Early infection and spread of a conditionally replicating adenovirus under conditions of plaque formation

Beyond the pair approximation: Modeling colonization population dynamics

The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.

Investigating Macrophages Plasticity Following Tumour-Immune Interactions During Oncolytic Therapies

Over the last few years, oncolytic virus therapy has been recognised as a promising approach in cancer treatment, due to the potential of these viruses to induce systemic anti-tumour immunity and selectively killing tumour cells. However, the effectiveness of these viruses depends significantly on their interactions with the host immune responses, both innate (e.g., macrophages, which accumulate in high numbers inside solid tumours) and adaptive (e.g., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells). In this article, we consider a mathematical approach to investigate the possible outcomes of the complex interactions between two extreme types of macrophages (M1 and M2 cells), effector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells and an oncolytic Vesicular Stomatitis Virus (VSV), on the growth/elimination of B16F10 melanoma. We discuss, in terms of VSV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ and macrophages levels, two different types of immune responses which could ensure tumour control and eventual elimination. We show that both innate and adaptive anti-tumour immune responses, as well as the oncolytic virus, could be very important in delaying tumour relapse and eventually eliminating the tumour. Overall this study supports the use mathematical modelling to increase our understanding of the complex immune interaction following oncolytic virotherapies. However, the complexity of the model combined with a lack of sufficient data for model parametrisation has an impact on the possibility of making quantitative predictions.

Inhibition of infection spread by co-transmitted defective interfering particles

Although virus release from host cells and tissues propels the spread of many infectious diseases, most virus particles are not infectious; many are defective, lacking essential genetic information needed for replication. When defective and viable particles enter the same cell, the defective particles can multiply while interfering with viable particle production. Defective interfering particles (DIPs) occur in nature, but their role in disease pathogenesis and spread is not known. Here, we engineered an RNA virus and its DIPs to express different fluorescent reporters, and we observed how DIPs impact viral gene expression and infection spread. Across thousands of host cells, co-infected with infectious virus and DIPs, gene expression was highly variable, but average levels of viral reporter expression fell at higher DIP doses. In cell populations spatial patterns of infection spread provided the first direct evidence for the co-transmission of DIPs with infectious virus. Patterns of spread were highly sensitive to the behavior of initial or early co-infected cells, with slower overall spread stemming from higher early DIP doses. Under such conditions striking patterns of patchy gene expression reflected localized regions of DIP or virus enrichment. From a broader perspective, these results suggest DIPs contribute to the ecological and evolutionary persistence of viruses in nature.

Complex Dynamics of Virus Spread from Low Infection Multiplicities: Implications for the Spread of Oncolytic Viruses

While virus growth dynamics have been well-characterized in several infections, data are typically collected once the virus population becomes easily detectable. Earlier dynamics, however, remain less understood. We recently reported unusual early dynamics in an experimental system using adenovirus infection of human embryonic kidney (293) cells. Under identical experimental conditions, inoculation at low infection multiplicities resulted in either robust spread, or in limited spread that eventually stalled, with both outcomes occurring with approximately equal frequencies. The reasons underlying these observations have not been understood. Here, we present further experimental data showing that inhibition of interferon-induced antiviral states in cells results in a significant increase in the percentage of robust infections that are observed, implicating a race between virus replication and the spread of the anti-viral state as a central mechanism. Analysis of a variety of computational models, however, reveals that this alone cannot explain the simultaneous occurrence of both viral growth outcomes under identical conditions, and that additional biological mechanisms have to be invoked to explain the data. One such mechanism is the ability of the virus to overcome the antiviral state through multiple infection of cells. If this is included in the model, two outcomes of viral spread are found to be simultaneously stable, depending on initial conditions. In stochastic versions of such models, the system can go by chance to either state from identical initial conditions, with the relative frequency of the outcomes depending on the strength of the interferon-based anti-viral response, consistent with the experiments. This demonstrates considerable complexity during the early phase of the infection that can influence the ability of a virus to become successfully established. Implications for the initial dynamics of oncolytic virus spread through tumors are discussed.

