Replication of viruses in a growing plaque: a reaction-diffusion model.

An understanding of the viral replication process commonly referred to as "plaque growth" is developed in the context of a reaction-diffusion model. The interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and diffusion. The solution to the full model reveals a maximum in the dependence of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data.     

Imaging the propagation of viruses

The propagation of viruses in a growing plaque has been measured using a digital image acquisition and analysis system. Plaques of phage T7 incubated at 37 degrees C and illuminated against a dark field emerged as dark growing spots against a background of host bacteria. Images of the growth were acquired using a charge-coupled device (CCD) camera at 1-h intervals over 24 h. The first 10 h of plaque development coincided with rapid growth of the agar-immobilized Escherichia coli host, measured as a reduction in gray value. Following this period, the average radial velocity of plaque growth remained constant at 0.059 mm/h while the standard deviation about this velocity increased. These results suggest the suitability of the system for spatially resolving the dynamics of viral evolution during plaque growth. (c) 1996 John Wiley & Sons, Inc.     

Antiserum inhibition of propagating viruses

The design and implementation of controlled environments to continuously culture and evolve viruses provides a means to track how their populations respond to natural and designed anti-viral agents. We have previously demonstrated how the growth of viruses in spreading plaques enables detection and characterization of their evolutionary dynamics. Using plaques of phage T7 growing on E. coli as a model system, we observe here that velocities of propagation can be readily controlled by the level of anti-viral antiserum incorporated into the propagation medium. Further, we develop a simple analytic expression for the radial velocity of propagation in terms of the microscopic rates of viral amplification, Fickian diffusion of the virions and their neutralization by antiserum. Our analysis captures the essential dependence of propagation velocity on antiserum concentration. This study provides an ex vivo foundation for exploring how medically relevant viruses escape suppression by the immune system. (c) 1997 John Wiley & Son, Inc. Biotechnol Bioeng 55: 542-546, 1997.     

Underwhelming the immune response: effect of slow virus growth on CD8+-T-lymphocyte responses

The speed of virus replication has typically been seen as an advantage for a virus in overcoming the ability of the immune system to control its population growth. Under some circumstances, the converse may also be true: more slowly replicating viruses may evoke weaker cellular immune responses and therefore enhance their likelihood of persistence. Using the model of lymphocytic choriomeningitis virus (LCMV) infection in mice, we provide evidence that slowly replicating strains induce weaker cytotoxic-T-lymphocyte (CTL) responses than a more rapidly replicating strain. Conceptually, we show a "bell-shaped" relationship between the LCMV growth rate and the peak CTL response. Quantitative analysis of human hepatitis C virus infections suggests that a reduction in virus growth rate between patients during the incubation period is associated with a spectrum of disease outcomes, from fulminant hepatitis at the highest rate of viral replication through acute resolving to chronic persistence at the lowest rate. A mathematical model for virus-CTL population dynamics (analogous to predator [CTL]-prey [virus] interactions) is applied in the clinical data-driven analysis of acute hepatitis B virus infection. The speed of viral replication, through its stimulus of host CTL responses, represents an important factor influencing the pathogenesis and duration of virus persistence within the human host. Viruses with lower growth rates may persist in the host because they "sneak through" immune surveillance.     

Bacterial Growth Rate and Marine Virus–Host Dynamics

Abstract The dynamics of a marine virus–host system were investigated at different steady state growth rates in chemostat cultures and the data were analyzed using a simple model. The virus–host interactions showed strong dependence on host cell growth rate. The duration of the infection cycle and the virus burst size were found to depend on bacterial growth rate, and the rate of cell lysis and virus production were positively correlated with steady state growth rate in the cultures (r ² > 0.96, p < 0.05). At bacterial growth rates of 0.02 to 0.10 h⁻¹ in the chemostats the virus burst size increased from 12 ± 4 to 56 ± 4, and the latent period decreased from 2.0 to 1.7 h. Resistant clones of the host strain were present in the cultures from the beginning of the experiment and replaced the sensitive host cells following viral lysis in the cultures. Regrowth of resistant cells correlated significantly (r ²= 1.000, p < 0.02) with the lysis rate of sensitive cells, indicating that release of viral lysates stimulated growth of the non-infected, resistant cells. The constructed model was suitable for simulating the observed dynamics of the sensitive host cells, viruses and resistant clones in the cultures. The model was therefore used in an attempt to predict the dynamics of this virus–host interaction in a natural marine environment during a certain set of growth conditions. The simulation indicated that a steady state relationship between the specific viruses and sensitive and resistant bacterial clones may occur at densities that are reasonable to assume for natural environments. The study demonstrates that basic characterization and modeling of specific virus–host interactions may improve our understanding of the behavior of bacteria and viruses in natural systems. Received: 12 November 1999; Accepted: 2 May 2000; Online Publication: 11 August 2000     

Host cell processes to accomplish mechanical and non-circulative virus transmission

Mechanical vector-less transmission of viruses, as well as vector-mediated non-circulative virus transmission, where the virus attaches only to the exterior of the vector during the passage to a new host, are apparently simple processes: the viruses are carried along with the wind, the food or by the vector to a new host. We discuss here, using the examples of the non-circulatively transmitted Cauliflower mosaic virus that binds to its aphid vector's exterior mouthparts, and that of the mechanically (during feeding activity) transmitted Autographa californica multicapsid nucleopolyhedrovirus, that transmission of these viruses is not so simple as previously thought. Rather, these viruses prepare their transmission carefully and long before the actual acquisition event. Host-virus interactions play a pivotal and specialised role in the future encounter with the vector or the new host. This ensures optimal propagation and enlarges the tremendous bottleneck transmission presents for viruses and other pathogens.     

Tobacco mosaic virus movement protein enhances the spread of RNA silencing

Eukaryotic cells restrain the activity of foreign genetic elements, including viruses, through RNA silencing. Although viruses encode suppressors of silencing to support their propagation, viruses may also exploit silencing to regulate host gene expression or to control the level of their accumulation and thus to reduce damage to the host. RNA silencing in plants propagates from cell to cell and systemically via a sequence-specific signal. Since the signal spreads between cells through plasmodesmata like the viruses themselves, virus-encoded plasmodesmata-manipulating movement proteins (MP) may have a central role in compatible virus:host interactions by suppressing or enhancing the spread of the signal. Here, we have addressed the propagation of GFP silencing in the presence and absence of MP and MP mutants. We show that the protein enhances the spread of silencing. Small RNA analysis indicates that MP does not enhance the silencing pathway but rather enhances the transport of the signal through plasmodesmata. The ability to enhance the spread of silencing is maintained by certain MP mutants that can move between cells but which have defects in subcellular localization and do not support the spread of viral RNA. Using MP expressing and non-expressing virus mutants with a disabled silencing suppressing function, we provide evidence indicating that viral MP contributes to anti-viral silencing during infection. Our results suggest a role of MP in controlling virus propagation in the infected host by supporting the spread of silencing signal. This activity of MP involves only a subset of its properties implicated in the spread of viral RNA.     

Tissue culture adaptation of foot-and-mouth disease virus selects viruses that bind to heparin and are attenuated in cattle.

