Computational modeling approaches to studying the dynamics of oncolytic viruses

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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), 127-131.
[2]	J. C. Bell, B. Lichty and D. Stojdl, Getting oncolytic virus therapies off the ground, Cancer Cell, 4 (2003), 7-11.
[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), 133-139.
[4]	J. J. Davis and B. Fang, Oncolytic virotherapy for cancer treatment: Challenges and solutions, J. Gene. Med., 7 (2005), 1380-1389.
[5]	J. M. Kaplan, Adenovirus-based cancer gene therapy, Curr. Gene Ther., 5 (2005), 595-605.
[6]	E. Kelly and S. J. Russell, History of oncolytic viruses: Genesis to genetic engineering, Mol. Ther., 15 (2007), 651-659.
[7]	D. H. Kirn and F. McCormick, Replicating viruses as selective cancer therapeutics, Mol. Med. Today, 2 (1996), 519-527.
[8]	F. McCormick, Cancer-specific viruses and the development of ONYX-015, Cancer Biol. Ther., 2 (2003), S157-60.
[9]	F. McCormick, Future prospects for oncolytic therapy, Oncogene, 24 (2005), 7817-7819.
[10]	C. C. O'Shea, Viruses - seeking and destroying the tumor program, Oncogene, 24 (2005), 7640-7655.
[11]	K. A. Parato, et. al., Recent progress in the battle between oncolytic viruses and tumours, Nat. Rev. Cancer, 5 (2005), 965-976.
[12]	D. E. Post, et. al., Cancer scene investigation: how a cold virus became a tumor killer, Future Oncol., 1 (2005), 247-258.
[13]	M. S. Roberts, et. al., Naturally oncolytic viruses, Curr. Opin. Mol. Ther., 8 (2006), 314-321. doi: 10.1080/08898480600950473.
[14]	M. J. Vaha-Koskela, J. E. Heikkila and A. E. Hinkkanen, Oncolytic viruses in cancer therapy, Cancer Lett., (2007).
[15]	H. H. Wong, N. R. Lemoine and Y. Wang, Oncolytic viruses for cancer therapy: Overcoming the obstacles, Viruses, 2 (2010), 78-106.
[16]	D. Koppers-Lalic and R. C. Hoeben, Non-human viruses developed as therapeutic agent for use in humans, Rev. Med. Virol, 21 (2011), 227-239.
[17]	R. L. Martuza, et. al., Experimental therapy of human glioma by means of a genetically engineered virus mutant, Science, 252 (1991), 854-856.
[18]	K. Garber, China approves world's first oncolytic virus therapy for cancer treatment, J. Natl. Cancer Inst., 98 (2006), 298-300.
[19]	R. M. Eager and J. Nemunaitis, Clinical development directions in oncolytic viral therapy, Cancer Gene. Ther., 18 (2011), 305-317.
[20]	D. Wodarz, Viruses as antitumor weapons: Defining conditions for tumor remission, Cancer Res., 61 (2001), 3501-3507.
[21]	D. Wodarz, Gene therapy for killing p53-negative cancer cells: Use of replicating versus nonreplicating agents, Hum. Gene. Ther., 14 (2003), 153-159.
[22]	Z. Bajzer, et. al., Modeling of cancer virotherapy with recombinant measles viruses, J. Theor. Biol., 252 (2008), 109-122. doi: 10.1016/j.jtbi.2008.01.016.
[23]	M. Biesecker, et. al., Optimization of virotherapy for cancer, Bull. Math. Biol., 72 (2010), 469-489. doi: 10.1007/s11538-009-9456-0.
[24]	D. Dingli, et. al., Mathematical modeling of cancer radiovirotherapy, Math. Biosci., 199 (2006), 55-78. doi: 10.1016/j.mbs.2005.11.001.
[25]	D. Dingli, et. al., Dynamics of multiple myeloma tumor therapy with a recombinant measles virus, Cancer Gene Ther., 16 (2009), 873-882.
[26]	A. Friedman, et. al., Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Cancer Res., 66 (2006), 2314-2319.
[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), pp. 30.
[28]	N. L. Komarova and D. Wodarz, ODE models for oncolytic virus dynamics, J. Theor. Biol., 263 (2010), 530-543. doi: 10.1016/j.jtbi.2010.01.009.
[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), pp. 6.
[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), 1317-1324.
[31]	D. Wodarz, Computational approaches to study oncolytic virus therapy: Insights and challenges, Gene Therapy and Molecular Biology, 8 (2004), 137-146.
[32]	D. Wodarz, Use of oncolytic viruses for the eradication of drug-resistant cancer cells, J. R. Soc. Interface, 6 (2009), 179-186.
[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), e4271.
[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), e1001085.
[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), 1-8. doi: 10.1016/j.jtbi.2006.09.029.
[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), 2352-2360.
[37]	L. R. Paiva, et. al., A multiscale mathematical model for oncolytic virotherapy, Cancer Res., 69 (2009), 1205-1211.
[38]	C. L. Reis, et. al., In silico evolutionary dynamics of tumour virotherapy, Integr. Biol. (Camb), 2 (2010), 41-45.
[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), 1009-1013.
[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), 162-169.
[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), 18983-18988.
[42]	D. Wodarz, et. al., Complex spatial dynamics of oncolytic viruses in vitro: Mathematical and experimental approaches, PLoS Comput. Biol., 8 (2012), e1002547.
[43]	K. Sato, H. Matsuda and A. Sasaki, Pathogen invasion and host extinction in lattice structured populations, Journal of Mathematical Biology, 32 (1994), 251-268.
[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), 117-122.
[45]	M. Pascual, P. Mazzega and S. A. Levin, Oscillatory dynamics and spatial scale: The role of noise and unresolved pattern, Ecology, 82 (2001), 2357-2369.
[46]	R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", 1991, ().
[47]	M. A. Nowak and R. M. May, "Virus Dynamics. Mathematical Principles of Immunology and Virology,", 2000: Oxford University Press., ().
[48]	M. P. Hassell, "The Spatial and Temporal Dynamics of Host-Parasitoid Interactions,", 2000, ().

show all references

References:

[1]	J. C. Bell, Oncolytic viruses: What's next?, Curr. Cancer Drug Targets, 7 (2007), 127-131.
[2]	J. C. Bell, B. Lichty and D. Stojdl, Getting oncolytic virus therapies off the ground, Cancer Cell, 4 (2003), 7-11.
[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), 133-139.
[4]	J. J. Davis and B. Fang, Oncolytic virotherapy for cancer treatment: Challenges and solutions, J. Gene. Med., 7 (2005), 1380-1389.
[5]	J. M. Kaplan, Adenovirus-based cancer gene therapy, Curr. Gene Ther., 5 (2005), 595-605.
[6]	E. Kelly and S. J. Russell, History of oncolytic viruses: Genesis to genetic engineering, Mol. Ther., 15 (2007), 651-659.
[7]	D. H. Kirn and F. McCormick, Replicating viruses as selective cancer therapeutics, Mol. Med. Today, 2 (1996), 519-527.
[8]	F. McCormick, Cancer-specific viruses and the development of ONYX-015, Cancer Biol. Ther., 2 (2003), S157-60.
[9]	F. McCormick, Future prospects for oncolytic therapy, Oncogene, 24 (2005), 7817-7819.
[10]	C. C. O'Shea, Viruses - seeking and destroying the tumor program, Oncogene, 24 (2005), 7640-7655.
[11]	K. A. Parato, et. al., Recent progress in the battle between oncolytic viruses and tumours, Nat. Rev. Cancer, 5 (2005), 965-976.
[12]	D. E. Post, et. al., Cancer scene investigation: how a cold virus became a tumor killer, Future Oncol., 1 (2005), 247-258.
[13]	M. S. Roberts, et. al., Naturally oncolytic viruses, Curr. Opin. Mol. Ther., 8 (2006), 314-321. doi: 10.1080/08898480600950473.
[14]	M. J. Vaha-Koskela, J. E. Heikkila and A. E. Hinkkanen, Oncolytic viruses in cancer therapy, Cancer Lett., (2007).
[15]	H. H. Wong, N. R. Lemoine and Y. Wang, Oncolytic viruses for cancer therapy: Overcoming the obstacles, Viruses, 2 (2010), 78-106.
[16]	D. Koppers-Lalic and R. C. Hoeben, Non-human viruses developed as therapeutic agent for use in humans, Rev. Med. Virol, 21 (2011), 227-239.
[17]	R. L. Martuza, et. al., Experimental therapy of human glioma by means of a genetically engineered virus mutant, Science, 252 (1991), 854-856.
[18]	K. Garber, China approves world's first oncolytic virus therapy for cancer treatment, J. Natl. Cancer Inst., 98 (2006), 298-300.
[19]	R. M. Eager and J. Nemunaitis, Clinical development directions in oncolytic viral therapy, Cancer Gene. Ther., 18 (2011), 305-317.
[20]	D. Wodarz, Viruses as antitumor weapons: Defining conditions for tumor remission, Cancer Res., 61 (2001), 3501-3507.
[21]	D. Wodarz, Gene therapy for killing p53-negative cancer cells: Use of replicating versus nonreplicating agents, Hum. Gene. Ther., 14 (2003), 153-159.
[22]	Z. Bajzer, et. al., Modeling of cancer virotherapy with recombinant measles viruses, J. Theor. Biol., 252 (2008), 109-122. doi: 10.1016/j.jtbi.2008.01.016.
[23]	M. Biesecker, et. al., Optimization of virotherapy for cancer, Bull. Math. Biol., 72 (2010), 469-489. doi: 10.1007/s11538-009-9456-0.
[24]	D. Dingli, et. al., Mathematical modeling of cancer radiovirotherapy, Math. Biosci., 199 (2006), 55-78. doi: 10.1016/j.mbs.2005.11.001.
[25]	D. Dingli, et. al., Dynamics of multiple myeloma tumor therapy with a recombinant measles virus, Cancer Gene Ther., 16 (2009), 873-882.
[26]	A. Friedman, et. al., Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Cancer Res., 66 (2006), 2314-2319.
[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), pp. 30.
[28]	N. L. Komarova and D. Wodarz, ODE models for oncolytic virus dynamics, J. Theor. Biol., 263 (2010), 530-543. doi: 10.1016/j.jtbi.2010.01.009.
[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), pp. 6.
[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), 1317-1324.
[31]	D. Wodarz, Computational approaches to study oncolytic virus therapy: Insights and challenges, Gene Therapy and Molecular Biology, 8 (2004), 137-146.
[32]	D. Wodarz, Use of oncolytic viruses for the eradication of drug-resistant cancer cells, J. R. Soc. Interface, 6 (2009), 179-186.
[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), e4271.
[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), e1001085.
[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), 1-8. doi: 10.1016/j.jtbi.2006.09.029.
[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), 2352-2360.
[37]	L. R. Paiva, et. al., A multiscale mathematical model for oncolytic virotherapy, Cancer Res., 69 (2009), 1205-1211.
[38]	C. L. Reis, et. al., In silico evolutionary dynamics of tumour virotherapy, Integr. Biol. (Camb), 2 (2010), 41-45.
[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), 1009-1013.
[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), 162-169.
[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), 18983-18988.
[42]	D. Wodarz, et. al., Complex spatial dynamics of oncolytic viruses in vitro: Mathematical and experimental approaches, PLoS Comput. Biol., 8 (2012), e1002547.
[43]	K. Sato, H. Matsuda and A. Sasaki, Pathogen invasion and host extinction in lattice structured populations, Journal of Mathematical Biology, 32 (1994), 251-268.
[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), 117-122.
[45]	M. Pascual, P. Mazzega and S. A. Levin, Oscillatory dynamics and spatial scale: The role of noise and unresolved pattern, Ecology, 82 (2001), 2357-2369.
[46]	R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", 1991, ().
[47]	M. A. Nowak and R. M. May, "Virus Dynamics. Mathematical Principles of Immunology and Virology,", 2000: Oxford University Press., ().
[48]	M. P. Hassell, "The Spatial and Temporal Dynamics of Host-Parasitoid Interactions,", 2000, ().

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