2011, 6(4): 597-624. doi: 10.3934/nhm.2011.6.597

Multiscale model of tumor-derived capillary-like network formation

1. 

Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

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, Italy

Received  January 2011 Revised  September 2011 Published  December 2011

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.
Citation: Marco Scianna, Luca Munaron. Multiscale model of tumor-derived capillary-like network formation. Networks & Heterogeneous Media, 2011, 6 (4) : 597-624. doi: 10.3934/nhm.2011.6.597
References:
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show all references

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.

[2]

D. Ambrosi, A. Gamba and G. Serini, Cell directional persistence and chemotaxis in vascular morphogenesis,, Bull. Math. Biol., 66 (2004), 1851. 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. 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, (2007), 157. 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. 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. 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. doi: 10.1016/0006-291X(84)91431-1.

[8]

J. Bennett and A. Weeds, Calcium and the cytoskeleton,, Br. Med. Bull., 42 (1985), 385.

[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. doi: 10.1038/nrm1155.

[10]

M. J. Berridge, Calcium signalling and cell proliferation,, Bioessays, 17 (1995), 491. 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.

[12]

M. D. Bootman, P. Lipp and M. J. Berridge, The organisation and functions of local Ca2+ signals,, J. Cell. Sci., 114 (2001), 2213.

[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. 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.

[15]

B. Bussolati, C. Grange and G. Camussi, Tumor exploits alternative strategies to achieve vascularization,, FASEB J., 25 (2011), 2874. 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, (2003), 1.

[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.

[18]

P. Carmeliet and R. K. Jain, Angiogenesis in cancer and other diseases,, Nature, 407 (2000), 249. doi: 10.1038/35025220.

[19]

P. Carmeliet, Angiogenesis in life, disease and medicine,, Nature, 438 (2005), 932. doi: 10.1038/nature04478.

[20]

P. Carmeliet, VEGF as a key mediator of angiogenesis in cancer,, Oncology, 69 (2005), 4. 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.

[22]

W. Coatesworth and S. Bolsover, Calcium signal transmission in chick sensory neurones is diffusion based,, Cell Calcium, 43 (2008), 236. 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. 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. doi: 10.1006/dbio.2000.9744.

[25]

N. Ferrara, VEGF and the quest for tumour angiogenesis factors,, Nat. Rev. Cancer, 2 (2002), 795. doi: 10.1038/nrc909.

[26]

N. Ferrara and R. S. Kerbel, Angiogenesis as a therapeutic target,, Nature, 438 (2005), 967. 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. 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.

[29]

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