The Force at the Tip - Modelling Tension and Proliferation in Sprouting Angiogenesis

PLoS Computational Biology

Volumn 11, Issue 8, 2015, Pages

  Santos Oliveira, Patrícia ^a   Correia, António ^b   Rodrigues, Tiago ^b   Ribeiro Rodrigues, Teresa M ^b   Matafome, Paulo ^b,c   Rodríguez Manzaneque, Juan Carlos ^d   Seiça, Raquel ^b   Girão, Henrique ^b   Travasso, Rui D M ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

^b UNIVERSITY OF COIMBRA   (Portugal)

^c POLYTECHNIC INSTITUTE OF COIMBRA   (Portugal)

^d PTS Granada   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD VESSELS; CELL ADHESION; CELL PROLIFERATION; ENZYME ACTIVITY; MOLECULAR BIOLOGY; STRAIN RATE; TRACTION (FRICTION);

ANGIOGENESIS; BIOCHEMICAL SIGNAL; BIOLOGICAL SIGNALS; CELL MOVEMENT; COMPLEX PROCESSES; ENDOTHELIAL CELL PROLIFERATION; ENDOTHELIAL-CELLS; MATHEMATICAL DESCRIPTIONS; MECHANICAL SIGNALS; TRACTION FORCES;

ENDOTHELIAL CELLS;

ANGIOGENIC FACTOR; VASCULOTROPIN; VASCULOTROPIN A;

ANGIOGENESIS; ARTICLE; CELL ADHESION; CELL ELONGATION; CELL PROLIFERATION; CELL STRESS; CELL STRUCTURE; CONTROLLED STUDY; ENDOTHELIUM CELL; GROWTH RATE; MATHEMATICAL MODEL; PREDICTION; SPROUTING ANGIOGENESIS; ANIMAL; BIOLOGICAL MODEL; BIOLOGY; BLOOD VESSEL; GROWTH, DEVELOPMENT AND AGING; HUMAN; METABOLISM; MOUSE; NEOVASCULARIZATION (PATHOLOGY); PATHOPHYSIOLOGY; PHYSIOLOGY;

ANIMALS; BLOOD VESSELS; CELL PROLIFERATION; COMPUTATIONAL BIOLOGY; HUMANS; MICE; MODELS, CARDIOVASCULAR; NEOVASCULARIZATION, PATHOLOGIC; NEOVASCULARIZATION, PHYSIOLOGIC; VASCULAR ENDOTHELIAL GROWTH FACTOR A;

EID: 84940778593     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1004436     Document Type: Article

References (85)

