Image-guided modeling of virus growth and spread

Towards a Mathematical Model for the Viral Progression in the Pharynx

In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.

Modeling the efficiency of filovirus entry into cells in vitro: Effects of SNP mutations in the receptor molecule

Interaction between filovirus glycoprotein (GP) and the Niemann-Pick C1 (NPC1) protein is essential for membrane fusion during virus entry. Some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity. However, the dependence of differences in entry efficiency on SNPs remains unclear. Using vesicular stomatitis virus pseudotyped with Ebola and Marburg virus GPs, we investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Eclipse and virus-producing phases were assessed by in vitro infection experiments, and we developed a mathematical model describing spatial-temporal virus spread. This mathematical model fit the plaque radius data well from day 2 to day 6. Based on the estimated parameters, we found that SNPs causing the P424A and D508N substitutions in NPC1 most effectively reduced the entry efficiency of Ebola and Marburg viruses, respectively. Our novel approach could be broadly applied to other virus plaque assays.

Ebola (EBOV) and Marburg (MARV) viruses, which are included viruses of the family Filoviridae, cause severe hemorrhagic fever in humans. Filovirus particles is adsorbed to the cell through glycoprotein (GP), which is the only viral surface protein. Interaction between the filovirus sugar protein (GP) and the Niemann-Pick C1 (NPC1) protein plays a key role in membrane fusion during virus entry. Although some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity, the dependence of differences in entry efficiency on SNPs has not been studied. We therefore investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Using a mathematical model describing spatial-temporal virus spread, we quantitatively analyze viral entry efficiency and how this affected cell-to-cell spread. Our approach may be applied to not only understanding the roles of genetic polymorphisms in human susceptibility to filoviruses, but also other virus plaque assays.

Pixel precise unsupervised detection of viral particle proliferation in cellular imaging data

Cellular and molecular imaging techniques and models have been developed to characterize single stages of viral proliferation after focal infection of cells in vitro. The fast and automatic classification of cell imaging data may prove helpful prior to any further comparison of representative experimental data to mathematical models of viral propagation in host cells. Here, we use computer generated images drawn from a reproduction of an imaging model from a previously published study of experimentally obtained cell imaging data representing progressive viral particle proliferation in host cell monolayers. Inspired by experimental time-based imaging data, here in this study viral particle increase in time is simulated by a one-by-one increase, across images, in black or gray single pixels representing dead or partially infected cells, and hypothetical remission by a one-by-one increase in white pixels coding for living cells in the original image model. The image simulations are submitted to unsupervised learning by a Self-Organizing Map (SOM) and the Quantization Error in the SOM output (SOM-QE) is used for automatic classification of the image simulations as a function of the represented extent of viral particle proliferation or cell recovery. Unsupervised classification by SOM-QE of 160 model images, each with more than three million pixels, is shown to provide a statistically reliable, pixel precise, and fast classification model that outperforms human computer-assisted image classification by RGB image mean computation. The automatic classification procedure proposed here provides a powerful approach to understand finely tuned mechanisms in the infection and proliferation of virus in cell lines in vitro or other cells.

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Automatic classification of cell imaging data for in vitro viral propagation in host cells.

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Economical in terms of computation times for rapid change/no change detection in large image data prior to human decision making.

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Simulating viral proliferation/cell recovery by progressive and selective single pixel changes in contrast polarity and/or intensity.

