Skip to main content
SpringerLink
Log in

Cell-Based Computational Modeling of Vascular Morphogenesis Using Tissue Simulation Toolkit

  • Protocol
  • First Online:
Book cover Vascular Morphogenesis

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1214))

Abstract

Computational modeling has become a widely used tool for unraveling the mechanisms of higher level cooperative cell behavior during vascular morphogenesis. However, experimenting with published simulation models or adding new assumptions to those models can be daunting for novice and even for experienced computational scientists. Here, we present a step-by-step, practical tutorial for building cell-based simulations of vascular morphogenesis using the Tissue Simulation Toolkit (TST). The TST is a freely available, open-source C++ library for developing simulations with the two-dimensional cellular Potts model, a stochastic, agent-based framework to simulate collective cell behavior. We will show the basic use of the TST to simulate and experiment with published simulations of vascular network formation. Then, we will present step-by-step instructions and explanations for building a recent simulation model of tumor angiogenesis. Demonstrated mechanisms include cell–cell adhesion, chemotaxis, cell elongation, haptotaxis, and haptokinesis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664

    Article  CAS  PubMed  Google Scholar 

  2. Folkman J, Hauenschild C (1980) Angiogenesis in vitro. Nature 288:551–556

    Article  CAS  PubMed  Google Scholar 

  3. Califano J, Reinhart-King C (2008) A balance of substrate mechanics and matrix chemistry regulates endothelial cell network assembly. Cell Mol Bioeng 1:122–132. doi:10.1007/s12195-008-0022-x

    Article  Google Scholar 

  4. Oster GF, Murray JD, Harris AK (1983) Mechanical aspects of mesenchymal morphogenesis. J Embryol Exp Morphol 78:83–125

    CAS  PubMed  Google Scholar 

  5. Manoussaki D, Lubkin S, Vernon R, Murray J (1996) A mechanical model for the formation of vascular networks in vitro. Acta Biotheor 44:271–282

    Article  CAS  PubMed  Google Scholar 

  6. Manoussaki D (2003) A mechanochemical model of angiogenesis and vasculogenesis. ESAIM: Math Model Num 37:581–599. doi:10.1051/m2an:2003046

    Article  Google Scholar 

  7. Gamba A, Ambrosi D, Coniglio A, de Candia A, Di Talia S et al (2003) Percolation, morphogenesis, and Burgers dynamics in blood vessels formation. Phys Rev Lett 90:118101. doi:10.1103/PhysRevLett.90.118101

    Article  CAS  PubMed  Google Scholar 

  8. Serini G, Ambrosi D, Giraudo E, Gamba A, Preziosi L et al (2003) Modeling the early stages of vascular network assembly. EMBO J 22:1771–1779. doi:10.1093/emboj/cdg176

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  9. Ambrosi D, Gamba A, Serini G (2004) Cell directional and chemotaxis in vascular morphogenesis. B Math Biol 66:1851–1873. doi:10.1016/j.blum.2004.04.004

    Article  CAS  Google Scholar 

  10. Keller E (1970) Initiation of slime mold aggregation viewed as an instability. J Theor Biol 26:399–415

    Article  CAS  PubMed  Google Scholar 

  11. Merks RMH, Glazier JA (2005) A cell-centered approach to developmental biology. Physica A 352:113–130. doi:10.1016/j.physa.2004.12.028

    Article  CAS  Google Scholar 

  12. Graner F, Glazier JA (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett 69:2013–2016

    Article  CAS  PubMed  Google Scholar 

  13. Merks RMH, Brodsky SV, Goligorksy MS, Newman SA, Glazier JA (2006) Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev Biol 289:44–54. doi:10.1016/j.ydbio.2005.10.003

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  14. Palm MM, Merks RMH (2013) Vascular networks due to dynamically arrested crystalline ordering of elongated cells. Phys Rev E 87:012725. doi:10.1103/PhysRevE.87.012725

    Article  Google Scholar 

  15. Merks RMH, 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

    Article  Google Scholar 

  16. Szabó A, Mehes E, Kosa E, Czirok A (2008) Multicellular sprouting in vitro. Biophys J 95:2702–2710. doi:10.1529/biophysj.108.129668

    Article  PubMed Central  PubMed  Google Scholar 

  17. Köhn-Luque A, De Back W, Starruß J, Mattiotti A, Deutsch A et al (2011) Early embryonic vascular patterning by matrix-mediated paracrine signalling: a mathematical model study. PLoS One 6:e24175. doi:10.1371/journal.pone.0024175.t001