1. Folkman J, (1995). Angiogenesis in cancer, vascular, rheumatoid and other disease. Nature Med 1: 27–30. doi: 10.1038/nm0195-27 7584949
2. Risau W, (1997). Mechanisms of angiogenesis. Nature 386: 671–674. doi: 10.1038/386671a0 9109485
3. Tonnesen MG, Feng X, Clark RA, (2000). Angiogenesis in wound healing. in Journal of Investigative Dermatology Symposium Proceedings (Vol. 5, No. 1, pp. 40–46). Nature Publishing Group.
4. Jackson JR, Seed MP, Kircher CH, Willoughby DA, Winkler JD, (1997). The codependence of angiogenesis and chronic inflammation. The FASEB J 11: 457–465. 9194526
5. Fiedler U, Augustin HG, (2006). Angiopoietins: a link between angiogenesis and inflammation. Trends in Immunology 27: 552–558. doi: 10.1016/j.it.2006.10.004 17045842
6. Carmeliet P, (2005). Angiogenesis in life, disease and medicine. Nature 438: 932–936. doi: 10.1038/nature04478 16355210
7. Carmeliet P, Jain RK, (2000). Angiogenesis in cancer and other diseases. Nature 407: 249–257. doi: 10.1038/35025220 11001068
8. Hanahan D, Folkman J, (1996). Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis. Cell 86: 353–364. doi: 10.1016/S0092-8674(00)80108-7 8756718
9. Kerbel RS, (2000). Tumor angiogenesis: past, present and the near future. Carcinogenesis 21: 505–515. doi: 10.1093/carcin/21.3.505 10688871
10. Ferrara N, Kerbel RS, (2005). Angiogenesis as a therapeutic target. Nature 438: 967–974. doi: 10.1038/nature04483 16355214
11. Mayer RJ, (2004). Two Steps Forward in the Treatment of Colorectal Cancer. N Engl J Med 350: 2406–2408. doi: 10.1056/NEJMe048098 15175443
12. Hurwitz H, Fehrenbacher L, Novotny W, Cartwright T, Hainsworth J, et al (2004). Bevacizumab plus Irinotecan, Fluorouracil, and Leucovorin for Metastatic Colorectal Cancer. N Engl J Med 350: 2335–2342. doi: 10.1056/NEJMoa032691 15175435
13. Jain RK, (2005). Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. Science 307: 58–62. doi: 10.1126/science.1104819 15637262
14. Gerhardt H, Golding M, Fruttiger M, et al (2003). VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia. J Cell Biol 161: 1163–1177 doi: 10.1083/jcb.200302047 12810700
15. Chatzizisis YS, Coskun AU, Jonas M, Edelman ER, Feldman CL, Stone PH, (2007). Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior. J Am Coll Cardio 49: 2379–2393. doi: 10.1016/j.jacc.2007.02.059
16. Secomb TW, Alberding JP, Hsu R, Dewhirst MW, Pries AR, (2013). Angiogenesis: an adaptive dynamic biological patterning problem. PLoS Comp Biol, 9: e1002983. doi: 10.1371/journal.pcbi.1002983
17. Travasso RDM, (2011). The mechanics of blood vessel growth. Vasculogenesis and angiogenesis—from embryonic development to regenerative medicine. inTechOpen, Rijeka Croatia, 187–204.
18. Mammoto A, Connor KM, Mammoto T, Yung CW, Huh D, Aderman CM, et al (2009). A mechanosensitive transcriptional mechanism that controls angiogenesis. Nature 457: 1103–1108. doi: 10.1038/nature07765 19242469
19. Hohberg M, Knöchel J, Hoffmann CJ, Chlench S, Wunderlich W, Alter A, et al (2010). Expression of ADAMTS1 in endothelial cells is induced by shear stress and suppressed in sprouting capillaries. J Cell Physiol 226: 350–361. doi: 10.1002/jcp.22340
20. Califano JP, Reinhart-King CA (2009). The effects of substrate elasticity on endothelial cell network formation and traction force generation. 31st Annual Inter. Conference of the IEEE EMBS, 3343–3345, Minneapolis.
21. Reinhart-King CA, Dembo M, Hammer DA, (2008). Cell-cell mechanical communication through compliant substrates. Biophys J 95: 6044–6051. doi: 10.1529/biophysj.107.127662 18775964
22. Shamloo A, Heilshorn SC, (2010). Matrix density mediates polarization and lumen formation of endothelial sprouts in VEGF gradients. Lab Chip 10: 3061–3068. doi: 10.1039/c005069e 20820484
23. Jain RK, Tong RT, Munn LL, (2007). Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model. Cancer Res 67: 2729–2735. doi: 10.1158/0008-5472.CAN-06-4102 17363594