Kinetic Modeling of Virus Growth in Cells

When a virus infects a host cell, it hijacks the biosynthetic capacity of the cell to produce virus progeny, a process that may take less than an hour or more than a week. The overall time required for a virus to reproduce depends collectively on the rates of multiple steps in the infection process, including initial binding of the virus particle to the surface of the cell, virus internalization and release of the viral genome within the cell, decoding of the genome to make viral proteins, replication of the genome, assembly of progeny virus particles, and release of these particles into the extracellular environment. For a large number of virus types, much has been learned about the molecular mechanisms and rates of the various steps. However, in only relatively few cases during the last 50 years has an attempt been made-using mathematical modeling-to account for how the different steps contribute to the overall timing and productivity of the infection cycle in a cell. Here we review the initial case studies, which include studies of the one-step growth behavior of viruses that infect bacteria (Qβ, T7, and M13), human immunodeficiency virus, influenza A virus, poliovirus, vesicular stomatitis virus, baculovirus, hepatitis B and C viruses, and herpes simplex virus. Further, we consider how such models enable one to explore how cellular resources are utilized and how antiviral strategies might be designed to resist escape. Finally, we highlight challenges and opportunities at the frontiers of cell-level modeling of virus infections.

Quantitative profiling of innate immune activation by viral infection in single cells

Cells infected by viruses can exhibit diverse patterns of viral and cellular gene expression. The patterns arise in part from the stochastic or noisy reaction kinetics associated with the small number of genomes, enzymes, and other molecules that typically initiate virus replication and activate cellular anti-viral defenses. It is not known what features, if any, of the early viral or cellular gene expression correlate with later processes of viral replication or cell survival. Here we used two fluorescent reporters to visualize innate immune activation of human prostate cancer (PC3) cells against infection by vesicular stomatitis virus. The cells were engineered to express green-fluorescent protein under control of the promoter for IFIT2, an interferon-sensitive component of the anti-viral response, while red-fluorescent protein was expressed as a byproduct of virus infection. To isolate and quantitatively analyze single-cells, we used a unique microwell array device and open-source image processing software. Kinetic analysis of viral and cellular reporter profiles from hundreds of cells revealed novel relationships between gene expression and the outcome of infection. Specifically, the relative timing rather than the magnitude of the viral gene expression and innate immune activation correlated with the infection outcome. Earlier viral or anti-viral gene expression favored or hindered virus growth, respectively. Further, analysis of kinetic parameters estimated from these data suggests a trade-off between robust antiviral signaling and cell death, as indicated by a higher rate of detectable cell lysis in infected cells with a detectable immune response. In short, cells that activate an immune response lyse at a higher rate. More broadly, we demonstrate how the intrinsic heterogeneity of individual cell behaviors can be exploited to discover features of viral and host gene expression that correlate with single-cell outcomes, which will ultimately impact whether or not infections spread.

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.

Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

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.

Rapid induction and persistence of paracrine-induced cellular antiviral states arrest viral infection spread in A549 cells

The virus/host interaction is a complex interplay between pro- and anti-viral factors that ultimately determines the spread or halt of virus infections in tissues. This interplay develops over multiple rounds of infection. The purpose of this study was to determine how cellular-level processes combine to impact the spatial spread of infection. We measured the kinetics of virus replication (VSV), antiviral paracrine signal upregulation and secretion, spatial spread of virus and paracrine antiviral signaling, and inhibition of virus production in antiviral-exposed A549 human lung epithelial cells. We found that initially infected cells released antiviral signals 4-to-7h following production of virus. However, the subsequent rapid dissemination of signal and fast induction of a robust and persistent antiviral state ultimately led to a suppression of infection spread. This work shows how cellular responses to infection and activation of antiviral responses can integrate to ultimately control infection spread across host cell populations.

A mathematical approach to virus therapy of glioblastomas

BACKGROUND

It is widely believed that the treatment of glioblastomas (GBM) could benefit from oncolytic virus therapy. Clinical research has shown that Vesicular Stomatitis Virus (VSV) has strong oncolytic properties. In addition, mathematical models of virus treatment of tumors have been developed in recent years. Some experiments in vitro and in vivo have been done and shown promising results, but have been never compared quantitatively with mathematical models. We use in vitro data of this virus applied to glioblastoma.

RESULTS

We describe three increasingly realistic mathematical models for the VSV-GBM in vitro experiment with progressive incorporation of time-delay effects. For the virus dynamics, we obtain results consistent with the in vitro experimental speed data only when applying the more complex and comprehensive model, with time-delay effects both in the reactive and diffusive terms. The tumor speed is given by the minimum of a very simple function that nonetheless yields results within the experimental measured range.

