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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

Observed (a) and predicted (b) spatial pattern of adenovirus (AdEGFPuci) growth for the experiment that exhibits a ring structure (time series given in Figure 3a).The predicted spatial pattern is the result of an individual run of the agent-based model with the parameter combination obtained from the model fitting procedure. Snapshots in time are shown, representing days 7, 9, 11, and 13 post infection. (a) The area of green fluorescence is shown, expressed by the infected cells, thus documenting the spatial spread of the virus through the population target cells arranged in a two dimensional setting. (b) In the computer simulation, green indicates infected cells, red infected cells, and grey empty spots.
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pcbi-1002547-g004: Observed (a) and predicted (b) spatial pattern of adenovirus (AdEGFPuci) growth for the experiment that exhibits a ring structure (time series given in Figure 3a).The predicted spatial pattern is the result of an individual run of the agent-based model with the parameter combination obtained from the model fitting procedure. Snapshots in time are shown, representing days 7, 9, 11, and 13 post infection. (a) The area of green fluorescence is shown, expressed by the infected cells, thus documenting the spatial spread of the virus through the population target cells arranged in a two dimensional setting. (b) In the computer simulation, green indicates infected cells, red infected cells, and grey empty spots.

Mentions: In order to go beyond the qualitative comparison of model and data, we fit the model to two sets of experimental data, one showing an expanding hollow ring, and the other the disperse growth pattern. A least squares algorithm (see Text S1) was used to fit the number of infected cells over time, and a relatively good fit was obtained for both cases (Figure 3). The types of spatial patterns that emerged matched the observed ones qualitatively (Figures 4 and 5). While this procedure found best fitting parameter values, their biological meaning remains questionable, since different parameter combinations can give rise to similarly good fits. A more solid validation would require an independent estimation of parameter values, and a subsequent generation of the predicted growth patterns. Due to the complexity of the experimental observations, this is not currently possible and is discussed in detail below. The fitting procedure does, however, indicate that the model is at least consistent with experimental data.


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)

Observed (a) and predicted (b) spatial pattern of adenovirus (AdEGFPuci) growth for the experiment that exhibits a ring structure (time series given in Figure 3a).The predicted spatial pattern is the result of an individual run of the agent-based model with the parameter combination obtained from the model fitting procedure. Snapshots in time are shown, representing days 7, 9, 11, and 13 post infection. (a) The area of green fluorescence is shown, expressed by the infected cells, thus documenting the spatial spread of the virus through the population target cells arranged in a two dimensional setting. (b) In the computer simulation, green indicates infected cells, red infected cells, and grey empty spots.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002547-g004: Observed (a) and predicted (b) spatial pattern of adenovirus (AdEGFPuci) growth for the experiment that exhibits a ring structure (time series given in Figure 3a).The predicted spatial pattern is the result of an individual run of the agent-based model with the parameter combination obtained from the model fitting procedure. Snapshots in time are shown, representing days 7, 9, 11, and 13 post infection. (a) The area of green fluorescence is shown, expressed by the infected cells, thus documenting the spatial spread of the virus through the population target cells arranged in a two dimensional setting. (b) In the computer simulation, green indicates infected cells, red infected cells, and grey empty spots.
Mentions: In order to go beyond the qualitative comparison of model and data, we fit the model to two sets of experimental data, one showing an expanding hollow ring, and the other the disperse growth pattern. A least squares algorithm (see Text S1) was used to fit the number of infected cells over time, and a relatively good fit was obtained for both cases (Figure 3). The types of spatial patterns that emerged matched the observed ones qualitatively (Figures 4 and 5). While this procedure found best fitting parameter values, their biological meaning remains questionable, since different parameter combinations can give rise to similarly good fits. A more solid validation would require an independent estimation of parameter values, and a subsequent generation of the predicted growth patterns. Due to the complexity of the experimental observations, this is not currently possible and is discussed in detail below. The fitting procedure does, however, indicate that the model is at least consistent with experimental data.

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