    Article  PubMed Central  PubMed  Google Scholar 

  18. Köhn-Luque A, de Back W, Yamaguchi Y, Yoshimura K, Herrero MA et al (2013) Dynamics of VEGF matrix-retention in vascular network patterning. Phys Biol 10:066007. doi:10.1088/1478-3975/10/6/066007

    Article  PubMed  Google Scholar 

  19. Daub JT, Merks RMH (2013) A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis. B Math Biol 75:1377–1399. doi:10.1007/s11538-013-9826-5

    Article  CAS  Google Scholar 

  20. Scianna M, Munaron L, Preziosi L (2011) A multiscale hybrid approach for vasculogenesis and related potential blocking therapies. Prog Biophys Mol Biol 106:450–462. doi:10.1016/j.pbiomolbio.2011.01.004

    Article  CAS  PubMed  Google Scholar 

  21. Boas SEM, Merks RMH (2014) Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation. J R Soc Interface 11:20131049. doi:10.1038/ncb1705

    Article  PubMed Central  PubMed  Google Scholar 

  22. Shirinifard A, Gens JS, Zaitlen BL, Popławski NJ, Swat M et al (2009) 3D multi-cell simulation of tumor growth and angiogenesis. PLoS One 4:e7190. doi:10.1371/journal.pone.0007190

    Article  PubMed Central  PubMed  Google Scholar 

  23. Shirinifard A, Glazier JA, Swat M, Gens JS, Family F et al (2012) Adhesion failures determine the pattern of choroidal neovascularization in the eye: a computer simulation study. PLoS Comput Biol 8:e1002440. doi:10.1371/journal.pcbi.1002440.s022

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  24. Kleinstreuer N, Dix D, Rountree M, Baker N, Sipes N et al (2013) A computational model predicting disruption of blood vessel development. PLoS Comput Biol 9:e1002996. doi:10.1371/journal.pcbi.1002996.s011

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  25. 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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  26. Bauer AL, Jackson TL, Jiang Y (2009) Topography of extracellular matrix mediates vascular morphogenesis and migration speeds in angiogenesis. PLoS Comput Biol 5:e1000445. doi:10.1371/journal.pcbi.1000445

    Article  PubMed Central  PubMed  Google Scholar 

  27. Scianna M, Bell CG, Preziosi L (2013) A review of mathematical models for the formation of vascular networks. J Theor Biol 333:174–209. doi:10.1016/j.jtbi.2013.04.037

    Article  CAS  PubMed  Google Scholar 

  28. Czirok A (2013) Endothelial cell motility, coordination and pattern formation during vasculogenesis. Wiley Interdiscip Rev Syst Biol Med 5:587–602. doi:10.1002/wsbm.1233

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  29. Wacker A, Gerhardt H (2011) Endothelial development taking shape. Curr Opin Cell Biol 23:676–685

    CAS  PubMed  Google Scholar 

  30. Swat MH, Thomas GL, Belmonte JM, Shirinifard A, Hmeljak D et al. (2012) Multi-scale modeling of tissues using CompuCell3D. Elsevier Inc. 42 pp. doi:10.1016/B978-0-12-388403-9.00013-8

  31. Szabó A, Varga K, Garay T, Hegedűs B, Czirok A (2012) Invasion from a cell aggregate – the roles of active cell motion and mechanical equilibrium. Phys Biol 9:016010. doi:10.1088/1478-3975/9/1/016010

    Article  PubMed Central  PubMed  Google Scholar 

  32. van Oers RFM, Ruimerman R, Tanck E, Hilbers PAJ, Huiskes R (2008) A unified theory for osteonal and hemi-osteonal remodeling. Bone 42:250–259. doi:10.1016/j.bone.2007.10.009

    Article  PubMed  Google Scholar 

  33. Starruß J, De Back W, Brusch L, Deutsch A (2014) Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics 30:1331–1332. doi:10.1093/bioinformatics/btt772

    Article  PubMed Central  PubMed  Google Scholar 

  34. Pitt-Francis J, Pathmanathan P, Bernabeu MO, Bordas R, Cooper J et al (2009) Chaste: a test-driven approach to software development for biological modelling. Comput Phys Commun 180:2452–2471. doi:10.1016/j.cpc.2009.07.019

    Article  CAS  Google Scholar 

  35. Merks RMH, Guravage M, Inze D, Beemster GTS (2011) VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol 155:656–666. doi:10.1104/pp. 110.167619

