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Spatial stochastic models of cancer: Fitness, migration, invasion
1. | Department of Mathematics, University of California Irvine, Irvine CA 92697, United States |
References:
[1] |
A. Anderson, M. Chaplain, K. Rejniak and J. Fozard, Single-cell based models in biology and medicine,, Math. Med. Biol., 25 (2008), 185. Google Scholar |
[2] |
A. Anderson and V. Quaranta, Integrative mathematical oncology,, Nature Reviews Cancer, 8 (2008), 227. Google Scholar |
[3] |
R. M. Anderson and R. M. May, Coevolution of hosts and parasites,, Parasitology, 85 (1982), 411. Google Scholar |
[4] |
M. Boots, P. J. Hudson and A. Sasaki, Large shifts in pathogen virulence relate to host population structure,, Science, 303 (2004), 842. Google Scholar |
[5] |
J. Breivik and G. Gaudernack, Carcinogenesis and natural selection: A new perspective to the genetics and epigenetics of colorectal cancer,, Adv. Cancer Res., 76 (1999), 187. Google Scholar |
[6] |
H. Byrne, T. Alarcón, M. Owen, S. Webb and P. Maini, Modeling aspects of cancer dynamics: A review,, Phi. Trans. R. Soc. A, 364 (2006), 1563.
doi: 10.1098/rsta.2006.1786. |
[7] |
A. Chauvière, L. Preziosi and C. Verdier, "Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling,", CRC Press, 32 (2009).
doi: 10.1201/9781420094558. |
[8] |
B. Chopard, R. Ouared, A. Deutsch, H. Hatzikirou and D. Wolf-Gladrow, Lattice-gas cellular automaton models for biology: from fluids to cells,, Acta Biotheoretica, 58 (2010), 329. Google Scholar |
[9] |
T. Deisboeck and G. Stamatakos, "Multiscale Cancer Modeling,", CRC Press, 34 (2010). Google Scholar |
[10] |
T. Deisboeck, L. Zhang, J. Yoon and J. Costa, In silico cancer modeling: is it ready for prime time?,, in press., (). Google Scholar |
[11] |
A. Deutsch and S. Dormann, "Cellular Automaton Modeling of Biological Pattern Formation,", Birkhauser, (2005).
|
[12] |
D. Drasdo and S. Höhme, On the role of physics in the growth and pattern of multicellular systems: What we learn from individual-cell based models?,, J. Stat. Phys., 128 (2007), 287.
doi: 10.1007/s10955-007-9289-x. |
[13] |
D. Ebert and E. A. Herre, The evolution of parasitic diseases,, Parasitol Today, 12 (1996), 96. Google Scholar |
[14] |
D. Ebert and K. L. Mangin, The influence of host demography on the evolution of virulence of a microsporidian gut parasite,, Evolution, 51 (1997), 1828. Google Scholar |
[15] |
A. Fasano, A. Bertuzzi and A. Gandolfi, Complex systems in biomedicine chapter mathematical modelling of tumour growth and treatment,, Milan: Springer, (2006), 71.
doi: 10.1007/88-470-0396-2_3. |
[16] |
S. A. Frank, Models of parasite virulence,, Q. Rev. Biol., 71 (1996), 37. Google Scholar |
[17] |
J. Galle, G. Aust, G. Schaller, T. Beyer and D. Drasdo, Individual cell-based models of the spatial temporal organization of multicellular systems- achievements and limitations,, Cytometry, 69A (2006), 704. Google Scholar |
[18] |
R. Gatenby and P. Maini, Mathematical oncology: Cancer summed up,, Nature, 421 (2003). Google Scholar |
[19] |
D. Hanahan and R. Weinberg, The hallmarks of cancer,, CELL, 100 (2000), 57. Google Scholar |
[20] |
P. Hinow,, P. Gerlee, L. McCawley, V. Quaranta, M. Ciobanu, S. Wang,, J. Graham, B. Ayati, J. Claridge, K. Swanson, et al., A spatial model of tumor-host interaction: Application of chemotherapy,, Mathematical Biosciences and Engineering: MBE, 6 (2009).
doi: 10.3934/mbe.2009.6.521. |
[21] |
Y. Iwasa, F. Michor and M. A. Nowak, Stochastic tunnels in evolutionary dynamics,, Genetics, 166 (2004), 1571. Google Scholar |
[22] |
Y. Jiao and S. Torquato, A cellular automaton model for tumor growth in heterogeneous environment,, Bulletin of the American Physical Society, 56 (2011). Google Scholar |
[23] |
N. Komarova, Loss- and gain-of-function mutations in cancer: Mass-action, spatial and hierarchical models,, Jour. Stat. Phys., 128 (2007), 413.
