A hybrid model for cell proliferation and migration in glioblastoma

Discrete and Continuous Dynamical Systems - Series B

Volumn 18, Issue 4, 2013, Pages 969-1015

  Kim, Yangjin ^a   Roh, Soyeon ^b  

^a Konkuk University   (South Korea)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Cancer progression; Glioblastoma; Hybrid model

Indexed keywords

EID: 84874746318     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2013.18.969     Document Type: Conference Paper

References (135)

1. B. D. Aguda, Y. Kim, M. G. Hunter, A. Friedman and C. B. Marsh, Microrna regulation of a cancer network: Consequences of the feedback loops involving mir-17-92, e2f, and myc, PNAS, 105 (2008), 19678-19683.
2. S. Alexander and P. Friedl, Cancer invasion and resistance: Interconnected processes of disease progression and therapy failure, Trends. Mol. Med., 18 (2012), 13-26.
3. D. Angeli, J. E Ferrell Jr. and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. USA, 101 (2004), 1822-1827.
4. R. P. Araujo and D. L. S. McElwain, A history of the study of solid tumour growth: The contribution of mathematical modelling, Bull. Math. Biol., 66 (2004), 1039-1091.
5. H. J. Aronen, F. S. Pardo, D. N. Kennedy, J. W. Belliveau, S. D. Packard, D. W. Hsu, F. H. Hochberg, A. J. Fischman and B. R. Rosen, High microvascular blood volume is associated with high glucose uptake and tumor angiogenesis in human gliomas, Clin. Cancer Res., 6 (2000), 2189-200.
6. K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pour-motabbed, Correlation of n-cadherin expression in high grade gliomas with tissue invasion, J. Neurooncol., 70 (2004), 3-15.
7. A. F. Baas, J. Kuipers, N. N. Wel, E. Batlle, H. K. Koerten, P. J. Peters and H. C. Clevers, Complete polarization of single intestinal epithelial cells upon activation of lkb1 by strad, Cell, 116 (2004), 457-466.
8. E. Bandres, N. Bitarte, F. Arias, J. Agorreta, P. Fortes, X. Agirre, R. Zarate, J. A. Diaz-Gonzalez, N. Ramirez and J. J. Sola, microrna-451 regulates macrophage migration inhibitory factor production and proliferation of gastrointestinal cancer cells, Clin. Cancer Res, 15 (2009), 2281-2290.
9. D. P. Bartel, Micrornas: target recognition and regulatory functions, Cell, 136 (2009), 215-233.
10. J. Boudeau, A. F. Baas, M. Deak, N. A. Morrice, A. Kieloch, M. Schutkowski, A. R. Prescott, H. C. Clevers and D. R. Alessi, Mo25alpha/beta interact with stradalpha/beta enhancing their ability to bind, activate and localize lkb1 in the cytoplasm, EMBO J., 22 (2003), 5102-5114.
11. H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures, Math. Med. Biol., 20 (2004), 341-360.
12. H. M. Byrne, Dissecting cancer through mathematics: From the cell to the animal model, Nature Reviews, 10 (2010), 221-230.
13. R. Cairns, I. Papandreou and N. Denko, Overcoming physiologic barriers to cancer treatment by molecularly targeting the tumor microenvironment, Mol. Cancer Res., 4 (2006), 61-70.
14. A. Chauviere, L. Preziosi and H. Byrne, A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism, Math. Med. Biol., 27 (2010), 255-281.
15. J. D. Cheng and L. M. Weiner, Tumors and their microenvironments: tilling the soil. Commentary re: A. M. Scott et al., A Phase I dose-escalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation protein-positive cancer, Clin. Cancer Res. 9 (2003), 1590-1595.
16. G. Cheng, J. Tse, R. K. Jain and L. L. Minn, Micro-environmental mechanical stress controls tumor spheroid size and morphology by supressing proliferation and inducing aopotosis in cancer cells, PLoS One, 4:e4632, 2009.
17. S. K. Chintala, J. C. Tonn and J. S. Rao, Matrix metalloproteinases and their biological function in human gliomas, Int. J. Dev. Neurosci., 17 (1999), 495-502.
18. D. G. Chiro, R. L. DeLaPaz, R. A. Brooks, L. Sokoloff, P. L. Kornblith, B. H. Smith, N. J. Patronas, C. V. Kufta, R. M. Kessler, G. S. Johnston, R. G. Manning and A. P. Wolf, Glucose utilization of cerebral gliomas measured by [18f] fluorodeoxyglucose and positron emission tomography, Neurology, 32 (1982), 1323-1329.
19. A. Cho, Life's patterns: No need to spell it out? Science, 303 (2004), 782-783.
20. G. Choe, J. K. Park, L. Jouben-Steele, T. J. Kremen, L. M. Liau, H. V. Vinters, T. F. Cloughesy and P. S. Mischel, Active matrix metalloproteinase 9 expression is associated with primary glioblastoma subtype, Clin. Cancer Res., 8(9) (2002), 2894-2901.
21. M. Crawford, E. Brawner, K. Batte, L. Yu, M. G. Hunter, G. A. Otterson, G. Nuovo, C. B. Marsh and S. P. Nana-Sinkam, Microrna-126 inhibits invasion in non-small cell lung carcinoma cell lines, Biochem. Biophys. Res. Commun., 373 (2008), 607-612.
22. B. E. Crute, K. Seefeld, J. Gamble, B. E. Kemp and L. A. Witters, Functional domains of the alpha1 catalytic subunit of the amp-activated protein kinase, J. Biol. Chem., 273 (1998), 35347-35354.
23. J. C. Dallon and H. G. Othmer, A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum, Phil. Trans. Roy. Soc. Lond, B352 (1997), 391-417.
24. J. C. Dallon and H. G. Othmer, How cellular movement determines the collective force generated by the dictyostelium discoideum slug, J. Theor. Biol., 231 (2004), 203-222.
25. F. G. Davis and B. J. McCarthy, Current epidemiological trends and surveillance issues in brain tumors, Expert Rev. Anticancer Ther., 1 (2001), 395-401.
26. S. J. Day and P. A. Lawrence, Measuring dimensions: The regulation of size and shape, Development, 127 (2000), 2977-2987.
27. T. S. Deisboeck, M. E. Berens, A. R. Kansal, S. Torquato, A. O. Stemmer-Rachamimov and E. A. Chiocca, Pattern of self-organization in tumour systems: Complex growth dynamics in a novel brain tumour spheroid model, Cell Prolif., 34 (2001), 115-134.
28. T. S. Deisboeck and I. D. Couzin, Collective behavior in cancer cell populations, Bioessays, 31 (2009), 190-197.
29. T. Demuth and M. E. Berens Molecular mechanisms of glioma cell migration and invasion, J. Neurooncol., 70 (2004), 217-228.
30. J. B. Easton and P. J. Houghton, mtor and cancer therapy, Oncogene, 25 (2006), 6436-6446.
31. A. Esquela-Kerscher and F. J. Slack, Oncomirs-micrornas with a role in cancer, Nat. Rev. Cancer, 6 (2006), 259-269.
32. J. E. Ferrell Jr, Self-perpetuating states in signal transduction: Positive feedback, doublenegative feedback and bistability, Curr. Opin. Cell Biol., 14 (2002), 140-148.
33. P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity, Cell, 147 (2011), 992-1009.
34. G. Gabriely, T. Wurdinger, S. Kesari, C. C. Esau, J. Burchard, P. S. Linsley and A. M. Krichevsky, Microrna 21 promotes glioma invasion by targeting matrix metalloproteinase regulators, Mol. Cell Biol., 28 (2008), 5369-5380.
35. H. Gal, G. Pandi, A. A. Kanner, Z. Ram, G. Lithwick-Yanai, N. Amariglio, G. Rechavi and D. Givol, Mir-451 and imatinib mesylate inhibit tumor growth of glioblastoma stem cells biochem., Biophys. Res. Commun., 376 (2008), 86-90.
36. J. Galle, M. Loeffler and D. Drasdo, Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro, Biophysical J., 88 (2005), 62-75.
37. M. P. Gantier, C. E. McCoy, I. Rusinova, D. Saulep, D. Wang, D. Xu, A. T. Irving, M. A. Behlke, P. J. Hertzog, F. Mackay and B. R. Williams, Analysis of microrna turnover in mammalian cells following dicer1 ablation, Nucleic Acids. Res., 39 (2011), 5692-5703.
38. R. A. Gatenby and R. J. Gillies, Why do cancers have high aerobic glycolysis? Nat. Rev. Cancer, 4 (2004), 891-899.
39. J. Godlewski, M. O. Nowicki, A. Bronisz, S. Williams, A. Otsuki, G. Nuovo, A. Raychaud-hury, H. B. Newton, E. A. Chiocca and S. Lawler, Targeting of the bmi-1 oncogene/stem cell renewal factor by microrna-128 inhibits glioma proliferation and self-renewal, Cancer Res., 68 (2008), 9125-9130.
40. J. Godlewski, A. Bronisz, M. O. Nowicki, E. A. Chiocca and S. Lawler, microRNA-451: A conditional switch controlling glioma cell proliferation and migration, Cell Cycle, 9 (2010), 2742-2748.
41. J. Godlewski, M. O. Nowicki, A. Bronisz, G. Nuovo J. Palatini, M. D. Lay, J. V. Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, MircroRNA-451 regulates lkb1/ampk signaling and allows adaptation to metabolic stress in glioma cells, Molecular Cell, 37 (2010), 620-632.
42. S. Goldman, M. Levivier, B. Pirotte, J. M. Brucher, D. Wikler, P. Damhaut, E. Stanus, J. Brotchi and J. Hildebrand, Regional glucose metabolism and histopathology of gliomas. A study based on positron emission tomography-guided stereotactic biopsy, Cancer, 78 (1996), 1098-106.
43. M. Gotte and G. W. Yip, Heparanase, hyaluronan, and CD44 in cancers: A breast carcinoma perspective, Cancer Research, 66 (2006), 10233-10237.
44. R. G. Hahn and T. Nystom, Plasma Volume Expansion Resulting from Intravenous Glucose Tolerance Test, Comput. Math. Methods Med., (2011), Article ID 965075, 4 pages.
45. D. G. Hardie, Amp-activated/snf1 protein kinases: Conserved guardians of cellular energy, Nat. Rev. Mol. Cell Biol., 8 (2007), 774-785.
46. D. G. Hardie, I. P. Salt, S. A. Hawley and S. P. Davies, Amp-activated protein kinase: An ultrasensitive system for monitoring cellular energy charge, Biochem. J., 338 (1999), 717-722.
47. H. L. Harpold, J.r. EC and K. R. Swanson, The evolution of mathematical modeling of glioma proliferation and invasion, J. Neuropathol. Exp. Neurol., 66 (2007), 1-9.
48. H. Hatzikirou, D. Basanta, M. Simon, K. Schaller and A. Deutsch, 'Go or grow': The key to the emergence of invasion in tumour progression? Math. Med. Biol., 27 (2010), 255-281.
49. S. A. Hawley, J. Boudeau, J. L. Reid, K. J. Mustard, L. Udd, T. P. Makela, D. R. Alessi and D. G. Hardie, Complexes between the lkb1 tumor suppressor, strad alpha/beta and mo25 alpha/beta are upstream kinases in the amp-activated protein kinase cascade, J. Biol., 2 (2003), 28.
50. S. A. Hawley, M. A. Selbert, E. G. Goldstein, A. M. Edelman, D. Carling and D. G. Hardie, 5'-amp activates the amp-activated protein kinase cascade, and ca2+/calmodulin activates the calmodulin-dependent protein kinase i cascade, via three independent mechanisms, J. Biol. Chem., 270 (1995), 27186-27191.
51. M. G. Heiden, L. C. Cantley and C. B. Thompson, Understanding the warburg effect: The metabolic requirements of cell proliferation, Science, 324 (2009), 1029-1033.
52. B. Hegedus, A. Czirok, I. Fazekas, T. Babel, E. Madarasz and T. Vicsek, Locomotion and proliferation of glioblastoma cells in vitro: Statistical evaluation of videomicroscopic observations, J. Neurosurg., 92 (2000), 428-434.
53. G. Helmlinger, P. A. Netti, H. C. Lichtenbeld, R. J. Melder and R. K. Jain, Solid stress inhibits the growth of multicellular tumor spheroids, Nature Biotechnology, 15(8) (1997), 778-783.
54. A. F. Hezel and N. Bardeesy, Lkb1; linking cell structure and tumor suppression, Oncogene, 27 (2008), 6908-6919.
55. O. Ilina, G. Bakker, A. Vasaturo, R. M. Hofmann and P. Friedl, Two-photon laser-generated microtracks in 3d collagen lattices: principles of mmp-dependent and-independent collective cancer cell invasion, Phys. Biol., 8 (2011), 015010.
56. K. Inoki, Y. Li, T. Xu and K. L. Guan, Rheb gtpase is a direct target of tsc2 gap activity and regulates mtor signaling, Genes. Dev., 17 (2003), 1829-1834.
57. K. Inoki, Y. Li, T. Zhu, J. Wu and K. L. Guan, Tsc2 is phosphorylated and inhibited by akt and suppresses mtor signalling, Nat. Cell Biol., 4 (2002), 648-657.
58. J. Jaalinoja, R. Herva, M. Korpela, M. Hoyhtya and T. Turpeenniemi-Hujanen, Matrix metalloproteinase 2 (mmp-2) immunoreactive protein is associated with poor grade and survival in brain neoplasms, J. Neurooncol., 46 (2000), 81-90.
59. V. L Jacobs, P. A. Valdes, W. F. Hickey and J. A. De Leo, Current review of in vivo gbm rodent models: emphasis on the cns-1 tumour model, ASN NEURO, 3 (2011), e00063.
60. R. K. Jain, Transport of molecules in the tumor interstitium: a review, Cancer Res., 47 (1987), 3039-3051.
61. R. G. Jones and C. B. Thompson, Tumor suppressors and cell metabolism: A recipe for cancer growth, Genes Dev., 23 (2009), 537-548.
62. L. J. Kaufma, C. P. Brangwynn, K. E. Kasz, E. Filippidi, V. D. Gordon, T. S. Deisboeck and D. A. Weitz, lioma expansion in Collagen I matrices: Analyzing Collagen concentration-dependent growth and motility patterns, Biophys. J., 89 (2005), 635-650.
63. E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth, Phys. Rev. Lett., 96 (2006), 188103.
64. R. Khanin and V. Vinciotti, Computational modeling of post-transcriptional gene regulation by micrornas, J. Comput. Biol., 15 (2008), 305-316.
65. J. W. Kim and C. V. Dang, Cancer's molecular sweet tooth and the warburg effect, Cancer Res., 66 (2006), 8927-8930.
66. H. D. Kim, T. W. Guo, A. P. Wu, A. Wells, F. B. Gertler and D. A. Lauffenburger, Epidermal growth factor induced enhancement of glioblastoma cell migration in 3D arises from an intrinsic increase in speed but an extrinsic matrix and proteolysis-dependent increase in persistence, Mol. Biol. Cell, 19 (2008), 4249-4259.
67. Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model, Bull. Math. Biol., 72 (2010), 1029-1068.
68. Y. Kim, S. Lawler, M. O. Nowicki, E. A Chiocca and A. Friedman, A mathematical model of brain tumor: Pattern formation of glioma cells outside the tumor spheroid core, J. Theo. Biol., 260 (2009), 359-371.
69. Y. Kim, M. Stolarska and H. G. Othmer, A hybrid model for tumor spheroid growth in vitro i: Theoretical development and early results, Math. Models Methods in Appl. Scis., 17 (2007), 1773-1798.
70. Y. Kim, S. Roh, S. Lawler and A. Friedman, miR451 and AMPK mutual antagonism in glioma cells migration and proliferation, PLoS One, 6 (2011), e28293.
71. Y. Kim, M. Stolarska and H. G. Othmer, The role of the microenvironment in tumor growth and invasion, Prog. Biophys. Mol. Biol., 106 (2011), 353-379.
72. Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments, J. Math. Biol., 61 (2010), 401-421.
73. W. P. Kloosterman and R. H. Plasterk, The diverse functions of micrornas in animal development and disease, Dev. Cell, 11 (2006), 441-450.
74. C. Koike, T. D. McKee, A. Pluen, S. Ramanujan, K. Burton, L. L. Munn, Y. Boucher and R. K. Jain, Solid stress facilitates spheroid formation: potential involvement of hyaluronan, British Journal of Cancer, 86 (2002), 947-953.
75. K. Lamszus, N. O. Schmidt, L. Jin, J. Laterra, D. Zagzag, D. Way, M. Witte, M. Weinand, I. D. Goldberg, M. Westphal and E. M. Rosen, Scatter factor promotes motility of human glioma and neuromicrovascular endothelial cells, Int. J. Cancer, 75 (1998), 19-28.
76. S. Lawler and E. A. Chiocca, Emerging functions of micrornas in glioblastoma, J. Neuroon-col., 92 (2009), 297-306.
77. J. H. Lee, H. Koh, M. Kim, Y. Kim, S. Y. Lee, R. E. Karess, S. H. Lee, M. Shong, J. M. Kim, J. Kim and J. Chung, Energy-dependent regulation of cell structure by amp-activated protein kinase, Nature, 447 (2007), 1017-1020.
78. C. K. Li, The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis, Cancer, 50 (1982), 2066-2073.
79. J. S. Lowengrub, H. B. Frieboes, F. Jin, Y. L. Chuang, X. Li, P. Macklin, S. M. Wise and V. Cristini, Nonlinear modelling of cancer: Bridging the gap between cells and tumours, Nonlinearity, 23 (2010), R1-R91.
80. A. D. Luca, Niccolo Arena, L. M. Sena and E. Medico, Met overexpression confers hgf-dependent invasive phenotype to human thyroid carcinoma cells in vitro, Journal of Cellular Physiology, 180 (1999), 365-371.
81. M. Lund-Johansen, R. Bjerkvig, P. A. Humphrey, S. H. Bigner, D. D. Bigner and O. D. Laerum, Effect of epidermal growth factor on glioma cell growth, migration, and invasion in vitro, Cancer Res., 50 (1990), 6039-6044.
82. L. Ma, J. Teruya-Feldstein and R. A. Weinberg, Tumour invasion and metastasis initiated by microrna-10b in breast cancer, Nature, 449 (2007), 682-688.
83. E. Mandonnet, J. Y. Delattre, M. L. Tanguy, K. R. Swanson, A. F. Carpentier, H. Duffau, P. Cornu, R. Effenterre, J.r. EC and L. Capelle, Continuous growth of mean tumor diameter in a subset of grade ii gliomas, Ann. Neurol., 53 (2003), 524-528.
84. S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178-196.
85. N. I. Markevich, J. B. Hoek and B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades, J. Cell Biol., 164 (2004), 353-359.
86. M. O. Nowicki, N. Dmitrieva, A. M. Stein, J. L. Cutter, J. Godlewski, Y. Saeki, M. Nita, M. E. Berens, L. M. Sander and H. B. Newton, Lithium inhibits invasion of glioma cells; possible involvement of glycogen synthase kinase-3, Neuro-oncol, 10 (2008), 690-699.
87. I. Papandreou, R. A. Cairns, L. Fontana, A. L. Lim and N. C. Denko, Hif-1 mediates adaptation to hypoxia by actively downregulating mitochondrial oxygen consumption, Cell Metab., 3 (2006), 187-197.
88. J. B. Park, H. J. Kwak and S. H. Lee, Role of hyaluronan in glioma invasion, Cell Adhesion and Migration, 2 (2008), 202-207.
89. M. J. Paszek and V. M. Weaver, The tension mounts: Mechanics meets morphogenesis and malignancy, J. Mammary Gland Biol. Neoplasia, 9 (2004), 325-342.
90. M. J. Paszek, N. Zahir, K. R. Johnson, J. N. Lakins, G. I. Rozenberg, A. Gefen, C. A. Reinhart-King, S. S. Margulies, M. Dembo, D. Boettiger, D. A. Hammer and V. M. Weaver, Tensional homeostasis and the malignant phenotype, Cancer cell, 8 (2005), 241-254.
91. C. Perego, C. Vanoni, S. Massari, A. Raimondi, S. Pola, M.G. Cattaneo, M. Francolini, L. M. Vicentini and G. Pietrini, Invasive behaviour of glioblastoma cell lines is associated with altered organisation of the cadherin-catenin adhesion system, J. Cell Sci., 115 (2002), 3331-3340.
92. K. Pham, A. Chauviere, H. Hatzikirou, X. Li, H. M. Byrne, V. Cristini and J. Lowengrub, Density-dependent quiescence in glioma invasion: Instability in a simple reaction-diffusion model for the migration/proliferation dichotomy, Journal of Biological dynamics, (2011).
93. M. Platten, W. Wick and M. Weller, Malignant glioma biology: role for tgf-beta in growth, motility, angiogenesis, and immune escape, Microsc. Res. Tech., 52 (2001), 401-410.
94. C. J. Potter, L. G. Pedraza and T. Xu, Akt regulates growth by directly phosphorylating tsc2, Nat. Cell Biol., 4 (2002), 658-665.
95. L. Preziosi and A. Tosin, Multiphase and multiscale trends in cancer modelling, Math. Model. Natl. Phenom., 4 (2009), 1-11.
96. L. Preziosi and G. Vitale, A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization, Math. Model. Method. Appl. Sci., 21 (2011), 1901-1932.
97. C. Ragan and M. Zuker amd M. A. Ragan, Quantitative prediction of miRNA-mRNA interaction based on equilibrium concentrations, PLoS Comput. Biol., 7 (2011), e1001090.
98. K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications, Experimental Biology and Medicine (Maywood), 235 (2010), 411-423.
99. K. A. Rejniak and A. R. A. Anderson, Hybrid models of tumor growth, WIRES Syst. Biol. Med., 3 (2011), 115-125.
100. K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications, Exp. Biol. Med. (Maywood), 235 (2010), 411-423
101. A. Ridley, M. Schwartz, K. Burridge, R. Firtel, M. Ginsberg, G. B. Parsons and A. Horwitz, Cell migration: Integrating signals from front to back, Science, 302 (2003), 1704-1709.
102. Z. Rong, U. Cheema and P. Vadgama, Needle enzyme electrode based glucose diffusive transport measurement in a collagen gel and validation of a simulation model, Analyst, 131 (2006), 816-821.
103. J. M. Rozental, R. L. Levine and R. J. Nickles, Changes in glucose uptake by malignant gliomas: Preliminary study of prognostic significance, J. Neurooncol., 10 (1991), 75-83.
104. O. Sampetrean, I. Saga, M. Nakanishi, E. Sugihara, R. Fukaya, N. Onishi, S. Osuka, M. Akahata, K. Kai, H. Sugimoto, A. Hirao and H. Saya, Invasion precedes tumor mass formation in a malignant brain tumor model of genetically modified neural stem cells, Neoplasia, 13 (2011), 784-791.
105. L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors, Phys. Rev. E, 66 (2002), 051901.
106. M. Scianna, R. M. Merks, L. Preziosi and E. Medico, Individual cell-based models of cell scatter of aro and mlp-29 cells in response to hepatocyte growth factor, J. Theor. Biol., 260, (2009) 151-160.
107. S. Sen, M. Dong and S. Kumar, Isoform-specific contributions of a-Actinin to Glioma cell mechanobiology, PLoS One, 4 (2009), e8427.
108. R. J. Shaw, N. Bardeesy, B. D. Manning, L. Lopez, M. Kosmatka, R. A. DePinho and L. C. Cantley, The lkb1 tumor suppressor negatively regulates mtor signaling, Cancer Cell, 6 (2004), 91-99.
109. B. I. Shraiman, Mechanicall feedback as a possible regulator of tissue growth, PNAS, 102 (2005), 3318-3323.
110. S. C. Stein, A. Woods, N. A. Jones, M. D. Davison and D. Carling, The regulation of amp-activated protein kinase by phosphorylation, Biochem. J., 345 (2000), 437-443.
111. A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment, Biophys. J., 92 (2007), 356-365.
112. A. Stein, D. Vader, D. Weitz and L. Sander, The micromechanics of three-dimensional collagen-I gels, Complexity, 16 (2011), 22-28.
113. M. C. Stella and P. M. Comoglio, HGF: A multifunctional growth factor controlling cell scattering, Int. J. Biochem. Cell Biol., 31(12) (1999), 1357-1362.
114. M. Stolarska, Y. Kim and H. G. Othmer, Multiscale models of cell and tissue dynamics, Phil. Trans. Roy. Soc. A, 367 (2009), 3525-3553.
115. S. S. Stylli, A. H. Kaye, L. MacGregor, M. Howes and P. Rajendra, Photodynamic therapy of high grade glioma-long term survival, J. Clin. Neurosci., 12 (2005), 389-398.
116. K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence, Math. Comp. Modelling, 37 (2003), 1177-1190.
117. K. R. Swanson, J.r. EC and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter, Cell Prolif., 33 (2000), 317-329.
118. L. Tamagnone and P. M. Comoglio, Control of invasive growth by hepatocyte growth factor (hgf) and related scatter factors, Cytokine Growth Factor Rev., 8(2) (1997), 129-142.
119. L. Trusolino and P. M. Comoglio, Scatter-factor and semaphorin receptors: Cell signalling for invasive growth, Nat. Rev. Cancer, 2 (2002), 289-300.
120. J. C. Valle-Casuso, A. Gonzalez-Sanchez, J. M. Medina and A. Tabernero, Hif-1 and c-src mediate increased glucose uptake induced by endothelin-1 and connexin43 in astrocytes, PLoS One, 7 (2012), e32448.
121. O. Warburg, On the origin of cancer cells, Science, 123 (1956), 309-314.
122. O. Wartlick, P. Mumcu, A. Kicheva, T. Bittig, C. Seum, F. Julicher and M. Gonzalez-Gaitan, Dynamics of DPP signaling and proliferation control, Science, 331 (2011), 1154-1159.
123. O. Wartlick, P. Mumcu, F. Julicher and M. Gonzalez-Gaitan, Understanding morphogenetic growth control-lessons from flies, Nat. Rev. Mol. Cell Biol., 12 (2011), 594-604.
124. J. J. Watters, J. M. Schartner and B. Badie, Microglia function in brain tumors, J. Neurosci. Res., 81 (2005), 447-455.
125. T. Williams and J. E. Brenman, Lkb1 and ampk in cell polarity and division, Trends. Cell Biol., 18 (2008), 193-198.
126. M. Wiranowska and M. V. Rojiani, "Extracellular Matrix Microenvironment in Glioma Progression," Glioma-Exploring Its Biology and Practical Relevance, Anirban Ghosh (Ed.), InTech, 2011.
127. K. Wolf, Y. Wu, Y. Liu, J. Geiger, E. Tam, C. Overall, M. Stack and P. Friedl, Multistep pericellular proteolysis controls the transition from individual to collective cancer cell invasion, Nat. Cell Biol., 9(8) (2007), 893-904.
128. K. Wolf, S. Alexander, V. Schacht, L. Coussens, U.H. von Andrian, J. van Rheenen, E. Deryugina and P. Friedl, Collagen-based cell migration models in vitro and in vivo, Semin. Cell Dev. Biol., 20(8) (2009), 931-941.
129. A. Woods, S. R. Johnstone, K. Dickerson, F. C. Leiper, L. G. Fryer, D. Neumann, U. Schlat-tner, T. Wallimann, M. Carlson and D. Carling, Lkb1 is the upstream kinase in the amp-activated protein kinase cascade, Curr. Biol., 13 (2003), 2004-2008.
130. W. Xiong and J. E. Ferrell Jr, A positive-feedback-based bistable 'memory module' that governs a cell fate decision, Nature, 426 (2003), 460-465.
131. R. H. Xu, H. Pelicano, Y. Zhou, J. S. Carew, L. Feng, K. N. Bhalla, M. J. Keating and P. Huang, Inhibition of glycolysis in cancer cells: A novel strategy to overcome drug resistance associated with mitochondrial respiratory defect and hypoxia, Cancer Res., 65 (2005), 613-621.
132. G. Yao, T. J. Lee, S. Mori, J. R. Nevins and L. You, A bistable rb-e2f switch underlies the restriction point, Nat. Cell Biol., 10 (2008), 476-482.
133. N. Young and J. R. Brocklyn, Roles of sphingosine-1-phosphate (s1p) receptors in malignant behavior of glioma cells. Differential effects of s1p2 on cell migration and invasiveness, Exp. Cell Res., 313 (2007), 1615-1627.
134. K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis, in "Cancer Metastasis-Biology and Treatment," Springer, Netherlands, (2006), 25-54.
135. Y. Zhou, P. H. Larsen, C. Hao and V. W. Yong, Cxcr4 is a major chemokine receptor on glioma cells and mediates their survival, J. Biol. Chem., 277 (2002), 49481-49487.