24. Wu J, Long Q, Xu S, Padhani AR, (2009). Study of tumor blood perfusion and its variation due to vascular normalization by anti-angiogenic therapy based on 3D angiogenic microvasculature. J Biomech 42: 712–721. doi: 10.1016/j.jbiomech.2009.01.009 19268290
25. Travasso RDM, Corvera Poiré E, Castro M, Rodríguez-Manzaneque JC, Hernández-Machado A, (2011). Tumor Angiogenesis and Vascular Patterning: A Mathematical Model. PLoS ONE 6: e19989. doi: 10.1371/journal.pone.0019989 21637756
26. Shiu Y-T, Weiss JA, Hoying JB, Iwamoto MN, Joung IS, Quam CT, (2005). The role of mechanical stresses in angiogenesis. Critical Rev Biomed Eng 33: 431–510. doi: 10.1615/CritRevBiomedEng.v33.i5.10
27. Neal ML, Trister AD, Cloke T, Sodt R, Ahn S, et al (2013). Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric. PloS ONE, 8: e51951. doi: 10.1371/journal.pone.0051951 23372647
28. Lowengrub JS, Frieboes HB, Jin F, Chuang Y-L, Li X, Macklin P, Wise SM, Cristini V, (2010). Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity 23: R1–R9. doi: 10.1088/0951-7715/23/1/R01 20808719
29. Frieboes HB, Jin F, Chuang Y-L, Wise SM, Lowengrub JS, Cristini V, (2010). Three-dimensional multispecies nonlinear tumor growth—II: tumor invasion and angiogenesis. J Theor Biol 264: 1254–1278. doi: 10.1016/j.jtbi.2010.02.036 20303982
30. Qutub AA, Popel AS, (2006). A computational model of intracellular oxygen sensing by hypoxia-inducible factor HIF1α. J Cell Sci 119: 3467–3480. doi: 10.1242/jcs.03087 16899821
31. Yu Y, Wang G, Simha R, Peng W, Turano F, Zeng C, (2007). Pathway switching explains the sharp response characteristic of hypoxia response network. PLoS Comp Biol 3: e171. doi: 10.1371/journal.pcbi.0030171
32. Gabhann FM, Popel AS, (2008). Systems biology of vascular endothelial growth factors. Microcirculation 15: 715–738. doi: 10.1080/10739680802095964
33. Karagiannis ED, Popel AS, (2006). Distinct modes of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell: insights from a computational model. J Theor Biol 238: 124–145. doi: 10.1016/j.jtbi.2005.05.020 16005020
34. Vempati P, Mac Gabhann F, Popel AS, (2010). Quantifying the proteolytic release of extracellular matrix-sequestered VEGF with a computational model. PLoS ONE 5: e11860. doi: 10.1371/journal.pone.0011860 20686621
35. Vempati P, Popel AS, Mac Gabhann F, (2011). Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis. BMC Sys Biol 5: 59. doi: 10.1186/1752-0509-5-59
36. Finley SD, Dhar M, Popel AS, (2013). Compartment model predicts VEGF secretion and investigates the effects of VEGF Trap in tumor-bearing mice. Front Oncol 3: 196. doi: 10.3389/fonc.2013.00196 23908970
37. Orme ME, Chaplain MAJ, (1996). A mathematical model of vascular tumour growth and invasion. Math Comp Model 23: 43–60. doi: 10.1016/0895-7177(96)00053-2
38. Orme ME, Chaplain MAJ, (1997). Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. Math Med Biol 14: 189–205. doi: 10.1093/imammb/14.3.189
39. Levine HA, Sleeman BD, Nilsen-Hamilton M, (2001). Mathematical modeling of the onset of capillary formation initiating angiogenesis. J Math Biol 42: 195–238. doi: 10.1007/s002850000037 11315313
40. Levine HA, Pamuk S, Sleeman BD, Nilsen-Hamilton M, (2001). Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull Math Biol 63: 801–863. doi: 10.1006/bulm.2001.0240 11565406
41. Levine HA, Sleeman BD, Nilsen-Hamilton M, (2000). A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Math Biosci 168: 77–115. doi: 10.1016/S0025-5564(00)00034-1 11121821
42. Plank MJ, Sleeman BD, Jones PF, (2004). A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins. J Theor Biol 229: 435–454. doi: 10.1016/j.jtbi.2004.04.012 15246783
43. Stokes CL, Lauffenburger DA, (1991). Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J Theor Biol 152: 377–403. doi: 10.1016/S0022-5193(05)80201-2 1721100
44. Anderson ARA, Chaplain MAJ, (1998). Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 60: 857–899. doi: 10.1006/bulm.1998.0042 9739618