Isolates of foot-and-mouth disease virus (FMDV) exist as complex mixtures of variants. Two different serotype O1 Campos preparations that we examined contained two variants with distinct plaque morphologies on BHK cells: a small, clear-plaque virus that replicates in BHK and CHO cells, and a large, turbid-plaque virus that only grows in BHK cells. cDNAs encoding the capsids of these two variants were inserted into a genome-length FMDV type A12 infectious cDNA and used to produce chimeric viruses that exhibited the phenotype of the original variants. Analyses of these viruses, and hybrids created by exchanging portions of the capsid gene, identified codon 56 in VP3 (3056) as the critical determinant of both cell tropism and plaque phenotype. Specifically, the CHO growth/clear-plaque phenotype is dependent on the presence of the highly charged Arg residue at 3056, and viruses with this phenotype and genotype were selected during propagation in tissue culture. The genetically engineered Arg 3056 virus was highly attenuated in bovines, but viruses recovered from animals inoculated with high doses of this virus had lost the ability to grow in CHO cells and contained either an uncharged residue at 3056 or a negatively charged Glu substituted for a Lys at a spatially and antigenically related position on VP2 (2134). Comparison of these animal-derived viruses to other natural and engineered viruses demonstrated that positively charged residues are required at both 2134 and 3056 for binding to heparin. Taken together, these results indicate that in vitro cultivation of FMDV type O selects viruses that bind to heparin and that viruses with the heparin-binding phenotype are attenuated in the natural host.     

Propagation of fluorescent viruses in growing plaques

To study virus propagation, we have developed a method by which the propagation of the Lambda bacteriophage can be observed and quantified. This is done by creating a fusion protein of the capsid protein gpD and the enhanced yellow fluorescent protein (EYFP). We show that this fusion allows capsid formation and that the modified viruses propagate on a surface covered with host bacteria thus forming fluorescent plaques. The intensity of fluorescence in a growing plaque determines the distribution of phages. This provides a new tool to study the propagation of infection at the microscopic level.     

Attenuation of Sindbis virus neurovirulence by using defined mutations in nontranslated regions of the genome RNA.

We examined a panel of Sindbis virus mutants containing defined mutations in the 5' nontranslated region of the genome RNA, in the 3' nontranslated region, or in both for their growth in cultured cells and virulence in newborn mice. In cultured cells, these viruses all had defects in RNA synthesis and displayed a wide range of growth rates. The growth properties of the mutants were often very different in mouse cells from those in chicken cells or in mosquito cells. We hypothesize that host factors, presumably proteins, interact with these nontranslated regions to promote viral replication and that the mammalian protein and the chicken or mosquito protein are sufficiently divergent that alterations in the viral RNA sequence can affect the interactions with these different host proteins in different ways. Some of the mutants were temperature sensitive for plaque formation, whereas one mutant was slightly cold sensitive in its growth in chicken cells. Upon inoculation into mice, viruses that grew well in cultured mouse cells retained their virulence, but mice that succumbed usually had extended survival times. One virulent mutant that grew slightly less well in cultured mouse cells than did the parental virus produced eight times as much virus in mouse brain following intracerebral inoculation, suggesting that changes in these regulatory regions may have tissue-specific as well as host-specific effects. Viruses that were severely crippled in their growth in mouse cells in culture were usually, but not always, attenuated in their virulence. In particular, temperature sensitivity was correlated with attenuation. The effect of two mutations was found to be cumulative, and double mutants that contained mutations in both the 5' and 3' nontranslated regions were more attenuated than was either single mutant. Three of four double mutants tested were severely crippled for virus production in cultured cells and were avirulent for mice, even when inoculated intracerebrally.     

The type 2 dengue virus envelope protein interacts with small ubiquitin-like modifier-1 (SUMO-1) conjugating enzyme 9 (Ubc9)

