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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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Dependence of outcomes on parameters in the agent-based model for (a) a relatively small 30×30 grid, and (b) a relatively large 300×300 grid.The plot is the result of at least 104 instances of the simulations, where the log10 of the parameters was varied between −4 and 4. The simulations were started by placing a small number of infected cells (5×5 cells) into a larger space filled with infected cells (13×13 cells). Identical results were observed over a very large range of initial conditions (differences were only observed if the initial number of cells is such that immediate stochastic extinction is likely, which are not regions of interest with respect to our study). Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and thus the virus. Red is used if extinction occurs before the boundary of the system has been reached, while orange is used if extinction occurs after cells have reached the boundary of the system. 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. This derives from ordinary differential equations that describe the dynamics within local neighborhoods where all cells can interact with each other (see Text S1). Below the yellow line, the virus can successfully invade its target cell population. This invasion threshold was determined by numerical simulations. The capital letters indicate different spatial patterns that are described in the text and in Figure 7. In these simulations, the probability for an uninfected cell to die was kept constant at D = 0.
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pcbi-1002547-g006: Dependence of outcomes on parameters in the agent-based model for (a) a relatively small 30×30 grid, and (b) a relatively large 300×300 grid.The plot is the result of at least 104 instances of the simulations, where the log10 of the parameters was varied between −4 and 4. The simulations were started by placing a small number of infected cells (5×5 cells) into a larger space filled with infected cells (13×13 cells). Identical results were observed over a very large range of initial conditions (differences were only observed if the initial number of cells is such that immediate stochastic extinction is likely, which are not regions of interest with respect to our study). Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and thus the virus. Red is used if extinction occurs before the boundary of the system has been reached, while orange is used if extinction occurs after cells have reached the boundary of the system. 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. This derives from ordinary differential equations that describe the dynamics within local neighborhoods where all cells can interact with each other (see Text S1). Below the yellow line, the virus can successfully invade its target cell population. This invasion threshold was determined by numerical simulations. The capital letters indicate different spatial patterns that are described in the text and in Figure 7. In these simulations, the probability for an uninfected cell to die was kept constant at D = 0.

Mentions: Here, we explore the long term dynamics, investigating how the above described patterns play out and correlate with the overall outcome if both the uninfected and infected cell population can expand in space. We seek to define conditions under which the virus can eliminate the target cell population in this system. All simulations are started with a small number of infected cells placed in a compact vicinity into a larger space filled with uninfected cells, which is in turn embedded into an even larger “empty” space (for the exact initial conditions for particular cases, see appropriate figure legends). In contrast to the simulations reported above, here we go beyond the initial virus growth stage, and focus on time-scales where the population of target cells experiences significant changes (grows in size in the absence of infection). The outcomes of this system include extinction of the target cells and thus the virus; extinction of the virus and persistence of the target cells; coexistence of virus and target cells. The dependency of these outcomes on the parameters is shown in Figure 6, which is the result of at least 104 instances of the simulation, where the log10 of all the parameters was varied between −4 and 4. Figures 7 and 8 show corresponding spatial and temporal patterns. We examine the outcomes first in a relatively small 30×30 grid, and subsequently in a larger, 300×300 grid.


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)

Dependence of outcomes on parameters in the agent-based model for (a) a relatively small 30×30 grid, and (b) a relatively large 300×300 grid.The plot is the result of at least 104 instances of the simulations, where the log10 of the parameters was varied between −4 and 4. The simulations were started by placing a small number of infected cells (5×5 cells) into a larger space filled with infected cells (13×13 cells). Identical results were observed over a very large range of initial conditions (differences were only observed if the initial number of cells is such that immediate stochastic extinction is likely, which are not regions of interest with respect to our study). Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and thus the virus. Red is used if extinction occurs before the boundary of the system has been reached, while orange is used if extinction occurs after cells have reached the boundary of the system. 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. This derives from ordinary differential equations that describe the dynamics within local neighborhoods where all cells can interact with each other (see Text S1). Below the yellow line, the virus can successfully invade its target cell population. This invasion threshold was determined by numerical simulations. The capital letters indicate different spatial patterns that are described in the text and in Figure 7. In these simulations, the probability for an uninfected cell to die was kept constant at D = 0.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3375216&req=5

pcbi-1002547-g006: Dependence of outcomes on parameters in the agent-based model for (a) a relatively small 30×30 grid, and (b) a relatively large 300×300 grid.The plot is the result of at least 104 instances of the simulations, where the log10 of the parameters was varied between −4 and 4. The simulations were started by placing a small number of infected cells (5×5 cells) into a larger space filled with infected cells (13×13 cells). Identical results were observed over a very large range of initial conditions (differences were only observed if the initial number of cells is such that immediate stochastic extinction is likely, which are not regions of interest with respect to our study). Blue indicates coexistence of virus and cells. Red and orange indicate extinction of the cells and thus the virus. Red is used if extinction occurs before the boundary of the system has been reached, while orange is used if extinction occurs after cells have reached the boundary of the system. 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. This derives from ordinary differential equations that describe the dynamics within local neighborhoods where all cells can interact with each other (see Text S1). Below the yellow line, the virus can successfully invade its target cell population. This invasion threshold was determined by numerical simulations. The capital letters indicate different spatial patterns that are described in the text and in Figure 7. In these simulations, the probability for an uninfected cell to die was kept constant at D = 0.
Mentions: Here, we explore the long term dynamics, investigating how the above described patterns play out and correlate with the overall outcome if both the uninfected and infected cell population can expand in space. We seek to define conditions under which the virus can eliminate the target cell population in this system. All simulations are started with a small number of infected cells placed in a compact vicinity into a larger space filled with uninfected cells, which is in turn embedded into an even larger “empty” space (for the exact initial conditions for particular cases, see appropriate figure legends). In contrast to the simulations reported above, here we go beyond the initial virus growth stage, and focus on time-scales where the population of target cells experiences significant changes (grows in size in the absence of infection). The outcomes of this system include extinction of the target cells and thus the virus; extinction of the virus and persistence of the target cells; coexistence of virus and target cells. The dependency of these outcomes on the parameters is shown in Figure 6, which is the result of at least 104 instances of the simulation, where the log10 of all the parameters was varied between −4 and 4. Figures 7 and 8 show corresponding spatial and temporal patterns. We examine the outcomes first in a relatively small 30×30 grid, and subsequently in a larger, 300×300 grid.

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