We investigate in vitro adenovirus spread starting from the lowest infection multiplicities. This phase of virus dynamics remains poorly understood and is likely critical for ensuring that engineered oncolytic viruses successfully spread and destroy tumors. We find unexpectedly complex dynamics, which are analyzed with a combination of experiments and mathematical models. The experiments indicate that the induction of an interferon-based anti-viral state is a crucial underlying mechanism. The mathematical models demonstrate that this mechanism alone cannot explain the experiments, and that additional mechanisms must be invoked to account for the data. The models suggest that the ability of the virus to overcome the anti-viral state through multiple infection of cells might be one such mechanism.

Spatial-Temporal Patterns of Viral Amplification and Interference Initiated by a Single Infected Cell

When viruses infect their host cells, they can make defective virus-like particles along with intact virus. Cells coinfected with virus and defective particles often exhibit interference with virus growth caused by the competition for resources by defective genomes. Recent reports of the coexistence and cotransmission of such defective interfering particles (DIPs) in vivo, across epidemiological length and time scales, suggest a role in viral pathogenesis, but it is not known how DIPs impact infection spread, even under controlled culture conditions. Using fluorescence microscopy, we quantified coinfections of vesicular stomatitis virus (VSV) expressing a fluorescent reporter protein and its DIPs on BHK-21 host cell monolayers. We found that viral gene expression was more delayed, infections spread more slowly, and patterns of spread became more “patchy” with higher DIP inputs to the initial cell. To examine how infection spread might depend on the behavior of the initial coinfected cell, we built a computational model, adapting a cellular automaton (CA) approach to incorporate kinetic data on virus growth for the first time. Specifically, changes in observed patterns of infection spread could be directly linked to previous high-throughput single-cell measures of virus-DIP coinfection. The CA model also provided testable hypotheses on the spatial-temporal distribution of the DIPs, which remain governed by their predator-prey interaction. More generally, this work offers a data-driven computational modeling approach for better understanding of how single infected cells impact the multiround spread of virus infections across cell populations.

IMPORTANCE Defective interfering particles (DIPs) compete with intact virus, depleting host cell resources that are essential for virus growth and infection spread. However, it is not known how such competition, strong or weak, ultimately affects the way in which infections spread and cause disease. In this study, we address this unmet need by developing an integrated experimental-computational approach, which sheds new light on how infections spread. We anticipate that our approach will also be useful in the development of DIPs as therapeutic agents to manage the spread of viral infections.

Computational modeling approaches to the dynamics of oncolytic viruses

Replicating oncolytic viruses represent a promising treatment approach against cancer, specifically targeting the tumor cells. Significant progress has been made through experimental and clinical studies. Besides these approaches, however, mathematical models can be useful when analyzing the dynamics of virus spread through tumors, because the interactions between a growing tumor and a replicating virus are complex and nonlinear, making them difficult to understand by experimentation alone. Mathematical models have provided significant biological insight into the field of virus dynamics, and similar approaches can be adopted to study oncolytic viruses. The review discusses this approach and highlights some of the challenges that need to be overcome in order to build mathematical and computation models that are clinically predictive. WIREs Syst Biol Med 2016, 8:242-252. doi: 10.1002/wsbm.1332 For further resources related to this article, please visit the WIREs website.

Infectio: a Generic Framework for Computational Simulation of Virus Transmission between Cells

Infectio presents a generalized platform to analyze virus infection spread between cells. It allows the simulation of plaque phenotypes from image-based assays. Viral plaques are the result of virus spreading from primary infected cells to neighboring cells. This is a complex process and involves neighborhood effects at cell-cell contact sites or fluid dynamics in the extracellular medium. Infectio differentiates between two major modes of virus transmission between cells, allowing in silico testing of hypotheses about spreading mechanisms of any virus which can be grown in cell cultures, based on experimentally measured parameters, such as infection intensity or cell killing. The results of these tests can be compared with experimental data and allow interpretations with regard to biophysical mechanisms. Infectio also facilitates characterizations of the mode of action of therapeutic agents, such as oncolytic viruses or other infectious or cytotoxic agents.

