in virion infectivity and HA-mediated membrane fusion.     

Glycoprotein gL-independent infectivity of pseudorabies virus is mediated by a gD-gH fusion protein

Envelope glycoproteins gH and gL, which form a complex, are conserved throughout the family Herpesviridae. The gH-gL complex is essential for the fusion between the virion envelope and the cellular cytoplasmic membrane during penetration and is also required for direct viral cell-to-cell spread from infected to adjacent noninfected cells. It has been proposed for several herpesviruses that gL is required for proper folding, intracellular transport, and virion localization of gH. In pseudorabies virus (PrV), glycoprotein gL is necessary for infectivity but is dispensable for virion localization of gH. A virus mutant lacking gL, PrV-DeltagLbeta, is defective in entry into target cells, and direct cell-to-cell spread is drastically reduced, resulting in only single or small foci of infected cells (B. G. Klupp, W. Fuchs, E. Weiland, and T. C. Mettenleiter, J. Virol. 71:7687-7695, 1997). We used this limited cell-to-cell spreading ability of PrV-DeltagLbeta for serial passaging of cells infected with transcomplemented virus by coseeding with noninfected cells. After repeated passaging, plaque formation was restored and infectivity in the supernatant was observed. One single-plaque isolate, designated PrV-DeltagLPass, was further characterized. To identify the mutation leading to this gL-independent infectious phenotype, Southern and Western blot analyses, radioimmunoprecipitations, and DNA sequencing were performed. The results showed that rearrangement of a genomic region comprising part of the gH gene into a duplicated copy of part of the unique short region resulted in a fusion fragment predicted to encode a protein consisting of the N-terminal 271 amino acids of gD fused to the C-terminal 590 residues of gH. Western blotting and radioimmunoprecipitation with gD- and gH-specific antibodies verified the presence of a gDH fusion protein. To prove that this fusion protein mediates infectivity of PrV-DeltagLPass, cotransfection of PrV-DeltagLbeta DNA with the cloned fusion fragment was performed, and a cell line, Nde-67, carrying the fusion gene was established. After cotransfection, infectious gL-negative PrV was recovered, and propagation of PrV-DeltagLbeta on Nde-67 cells produced infectious virions. Thus, a gDH fusion polypeptide can compensate for function of the essential gL in entry and cell-to-cell spread of PrV.     

Existence of traveling waves for integral recursions with nonmonotone growth functions

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94–121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers. B. Li’s research was partially supported by the National Science Foundation under Grant DMS-616445. M. A. Lewis research was supported by “The Canada Research Chairs program,” and a grant from the Natural Sciences and Engineering Research Council of Canada.     

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.     

Global dynamics of a reaction and diffusion model for Lyme disease

This paper is devoted to the mathematical analysis of a reaction and diffusion model for Lyme disease. In the case of a bounded spatial habitat, we obtain the global stability of either disease-free or endemic steady state in terms of the basic reproduction number R?. In the case of an unbounded spatial habitat, we establish the existence of the spreading speed of the disease and its coincidence with the minimal wave speed for traveling fronts. Our analytic results show that R? is a threshold value for the global dynamics and that the spreading speed is linearly determinate.     

Role of cytoplasmic vacuoles in varicella-zoster virus glycoprotein trafficking and virion envelopment.

Varicella-zoster virus (VZV) encodes several glycoproteins which are present on both mature viral envelopes and the surfaces of infected cell membranes. Mechanisms of VZV glycoprotein transport and virion envelopment were investigated by both continuous radiolabeling and pulse-chase analyses with tritiated fucose in VZV-infected cells. We studied in detail the large cytoplasmic vacuoles which were present in infected cells but absent from uninfected cells. The specific activity in each subcellular compartment was defined by quantitative electron microscope autoradiography, using a cross-fire probability matrix analysis to more accurately assess the individual compartment demarcated by the silver grains. By these techniques, we documented a progression of activity originating in the Golgi apparatus and traveling through the post-Golgi region into virus-induced cytoplasmic vacuoles and finally to areas of the cellular membrane associated with the egress of viral particles. Significant amounts of radiolabel were not observed in the nucleus, and only low levels of radiolabel were associated with the cellular membrane not involved with the egress of viral particles. In addition, immunolabeling of Lowicryl-embedded VZV-infected cells demonstrated the presence of VZV glycoproteins within cytoplasmic vacuole membranes as well as on virion envelopes. These observations suggested that cytoplasmic vacuoles harbored VZV-specified glycoproteins and were also the predominant site of VZV virion envelopment within the infected cell. Neither enveloped nor unenveloped viral particles were observed within the Golgi apparatus itself.     

Plant Dynamics,Birth-Jump Processes,and Sharp Traveling Waves

Motivated by the importance of understanding the dynamics of the growth and dispersal of plants in various environments, we introduce and analyze a discrete agent-based model based on a birth-jump process, which exhibit wave-like solutions. To rigorously analyze these traveling wave phenomena, we derive the diffusion limit of the discrete model and prove the existence of traveling wave solutions (sharp and continuously differentiable) assuming a logarithmic-type growth. Furthermore, we provide a variational speed for the minimum speed of the waves and perform numerical experiments that confirm our results.     

