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

Wodarz D, Hofacre A, Lau JW, Sun Z, Fan H, Komarova NL - PLoS Comput. Biol. (2012)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, University of California, Irvine, California, United States of America. dwodarz@uci.edu

ABSTRACT
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.

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Related in: MedlinePlus

The phase diagram of the metapopulation model showing different outcomes of the dynamics depending on the parameters.The plot is a result of at least 104 instances of the simulations, where log10 of the parameters was varied between −4 and 4. The metapopulation consisted of 100 local populations or spots, each characterized by a carrying capacity k = 100. In the middle spot, the simulation was started with 30 infected and 70 uninfected cells. In the subsequent five spots to the left and to the right of the middle spot, the uninfected cell population was at carrying capacity, without the presence of infected cells. The rest of the spots were initially empty. Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and the virus. Grey indicates extinction of the virus while cells persist. Above the white line and below the black line, the local equilibrium number of uninfected and infected cells, respectively, is greater than one. Below the yellow line, the virus can successfully invade its target cell population, derived from the basic reproductive ratio of the virus. See text for more details and a description of all the outcomes.
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pcbi-1002547-g009: The phase diagram of the metapopulation model showing different outcomes of the dynamics depending on the parameters.The plot is a result of at least 104 instances of the simulations, where log10 of the parameters was varied between −4 and 4. The metapopulation consisted of 100 local populations or spots, each characterized by a carrying capacity k = 100. In the middle spot, the simulation was started with 30 infected and 70 uninfected cells. In the subsequent five spots to the left and to the right of the middle spot, the uninfected cell population was at carrying capacity, without the presence of infected cells. The rest of the spots were initially empty. Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and the virus. Grey indicates extinction of the virus while cells persist. Above the white line and below the black line, the local equilibrium number of uninfected and infected cells, respectively, is greater than one. Below the yellow line, the virus can successfully invade its target cell population, derived from the basic reproductive ratio of the virus. See text for more details and a description of all the outcomes.

Mentions: As initial conditions we assume that in a subset of adjacent local patches in the middle of the metapopulation, target cells are present at their infection-free equilibrium levels. The rest of the patches are initially empty. A small amount of infected cells are placed into the middle patch, and the infection is allowed to spread from there (See appropriate figures for exact initial conditions). Figure 9 shows the diagram of various outcomes observed in this model, and it is remarkably similar to the diagrams produced by the agent-based models. The same basic outcomes are observed: extinction of the target cells and consequently the infected cells; extinction of the infection and persistence of the target cells; coexistence of infected and uninfected cells. As before, there are two modes of extinction: in scenario MA, the virus is sufficiently strong, such that when it expands as a wave, it leaves no target cells behind in its wake, and overtakes the expanding target cell wave, leading to extinction of both populations. In scenario MB, a weaker virus can still expand as a wave, leave no susceptible cells in its wake, and catch up with the target cell wave. However, it fails to destroy the target cell wave. Instead, the two waves travel together with the same velocity until the boundary is reached, at which point extinction occurs. In region MB1, the same basic dynamics occur as in region MB. However, the traveling waves can split and travel independently in different directions, thus avoiding extinction when the boundary is reached (i.e. before a wave hits the boundary and goes extinct, it gives rise to another waves that travels independently). Thus, while local extinction occurs, the populations are maintained globally through the traveling waves. In region MC we observe “true coexistence”, where populations eventually persist locally across most of the patches. Finally, virus extinction can be observed either following initial invasion (region MD) or if the local basic reproductive ratio of the virus is less than one resulting in failure to invade (region ME).


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

Wodarz D, Hofacre A, Lau JW, Sun Z, Fan H, Komarova NL - PLoS Comput. Biol. (2012)

The phase diagram of the metapopulation model showing different outcomes of the dynamics depending on the parameters.The plot is a result of at least 104 instances of the simulations, where log10 of the parameters was varied between −4 and 4. The metapopulation consisted of 100 local populations or spots, each characterized by a carrying capacity k = 100. In the middle spot, the simulation was started with 30 infected and 70 uninfected cells. In the subsequent five spots to the left and to the right of the middle spot, the uninfected cell population was at carrying capacity, without the presence of infected cells. The rest of the spots were initially empty. Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and the virus. Grey indicates extinction of the virus while cells persist. Above the white line and below the black line, the local equilibrium number of uninfected and infected cells, respectively, is greater than one. Below the yellow line, the virus can successfully invade its target cell population, derived from the basic reproductive ratio of the virus. See text for more details and a description of all the outcomes.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3375216&req=5

pcbi-1002547-g009: The phase diagram of the metapopulation model showing different outcomes of the dynamics depending on the parameters.The plot is a result of at least 104 instances of the simulations, where log10 of the parameters was varied between −4 and 4. The metapopulation consisted of 100 local populations or spots, each characterized by a carrying capacity k = 100. In the middle spot, the simulation was started with 30 infected and 70 uninfected cells. In the subsequent five spots to the left and to the right of the middle spot, the uninfected cell population was at carrying capacity, without the presence of infected cells. The rest of the spots were initially empty. Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and the virus. Grey indicates extinction of the virus while cells persist. Above the white line and below the black line, the local equilibrium number of uninfected and infected cells, respectively, is greater than one. Below the yellow line, the virus can successfully invade its target cell population, derived from the basic reproductive ratio of the virus. See text for more details and a description of all the outcomes.
Mentions: As initial conditions we assume that in a subset of adjacent local patches in the middle of the metapopulation, target cells are present at their infection-free equilibrium levels. The rest of the patches are initially empty. A small amount of infected cells are placed into the middle patch, and the infection is allowed to spread from there (See appropriate figures for exact initial conditions). Figure 9 shows the diagram of various outcomes observed in this model, and it is remarkably similar to the diagrams produced by the agent-based models. The same basic outcomes are observed: extinction of the target cells and consequently the infected cells; extinction of the infection and persistence of the target cells; coexistence of infected and uninfected cells. As before, there are two modes of extinction: in scenario MA, the virus is sufficiently strong, such that when it expands as a wave, it leaves no target cells behind in its wake, and overtakes the expanding target cell wave, leading to extinction of both populations. In scenario MB, a weaker virus can still expand as a wave, leave no susceptible cells in its wake, and catch up with the target cell wave. However, it fails to destroy the target cell wave. Instead, the two waves travel together with the same velocity until the boundary is reached, at which point extinction occurs. In region MB1, the same basic dynamics occur as in region MB. However, the traveling waves can split and travel independently in different directions, thus avoiding extinction when the boundary is reached (i.e. before a wave hits the boundary and goes extinct, it gives rise to another waves that travels independently). Thus, while local extinction occurs, the populations are maintained globally through the traveling waves. In region MC we observe “true coexistence”, where populations eventually persist locally across most of the patches. Finally, virus extinction can be observed either following initial invasion (region MD) or if the local basic reproductive ratio of the virus is less than one resulting in failure to invade (region ME).

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, University of California, Irvine, California, United States of America. dwodarz@uci.edu

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus