Computational modeling approaches to studying the dynamics of oncolytic viruses

Dominik Wodarz

doi:10.3934/mbe.2013.10.939

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2013, 10(3): 939-957. doi: 10.3934/mbe.2013.10.939

Computational modeling approaches to studying the dynamics of oncolytic viruses

Dominik Wodarz ^1,

1.	Department of Ecology and Evolutionary Biology, University of California, 321 Steinhaus Hall, Irvine, CA 92617, United States

Received July 2012 Revised February 2013 Published April 2013

Abstract
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Oncolytic viruses specifically infect cancer cells, replicate in them, kill them, and spread to further tumor cells. They represent a targeted treatment approach that is promising in principle, but consistent success has yet to be observed. Mathematical models can play an important role in analyzing the dynamics between oncolytic viruses and a growing tumor cell population, providing insights that can be useful for the further development of this therapy approach. This article reviews different mathematical modeling approaches ranging from ordinary differential equations to spatially explicit agent-based models. Problems of model robustness are discussed and so are some clinically important insight derived from the models.

Keywords: therapy, mathematical models, Oncolytic viruses, spatial dynamics., cancer, population dynamics.

Mathematics Subject Classification: 92D2.

Citation: Dominik Wodarz. Computational modeling approaches to studying the dynamics of oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 939-957. doi: 10.3934/mbe.2013.10.939

References:

[1]	J. C. Bell, Oncolytic viruses: What's next?,, Curr. Cancer Drug Targets, 7 (2007), 127. Google Scholar
[2]	J. C. Bell, B. Lichty and D. Stojdl, Getting oncolytic virus therapies off the ground,, Cancer Cell, 4 (2003), 7. Google Scholar
[3]	A. M. Crompton and D. H. Kirn, From ONYX-015 to armed vaccinia viruses: The education and evolution of oncolytic virus development,, Curr. Cancer Drug Targets, 7 (2007), 133. Google Scholar
[4]	J. J. Davis and B. Fang, Oncolytic virotherapy for cancer treatment: Challenges and solutions,, J. Gene. Med., 7 (2005), 1380. Google Scholar
[5]	J. M. Kaplan, Adenovirus-based cancer gene therapy,, Curr. Gene Ther., 5 (2005), 595. Google Scholar
[6]	E. Kelly and S. J. Russell, History of oncolytic viruses: Genesis to genetic engineering,, Mol. Ther., 15 (2007), 651. Google Scholar
[7]	D. H. Kirn and F. McCormick, Replicating viruses as selective cancer therapeutics,, Mol. Med. Today, 2 (1996), 519. Google Scholar
[8]	F. McCormick, Cancer-specific viruses and the development of ONYX-015,, Cancer Biol. Ther., 2 (2003), 157. Google Scholar
[9]	F. McCormick, Future prospects for oncolytic therapy,, Oncogene, 24 (2005), 7817. Google Scholar
[10]	C. C. O'Shea, Viruses - seeking and destroying the tumor program,, Oncogene, 24 (2005), 7640. Google Scholar
[11]	K. A. Parato, et. al., Recent progress in the battle between oncolytic viruses and tumours,, Nat. Rev. Cancer, 5 (2005), 965. Google Scholar
[12]	D. E. Post, et. al., Cancer scene investigation: how a cold virus became a tumor killer,, Future Oncol., 1 (2005), 247. Google Scholar
[13]	M. S. Roberts, et. al., Naturally oncolytic viruses,, Curr. Opin. Mol. Ther., 8 (2006), 314. doi: 10.1080/08898480600950473. Google Scholar
[14]	M. J. Vaha-Koskela, J. E. Heikkila and A. E. Hinkkanen, Oncolytic viruses in cancer therapy,, Cancer Lett., (2007). Google Scholar
[15]	H. H. Wong, N. R. Lemoine and Y. Wang, Oncolytic viruses for cancer therapy: Overcoming the obstacles,, Viruses, 2 (2010), 78. Google Scholar
[16]	D. Koppers-Lalic and R. C. Hoeben, Non-human viruses developed as therapeutic agent for use in humans,, Rev. Med. Virol, 21 (2011), 227. Google Scholar
[17]	R. L. Martuza, et. al., Experimental therapy of human glioma by means of a genetically engineered virus mutant,, Science, 252 (1991), 854. Google Scholar
[18]	K. Garber, China approves world's first oncolytic virus therapy for cancer treatment,, J. Natl. Cancer Inst., 98 (2006), 298. Google Scholar
[19]	R. M. Eager and J. Nemunaitis, Clinical development directions in oncolytic viral therapy,, Cancer Gene. Ther., 18 (2011), 305. Google Scholar
[20]	D. Wodarz, Viruses as antitumor weapons: Defining conditions for tumor remission,, Cancer Res., 61 (2001), 3501. Google Scholar
[21]	D. Wodarz, Gene therapy for killing p53-negative cancer cells: Use of replicating versus nonreplicating agents,, Hum. Gene. Ther., 14 (2003), 153. Google Scholar
[22]	Z. Bajzer, et. al., Modeling of cancer virotherapy with recombinant measles viruses,, J. Theor. Biol., 252 (2008), 109. doi: 10.1016/j.jtbi.2008.01.016. Google Scholar
[23]	M. Biesecker, et. al., Optimization of virotherapy for cancer,, Bull. Math. Biol., 72 (2010), 469. doi: 10.1007/s11538-009-9456-0. Google Scholar
[24]	D. Dingli, et. al., Mathematical modeling of cancer radiovirotherapy,, Math. Biosci., 199 (2006), 55. doi: 10.1016/j.mbs.2005.11.001. Google Scholar
[25]	D. Dingli, et. al., Dynamics of multiple myeloma tumor therapy with a recombinant measles virus,, Cancer Gene Ther., 16 (2009), 873. Google Scholar
[26]	A. Friedman, et. al., Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity,, Cancer Res., 66 (2006), 2314. Google Scholar
[27]	G. P. Karev, A. S. Novozhilov and E. V. Koonin, Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics,, Biol. Direct, 1 (2006). Google Scholar
[28]	N. L. Komarova and D. Wodarz, ODE models for oncolytic virus dynamics,, J. Theor. Biol., 263 (2010), 530. doi: 10.1016/j.jtbi.2010.01.009. Google Scholar
[29]	A. S. Novozhilov, et. al., Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models,, Biol. Direct, 1 (2006). Google Scholar
[30]	L. M. Wein, J. T. Wu and D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: Implications for virus design and delivery,, Cancer Res., 63 (2003), 1317. Google Scholar
[31]	D. Wodarz, Computational approaches to study oncolytic virus therapy: Insights and challenges,, Gene Therapy and Molecular Biology, 8 (2004), 137. Google Scholar
[32]	D. Wodarz, Use of oncolytic viruses for the eradication of drug-resistant cancer cells,, J. R. Soc. Interface, 6 (2009), 179. Google Scholar
[33]	D. Wodarz and N. Komarova, Towards predictive computational models of oncolytic virus therapy: Basis for experimental validation and model selection,, PLoS ONE, 4 (2009). Google Scholar
[34]	N. Bagheri, et. al., A dynamical systems model for combinatorial cancer therapy enhances oncolytic adenovirus efficacy by MEK-inhibition,, PLoS Comput. Biol., 7 (2011). Google Scholar
[35]	R. Zurakowski and D. Wodarz, Model-driven approaches for in vitro combination therapy using ONYX-015 replicating oncolytic adenovirus,, J. Theor. Biol., 245 (2007), 1. doi: 10.1016/j.jtbi.2006.09.029. Google Scholar
[36]	W. Mok, et. al., Mathematical modeling of herpes simplex virus distribution in solid tumors: Implications for cancer gene therapy,, Clin. Cancer Res., 15 (2009), 2352. Google Scholar
[37]	L. R. Paiva, et. al., A multiscale mathematical model for oncolytic virotherapy,, Cancer Res., 69 (2009), 1205. Google Scholar
[38]	C. L. Reis, et. al., In silico evolutionary dynamics of tumour virotherapy,, Integr. Biol. (Camb), 2 (2010), 41. Google Scholar
[39]	L. You, C. T. Yang and D. M. Jablons, ONYX-015 works synergistically with chemotherapy in lung cancer cell lines and primary cultures freshly made from lung cancer patients,, Cancer Res., 60 (2000), 1009. Google Scholar
[40]	A. Chahlavi, et. al., Replication-competent herpes simplex virus vector G207 and cisplatin combination therapy for head and neck squamous cell carcinoma,, Neoplasia, 1 (1999), 162. Google Scholar
[41]	I. A. Rodriguez-Brenes, N. L. Komarova and D. Wodarz, Evolutionary dynamics of feedback escape and the development of stem-cell-driven cancers,, Proc. Natl. Acad. Sci. U S A, 108 (2011), 18983. Google Scholar
[42]	D. Wodarz, et. al., Complex spatial dynamics of oncolytic viruses in vitro: Mathematical and experimental approaches,, PLoS Comput. Biol., 8 (2012). Google Scholar
[43]	K. Sato, H. Matsuda and A. Sasaki, Pathogen invasion and host extinction in lattice structured populations,, Journal of Mathematical Biology, 32 (1994), 251. Google Scholar
[44]	A. M. Deroos, E. Mccauley and W. G. Wilson, Mobility versus density-limited predator prey dynamics on different spatial scales,, Proceedings of the Royal Society of London Series B-Biological Sciences, 246 (1991), 117. Google Scholar
[45]	M. Pascual, P. Mazzega and S. A. Levin, Oscillatory dynamics and spatial scale: The role of noise and unresolved pattern,, Ecology, 82 (2001), 2357. Google Scholar
[46]	R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", 1991, (). Google Scholar
[47]	M. A. Nowak and R. M. May, "Virus Dynamics. Mathematical Principles of Immunology and Virology,", 2000: Oxford University Press., (). Google Scholar
[48]	M. P. Hassell, "The Spatial and Temporal Dynamics of Host-Parasitoid Interactions,", 2000, (). Google Scholar

show all references

References:

[1]	J. C. Bell, Oncolytic viruses: What's next?,, Curr. Cancer Drug Targets, 7 (2007), 127. Google Scholar
[2]	J. C. Bell, B. Lichty and D. Stojdl, Getting oncolytic virus therapies off the ground,, Cancer Cell, 4 (2003), 7. Google Scholar
[3]	A. M. Crompton and D. H. Kirn, From ONYX-015 to armed vaccinia viruses: The education and evolution of oncolytic virus development,, Curr. Cancer Drug Targets, 7 (2007), 133. Google Scholar
[4]	J. J. Davis and B. Fang, Oncolytic virotherapy for cancer treatment: Challenges and solutions,, J. Gene. Med., 7 (2005), 1380. Google Scholar
[5]	J. M. Kaplan, Adenovirus-based cancer gene therapy,, Curr. Gene Ther., 5 (2005), 595. Google Scholar
[6]	E. Kelly and S. J. Russell, History of oncolytic viruses: Genesis to genetic engineering,, Mol. Ther., 15 (2007), 651. Google Scholar
[7]	D. H. Kirn and F. McCormick, Replicating viruses as selective cancer therapeutics,, Mol. Med. Today, 2 (1996), 519. Google Scholar
[8]	F. McCormick, Cancer-specific viruses and the development of ONYX-015,, Cancer Biol. Ther., 2 (2003), 157. Google Scholar
[9]	F. McCormick, Future prospects for oncolytic therapy,, Oncogene, 24 (2005), 7817. Google Scholar
[10]	C. C. O'Shea, Viruses - seeking and destroying the tumor program,, Oncogene, 24 (2005), 7640. Google Scholar
[11]	K. A. Parato, et. al., Recent progress in the battle between oncolytic viruses and tumours,, Nat. Rev. Cancer, 5 (2005), 965. Google Scholar
[12]	D. E. Post, et. al., Cancer scene investigation: how a cold virus became a tumor killer,, Future Oncol., 1 (2005), 247. Google Scholar
[13]	M. S. Roberts, et. al., Naturally oncolytic viruses,, Curr. Opin. Mol. Ther., 8 (2006), 314. doi: 10.1080/08898480600950473. Google Scholar
[14]	M. J. Vaha-Koskela, J. E. Heikkila and A. E. Hinkkanen, Oncolytic viruses in cancer therapy,, Cancer Lett., (2007). Google Scholar
[15]	H. H. Wong, N. R. Lemoine and Y. Wang, Oncolytic viruses for cancer therapy: Overcoming the obstacles,, Viruses, 2 (2010), 78. Google Scholar
[16]	D. Koppers-Lalic and R. C. Hoeben, Non-human viruses developed as therapeutic agent for use in humans,, Rev. Med. Virol, 21 (2011), 227. Google Scholar
[17]	R. L. Martuza, et. al., Experimental therapy of human glioma by means of a genetically engineered virus mutant,, Science, 252 (1991), 854. Google Scholar
[18]	K. Garber, China approves world's first oncolytic virus therapy for cancer treatment,, J. Natl. Cancer Inst., 98 (2006), 298. Google Scholar
[19]	R. M. Eager and J. Nemunaitis, Clinical development directions in oncolytic viral therapy,, Cancer Gene. Ther., 18 (2011), 305. Google Scholar
[20]	D. Wodarz, Viruses as antitumor weapons: Defining conditions for tumor remission,, Cancer Res., 61 (2001), 3501. Google Scholar
[21]	D. Wodarz, Gene therapy for killing p53-negative cancer cells: Use of replicating versus nonreplicating agents,, Hum. Gene. Ther., 14 (2003), 153. Google Scholar
[22]	Z. Bajzer, et. al., Modeling of cancer virotherapy with recombinant measles viruses,, J. Theor. Biol., 252 (2008), 109. doi: 10.1016/j.jtbi.2008.01.016. Google Scholar
[23]	M. Biesecker, et. al., Optimization of virotherapy for cancer,, Bull. Math. Biol., 72 (2010), 469. doi: 10.1007/s11538-009-9456-0. Google Scholar
[24]	D. Dingli, et. al., Mathematical modeling of cancer radiovirotherapy,, Math. Biosci., 199 (2006), 55. doi: 10.1016/j.mbs.2005.11.001. Google Scholar
[25]	D. Dingli, et. al., Dynamics of multiple myeloma tumor therapy with a recombinant measles virus,, Cancer Gene Ther., 16 (2009), 873. Google Scholar
[26]	A. Friedman, et. al., Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity,, Cancer Res., 66 (2006), 2314. Google Scholar
[27]	G. P. Karev, A. S. Novozhilov and E. V. Koonin, Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics,, Biol. Direct, 1 (2006). Google Scholar
[28]	N. L. Komarova and D. Wodarz, ODE models for oncolytic virus dynamics,, J. Theor. Biol., 263 (2010), 530. doi: 10.1016/j.jtbi.2010.01.009. Google Scholar
[29]	A. S. Novozhilov, et. al., Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models,, Biol. Direct, 1 (2006). Google Scholar
[30]	L. M. Wein, J. T. Wu and D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: Implications for virus design and delivery,, Cancer Res., 63 (2003), 1317. Google Scholar
[31]	D. Wodarz, Computational approaches to study oncolytic virus therapy: Insights and challenges,, Gene Therapy and Molecular Biology, 8 (2004), 137. Google Scholar
[32]	D. Wodarz, Use of oncolytic viruses for the eradication of drug-resistant cancer cells,, J. R. Soc. Interface, 6 (2009), 179. Google Scholar
[33]	D. Wodarz and N. Komarova, Towards predictive computational models of oncolytic virus therapy: Basis for experimental validation and model selection,, PLoS ONE, 4 (2009). Google Scholar
[34]	N. Bagheri, et. al., A dynamical systems model for combinatorial cancer therapy enhances oncolytic adenovirus efficacy by MEK-inhibition,, PLoS Comput. Biol., 7 (2011). Google Scholar
[35]	R. Zurakowski and D. Wodarz, Model-driven approaches for in vitro combination therapy using ONYX-015 replicating oncolytic adenovirus,, J. Theor. Biol., 245 (2007), 1. doi: 10.1016/j.jtbi.2006.09.029. Google Scholar
[36]	W. Mok, et. al., Mathematical modeling of herpes simplex virus distribution in solid tumors: Implications for cancer gene therapy,, Clin. Cancer Res., 15 (2009), 2352. Google Scholar
[37]	L. R. Paiva, et. al., A multiscale mathematical model for oncolytic virotherapy,, Cancer Res., 69 (2009), 1205. Google Scholar
[38]	C. L. Reis, et. al., In silico evolutionary dynamics of tumour virotherapy,, Integr. Biol. (Camb), 2 (2010), 41. Google Scholar
[39]	L. You, C. T. Yang and D. M. Jablons, ONYX-015 works synergistically with chemotherapy in lung cancer cell lines and primary cultures freshly made from lung cancer patients,, Cancer Res., 60 (2000), 1009. Google Scholar
[40]	A. Chahlavi, et. al., Replication-competent herpes simplex virus vector G207 and cisplatin combination therapy for head and neck squamous cell carcinoma,, Neoplasia, 1 (1999), 162. Google Scholar
[41]	I. A. Rodriguez-Brenes, N. L. Komarova and D. Wodarz, Evolutionary dynamics of feedback escape and the development of stem-cell-driven cancers,, Proc. Natl. Acad. Sci. U S A, 108 (2011), 18983. Google Scholar
[42]	D. Wodarz, et. al., Complex spatial dynamics of oncolytic viruses in vitro: Mathematical and experimental approaches,, PLoS Comput. Biol., 8 (2012). Google Scholar
[43]	K. Sato, H. Matsuda and A. Sasaki, Pathogen invasion and host extinction in lattice structured populations,, Journal of Mathematical Biology, 32 (1994), 251. Google Scholar
[44]	A. M. Deroos, E. Mccauley and W. G. Wilson, Mobility versus density-limited predator prey dynamics on different spatial scales,, Proceedings of the Royal Society of London Series B-Biological Sciences, 246 (1991), 117. Google Scholar
[45]	M. Pascual, P. Mazzega and S. A. Levin, Oscillatory dynamics and spatial scale: The role of noise and unresolved pattern,, Ecology, 82 (2001), 2357. Google Scholar
[46]	R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", 1991, (). Google Scholar
[47]	M. A. Nowak and R. M. May, "Virus Dynamics. Mathematical Principles of Immunology and Virology,", 2000: Oxford University Press., (). Google Scholar
[48]	M. P. Hassell, "The Spatial and Temporal Dynamics of Host-Parasitoid Interactions,", 2000, (). Google Scholar

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