Viruses spread between cells, tissues, and organisms by cell-free and cell-cell mechanisms, depending on the cell type, the nature of the virus, or the phase of the infection cycle. The mode of viral transmission has a large impact on disease development, the outcome of antiviral therapies or the efficacy of gene therapy protocols. The transmission mode of viruses can be addressed in tissue culture systems using live-cell imaging. Yet even in relatively simple cell cultures, the mechanisms of viral transmission are difficult to distinguish. Here we present a cross-platform software framework called “Infectio,” which is capable of simulating transmission phenotypes in tissue culture of virtually any virus. Infectio can estimate interdependent biological parameters, for example for vaccinia virus infection, and differentiate between cell-cell and cell-free virus spreading. Infectio assists in elucidating virus transmission mechanisms, a feature useful for designing strategies of perturbing or enhancing viral transmission. The complexity of the Infectio software is low compared to that of other software commonly used to quantitate features of cell biological images, which yields stable and relatively error-free output from Infectio. The software is open source (GPLv3 license), and operates on the major platforms (Windows, Mac, and Linux). The complete source code can be downloaded from http://infectio.github.io/index.html.

IMPORTANCE Infectio presents a generalized platform to analyze virus infection spread between cells. It allows the simulation of plaque phenotypes from image-based assays. Viral plaques are the result of virus spreading from primary infected cells to neighboring cells. This is a complex process and involves neighborhood effects at cell-cell contact sites or fluid dynamics in the extracellular medium. Infectio differentiates between two major modes of virus transmission between cells, allowing in silico testing of hypotheses about spreading mechanisms of any virus which can be grown in cell cultures, based on experimentally measured parameters, such as infection intensity or cell killing. The results of these tests can be compared with experimental data and allow interpretations with regard to biophysical mechanisms. Infectio also facilitates characterizations of the mode of action of therapeutic agents, such as oncolytic viruses or other infectious or cytotoxic agents.

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1

Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4(+) T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that ∼2,000-fold reductions are required to permit a majority of patients to interrupt ART for 1 y without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the laboratory to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.

Complex role of space in the crossing of fitness valleys by asexual populations

The evolution of complex traits requires the accumulation of multiple mutations, which can be disadvantageous, neutral or advantageous relative to the wild-type. We study two spatial (two-dimensional) models of fitness valley crossing (the constant-population Moran process and the non-constant-population contact process), varying the number of loci involved and the degree of mixing. We find that spatial interactions accelerate the crossing of fitness valleys in the Moran process in the context of neutral and disadvantageous intermediate mutants because of the formation of mutant islands that increase the lifespan of mutant lineages. By contrast, in the contact process, spatial structure can accelerate or delay the emergence of the complex trait, and there can even be an optimal degree of mixing that maximizes the rate of evolution. For advantageous intermediate mutants, spatial interactions always delay the evolution of complex traits, in both the Moran and contact processes. The role of the mutant islands here is the opposite: instead of protecting, they constrict the growth of mutants. We conclude that the laws of population growth can be crucial for the effect of spatial interactions on the rate of evolution, and we relate the two processes explored here to different biological situations.

Mathematical models of HIV replication and pathogenesis

This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.

Visualizing infection spread: dual-color fluorescent reporting of virus-host interactions

Although the molecular mechanisms by which host cells defend themselves against viral infection have been studied in great depth, and countermeasures viruses employ to suppress such defensive responses have been widely documented, relatively little attention has been devoted toward elucidating how such interactions between virus and host are resolved over multiple rounds of infection. Here, we describe the design, synthesis, and validation of a dual-color fluorescent reporter system to study how viral infections spread through a host cell monolayer and how the cellular innate immune system mounts an antiviral response. We employed recombinant, red fluorescent protein expressing mutants of a prototypical RNA virus, vesicular stomatitis virus to enable identification and tracking of infected cells. Further, we generated stable reporter cells that use green fluorescent protein to report on the expression of IFIT2, an interferon stimulated gene involved in the interference of viral protein translation, and a marker of antiviral defense activation. The presence of the fluorescent protein reporters had minimal effects on the normal behavior of the cells or viruses. Moreover, expression of the virus and cell reporters correlated with the kinetics of viral replication and activation of an anti-viral response, respectively. This two-color system enabled us to track and quantify in live cells how viral replication and activation of host defensive responses play out over multiple rounds of infection. Initial study of propagating infections demonstrated that antiviral activation over multiple rounds was critical for slowing and ultimately halting the spread of infection.

Complex spatial dynamics of oncolytic viruses in vitro: mathematical and experimental approaches

Oncolytic viruses replicate selectively in tumor cells and can serve as targeted treatment agents. While promising results have been observed in clinical trials, consistent success of therapy remains elusive. The dynamics of virus spread through tumor cell populations has been studied both experimentally and computationally. However, a basic understanding of the principles underlying virus spread in spatially structured target cell populations has yet to be obtained. This paper studies such dynamics, using a newly constructed recombinant adenovirus type-5 (Ad5) that expresses enhanced jellyfish green fluorescent protein (EGFP), AdEGFPuci, and grows on human 293 embryonic kidney epithelial cells, allowing us to track cell numbers and spatial patterns over time. The cells are arranged in a two-dimensional setting and allow virus spread to occur only to target cells within the local neighborhood. Despite the simplicity of the setup, complex dynamics are observed. Experiments gave rise to three spatial patterns that we call "hollow ring structure", "filled ring structure", and "disperse pattern". An agent-based, stochastic computational model is used to simulate and interpret the experiments. The model can reproduce the experimentally observed patterns, and identifies key parameters that determine which pattern of virus growth arises. The model is further used to study the long-term outcome of the dynamics for the different growth patterns, and to investigate conditions under which the virus population eliminates the target cells. We find that both the filled ring structure and disperse pattern of initial expansion are indicative of treatment failure, where target cells persist in the long run. The hollow ring structure is associated with either target cell extinction or low-level persistence, both of which can be viewed as treatment success. Interestingly, it is found that equilibrium properties of ordinary differential equations describing the dynamics in local neighborhoods in the agent-based model can predict the outcome of the spatial virus-cell dynamics, which has important practical implications. This analysis provides a first step towards understanding spatial oncolytic virus dynamics, upon which more detailed investigations and further complexity can be built.

Increased burst size in multiply infected cells can alter basic virus dynamics

BACKGROUND

The dynamics of viral infections have been studied extensively in a variety of settings, both experimentally and with mathematical models. The majority of mathematical models assumes that only one virus can infect a given cell at a time. It is, however, clear that especially in the context of high viral load, cells can become infected with multiple copies of a virus, a process called coinfection. This has been best demonstrated experimentally for human immunodeficiency virus (HIV), although it is thought to be equally relevant for a number of other viral infections. In a previously explored mathematical model, the viral output from an infected cell does not depend on the number of viruses that reside in the cell, i.e. viral replication is limited by cellular rather than viral factors. In this case, basic virus dynamics properties are not altered by coinfection.

RESULTS

Here, we explore the alternative assumption that multiply infected cells are characterized by an increased burst size and find that this can fundamentally alter model predictions. Under this scenario, establishment of infection may not be solely determined by the basic reproductive ratio of the virus, but can depend on the initial virus load. Upon infection, the virus population need not follow straight exponential growth. Instead, the exponential rate of growth can increase over time as virus load becomes larger. Moreover, the model suggests that the ability of anti-viral drugs to suppress the virus population can depend on the virus load upon initiation of therapy. This is because more coinfected cells, which produce more virus, are present at higher virus loads. Hence, the degree of drug resistance is not only determined by the viral genotype, but also by the prevalence of coinfected cells.

CONCLUSIONS

Our work shows how an increased burst size in multiply infected cells can alter basic infection dynamics. This forms the basis for future experimental testing of model assumptions and predictions that can distinguish between the different scenarios.