Dengue viruses are mosquito-borne flaviviruses and may cause the life-threatening dengue hemorrhagic fever and dengue shock syndrome. Its envelope protein is responsible mainly for the virus attachment and entry to host cells. To identify the human cellular proteins interacting with the envelope protein of dengue virus serotype 2 inside host cells, we have performed a screening with the yeast-two-hybrid-based “Functional Yeast Array”. Interestingly, the small ubiquitin-like modifier-1 conjugating enzyme 9 protein, modulating cellular processes such as those regulating signal transduction and cell growth, was one of the candidates interacting with the dengue virus envelope protein. With co-precipitation assay, we have demonstrated that it indeed could interact directly with the Ubc9 protein. Site-directed mutagenesis has demonstrated that Ubc9 might interact with the E protein via amino acid residues K51 and K241. Furthermore, immunofluorescence microscopy has shown that the DV2E-EGFP proteins tended to progress toward the nuclear membrane and co-localized with Flag-Ubc9 proteins around the nuclear membrane in the cytoplasmic side, and DV2E-EGFP also shifted the distribution of Flag-Ubc9 from evenly in the nucleus toward concentrating around the nuclear membrane in the nucleic side. In addition, over-expression of Ubc9 could reduce the plaque formation of the dengue virus in mammalian cells. This is the first report that DV envelope proteins can interact with the protein of sumoylation system and Ubc9 may involve in the host defense system to prevent virus propagation.     

Viral infection in internally structured hosts. I. Conditions for persistent infection

For a virus population within its host, two important levels of structure can be considered: multiple cell types which can be infected, and tissue types or body compartments which may be coupled via movement. We develop a model with both types of structure. Migration between compartments can create "sources" and "sinks" within the virus population, where realized viral growth rate and abundance is lowered in some compartments compared to what would be observed in isolation. Using both analytical and numerical methods, we investigate how this within-host spatial structure affects the conditions for persistent viral infection. We find that migration between compartments makes the establishment of infection more difficult than it would be in the absence of migration, implying that within-host spatial structure combined with viral movement decreases the likelihood of viral establishment. If migration is symmetrical and compartments are heterogeneous, an increase in migration rates between compartments generally makes establishment less likely. This may help to explain the tissue specificity observed for many viruses. There are, however, important exceptions to this result. These include circumstances where the virus initially invades a compartment that is unfavorable to population growth and migration is necessary to infect other parts of the host body. Stochastic aspects of viral establishment may also favor increased migration as it tends to dampen the amplitude of fluctuations in population size during the initial transient phase of establishment.     

Severe hindrance of viral infection propagation in spatially extended hosts

The production of large progeny numbers affected by high mutation rates is a ubiquitous strategy of viruses, as it promotes quick adaptation and survival to changing environments. However, this situation often ushers in an arms race between the virus and the host cells. In this paper we investigate in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Our analytical and numerical analyses are developed in close connection to directed percolation models. In fact, we show that making the space explicit in the model, which in turn amounts to reducing viral mobility and hindering the infective ability of the virus, connects our work with similar dynamical models that lie in the universality class of directed percolation. In addition, we use the fact that our model is a multicomponent generalization of the Domany-Kinzel probabilistic cellular automaton to employ several techniques developed in the past in that context, such as the two-site approximation to the extinction transition line. Our aim is to better understand propagation of viral infections with mobility restrictions, e.g., in crops or in plant leaves, in order to inspire new strategies for effective viral control.     

Multicellular spatial model of RNA virus replication and interferon responses reveals factors controlling plaque growth dynamics

Respiratory viruses present major public health challenges, as evidenced by the 1918 Spanish Flu, the 1957 H2N2, 1968 H3N2, and 2009 H1N1 influenza pandemics, and the ongoing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Severe RNA virus respiratory infections often correlate with high viral load and excessive inflammation. Understanding the dynamics of the innate immune response and its manifestations at the cell and tissue levels is vital to understanding the mechanisms of immunopathology and to developing strain-independent treatments. Here, we present a novel spatialized multicellular computational model of RNA virus infection and the type-I interferon-mediated antiviral response that it induces within lung epithelial cells. The model is built using the CompuCell3D multicellular simulation environment and is parameterized using data from influenza virus-infected cell cultures. Consistent with experimental observations, it exhibits either linear radial growth of viral plaques or arrested plaque growth depending on the local concentration of type I interferons. The model suggests that modifying the activity of signaling molecules in the JAK/STAT pathway or altering the ratio of the diffusion lengths of interferon and virus in the cell culture could lead to plaque growth arrest. The dependence of plaque growth arrest on diffusion lengths highlights the importance of developing validated spatial models of cytokine signaling and the need for in vitro measurement of these diffusion coefficients. Sensitivity analyses under conditions leading to continuous or arrested plaque growth found that plaque growth is more sensitive to variations of most parameters and more likely to have identifiable model parameters when conditions lead to plaque arrest. This result suggests that cytokine assay measurements may be most informative under conditions leading to arrested plaque growth. The model is easy to extend to include SARS-CoV-2-specific mechanisms or to use as a component in models linking epithelial cell signaling to systemic immune models.     

