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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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Two different experimentally observed time series of adenovirus (AdEGFPuci) growth on human 293 embryonic kidney epithelial cells, arranged in a two dimensional layer.The number of cells was determined by measuring the fluorescent area of the infected cell population, divided by the fluorescent area of individual infected cells, using Photoshop (see Methods as well as Text S1). The graph is based on a single experimental run. The area however, was measured independently four times, giving rise to the plotted error bars. The black middle line through the data represents the time series predicted by the agent-based model, using a parameter combination that was obtained by a least squares fitting procedure. Since the model is stochastic, the predicted time series represents the average over 1000 instances of the simulation. The upper and lower lines show the standard deviations added to and subtracted from the average. (a) This experiment shows virus growth characterized by the formation of a ring structure. Consequently there is a relatively short phase of quadratic growth, followed by a transition to linear growth. (b) This experiment shows disperse virus growth characterized by quadratic growth throughout time. The corresponding observed and predicted spatial patterns are shown in Figures 4 and 5. Values for parameters R, B, and A were obtained from the fitting procedures and are given as follows: (a) R = 0.18, B = 0.26, A = 1.85×10−2. (b) R = 0.19, B = 0.52, A = 0.12. The parameter D was kept constant at D = 0. For further details of the fit, including initial conditions and the time step of the simulation, see Text S1.
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pcbi-1002547-g003: Two different experimentally observed time series of adenovirus (AdEGFPuci) growth on human 293 embryonic kidney epithelial cells, arranged in a two dimensional layer.The number of cells was determined by measuring the fluorescent area of the infected cell population, divided by the fluorescent area of individual infected cells, using Photoshop (see Methods as well as Text S1). The graph is based on a single experimental run. The area however, was measured independently four times, giving rise to the plotted error bars. The black middle line through the data represents the time series predicted by the agent-based model, using a parameter combination that was obtained by a least squares fitting procedure. Since the model is stochastic, the predicted time series represents the average over 1000 instances of the simulation. The upper and lower lines show the standard deviations added to and subtracted from the average. (a) This experiment shows virus growth characterized by the formation of a ring structure. Consequently there is a relatively short phase of quadratic growth, followed by a transition to linear growth. (b) This experiment shows disperse virus growth characterized by quadratic growth throughout time. The corresponding observed and predicted spatial patterns are shown in Figures 4 and 5. Values for parameters R, B, and A were obtained from the fitting procedures and are given as follows: (a) R = 0.18, B = 0.26, A = 1.85×10−2. (b) R = 0.19, B = 0.52, A = 0.12. The parameter D was kept constant at D = 0. For further details of the fit, including initial conditions and the time step of the simulation, see Text S1.

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)

Two different experimentally observed time series of adenovirus (AdEGFPuci) growth on human 293 embryonic kidney epithelial cells, arranged in a two dimensional layer.The number of cells was determined by measuring the fluorescent area of the infected cell population, divided by the fluorescent area of individual infected cells, using Photoshop (see Methods as well as Text S1). The graph is based on a single experimental run. The area however, was measured independently four times, giving rise to the plotted error bars. The black middle line through the data represents the time series predicted by the agent-based model, using a parameter combination that was obtained by a least squares fitting procedure. Since the model is stochastic, the predicted time series represents the average over 1000 instances of the simulation. The upper and lower lines show the standard deviations added to and subtracted from the average. (a) This experiment shows virus growth characterized by the formation of a ring structure. Consequently there is a relatively short phase of quadratic growth, followed by a transition to linear growth. (b) This experiment shows disperse virus growth characterized by quadratic growth throughout time. The corresponding observed and predicted spatial patterns are shown in Figures 4 and 5. Values for parameters R, B, and A were obtained from the fitting procedures and are given as follows: (a) R = 0.18, B = 0.26, A = 1.85×10−2. (b) R = 0.19, B = 0.52, A = 0.12. The parameter D was kept constant at D = 0. For further details of the fit, including initial conditions and the time step of the simulation, see Text S1.
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pcbi-1002547-g003: Two different experimentally observed time series of adenovirus (AdEGFPuci) growth on human 293 embryonic kidney epithelial cells, arranged in a two dimensional layer.The number of cells was determined by measuring the fluorescent area of the infected cell population, divided by the fluorescent area of individual infected cells, using Photoshop (see Methods as well as Text S1). The graph is based on a single experimental run. The area however, was measured independently four times, giving rise to the plotted error bars. The black middle line through the data represents the time series predicted by the agent-based model, using a parameter combination that was obtained by a least squares fitting procedure. Since the model is stochastic, the predicted time series represents the average over 1000 instances of the simulation. The upper and lower lines show the standard deviations added to and subtracted from the average. (a) This experiment shows virus growth characterized by the formation of a ring structure. Consequently there is a relatively short phase of quadratic growth, followed by a transition to linear growth. (b) This experiment shows disperse virus growth characterized by quadratic growth throughout time. The corresponding observed and predicted spatial patterns are shown in Figures 4 and 5. Values for parameters R, B, and A were obtained from the fitting procedures and are given as follows: (a) R = 0.18, B = 0.26, A = 1.85×10−2. (b) R = 0.19, B = 0.52, A = 0.12. The parameter D was kept constant at D = 0. For further details of the fit, including initial conditions and the time step of the simulation, see Text S1.
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