Multiscale model of tumor-derivedcapillary-like network formation

Marco Scianna; Luca Munaron

doi:10.3934/nhm.2011.6.597

Article Contents

2011, Volume 6, Issue 4: 597-624. Doi: 10.3934/nhm.2011.6.597

This issue Previous Article Next Article Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model

Multiscale model of tumor-derived capillary-like network formation

Marco Scianna^1, and
Luca Munaron^2,

1.
Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino
2.
Department of Animal and Human Biology, Nanostructured Interfaces and Surfaces Centre of Excellence (NIS), Center for Complex Systems in Molecular Biology and Medicine (SysBioM), Universitá degli Studi di Torino Via Accademia Albertina 13 10123, Torino

Received: January 2011

Revised: September 2011

Published: December 2011

Abstract / Introduction Related Papers Cited by

Abstract

Solid tumors recruit and form blood vessels, used for maintenance and growth as well as for formation and spread of metastases. Vascularization is therefore a pivotal switch in cancer malignancy: an accurate analysis of its driving processes is a big issue for the development of treatments. In vitro experiments have demonstrated that cultured tumor-derived endothelial cells (TECs) are able to organize in a connected network, which mimics an in vivo capillary-plexus. The process, called tubulogenesis, is promoted by the activity of soluble peptides (such as VEGFs), as well as by the following intracellular calcium signals. We here propose a multilevel approach, reproducing selected features of the experimental system: it incorporates a continuous model of microscopic VEGF-induced events in a discrete mesoscopic Cellular Potts Model (CPM). The two components are interfaced, producing a multiscale framework characterized by a constant flux of information from finer to coarser levels. The simulation results, in agreement with experimental analysis, allow to identify the key mechanisms of network formation. In particular, we provide evidence that the nascent pattern is characterized by precise topological properties, regulated by the initial cell density in conjunction with the degree of the chemotactic response and the directional persistence of cell migration.

Keywords:

Mathematics Subject Classification: Primary: 92B05, 92C15; Secondary: 92C42, 92C17.

Citation:

Related Papers

Cited by

References

[1]	M. A. Albrecht, S. L. Colegrove and D. D. Friel, Differential 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.doi: 10.1016/j.bulm.2004.04.004.
[3]	D. Ambrosi, F. Bussolino and L. Preziosi, A review of vasculogenesis models, J. Theor. Med., 6 (2005), 1-19.doi: 10.1080/1027366042000327098.
[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.doi: 10.1007/978-3-7643-8123-3_7.
[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.doi: 10.1016/S0002-9440(10)63540-7.
[6]	A. L. Bauer, T. L. Jackson and Y. Jiang, A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis, Biophys. J., 92 (2007), 3105-3121.doi: 10.1529/biophysj.106.101501.
[7]	P. Bayley, P. Ahlstrom, S. R. Martin and S. Forsen, The kinetics of calcium binding to calmodulin: Quin 2 and ANS stopped-flow fluorescence studies, Biochem. Biophys. Res. Commun., 120 (1984), 185-191.doi: 10.1016/0006-291X(84)91431-1.
[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, homeostasis and remodelling, Nat. Rev. Mol. Cell Biol., 4 (2003), 517-529.doi: 10.1038/nrm1155.
[10]	M. J. Berridge, Calcium signalling and cell proliferation, Bioessays, 17 (1995), 491-500.doi: 10.1002/bies.950170605.
[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.doi: 10.2174/157016110790887036.
[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.doi: 10.1096/fj.10-180323.
[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 endothelial growth factor. Endothelial activity, tumor cell expression, and high affinity binding to flk-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.doi: 10.1038/35025220.
[19]	P. Carmeliet, Angiogenesis in life, disease and medicine, Nature, 438 (2005), 932-936.doi: 10.1038/nature04478.
[20]	P. Carmeliet, VEGF as a key mediator of angiogenesis in cancer, Oncology, 69 (2005), 4-10.doi: 10.1159/000088478.
[21]	P. D. Chilibeck, D. H. Paterson, D. A. Cunningham, A. W. Taylor and E. G. Noble, Muscle capillarization O2 diffusion 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 diffusion based, Cell Calcium, 43 (2008), 236-249.doi: 10.1016/j.ceca.2007.05.016.
[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.doi: 10.1016/j.gde.2010.10.008.
[24]	C. J. Drake, A. LaRue, N. Ferrara and C. D. Little, VEGF regulates cell behavior during vasculogenesis, Dev. Biol., 224 (2000), 178-188.doi: 10.1006/dbio.2000.9744.
[25]	N. Ferrara, VEGF and the quest for tumour angiogenesis factors, Nat. Rev. Cancer, 2 (2002), 795-803.doi: 10.1038/nrc909.
[26]	N. Ferrara and R. S. Kerbel, Angiogenesis as a therapeutic target, Nature, 438 (2005), 967-974.doi: 10.1038/nature04483.
[27]	C. C. Fink, B. Slepchenko, Moraru, II, J. Watras, J. C. Schaff and L. M. Loew, An image-based model of calcium waves in differentiated neuroblastoma cells, Biophys. J., 79 (2000), 163-183.doi: 10.1016/S0006-3495(00)76281-3.
[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 influx, arachidonic acid, and control of endothelial cell proliferation, Cell Calcium, 30 (2001), 235-244.doi: 10.1054/ceca.2001.0234.
[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.doi: 10.1158/1541-7786.MCR-10-0002.
[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.doi: 10.1038/onc.2011.231.
[32]	D. Fukumura, D. G. Duda, L. L. Munn and R. K. Jain, Tumor microvasculature and microenvironment: Novel insights through intravital imaging in pre-clinical models, Microcirculation, 17 (2010), 206-225.doi: 10.1111/j.1549-8719.2010.00029.x.
[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.doi: 10.1103/PhysRevLett.90.118101.
[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 differential adhesion driven rearrangement of biological cells, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 47 (1993), 2128-2154.doi: 10.1103/PhysRevE.47.2128.
[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.doi: 10.1016/S0014-2999(96)00532-8.
[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.doi: 10.1103/PhysRevLett.69.2013.
[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," 10^th 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.doi: 10.1007/BF00794067.
[41]	S. Huang, C. P. Brangwynne, K. K. Parker and D. E. Ingber, Symmetry-breaking in mammalian cell cohort migration during tissue pattern formation: Role of random-walk persistence, Cell Motil. Cytoskeleton., 61 (2005), 201-213.doi: 10.1002/cm.20077.
[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 buffered Ca2+ diffusion 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.doi: 10.1016/j.jmaa.2004.12.009.
[45]	M. Kowanetz and N. Ferrara, Vascular endothelial growth factor signaling pathways: Therapeutic perspective, Clin. Cancer Res., 12 (2006), 5018-5022.doi: 10.1158/1078-0432.CCR-06-1520.
[46]	J. R. Lancaster, A tutorial on the diffusibility and reactivity of free nitric oxide, Nitric Oxide, 1 (1997), 18-30.doi: 10.1006/niox.1996.0112.
[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.doi: 10.1007/BF00046533.
[49]	A. F. M arée, 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. Marée, 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.doi: 10.1007/s11538-006-9131-7.
[51]	R. M. Merks and J. A. Glazier, Dynamic mechanisms of blood vessel growth, Nonlinearity, 19 (2006), C1-C10.doi: 10.1088/0951-7715/19/1/000.
[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.doi: 10.1016/j.ydbio.2005.10.003.
[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 quantitative, predictive, cell-based modeling, Math. Model Nat. Phenom., 4 (2009), 149-171.doi: 10.1051/mmnp/20094406.
[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.doi: 10.1063/1.1699114.
[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.doi: 10.2174/157489206775246502.
[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.doi: 10.2174/1874196700902010114.
[61]	L. Munaron and A. Fiorio Pla, Endothelial calcium machinery and angiogenesis: Understanding physiology to interfere with pathology, Curr. Med. Chem., 16 (2009), 4691-4703.doi: 10.2174/092986709789878210.
[62]	P. Namy, J. Ohayon and P. Tracqui, Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields, J. Theor. Biol., 227 (2004), 103-120.doi: 10.1016/j.jtbi.2003.10.015.
[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.doi: 10.1158/0008-5472.CAN-04-1976.
[64]	A. M. Patton, J. Kassis, H. Doong and E. C. Kohn, Calcium as a molecular target in angiogenesis, Curr. Pharm. Des., 9 (2003), 543-551.doi: 10.2174/1381612033391559.
[65]	E. D. Perryn, A. Czirok and C. D. Little, Vascular sprout formation entails tissue deformations and VE-cadherin-dependent cell-autonomous motility, Dev. Biol., 313 (2008), 545-555.doi: 10.1016/j.ydbio.2007.10.036.
[66]	J. S. Pollock, U. Forstermann, J. A. Mitchell, T. D. Warner, H. H. Schmidt, M. Nakane and F. Murad, Purification 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.doi: 10.1073/pnas.88.23.10480.
[67]	N. J. Poplawski, A. Shirinifard, M. Swat and J. A. Glazier, Simulation od single-species bacterical-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment, Math. Biosci. Eng., 5 (2008), 355-388.doi: 10.3934/mbe.2008.5.355.
[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.doi: 10.1073/pnas.0600137103.
[69]	N. J. Savill and P. Hogeweg, Modelling morphogenesis: From single cells to crawling slugs, J. Theor. Biol., 184 (1997), 118-124.doi: 10.1006/jtbi.1996.0237.
[70]	M. Scianna, A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell, Bull. Math. Biol., (2011), in press.doi: 10.1007/s11538-011-9695-8.
[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.doi: 10.1016/j.pbiomolbio.2011.01.004.
[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. Graff-Cherry and B. St Croix, Genes that distinguish physiological and pathological angiogenesis, Cancer Cell, 11 (2007), 539-554.doi: 10.1016/j.ccr.2007.04.017.
[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.doi: 10.1093/emboj/cdg176.
[75]	F. Shojaei and N. Ferrara, Antiangiogenic therapy for cancer: An update, Cancer J., 13 (2007), 345-348.doi: 10.1097/PPO.0b013e31815a7b69.
[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.doi: 10.1126/science.141.3579.401.
[78]	M. S. Steinberg, Does differential adhesion govern self-assembly processes in histogenesis? Equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells, J. Exp. Zool., 171 (1970), 395-433.doi: 10.1002/jez.1401730406.
[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.doi: 10.1016/j.ceca.2006.07.003.
[81]	A. Tosin, D. Ambrosi and L. Preziosi,, Mechanics and chemotaxis in the morphogenesis of vascular networks, Bull. Math. Biol., 68 (2006), 1819-1836.doi: 10.1007/s11538-006-9071-2.
[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.doi: 10.1007/BF00233739.
[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.doi: 10.1016/S0898-6568(03)00102-5.