45. McDougall SR, Anderson ARA, Chaplain MAJ, Sherratt JA, (2002). Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull Math Biol 64: 673–702. doi: 10.1006/bulm.2002.0293 12216417
46. Chaplain MAJ, McDougall SR, Anderson ARA, (2006). Mathematical modeling of tumor-induced angiogenesis. Annu Rev Biomed Eng 8: 233–257. doi: 10.1146/annurev.bioeng.8.061505.095807 16834556
47. Macklin P, McDougall S, Anderson ARA, Chaplain MAJ, Cristini V, Lowengrub J, (2009). Multiscale modelling and nonlinear simulation of vascular tumour growth. J Math Biol 58: 765–798. doi: 10.1007/s00285-008-0216-9 18781303
48. Perfahl H, Byrne HM, Chen T, Estrella V, Alarcón T, Lapin A, et al (2011). Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions. PloS ONE 6: e14790. doi: 10.1371/journal.pone.0014790 21533234
49. McDougall SR, Watson MG, Devlin AH, Mitchell CA, Chaplain MAJ, (2012). A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature. Bull Math Biol 74: 2272–2314. doi: 10.1007/s11538-012-9754-9 22829182
50. Bauer AL, Jackson TL, Jiang Y, (2007). A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys J 92: 3105–3121. doi: 10.1529/biophysj.106.101501 17277180
51. Merks RM, Perryn ED, Shirinifard A, Glazier JA, (2008). Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoS Comp Biol 4: e1000163. doi: 10.1371/journal.pcbi.1000163
52. Bentley K, Gerhardt H, Bates PA, (2008). Agent-based simulation of notch-mediated tip cell selection in angiogenic sprout initialisation. J Theor Biol 250: 25–36. doi: 10.1016/j.jtbi.2007.09.015 18028963
53. Shirinifard A, Gens JS, Zaitlen BL, Poplawski NJ, Swat M, Glazier JA, (2009). 3D multi-cell simulation of tumor growth and angiogenesis. PLoS ONE 4: e7190. doi: 10.1371/journal.pone.0007190 19834621
54. Milde F, Bergdorf M, Koumoutsakos P, (2008). A hybrid model for three-dimensional simulations of sprouting angiogenesis. Biophys J 95: 3146–3160. doi: 10.1529/biophysj.107.124511 18586846
55. Vilanova G, Colominas I, Gomez H, (2014). Coupling of discrete random walks and continuous modeling for three-dimensional tumor-induced angiogenesis. Comp Mech 53: 449–464. doi: 10.1007/s00466-013-0958-0
56. Mantzaris N, Webb S, Othmer H, (2004). Mathematical modeling of tumor-induced angiogenesis. J Math Biol 49: 111–187. doi: 10.1007/s00285-003-0262-2 15293017
57. Spill F, Guerrero P, Alarcón T, Maini PK, Byrne HM, (2014). Mesoscopic and continuum modelling of angiogenesis. J Math Biol 70: 485–532. doi: 10.1007/s00285-014-0771-1 24615007
58. Quinas-Guerra MM, Ribeiro-Rodrigues TM, Rodríguez-Manzaneque JC, Travasso RDM, (2012). Understanding the dynamics of tumor angiogenesis: A systems biology approach. in Systems Biology in Cancer Research and Drug Discovery (pp. 197–227). Springer Netherlands.
59. Heck T, Vaeyens MM, Van Oosterwyck H, (2015). Computational models of sprouting angiogenesis and cell migration: towards multiscale mechanochemical models of angiogenesis. Math Model Nat Phen 10: 108–141. doi: 10.1051/mmnp/201510106
60. Bentley K, Mariggi G, Gerhardt H, Bates PA, (2009). Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis. PLoS Comp Biol 5: e1000549. doi: 10.1371/journal.pcbi.1000549
61. van Oers RFM, Rens EG, LaValley DJ, Reinhart-King CA, Merks RMH, (2014). Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro. PLoS Comp Biol 10: e1003774. doi: 10.1371/journal.pcbi.1003774
62. Jakobsson L, Franco C, Bentley K, Collins R, Ponsioen B, et al (2010) Endothelial cells dynamically compete for the tip cell position during angiogenic sprouting. Nat Cell Biol 12(10): 943–953. doi: 10.1038/ncb2103 20871601
63. Zheng X, Xie C, (2014). A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation. J Math Biol 68: 57–80. doi: 10.1007/s00285-012-0624-8 23149501
64. Arima S, Nishiyama K, Ko T, Arima Y, Hakozaki Y, Sugihara K, et al (2011). Angiogenic morphogenesis driven by dynamic and heterogeneous collective endothelial cell movement. Development 138: 4763–4776. doi: 10.1242/dev.068023 21965612
