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Computational Particle Mechanics

, Volume 6, Issue 1, pp 85–96 | Cite as

An agent-based and FE approach to simulate cell jamming and collective motion in epithelial layers

  • Ismael González-Valverde
  • José Manuel García-AznarEmail author
Article
  • 88 Downloads

Abstract

The collective cell motion in epithelial layers is still poorly understood, despite this phenomenon being fundamental to explain several biological processes. Indeed, it has been experimentally observed that epithelial cells can behave either as a fluid or as a solid in the tissue. The transition between both states is related to cell–cell adhesions and cell morphology. In fact, cell motility can be limited by the interaction with its neighboring cells. Moreover, cells can even enter in a frozen state, and in that case, the system behaves as a solid. However, this state is reversible under certain circumstances, and cells may return to a fluidized state. This phenomenon is known as cell jamming. Here, we propose a hybrid approach that couples a discrete agent-based model and a continuum finite element-based model to simulate cell dynamics and cell jamming in epithelial monolayers. Our hybrid approach is able to simulate cell motion individually, but it also reproduces the mechanical properties at tissue level that emerge from cell–cell interactions. This study helps to understand how cell–cell interactions regulate the cell jamming phenomenon and provides a deeper insight into the role of the passive mechanics in collective cell motion.

Keywords

Finite element method Tissue mechanics Hybrid model Cell mechanics 

Notes

Acknowledgements

This research was supported by the European Research Council (ERC) through Project (ERC-2012-StG 306571) and the Spanish Ministry of Economy and Competitiveness (DPI2015-64221-C2-1-R). We would like to acknowledge open-source projects that were used in this research: deal.II library [24] for FE analysis, CGAL library [25] for geometrical representation, Seaborn [26] for data analysis and Paraview [27] for data representation.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Supplementary material

40571_2018_199_MOESM1_ESM.mp4 (10 mb)
S1 Video Collective cell motion for different values of epsilon.
40571_2018_199_MOESM2_ESM.mp4 (4.9 mb)
S2 Video Collective motion generates heterogeneity in the monolayer.