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  36. Holcombe M, Adra S, Bicak M, Chin S, Coakley S et al (2012) Modelling complex biological systems using an agent-based approach. Integr Biol 4:53–64

    Article  CAS  Google Scholar 

  37. Glazier JA, Graner F (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E 47:2128–2154

    Article  Google Scholar 

  38. Savill NJ, Hogeweg P (1997) Modelling morphogenesis: from single cells to crawling slugs. J Theor Biol 184:229–235

    Article  Google Scholar 

  39. Eden M (1961) A two-dimensional growth process. Proc 4th Berkeley Symp Math Statist Prob 4:223–239

    Google Scholar 

  40. Merks RMH, Glazier JA (2006) Dynamic mechanisms of blood vessel growth. Nonlinearity 19:C1–C10. doi:10.1088/0951-7715/19/1/000

    Article  PubMed Central  PubMed  Google Scholar 

  41. Folkman J (2007) Angiogenesis: an organizing principle for drug discovery? Nat Rev Drug Discov 6:273–286. doi:10.1038/nrd2115

    Article  CAS  PubMed  Google Scholar 

  42. Pepper MS (2001) Role of the matrix metalloproteinase and plasminogen activator-plasmin systems in angiogenesis. Arterioscler Thromb Vasc Biol 21:1104–1117

    Article  CAS  PubMed  Google Scholar 

  43. van Hinsbergh VWM, Koolwijk P (2008) Endothelial sprouting and angiogenesis: matrix metalloproteinases in the lead. Cardiovasc Res 78:203–212. doi:10.1093/cvr/cvm102

    Article  PubMed  Google Scholar 

  44. Gerhardt H, Betsholtz C (2003) Endothelial-pericyte interactions in angiogenesis. Cell Tissue Res 314:15–23. doi:10.1007/s00441-003-0745-x

    Article  PubMed  Google Scholar 

  45. Gerhardt H (2008) VEGF and endothelial guidance in angiogenic sprouting. Organogenesis 4:241–246

    Article  PubMed Central  PubMed  Google Scholar 

  46. Senger DR, Perruzzi CA, Streit M, Koteliansky VE, de Fougerolles AR et al (2002) The and integrins provide critical support for vascular endothelial growth factor signaling, endothelial cell migration, and tumor angiogenesis. Am J Pathol 160:195–204

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  47. Lamalice L, Le Boeuf F, Huot J (2007) Endothelial cell migration during angiogenesis. Circ Res 100:782–794. doi:10.1161/01.RES.0000259593.07661.1e

    Article  CAS  PubMed  Google Scholar 

  48. DiMilla PA, Stone JA, Quinn JA, Albelda SM, Lauffenburger DA (1993) Maximal migration of human smooth muscle cells on fibronectin and type IV collagen occurs at an intermediate attachment strength. J Cell Biol 122:729–737

    Article  CAS  PubMed  Google Scholar 

  49. Cox E, Sastry S, Huttenlocher A (2001) Integrin-mediated adhesion regulates cell polarity and membrane protrusion through the Rho family of GTPases. Mol Biol Cell 12:265–277

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  50. Coomber BL, Gotlieb AI (1990) In vitro endothelial wound repair. Interaction of cell migration and proliferation. Arteriosclerosis 10:215–222

    Article  CAS  PubMed  Google Scholar 

  51. Keller EF, Segel LA (1971) Model for chemotaxis. J Theor Biol 30:225–234. doi:10.1016/0022-5193(71)90050-6

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Ecology and Evolution, University of Bern, Bern, Switzerland

    Josephine T. Daub

  2. Swiss Institute of Bioinformatics, Lausanne, Switzerland

    Josephine T. Daub

  3. Department of Ecology and Evolution, University of Lausanne, Lausanne, 1015, Switzerland

    Josephine T. Daub

  4. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Roeland M. H. Merks

  5. Mathematical Institute, University Leiden, 9512, Leiden, The Netherlands

    Roeland M. H. Merks

Authors
  1. Josephine T. Daub
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roeland M. H. Merks
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roeland M. H. Merks .

Editor information

Editors and Affiliations

  1. University of Bari Aldo Moro, Bari, Italy

    Domenico Ribatti

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this protocol

Cite this protocol

Daub, J.T., Merks, R.M.H. (2015). Cell-Based Computational Modeling of Vascular Morphogenesis Using Tissue Simulation Toolkit . In: Ribatti, D. (eds) Vascular Morphogenesis. Methods in Molecular Biology, vol 1214. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-1462-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-1462-3_6

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-1461-6

  • Online ISBN: 978-1-4939-1462-3

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation