Multiscale model of tumor-derived capillary-like network formation

Networks and Heterogeneous Media

Volumn 6, Issue 4, 2011, Pages 597-624

  Scianna, Marco ^a   Munaron, Luca ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Cellular potts model; In vitro tubulogenesis; Proangiogenic calcium signals; Vascular endothelial growth factor

Indexed keywords

EID: 84055193621     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2011.6.597     Document Type: Article

References (83)

1. M. A. Albrecht, S. L. Colegrove and D. D. Friel, Diffierential regulation of ER Ca2+ uptake and release rates accounts for multiple modes of Ca2+-induced Ca2+ release, J. Gen. Physiol., 119 (2002), 211-233.
2. D. Ambrosi, A. Gamba and G. Serini, Cell directional persistence and chemotaxis in vascular morphogenesis, Bull. Math. Biol., 66 (2004), 1851-1873.
3. D. Ambrosi, F. Bussolino and L. Preziosi, A review of vasculogenesis models, J. Theor. Med., 6 (2005), 1-19.
4. A. Balter, R. M. Merks, N. J. Poplawski, M. Swat and J. A. Glazier, The Glazier-Graner-Hogeweg model: Extensions, future directions, and opportunities for further study, in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions"(eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 157-167.
5. P. Baluk, S. Morikawa, A. Haskell, M. Mancuso and D. M. McDonald, Abnormalities of basement membrane on blood vessels and endothelial sprouts in tumors, Am. J. Pathol., 163 (2003), 1801-1815.
6. A. L. Bauer, T. L. Jackson and Y. Jiang, A cell-based model exhibiting branching and anas-tomosis during tumor-induced angiogenesis, Biophys. J., 92 (2007), 3105-3121.
7. P. Bayley, P. Ahlstrom, S. R. Martin and S. Forsen, The kinetics of calcium binding to calmod-ulin: Quin 2 and ANS stopped-ow uorescence studies, Biochem. Biophys. Res. Commun., 120 (1984), 185-191.
8. J. Bennett and A. Weeds, Calcium and the cytoskeleton, Br. Med. Bull., 42 (1985), 385-390.
9. M. J. Berridge, M. D. Bootman and H. L. Roderick, Calcium signalling: Dynamics, home-ostasis and remodelling, Nat. Rev. Mol. Cell Biol., 4 (2003), 517-529.
10. M. J. Berridge, Calcium signalling and cell proliferation, Bioessays, 17 (1995), 491-500.
11. L. A. Blatter, Z. Taha, S. Mesaros, P. S. Shacklock, W. G. Wier and T. Malinski, Simultaneous measurements of Ca2+ and nitric oxide in bradykinin-stimulated vascular endothelial cells, Circ. Res., 76 (1995), 922-924.
12. M. D. Bootman, P. Lipp and M. J. Berridge, The organisation and functions of local Ca2+ signals, J. Cell. Sci., 114 (2001), 2213-2222.
13. B. Bussolati, M. C. Deregibus and G. Camussi, Characterization of molecular and functional alterations of tumor endothelial cells to design anti-angiogenic strategies, Curr. Vasc. Pharmacol., 8 (2010), 220-232.
14. B. Bussolati, I. Deambrosis, S. Russo, M. C. Deregibus and G. Camussi, Altered angiogenesis and survival in human tumor-derived endothelial cells, FASEB J., 17 (2003), 1159-1161.
15. B. Bussolati, C. Grange and G. Camussi, Tumor exploits alternative strategies to achieve vascularization, FASEB J., 25 (2011), 2874-2882.
16. F. Bussolino, M. Arese, E. Audero, E. Giraudo, S. Marchio, S. Mitola, L. Primo and G. Serini, Biological aspects in tumor angiogenesis, in "Cancer Modeling and Simulation, Mathematical Biology and Medicine Sciences"(ed. L. Preziosi), Chapman & Hall/CRC, (2003), 1-16.
17. Y. Cao, H. Chen, L. Zhou, M. K. Chiang, B. Anand-Apte, J. A. Weatherbee, Y. Wang, F. Fang, J. G. Flanagan and M. L. Tsang, Heterodimers of placenta growth factor/ vascular en-dothelial growth factor. Endothelial activity, tumor cell expression, and high affinity binding to k-1/kdr, J. Biol. Chem., 271 (1996), 3154-3162.
18. P. Carmeliet and R. K. Jain, Angiogenesis in cancer and other diseases, Nature, 407 (2000), 249-257.
19. P. Carmeliet, Angiogenesis in life, disease and medicine, Nature, 438 (2005), 932-936.
20. P. Carmeliet, VEGF as a key mediator of angiogenesis in cancer, Oncology, 69 (2005), 4-10.
21. P. D. Chilibeck, D. H. Paterson, D. A. Cunningham, A. W. Taylor and E. G. Noble, Muscle capillarization O2 diffiusion distance, and VO2 kinetics in old and young individuals, J. Appl. Physiol., 82 (1997), 63-69.
22. W. Coatesworth and S. Bolsover, Calcium signal transmission in chick sensory neurones is diffiusion based, Cell Calcium, 43 (2008), 236-249.
23. K. De Bock, S. Cauwenberghs and P. Carmeliet, Vessel abnormalization: Another hallmark of cancer? Molecular mechanisms and therapeutic implications, Curr. Opin. Genet. Dev., 21 (2011), 73-79.
24. C. J. Drake, A. LaRue, N. Ferrara and C. D. Little, VEGF regulates cell behavior during vasculogenesis, Dev. Biol., 224 (2000), 178-188.
25. N. Ferrara, VEGF and the quest for tumour angiogenesis factors, Nat. Rev. Cancer, 2 (2002), 795-803.
26. N. Ferrara and R. S. Kerbel, Angiogenesis as a therapeutic target, Nature, 438 (2005), 967-974.
27. C. C. Fink, B. Slepchenko, Moraru, II, J. Watras, J. C. Schaffiand L. M. Loew, An image-based model of calcium waves in diffierentiated neuroblastoma cells, Biophys. J., 79 (2000), 163-183.
28. A. Fiorio Pla, C. Grange, S. Antoniotti, C. Tomatis, A. Merlino, B. Bussolati and L. Munaron, Arachidonic acid-induced Ca2+ entry is involved in early steps of tumor angiogenesis, Mol. Cancer Res., 6 (2008), 535-545.
29. A. Fiorio Pla and L. Munaron, Calcium inux, arachidonic acid, and control of endothelial cell proliferation, Cell Calcium, 30 (2001), 235-244.
30. A. Fiorio Pla, T. Genova, E. Pupo, C. Tomatis, A. Genazzani, R. Zaninetti and L. Munaron, Multiple roles of protein kinase a in arachidonic acid-mediated ca2+ entry and tumor-derived human endothelial cell migration, Mol. Cancer Res., 8 (2010), 1466-1476.
31. A. Fiorio Pla, H. L. Ong, K. T. Cheng, A. Brossa, B. Bussolati, T. Lockwich, B. Paria, L. Munaron and I. S. Ambudkar, TRPV4 mediates tumor-derived endothelial cell migration via arachidonic acid-activated actin remodeling, Oncogene, (2011), in press.
32. D. Fukumura, D. G. Duda, L. L. Munn and R. K. Jain, Tumor microvasculature and microen-vironment: Novel insights through intravital imaging in pre-clinical models, Microcirculation, 17 (2010), 206-225.
33. A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. Di Talia, E. Giraudo, G. Serini, L. Preziosi and F. Bussolino, Percolation, morphogenesis, and burgers dynamics in blood vessels formation, Phys. Rev. Letters, 90 (2003), 118101-118104.
34. J. A. Glazier, A. Balter and N. J. Poplawski, Magnetization to morphogenesis: A brief history of the Glazier-Graner-Hogeweg model, in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions"(eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 79-106.
35. J. A. Glazier and F. Graner, Simulation of the diffierential adhesion driven rearrangement of biological cells, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 47 (1993), 2128-2154.
36. Y. Goto, M. Miura and T. Iijima, Extrusion mechanisms of intracellular Ca2+ in human aortic endothelial cells, Eur. J. Pharmacol., 314 (1996), 185-192.
37. F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.
38. C. Grange, B. Bussolati, S. Bruno, V. Fonsato, A. Sapino and G. Camussi, Isolation and characterization of human breast tumor-derived endothelial cells, Oncol. Rep., 15 (2006), 381-386.
39. A. C. Guyton and J. E. Hall, "Textbook of Medical Physiology,"10th edition, W. B. Sauders, 2000.
40. L. V. Hryshko and K. D. Philipson, Sodium-calcium exchange: recent advances, Basic Res. Cardiol., 92 (1997), 45-51.