Amplification of Epstein-Barr virus (EBV) DNA by superinfection with a strain of EBV derived from nasopharyngeal carcinoma.

Epstein-Barr virus (EBV) from a nasopharyngeal carcinoma (NPC) hybrid cell line (NPC-KT) lacking defective viral DNA molecules superinfected Raji cells and induced EBV early antigens (EA), as did virus from P3HR-1 cells, which contained defective molecules. The EBV polypeptides induced by NPC-KT appeared to be identical to those induced by P3HR-1 virus. The ability of NPC-KT virus to induce EA was enhanced more than 10-fold by treatment of superinfected cells with dimethyl sulfoxide; however, dimethyl sulfoxide treatment did not enhance superinfection by P3HR-1 virus. After infection, DNA synthesis of both the superinfecting NPC-KT virus and the resident Raji viral genome was induced. In addition to amplified Raji EBV episomal DNA, a fused terminal fragment of NPC-KT viral DNA was detected. The detection of fused terminal DNA fragments suggests that the superinfecting virion DNA either circularizes or polymerizes after superinfection and is possibly amplified through circular or concatenated replicative intermediates.     

Photodynamic treatment of herpes simplex virus during its replicative cycle.

Photodynamic treatment of herpes simplex virus type 1-infected hamster embryo fibroblasts (LSH strain) with a low concentration of proflavine (0.08 mug/10(5) cells per ml), a 3-9-diamine acridine dye, inhibited production not only of infectious progeny but also of virion particles. However, there was no appreciable inhibition of viral or cellular DNA synthesis, even when the infected cells were repeatedly exposed to this low concentration of dye and light during the replication cycle of the virus. It thus appears that photodynamic treatment of infected cells interferes with the processes involved in virus maturation.     

A Traveling Wave Model for Invasion by Precursor and Differentiated Cells

We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired migration and proliferation. The equation describing the precursor cells is based on Fisher’s equation with the addition of a carrying-capacity limited differentiation term. Two variations of the proliferation term are considered and compared. For most parameter values, the model admits a traveling wave solution for each population, both traveling at the same speed. The traveling wave solutions are investigated using perturbation analysis, phase plane methods, and numerical techniques. Analytical and numerical results suggest the existence of two wavespeed selection regimes. Regions of the parameter space are characterized according to existence, shape, and speed of traveling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, our results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells.     

Polar appearance and nonligand induced spreading of measles virus hemagglutinin at the surface of chronically infected cells

Fixation with glutaraldehyde (GA) and paraformaldehyde (PFA) preserved measles virus hemagglutinin at the surface of chronically infected cells. Cells fixed with PFA but not with GA exhibited hemadsorption with green monkey cells. PFA fixation, in contrast to GA fixation, also preserved the immunogenicity of measles virus hemolysin.These fixatives and the removal of the measles virus hemagglutinin from the cell surface by trypsin enabled studies of the appearance of the hemagglutinin at the surface membrane. Results obtained by immunofluorescence technique and by hemadsorption indicated that measles virus hemagglutinin appeared polarly at the cell membrane and then spread around the surface. This was substantiated by measurements of the immunofluorescence intensity at the single cell level per membrane unit and per cell, and by measuring the binding of iodinated immunoglobulins per 10⁶ cells. The appearance was inhibited by sodium azide and cytochalasin B. The spreading was not inhibited by sodium azide, but was influenced by cytochalasin B. The spreading did not proceed at 4°C. On the basis of these findings, a hypothetical model for appearance and spreading of measles virus hemagglutinin was proposed.     

Traveling waves in a model of influenza A drift

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease.     

Endocytosis and a low-pH step are required for productive entry of equine infectious anemia virus

Recently, it has become evident that entry of some retroviruses into host cells is dependent upon a vesicle-localized, low-pH step. The entry mechanism of equine infectious anemia virus (EIAV) has yet to be examined. Here, we demonstrate that wild-type strains of EIAV require a low-pH step for productive entry. Lysosomotropic agents that inhibit the acidification of internal vesicles inhibited productive entry of EIAV. The presence of ammonium chloride (30 mM), monensin (30 microM), or bafilomycin A (50 nM) in the medium dramatically decreased the number of EIAV antigen-positive cells. We found that a low-pH step was required for EIAV infection of tissue culture cell lines as well as primary cells, such as endothelial cells and monocyte-derived macrophages. The ammonium chloride treatment did not reduce virion stability, nor did the treatment prevent virion binding to cells. Consistent with a requirement for a low-pH step, virion infectivity was enhanced more than threefold by brief low-pH treatment following binding of viral particles to permissive cells. A superinfecting variant strain of EIAV, vMA-1c, did not require a low-pH step for productive infection of fibroblasts. However, lysosomotropic agents were inhibitory to vMA-1c infection in the other cell types that vMA-1c infected but did not superinfect, indicating that the entry pathway used by vMA-1c for superinfection abrogates the need for the low-pH step.