Bacteriophage evolution given spatial constraint

Spatial structure can impede mixing, diffusion, and motility. In microbiology laboratories, spatial structure is commonly achieved via formation of agar gels, within which bacteriophage (phage) replication results in localized clearings called plaques. Developing a better understanding of phage plaque formation is relevant because of the ubiquity of phage plaquing in the laboratory; because plaque size has been employed as a measure of phage fitness; because many bacteria exist within environments that display significant spatial structure (e.g., biofilms, soils, sediments, and in or on plant or animal tissues); and because spatial structure could impede phage exploitation of bacterial communities. There is, however, a relative dearth of experimentation and analysis considering phage plaque formation from the perspective of selection acting on individual phage growth parameters-latent period, burst size, and adsorption rate. Here we consider the impact of these parameters on rates of plaque wavefront velocity (rates of radial plaque enlargement), especially as functions of existing phage and environmental properties. We do so based on analyses of published equations which predict plaque enlargement rates. These indicate that greater wavefront velocities should be associated with (i) latent period reductions, (ii) larger burst sizes, or (iii) faster virion binding to bacteria. We suggest, however, that deviations could occur, respectively, (i) if virion adsorption is "slow" or if burst sizes are large, (ii) if burst sizes are already large, or (iii) if virion binding rates are already fast, bacterial densities are especially high, or burst sizes are large. Higher initial lawn bacterial densities could also contribute to faster plaque expansion, but only if adsorption is otherwise slow or burst sizes are large. By contrast, faster virion diffusion is always expected to result in greater plaque wavefront velocities. Overall, we provide a snapshot of how phage populations may respond evolutionarily to selection for more-rapid propagation during spatially constrained growth.     

Structured model of influenza virus replication in MDCK cells

Intracellular events that take place during influenza virus replication in animal cells are well understood qualitatively. However, to better understand the complex interaction of the virus with its host cell and to quantitatively analyze the use of cellular resources for virion formation or the overall dynamic for the entire infection cycle, a mathematical model for influenza virus replication has to be formulated. Here, we present a structured model for the single-cell reproductive cycle of influenza A virus in animal cells that accounts for the individual steps of the process such as attachment, internalization, genome replication and translation, and progeny virion assembly. The model describes an average cell surrounded by a small quantity of medium and infected by a low number of virus particles. The model allows estimation of the cellular resources consumed by virus replication. Simulation results show that the number of cellular surface receptors and endosomes, as well as other resources, such as the number of free nucleotides or amino acids, is not significantly influenced by influenza virus propagation. A factor that limits the growth rate of progeny viruses and their release is the total amount of matrix proteins (M1) in the nucleus while other newly synthesized viral proteins (e.g., nucleoprotein NP) and viral RNAs accumulate. During budding, synthesis of vRNPs (viral ribonucleoprotein complexes) represents another limiting factor. Based on this model it is also possible to analyze effects of parameter changes on the dynamics of virus replication, to identify possible targets for molecular engineering, or to develop strategies for improving yields in vaccine production processes. Furthermore, a better insight into the interactions of viruses and host cells might help to improve our understanding of virus-related diseases and to develop therapies.     