41. S. Huang, C. P. Brangwynne, K. K. Parker and D. E. Ingber, Symmetry-breaking in mam-malian cell cohort migration during tissue pattern formation: Role of random-walk persistence, Cell Motil. Cytoskeleton., 61 (2005), 201-213.
42. H. Kimura and H. Esumi, Reciprocal regulation between nitric oxide and vascular endothelial growth factor in angiogenesis, Acta Biochim. Pol., 50 (2003), 49-59.
43. J. Klingauf and E. Neher, Modeling buffiered Ca2+ diffiusion near the membrane: Implications for secretion in neuroendocrine cells, Biophys. J., 72 (1997), 674-690.
44. R. Kowalczyk, Preventing blow-up in a chemotaxis model, Journal of Mathematical Analysis and Applications, 305 (2005), 566-588.
45. M. Kowanetz and N. Ferrara, Vascular endothelial growth factor signaling pathways: Thera-peutic perspective, Clin. Cancer Res., 12 (2006), 5018-5022.
46. J. R. Lancaster, A tutorial on the diffiusibility and reactivity of free nitric oxide, Nitric Oxide, 1 (1997), 18-30.
47. A. W. Mahoney, B. G. Smith, N. S. Flann and G. J. Podgorski, Discovering novel cancer therapies: A computational modeling and search approach, in "IEEE conference on Computational Intelligence in Bioinformatics and Bioengineering,"(2008), 233-240.
48. D. Manoussaki, S. R. Lubkin, R. B. Vernon and J. D. Murray, A mechanical model for the formation of vascular networks in vitro, Acta Biotheor., 44 (1996), 271-282.
49. A. F. M arffiee, V. A. Grieneisen and P. Hogeweg, The Cellular Potts Model and biophysical properties of cells, tissues and morphogenesis, in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions"(eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 107-136.
50. A. F. Marffiee, A. Jilkine, A. Dawes, V. A. Grieneisen and L. Edelstein-Keshet, Polarization and movement of keratocytes: A multiscale modelling approach, Bull. Math. Biol., 68 (2006), 1169-1211.
51. R. M. Merks and J. A. Glazier, Dynamic mechanisms of blood vessel growth, Nonlinearity, 19 (2006), C1-C10.
52. R. M. Merks, S. V. Brodsky, M. S. Goligorksy, S. A. Newman and J. A. Glazier, Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling, Dev. Biol., 289 (2006), 44-54.
53. R. M. Merks, E. D. Perryn, A. Shirinifard and J. A. Glazier, Contact-inhibited chemotaxis in de novo and sprouting blood vessel growth, PLoS Comput. Biol., 4 (2008), e1000163, 16 pp.
54. R. M. Merks and P. Koolwijk, Modeling morphogenesis in silico and in vitro: Towards quan-titative, predictive, cell-based modeling, Math. Model Nat. Phenom., 4 (2009), 149-171.
55. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), 1087-1092.
56. A. Mottola, S. Antoniotti, D. Lovisolo and L. Munaron, Regulation of noncapacitative calcium entry by arachidonic acid and nitric oxide in endothelial cells, FASEB J., 19 (2005), 2075-2077.
57. L. Munaron, Calcium signalling and control of cell proliferation by tyrosine kinase receptors (review), Int. J. Mol. Med., 10 (2002), 671-676.
58. L. Munaron, Intracellular calcium, endothelial cells and angiogenesis, Recent Patents Anticancer Drug Discov., 1 (2002), 105-119.
59. L. Munaron, C. Tomatis and A. Fiorio Pla, The secret marriage between calcium and tumor angiogenesis, Technol. Cancer Res. Treat., 7 (2008), 335-339.
60. L. Munaron, A tridimensional model of proangiogenic calcium signals in endothelial cells, The Open Biology Journal, 2 (2009), 114-129.
61. L. Munaron and A. Fiorio Pla, Endothelial calcium machinery and angiogenesis: Under-standing physiology to interfere with pathology, Curr. Med. Chem., 16 (2009), 4691-4703.
62. P. Namy, J. Ohayon and P. Tracqui, Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction ffields, J. Theor. Biol., 227 (2004), 103-120.
63. B. S. Parker, P. Argani, B. P. Cook, H. Liangfeng, S. D. Chartrand, M. Zhang, S. Saha, A. Bardelli, Y. Jiang, T. B. St Martin, M. Nacht, B. A. Teicher, K. W. Klinger, S. Sukumar and S. L. Madden, Alterations in vascular gene expression in invasive breast carcinoma, Cancer Res., 64 (2004), 7857-7866.
64. A. M. Patton, J. Kassis, H. Doong and E. C. Kohn, Calcium as a molecular target in angio-genesis, Curr. Pharm. Des., 9 (2003), 543-551.
65. E. D. Perryn, A. Czirok and C. D. Little, Vascular sprout formation entails tissue deforma-tions and VE-cadherin-dependent cell-autonomous motility, Dev. Biol., 313 (2008), 545-555.
66. J. S. Pollock, U. Forstermann, J. A. Mitchell, T. D. Warner, H. H. Schmidt, M. Nakane and F. Murad, Puriffication and characterization of particulate endothelium-derived relaxing factor synthase from cultured and native bovine aortic endothelial cells, Proc. Natl. Acad. Sci. USA, 88 (1991), 10480-10484.
67. N. J. Poplawski, A. Shirinifard, M. Swat and J. A. Glazier, Simulation od single-species bacterical-bioffilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment, Math. Biosci. Eng., 5 (2008), 355-388.
68. J. J. Saucerman, J. Zhang, J. C. Martin, L. X. Peng, A. E. Stenbit, R. Y. Tsien and A. D. McCulloch, Systems analysis of PKA-mediated phosphorylation gradients in live cardiac myocytes, Proc. Natl. Acad. Sci. USA, 103 (2006), 12923-12928.
69. N. J. Savill and P. Hogeweg, Modelling morphogenesis: From single cells to crawling slugs, J. Theor. Biol., 184 (1997), 118-124.
70. M. Scianna, A multiscale hybrid model for pro-angiogenic calcium signals in a vascular en-dothelial cell, Bull. Math. Biol., (2011), in press.
71. M. Scianna, L. Munaron and L. Preziosi, A multiscale hybrid approach for vasculogenesis and related potential blocking therapies, Prog. Biophys. Mol. Biol., 106 (2011), 450-462.
72. M. Scianna and L. Preziosi, Multiscale developments of the Cellular Potts Model, (2011), submitted for publication.
73. S. Seaman, J. Stevens, M. Y. Yang, D. Logsdon, C. Graffi-Cherry and B. St Croix, Genes that distinguish physiological and pathological angiogenesis, Cancer Cell, 11 (2007), 539-554.
74. G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi and F. Bussolino, Modeling the early stages of vascular network assembly, EMBO J., 22 (2003), 1771-1779.
75. F. Shojaei and N. Ferrara, Antiangiogenic therapy for cancer: An update, Cancer J., 13 (2007), 345-348.
76. J. Sneyd, J. Keizer and M. J. Sanderson, Mechanisms of calcium oscillations and waves: A quantitative analysis, FASEB J., 9 (1995), 1463-1472.
77. M. S. Steinberg, Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation, Science, 141 (1963), 401-408.
78. M. S. Steinberg, Does diffierential adhesion govern self-assembly processes in histogenesis? Equilibrium conffigurations and the emergence of a hierarchy among populations of embryonic cells, J. Exp. Zool., 171 (1970), 395-433.
79. O. Straume, H. B. Salvesen and L. A. Akslen, Angiogenesis is prognostically important in vertical growth phase melanomas, Int. J. Oncol., 5 (1999), 595-599.
80. C. Tomatis, A. Fiorio Pla and L. Munaron, Cytosolic calcium microdomains by arachidonic acid and nitric oxide in endothelial cells, Cell Calcium, 41 (2007), 261-269.
81. A. Tosin, D. Ambrosi and L. Preziosi,, Mechanics and chemotaxis in the morphogenesis of vascular networks, Bull. Math. Biol., 68 (2006), 1819-1836.
82. P. A. Valant, P. N. Adjei and D. H. Haynes, Rapid Ca2+ extrusion via the Na+/Ca2+ exchanger of the human platelet, J. Membr. Biol., 130 (1992), 63-82.
83. E. L. Watson, K. L. Jacobson, J. C. Singh and D. H. Di Julio, Arachidonic acid regulates two Ca2+ entry pathways via nitric oxide, Cell Signal, 13 (2004), 157-165.