CONCLUSIONS

We have improved a previous model with new ideas and carefully incorporated concepts from experimental results. We have shown that the delay time τ is the crucial parameter in this kind of models. We have demonstrated that our new model can satisfactorily predict the front speed for the lytic action of oncolytic VSV on glioblastoma observed in vitro. We provide a basis that can be applied in the near future to realistically simulate in vivo virus treatments of several cancers.

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.

Stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Finally, numerical simulations are presented to verify the results.

A quantitative infection assay for human type I, II, and III interferon antiviral activities

Background

Upon virus infection, cells secrete a diverse group of antiviral molecules that signal proximal cells to enter into an antiviral state, slowing or preventing viral spread. These paracrine signaling molecules can work synergistically, so measurement of any one antiviral molecule does not reflect the total antiviral activity of the system.

Results

We have developed an antiviral assay based on replication inhibition of an engineered fluorescent vesicular stomatitis virus reporter strain on A549 human lung epithelial cells. Our assay provides a quantitative functional readout of human type I, II, and III interferon activities, and it provides better sensitivity, intra-, and inter-assay reproducibility than the traditional crystal violet based assay. Further, it eliminates cell fixation, rinsing, and staining steps, and is inexpensive to implement.

Conclusions

A dsRed2-strain of vesicular stomatitis virus that is sensitive to type I, II, and III interferons was used to develop a convenient and sensitive assay for interferon antiviral activity. We demonstrate use of the assay to quantify the kinetics of paracrine antiviral signaling from human prostate cancer (PC3) cells in response to viral infection. The assay is applicable to high-throughput screening for anti-viral compounds as well as basic studies of cellular antiviral signaling.

Towards multiscale modeling of influenza infection

Aided by recent advances in computational power, algorithms, and higher fidelity data, increasingly detailed theoretical models of infection with influenza A virus are being developed. We review single scale models as they describe influenza infection from intracellular to global scales, and, in particular, we consider those models that capture details specific to influenza and can be used to link different scales. We discuss the few multiscale models of influenza infection that have been developed in this emerging field. In addition to discussing modeling approaches, we also survey biological data on influenza infection and transmission that is relevant for constructing influenza infection models. We envision that, in the future, multiscale models that capitalize on technical advances in experimental biology and high performance computing could be used to describe the large spatial scale epidemiology of influenza infection, evolution of the virus, and transmission between hosts more accurately.

Kinetics of virus production from single cells

The production of virus by infected cells is an essential process for the spread and persistence of viral diseases, the effectiveness of live-viral vaccines, and the manufacture of viruses for diverse applications. Yet despite its importance, methods to precisely measure virus production from cells are lacking. Most methods test infected-cell populations, masking how individual cells behave. Here we measured the kinetics of virus production from single cells. We combined simple steps of liquid-phase infection, serial dilution, centrifugation, and harvesting, without specialized equipment, to track the production of virus particles from BHK cells infected with vesicular stomatitis virus. Remarkably, cell-to-cell differences in latent times to virus release were within a factor of two, while production rates and virus yields spanned over 300-fold, highlighting an extreme diversity in virus production for cells from the same population. These findings have fundamental and technological implications for health and disease.

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

Conditionally-replicating adenoviruses (CRAds) and other oncolytic viruses replicate selectively in tumor cells, presenting a potential cancer treatment approach. To optimize application of these viruses, understanding of early spread of these viruses in target cells is important. Here we used a recombinant adenovirus expressing enhanced jellyfish green fluorescent protein (EGFP) in place of the EIA and EIB genes (AdEGFPuci). Infection of susceptible cells (AD-293) under plaque formation conditions (MOI<<1) on gridded culture dishes and daily monitoring allowed visualization of initially infected cells, as well as spread to neighboring cells. We determined key parameters of early infection, including the rate and efficiency of spread from the initially infected cell to other cells. It was noteworthy that a minority of initially infected cells ultimately resulted in plaques. The approaches elucidated here will be useful for determining early infection parameters for CRAds of therapeutic interest.

Viral epidemics in a cell culture: novel high resolution data and their interpretation by a percolation theory based model

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation.

Virus infection speeds: theory versus experiment

In order to explain the speed of Vesicular Stomatitis Virus (VSV) infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a very important effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections.

Theoretical aspects of immunity

The immune system recognizes a myriad of invading pathogens and their toxic products. It does so with a finite repertoire of antibodies and T cell receptors. We here describe theories that quantify the dynamics of the immune system. We describe how the immune system recognizes antigens by searching the large space of receptor molecules. We consider in some detail the theories that quantify the immune response to influenza and dengue fever. We review theoretical descriptions of the complementary evolution of pathogens that occurs in response to immune system pressure. Methods including bioinformatics, molecular simulation, random energy models, and quantum field theory contribute to a theoretical understanding of aspects of immunity.

Dynamics of virus spread in the presence of fluid flow

The dynamics of viral infection spread, whether in laboratory cultures or in naturally infected hosts, reflects a coupling of biological and physical processes that remain to be fully elucidated. Biological processes include the kinetics of virus growth in infected cells while physical processes include transport of virus progeny from infected cells, where they are produced, to susceptible cells, where they initiate new infections. Mechanistic models of infection spread have been widely developed for systems where virus growth is coupled with transport of virus particles by diffusion, but they have yet to be developed for systems where viruses move under the influence of fluid flows. Recent experimental observations of flow-enhanced infection spread in laboratory cultures motivate here the development of initial continuum and discrete virus-particle models of infection spread. The magnitude of a dimensionless group, the Damköhler number, shows how parameters that characterize particle adsorption to cells, strain rates that reflect flow profiles, and diffusivities of virus particles combine to influence the spatial pattern of infection spread.

Virus-host interactions: from systems biology to translational research

Research embracing systems biology approaches and careful analysis of the critical host response has greatly expanded our understanding of infectious diseases. First-generation studies based on genomics and proteomics have made significant progress in establishing the foundation for network-based investigations on virus-host interactions. More recently, data from complementary high-throughput technologies, such as siRNA and microRNA screens and next-generation sequencing, are augmenting systems level analyses and are providing a more detailed and insightful multidimensional view of virus-host networks. Together with advances in data integration, systems biology approaches now have the potential to provide profound impacts on translational research, leading to the more rapid development of new therapeutics and vaccines for infectious diseases. In this review, we highlight new high-throughput technologies, a new philosophy for studying virus-host interactions, and discuss the potential of systems biology to facilitate bench-to-bedside research and create novel strategies to combat disease. Can we save the world using these approaches? Read on.

Implications of decoupling the intracellular and extracellular levels in multi-level models of virus growth

Virus infections are characterized by two distinct levels of detail: the intracellular level describing how viruses hijack the host machinery to replicate, and the extracellular level describing how populations of virus and host cells interact. Deterministic, population balance models for viral infections permit incorporation of both the intracellular and extracellular levels of information. In this work, we identify assumptions that lead to exact, selective decoupling of the interaction between the intracellular and extracellular levels, effectively permitting solution of first the intracellular level, and subsequently the extracellular level. This decoupling leads to (1) intracellular and extracellular models of viral infections that have been previously reported and (2) a significant reduction in the computational expense required to solve the model. However, the decoupling restricts the behaviors that can be modeled. Simulation of a previously reported multi-level model demonstrates this decomposition when the intracellular level of description consists of numerous reaction events. Additionally, examples demonstrate that viruses can persist even when the intracellular level of description cannot sustain a steady-state production of virus (i.e., has only a trivial equilibrium). We expect the combination of this modeling framework with experimental data to result in a quantitative, systems-level understanding of viral infections and cellular antiviral strategies that will facilitate controlling both these infections and antiviral strategies.