65. Emmerich H, (2008). Advances of and by phase field modeling in condensed-matter physics. Adv Phys 57: 1. doi: 10.1080/00018730701822522
66. Lázaro GR, Hernández-Machado A, Pagonabarraga I, (2014). Rheology of red blood cells under flow in highly confined microchannels: I. effect of elasticity. Soft Matter 10: 7195–7206. doi: 10.1039/C4SM00894D 25105872
67. Nonomura M, (2012). Study on multicellular systems using a phase field model. PloS ONE 7: e33501. doi: 10.1371/journal.pone.0033501 22539943
68. Camley BA, Zhang Y, Zhao Y, Li B, Ben-Jacob E, Levine H, Rappel WJ, (2014). Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns. Proc Natl Acad Sci USA 111: 14770–14775. doi: 10.1073/pnas.1414498111 25258412
69. Travasso RDM, Castro M, Oliveira JCRE, (2011). The phase-field model in tumor growth. Philos Mag 91: 183–206. doi: 10.1080/14786435.2010.501771
70. Zheng X, Koh GY, Jackson T, (2013). A continuous model of angiogenesis: initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Disc Cont Dyn Syst Ser B 18: 1109–1154. doi: 10.3934/dcdsb.2013.18.1109
71. Köhn-Luque A, de Back W, Yamaguchi Y, Yoshimura K, Herrero MA, Miura T, (2013). Dynamics of VEGF matrix-retention in vascular network patterning. Phys Biol 10: 066007. doi: 10.1088/1478-3975/10/6/066007 24305433
72. Onuki A, (2004). Phase transition dynamics, Cambridge University Press, Cambridge, UK
73. Gerhardt H, Betsholtz C, (2005). How do endothelial cells orientate?. in Mechanisms of angiogenesis (pp. 3–15). Birkhäuser Basel.
74. Landau LD, Lifchits EM, Kosevitch AM, Pitaevski LP, Kosevitch A. M., Pitaevski L. P., (1986). Course of theoretical physics: theory of elasticity (p. 4). (Eds.). Butterworth-Heinemann.
75. Schugart RC, Friedman A, Zhao R, Sen CK, (2008). Wound angiogenesis as a function of tissue oxygen tension: A mathematical model. Proc Natl Acad Sci USA 105: 2628–2633. doi: 10.1073/pnas.0711642105 18272493
76. Nelson CM, Pirone DM, Tan JL, Chen CS, (2004). Vascular endothelial-cadherin regulates cytoskeletal tension, cell spreading, and focal adhesions by stimulating RhoA. Mol Biol Cell 15: 2943–2953. doi: 10.1091/mbc.E03-10-0745 15075376
77. Liu J, Agarwal S, (2010). Mechanical signals activate vascular endothelial growth factor receptor-2 to upregulate endothelial cell proliferation during inflammation. Journal Immun 185: 1215–1221. doi: 10.4049/jimmunol.0903660
78. Provenzano PP, Keely PJ, (2011). Mechanical signaling through the cytoskeleton regulates cell proliferation by coordinated focal adhesion and Rho GTPase signaling. J Cell Sci 124: 1195–1205. doi: 10.1242/jcs.067009 21444750
79. Raub CB, Putnam AJ, Tromberg BJ, George SC, (2010). Predicting bulk mechanical properties of cellularized collagen gels using multiphoton microscopy. Acta Biomater 6: 4657–4665. doi: 10.1016/j.actbio.2010.07.004 20620246
80. Muller DJ, Dufrêne YF, (2011). Atomic force microscopy: a nanoscopic window on the cell surface. Trend Cell Biol 21: 461–469. doi: 10.1016/j.tcb.2011.04.008
81. McCain ML, Lee H, Aratyn-Schaus Y, Kléber AG, Parker KK, (2012). Cooperative coupling of cell-matrix and cell-cell adhesions in cardiac muscle. Proc Natl Acad Sci USA 109: 9881–9886. doi: 10.1073/pnas.1203007109 22675119
82. Lamura A, Gonnella G, Yeomans JM, (1998). Modeling the dynamics of amphiphilic fluids. Int J Mod Phys C 9: 1469–1478. doi: 10.1142/S0129183198001333
83. Good K, Kuksenok O, Buxton GA, Ginzburg VV, Balazs AC, (2004). Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures. J Chem Phys 121: 6052–6063. doi: 10.1063/1.1783872 15367034
84. D’Antonio G, Macklin P, Preziosi L, (2012). An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix. Math Biosci Eng 10: 75–101. doi: 10.3934/mbe.2013.10.75
85. Welter M, Rieger H, (2013). Interstitial fluid flow and drug delivery in vascularized tumors: a computational model. PloS ONE 8: e70395. doi: 10.1371/journal.pone.0070395 23940570