doi: 10.1007/s10955-006-9238-0. |
[24] |
N. L. Komarova, Spatial stochastic models for cancer initiation and progression,, Bull. Math. Biol., 68 (2006), 1573.
doi: 10.1007/s11538-005-9046-8. |
[25] |
N. L. Komarova, A. Sengupta and M. A. Nowak, Mutation-selection networks of cancer initiation: Tumor suppressor genes and chromosomal instability,, J. Theor. Biol., 223 (2003), 433.
doi: 10.1016/S0022-5193(03)00120-6. |
[26] |
B. R. Levin, The evolution and maintenance of virulence in microparasites,, Emerg. Infect. Dis., 2 (1996), 93. Google Scholar |
[27] |
L. Merlo, J. Pepper, B. Reid and C. Maley, Cancer as an evolutionary and ecological process,, Nat. Rev. Cancer, 6 (2006), 924. Google Scholar |
[28] |
F. Michor, Y. Iwasa, H. Rajagopalan, C. Lengauer and M. A. Nowak, Linear model of colon cancer initiation,, Cell Cycle, 3 (2004), 358. Google Scholar |
[29] |
P. Moran, "The Statistical Processes of Evolutionary Theory,", Clarendon, (1962). Google Scholar |
[30] |
M. Nowak and K. Sigmund, Evolutionary dynamics of biological games,, Science, 303 (2004), 793. Google Scholar |
[31] |
M. A. Nowak, N. L. Komarova, A. Sengupta, P. V. Jallepalli, I.-M. Shih, B. Vogelstein and C. Lengauer, The role of chromosomal instability in tumor initiation,, Proc. Natl. Acad. Sci. U S A, 99 (2002), 16226. Google Scholar |
[32] |
M. A. Nowak and R. M. May, Superinfection and the evolution of parasite virulence,, Proc. Biol. Sci., 255 (1994), 81. Google Scholar |
[33] |
M. A. Nowak, F. Michor, N. L. Komarova and Y. Iwasa, Evolutionary dynamics of tumor suppressor gene inactivation,, Proc. Natl. Acad. Sci. U S A, 101 (2004), 10635. Google Scholar |
[34] |
P. Nowell, The clonal evolution of tumor cell populations,, Science, 194 (1976), 23. Google Scholar |
[35] |
V. Quaranta, K. Rejniak, P. Gerlee and A. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models,, Sem. Cancer Biol., (2008). Google Scholar |
[36] |
K. Rejniak and A. Anderson, Hybrid models of tumor growth,, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3 (2011), 115. Google Scholar |
[37] |
C. W. Rinker-Schaeffer, J. P. O'Keefe, D. R. Welch and D. Theodorescu, Metastasis suppressor proteins: Discovery, molecular mechanisms, and clinical application,, CLINICAL CANCER RESEARCH, 12 (2006), 3882. Google Scholar |
[38] |
J. Sagotsky and T. Deisboeck, Simulating cancer growth with agent-based models,, Multiscale Cancer Modeling, 34 (2010). Google Scholar |
[39] |
A. Sasaki and M. Boots, Parasite evolution and extinctions,, Ecology Letters, 6 (2003). Google Scholar |
[40] |
J. M. Smith, "Evolution and the Theory of Games,", Cambridge University Press, (1982). Google Scholar |
[41] |
C. Thalhauser, J. Lowengrub, D. Stupack and N. Komarova, Research selection in spatial stochastic models of cancer: Migration as a key modulator of fitness,, Biology Direct, 5 (2010). Google Scholar |
[42] |
T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics,", Cambridge University Press, (2005). Google Scholar |
[43] |
P. Vineis and M. Berwick, The population dynamics of cancer: A Darwinian perspective,, Int. J. Epidemiol, 35 (2006), 1151. Google Scholar |
[44] |
D. Wodarz and N. Komarova, "Computational Biology of Cancer: Lecture Notes and Mathematical Modeling,", World Scientific, (2005). Google Scholar |
[45] |
S. Wright, The roles of mutation, inbreeding, crossbreeding, and selection in evolution,, in, (1932), 355. Google Scholar |
[46] |
L. Zhang, Z. Wang, J. Sagotsky and T. Deisboeck, Multiscale agent-based cancer modeling,, Journal of Mathematical Biology, 58 (2009), 545.
doi: 10.1007/s00285-008-0211-1. |
show all references
References:
[1] |
A. Anderson, M. Chaplain, K. Rejniak and J. Fozard, Single-cell based models in biology and medicine,, Math. Med. Biol., 25 (2008), 185. Google Scholar |
[2] |
A. Anderson and V. Quaranta, Integrative mathematical oncology,, Nature Reviews Cancer, 8 (2008), 227. Google Scholar |
[3] |
R. M. Anderson and R. M. May, Coevolution of hosts and parasites,, Parasitology, 85 (1982), 411. Google Scholar |
[4] |
M. Boots, P. J. Hudson and A. Sasaki, Large shifts in pathogen virulence relate to host population structure,, Science, 303 (2004), 842. Google Scholar |
[5] |
J. Breivik and G. Gaudernack, Carcinogenesis and natural selection: A new perspective to the genetics and epigenetics of colorectal cancer,, Adv. Cancer Res., 76 (1999), 187. Google Scholar |
[6] |
H. Byrne, T. Alarcón, M. Owen, S. Webb and P. Maini, Modeling aspects of cancer dynamics: A review,, Phi. Trans. R. Soc. A, 364 (2006), 1563.
doi: 10.1098/rsta.2006.1786. |
[7] |
A. Chauvière, L. Preziosi and C. Verdier, "Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling,", CRC Press, 32 (2009).
doi: 10.1201/9781420094558. |
[8] |
B. Chopard, R. Ouared, A. Deutsch, H. Hatzikirou and D. Wolf-Gladrow, Lattice-gas cellular automaton models for biology: from fluids to cells,, Acta Biotheoretica, 58 (2010), 329. Google Scholar |
[9] |
T. Deisboeck and G. Stamatakos, "Multiscale Cancer Modeling,", CRC Press, 34 (2010). Google Scholar |
[10] |
T. Deisboeck, L. Zhang, J. Yoon and J. Costa, In silico cancer modeling: is it ready for prime time?,, in press., (). Google Scholar |
[11] |
A. Deutsch and S. Dormann, "Cellular Automaton Modeling of Biological Pattern Formation,", Birkhauser, (2005).
|
[12] |
D. Drasdo and S. Höhme, On the role of physics in the growth and pattern of multicellular systems: What we learn from individual-cell based models?,, J. Stat. Phys., 128 (2007), 287.
doi: 10.1007/s10955-007-9289-x. |
[13] |
D. Ebert and E. A. Herre, The evolution of parasitic diseases,, Parasitol Today, 12 (1996), 96. Google Scholar |
[14] |
D. Ebert and K. L. Mangin, The influence of host demography on the evolution of virulence of a microsporidian gut parasite,, Evolution, 51 (1997), 1828. Google Scholar |
[15] |
A. Fasano, A. Bertuzzi and A. Gandolfi, Complex systems in biomedicine chapter mathematical modelling of tumour growth and treatment,, Milan: Springer, (2006), 71.
doi: 10.1007/88-470-0396-2_3. |
[16] |
S. A. Frank, Models of parasite virulence,, Q. Rev. Biol., 71 (1996), 37. Google Scholar |
[17] |
J. Galle, G. Aust, G. Schaller, T. Beyer and D. Drasdo, Individual cell-based models of the spatial temporal organization of multicellular systems- achievements and limitations,, Cytometry, 69A (2006), 704. Google Scholar |
[18] |
R. Gatenby and P. Maini, Mathematical oncology: Cancer summed up,, Nature, 421 (2003). Google Scholar |
[19] |
D. Hanahan and R. Weinberg, The hallmarks of cancer,, CELL, 100 (2000), 57. Google Scholar |
[20] |
P. Hinow,, P. Gerlee, L. McCawley, V. Quaranta, M. Ciobanu, S. Wang,, J. Graham, B. Ayati, J. Claridge, K. Swanson, et al., A spatial model of tumor-host interaction: Application of chemotherapy,, Mathematical Biosciences and Engineering: MBE, 6 (2009).
doi: 10.3934/mbe.2009.6.521. |
[21] |
Y. Iwasa, F. Michor and M. A. Nowak, Stochastic tunnels in evolutionary dynamics,, Genetics, 166 (2004), 1571. Google Scholar |
[22] |
Y. Jiao and S. Torquato, A cellular automaton model for tumor growth in heterogeneous environment,, Bulletin of the American Physical Society, 56 (2011). Google Scholar |
[23] |
N. Komarova, Loss- and gain-of-function mutations in cancer: Mass-action, spatial and hierarchical models,, Jour. Stat. Phys., 128 (2007), 413.
doi: 10.1007/s10955-006-9238-0. |
[24] |
N. L. Komarova, Spatial stochastic models for cancer initiation and progression,, Bull. Math. Biol., 68 (2006), 1573.
doi: 10.1007/s11538-005-9046-8. |
[25] |
N. L. Komarova, A. Sengupta and M. A. Nowak, Mutation-selection networks of cancer initiation: Tumor suppressor genes and chromosomal instability,, J. Theor. Biol., 223 (2003), 433.
doi: 10.1016/S0022-5193(03)00120-6. |
[26] |
B. R. Levin, The evolution and maintenance of virulence in microparasites,, Emerg. Infect. Dis., 2 (1996), 93. Google Scholar |
[27] |
L. Merlo, J. Pepper, B. Reid and C. Maley, Cancer as an evolutionary and ecological process,, Nat. Rev. Cancer, 6 (2006), 924. Google Scholar |
[28] |
F. Michor, Y. Iwasa, H. Rajagopalan, C. Lengauer and M. A. Nowak, Linear model of colon cancer initiation,, Cell Cycle, 3 (2004), 358. Google Scholar |
[29] |
P. Moran, "The Statistical Processes of Evolutionary Theory,", Clarendon, (1962). Google Scholar |
[30] |
M. Nowak and K. Sigmund, Evolutionary dynamics of biological games,, Science, 303 (2004), 793. Google Scholar |
[31] |
M. A. Nowak, N. L. Komarova, A. Sengupta, P. V. Jallepalli, I.-M. Shih, B. Vogelstein and C. Lengauer, The role of chromosomal instability in tumor initiation,, Proc. Natl. Acad. Sci. U S A, 99 (2002), 16226. Google Scholar |
[32] |
M. A. Nowak and R. M. May, Superinfection and the evolution of parasite virulence,, Proc. Biol. Sci., 255 (1994), 81. Google Scholar |
[33] |
M. A. Nowak, F. Michor, N. L. Komarova and Y. Iwasa, Evolutionary dynamics of tumor suppressor gene inactivation,, Proc. Natl. Acad. Sci. U S A, 101 (2004), 10635. Google Scholar |
[34] |
P. Nowell, The clonal evolution of tumor cell populations,, Science, 194 (1976), 23. Google Scholar |
[35] |
V. Quaranta, K. Rejniak, P. Gerlee and A. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models,, Sem. Cancer Biol., (2008). Google Scholar |
[36] |
K. Rejniak and A. Anderson, Hybrid models of tumor growth,, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3 (2011), 115. Google Scholar |
[37] |
C. W. Rinker-Schaeffer, J. P. O'Keefe, D. R. Welch and D. Theodorescu, Metastasis suppressor proteins: Discovery, molecular mechanisms, and clinical application,, CLINICAL CANCER RESEARCH, 12 (2006), 3882. Google Scholar |
[38] |
J. Sagotsky and T. Deisboeck, Simulating cancer growth with agent-based models,, Multiscale Cancer Modeling, 34 (2010). Google Scholar |
[39] |
A. Sasaki and M. Boots, Parasite evolution and extinctions,, Ecology Letters, 6 (2003). Google Scholar |
[40] |
J. M. Smith, "Evolution and the Theory of Games,", Cambridge University Press, (1982). Google Scholar |
[41] |
C. Thalhauser, J. Lowengrub, D. Stupack and N. Komarova, Research selection in spatial stochastic models of cancer: Migration as a key modulator of fitness,, Biology Direct, 5 (2010). Google Scholar |
[42] |
T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics,", Cambridge University Press, (2005). Google Scholar |
[43] |
P. Vineis and M. Berwick, The population dynamics of cancer: A Darwinian perspective,, Int. J. Epidemiol, 35 (2006), 1151. Google Scholar |
[44] |
D. Wodarz and N. Komarova, "Computational Biology of Cancer: Lecture Notes and Mathematical Modeling,", World Scientific, (2005). Google Scholar |
[45] |
S. Wright, The roles of mutation, inbreeding, crossbreeding, and selection in evolution,, in, (1932), 355. Google Scholar |
[46] |
L. Zhang, Z. Wang, J. Sagotsky and T. Deisboeck, Multiscale agent-based cancer modeling,, Journal of Mathematical Biology, 58 (2009), 545.
doi: 10.1007/s00285-008-0211-1. |
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