The dependence of viral RNA replication on co-opted host factors

Positive-sense RNA ((+)RNA) viruses such as hepatitis C virus exploit host cells by subverting host proteins, remodelling subcellular membranes, co-opting and modulating protein and ribonucleoprotein complexes, and altering cellular metabolic pathways during infection. To facilitate RNA replication, (+)RNA viruses interact with numerous host molecules through protein-protein, RNA-protein and protein-lipid interactions. These interactions lead to the formation of viral replication complexes, which produce new viral RNA progeny in host cells. This Review presents the recent progress that has been made in understanding the role of co-opted host proteins and membranes during (+)RNA virus replication, and discusses common themes employed by different viruses.     

Emergence of Variability in Isogenic Escherichia coli Populations Infected by a Filamentous Virus

The spread of epidemics not only depends on the average number of parasites produced per host, but also on the existence of highly infectious individuals. It is widely accepted that infectiousness depends on genetic and environmental determinants. However, even in clonal populations of host and viruses growing in homogeneous conditions, high variability can exist. Here we show that Escherichia coli cells commonly display high differentials in viral burst size, and address the kinetics of emergence of such variability with the non-lytic filamentous virus M13. By single-cell imaging of a virally-encoded fluorescent reporter, we monitor the viral charge distribution in infected bacterial populations at different time following infection. A mathematical model assuming autocatalytic virus replication and inheritance of bacterial growth rates quantitatively reproduces the experimental distributions, demonstrating that deterministic amplification of small host inhomogeneities is a mechanism sufficient to explain large and highly skewed distributions. This mechanism of amplification is general and may occur whenever a parasite has an initial phase of exponential growth within its host. Moreover, it naturally reproduces the shift towards higher virulence when the host is experimenting poor conditions, as observed commonly in host-parasite systems.     

Repulsion Effect on Superinfecting Virions by Infected Cells

In this paper, the repulsion effect of superinfecting virion by infected cells is studied by a reaction diffusion equation model for virus infection dynamics. In this model, the diffusion of virus depends not only on its concentration gradient but also on the concentration of infected cells. The basic reproduction number, linear stability of steady states, spreading speed and existence of traveling wave solutions for the model are discussed. It is shown that viruses spread more rapidly with the repulsion effect of infected cells on superinfecting virions, than with random diffusion only. For our model, the spreading speed of free virus is not consistent with the minimal traveling wave speed. With our general model, numerical computations of the spreading speed show that the repulsion of superinfecting virion promotes the spread of virus, which confirms, not only qualitatively but also quantitatively, the experimental result of Doceul et al. (Science 327:873–876, 2010).     

Polarized Cell Migration during Cell-to-Cell Transmission of Herpes Simplex Virus in Human Skin Keratinocytes

In addition to transmission involving extracellular free particles, a generally accepted model of virus propagation is one wherein virus replicates in one cell, producing infectious particles that transmit to the next cell via cell junctions or induced polarized contacts. This mechanism of spread is especially important in the presence of neutralizing antibody, and the concept underpins analysis of virus spread, plaque size, viral and host functions, and general mechanisms of virus propagation. Here, we demonstrate a novel process involved in cell-to-cell transmission of herpes simplex virus (HSV) in human skin cells that has not previously been appreciated. Using time-lapse microscopy of fluorescent viruses, we show that HSV infection induces the polarized migration of skin cells into the site of infection. In the presence of neutralizing antibody, uninfected skin cells migrate to the initial site of infection and spread over infected cells to become infected in a spatially confined cluster containing hundreds of cells. The cells in this cluster do not undergo cytocidal cell lysis but harbor abundant enveloped particles within cells and cell-free virus within interstitial regions below the cluster surface. Cells at the base and outside the cluster were generally negative for virus immediate-early expression. We further show, using spatially separated monolayer assays, that at least one component of this induced migration is the paracrine stimulation of a cytotactic response from infected cells to uninfected cells. The existence of this process changes our concept of virus transmission and the potential functions, virus, and host factors involved.