References

  1. 1.
    Trepat X, Fredberg J (2011) Plithotaxis and emergent dynamics in collective cellular migration. Trends Cell Biol 21:638–646.  https://doi.org/10.1016/j.tcb.2011.06.006.Plithotaxis CrossRefGoogle Scholar
  2. 2.
    Sadati M, Taheri Qazvini N, Krishnan R et al (2013) Collective migration and cell jamming. Differentiation 86:121–125.  https://doi.org/10.1016/j.diff.2013.02.005 CrossRefGoogle Scholar
  3. 3.
    Park J-A, Kim JH, Bi D et al (2015) Unjamming and cell shape in the asthmatic airway epithelium. Nat Mater 14:1040–1048.  https://doi.org/10.1038/nmat4357 CrossRefGoogle Scholar
  4. 4.
    Park J-A, Atia L, Mitchel JA et al (2016) Collective migration and cell jamming in asthma, cancer and development. J Cell Sci 129:3375–3383.  https://doi.org/10.1242/jcs.187922 CrossRefGoogle Scholar
  5. 5.
    Garcia S, Hannezo E, Elgeti J et al (2015) Physics of active jamming during collective cellular motion in a monolayer. Proc Natl Acad Sci 112:15314–15319.  https://doi.org/10.1073/pnas.1510973112 CrossRefGoogle Scholar
  6. 6.
    Tambe DT, Corey Hardin C, Angelini TE et al (2011) Collective cell guidance by cooperative intercellular forces. Nat Mater 10:469–475.  https://doi.org/10.1038/nmat3025 CrossRefGoogle Scholar
  7. 7.
    Harris AR, Peter L, Bellis J et al (2012) Characterizing the mechanics of cultured cell monolayers. Proc Natl Acad Sci 109:16449–16454.  https://doi.org/10.1073/pnas.1213301109 CrossRefGoogle Scholar
  8. 8.
    Harris AR, Daeden A, Charras GT (2014) Formation of adherens junctions leads to the emergence of a tissue-level tension in epithelial monolayers. J Cell Sci 127:2507–2517.  https://doi.org/10.1242/jcs.142349 CrossRefGoogle Scholar
  9. 9.
    Bi D, Lopez JH, Schwarz JM, Manning ML (2015) A density-independent rigidity transition in biological tissues. Nat Phys 11:1074–1079.  https://doi.org/10.1038/nphys3471 CrossRefGoogle Scholar
  10. 10.
    Bi D, Yang X, Marchetti MC, Manning ML (2016) Motility-driven glass and jamming transitions in biological tissues. Phys Rev X 6:1–12.  https://doi.org/10.1103/PhysRevX.6.021011 Google Scholar
  11. 11.
    Angelini TE, Hannezo E, Trepat X et al (2011) Glass-like dynamics of collective cell migration. Proc Natl Acad Sci 108:4714–4719.  https://doi.org/10.1073/pnas.1010059108 CrossRefGoogle Scholar
  12. 12.
    Rey R, García-Aznar JM (2013) A phenomenological approach to modelling collective cell movement in 2D. Biomech Model Mechanobiol 12:1089–1100.  https://doi.org/10.1007/s10237-012-0465-9 CrossRefGoogle Scholar
  13. 13.
    Sepúlveda N, Petitjean L, Cochet O et al (2013) Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model. PLoS Comput Biol 9:e1002944.  https://doi.org/10.1371/journal.pcbi.1002944 MathSciNetCrossRefGoogle Scholar
  14. 14.
    Smeets B, Alert R, Pešek J et al (2016) Emergent structures and dynamics of cell colonies by contact inhibition of locomotion. Proc Natl Acad Sci 113:14621–14626.  https://doi.org/10.1073/pnas.1521151113 CrossRefGoogle Scholar
  15. 15.
    Van Liedekerke P, Palm MM, Jagiella N, Drasdo D (2015) Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Comput Part Mech 2:401–444.  https://doi.org/10.1007/s40571-015-0082-3 CrossRefGoogle Scholar
  16. 16.
    Farhadifar R, Röper J-C, Aigouy B et al (2007) The influence of cell mechanics, cell–cell interactions, and proliferation on epithelial packing. Curr Biol 17:2095–2104.  https://doi.org/10.1016/j.cub.2007.11.049 CrossRefGoogle Scholar
  17. 17.
    Staple DB, Farhadifar R, Röper J-C et al (2010) Mechanics and remodelling of cell packings in epithelia. Eur Phys J E 33:117–127.  https://doi.org/10.1140/epje/i2010-10677-0 CrossRefGoogle Scholar
  18. 18.
    Aegerter-Wilmsen T, Smith AC, Christen AJ et al (2010) Exploring the effects of mechanical feedback on epithelial topology. Development 137:499–506.  https://doi.org/10.1242/dev.041731 CrossRefGoogle Scholar
  19. 19.
    Li B, Sun SX (2014) Coherent motions in confluent cell monolayer sheets. Biophys J 107:1532–1541.  https://doi.org/10.1016/j.bpj.2014.08.006 CrossRefGoogle Scholar
  20. 20.
    Malinverno C, Corallino S, Giavazzi F et al (2017) Endocytic reawakening of motility in jammed epithelia. Nat Mater 16:587–596.  https://doi.org/10.1038/nmat4848 CrossRefGoogle Scholar
  21. 21.
    González-Valverde I, García-Aznar JM (2017) A hybrid computational model to explore the topological characteristics of epithelial tissues. Int J Numer Methods Biomed Eng.  https://doi.org/10.1002/cnm.2877 MathSciNetGoogle Scholar
  22. 22.
    Pawlizak S, Fritsch AW, Grosser S et al (2015) Testing the differential adhesion hypothesis across the epithelial–mesenchymal transition. New J Phys 17:083049.  https://doi.org/10.1088/1367-2630/17/8/083049 CrossRefGoogle Scholar
  23. 23.
    Wyatt TPJ, Harris AR, Lam M et al (2015) Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis. Proc Natl Acad Sci 112:5726–5731.  https://doi.org/10.1073/pnas.1420585112 CrossRefGoogle Scholar
  24. 24.
    Arndt D, Bangerth W, Davydov D et al (2017) The deal. II library, version 8.5. J Numer Math 25:137–145.  https://doi.org/10.1515/jnma-2017-0058 MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    The CGAL Project (2017) CGAL user and reference manual. CGAL Editor, BoardGoogle Scholar
  26. 26.
    Waskom M, Botvinnik O, O’Kane D et al (2017) mwaskom/seaborn: v0.8.1.  https://doi.org/10.5281/ZENODO.883859
  27. 27.
    Ayachit U (2015) The ParaView guide: a parallel visualization application. Kitware, New YorkGoogle Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A)University of ZaragozaZaragozaSpain

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