Skip to main content
SpringerLink
Log in

Mechanical waves caused by collective cell migration: generation

  • Review
  • Published:
European Biophysics Journal Aims and scope Submit manuscript

Abstract

Long-timescale viscoelasticity caused by collective cell migration (CCM) significantly influences cell rearrangement and induces generation of mechanical waves. The phenomenon represents a product of the active turbulence occurring at low Reynolds number. The generation of mechanical waves has been a subject of intensive research primarily in 2D multicellular systems, while 3D systems have not been considered in this context. The aim of this contribution is to discuss the generation of mechanical waves during 3D CCM in two model systems: (1) the fusion of two-cell aggregates and (2) cell aggregate rounding after uni-axial compression, pointing out that mechanical waves represent a characteristic of CCM in general. Such perturbations are also involved in various biological processes, such as embryogenesis, wound healing and cancer invasion. The inter-relation between the viscoelasticity and the appearance of active turbulence remains poorly understood even in 2D. The phenomenon represents a consequence of the competition between the viscoelastic force and the surface tension force which induces successive stiffening and softening of parts of multicellular systems. The viscoelastic force is a product of the residual cell stress accumulation and its inhomogeneous distribution caused by CCM. This modeling consideration represents a powerful tool to address the generation of mechanical waves in CCM towards an understanding of this important but still controversial topic.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Alert R, Casademunt J, Joanny J-F (2021) Active turbulence. arXiv:2104.02122v1

  • Alert R, Trepat X (2020) Physical models of collective cell migration. Annu Rev Condens Matter Phys 11:77–101

    Article  Google Scholar 

  • Ban E, Wang H, J. Franklin M, Liphardt JT, Janmey PA, Shenoy VB. (2019) Strong triaxial coupling and anomalous Poisson effect in collagen networks. PNAS 116(4):6790-6799

  • Barriga EH, Mayor R (2019) Adjustable viscoelasticity allows for efficient collective cell migration. Sem Cell Dev Biol 93:55–68

    Article  Google Scholar 

  • Blanchard GB, Fletcher AG, Schumacher LJ (2019) The devil is in the mesoscale: mechanical and behavioural heterogeneity in collective cell movement. Sem Cell Dev Biol 93:46–54

    Article  Google Scholar 

  • Casas-Vazquez J, Jou D (2003) Temperature in non-equilibrium states: a review of open problems and current proposals. Rep Prog Phys 66:1937–2023

    Article  Google Scholar 

  • Dechristé G, Fehrenbach J, Griseti E, Lobjois V, Clair PC (2018) Viscoelastic modeling of the fusion of multicellular tumor spheroids in growth phase. J Theor Biol 454:102–109

    Article  Google Scholar 

  • Deforet M, Hakim V, Yevick H, Duclos G, Silberzan P (2014) Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nature Comm 5(1):3747. https://doi.org/10.1038/ncomms4747

    Article  CAS  Google Scholar 

  • Gongora C, Candeil L, Vezzio N, Copois V, Denis V, Breil C, Molina F, Fraslon C, Conseiller E et al (2008) Altered expression of cell proliferation-related and interferon-stimulated genes in colon cancer cells resistant to SN38. Cancer Biol & Therapy 7(6):822–832

    Article  CAS  Google Scholar 

  • Groisman A, Steinberg V (1998) Mechanism of elastic instability in Couette flow of polymer solutions: Experiment. Phys Fluids 10(10):2451–2463

    Article  CAS  Google Scholar 

  • Groisman A, Steinberg V (2000) Elastic turbulence in a polymer solution flow. Nature 405:53–55

    Article  CAS  Google Scholar 

  • Grosser S, Lippoldt J, Oswald L, Merkel M , Sussman DM, Renner F, Gottheil P, Morawetz EW , Fuhs T, Xie X, et al. (2021) Cell and Nucleus Shape as an Indicator of Tissue Fluidity in Carcinoma. Phys Rev X 11, 011033.

  • Guevorkian K, Gonzalez-Rodriguez D, Carlier C, Dufour S, Brochard-Wyart F (2011) Mechanosensitive shivering of model tissues under controlled aspiration. PNAS 108(33):13387–13392

    Article  CAS  Google Scholar 

  • Kosztin I, Vunjak-Novakovic G, Forgacs G (2012) Colloquium: Modeling the dynamics of multicellular systems: Application to tissue engineering. Rev Mod Phys 84(4):1791–1805

    Article  Google Scholar 

  • Lange JP, Fabry B (2013) Cell and tissue mechanics in cell migration. Exp Cell Res 319:2418–2423

    Article  CAS  Google Scholar 

  • Lee P and Wolgemuth CW. (2011) Crawling Cells Can Close Wounds without Purse Strings or Signaling. PLoS Comput Biol 7(3):e1002007 1–8.

  • Marmottant P, Mgharbel A, Kafer J, Audren B, Rieu JP, Vial JC, van der Sanden B, Maree AFM, Graner F, Delanoe-Ayari H (2009) The role of fluctuations and stress on the effective viscosity of cell aggregates. PNAS 106(41):17271–17275

    Article  CAS  Google Scholar 

  • Mc Cann C, Kriebel PW, Parent CA, Losert W (2010) Cell speed, persistence and information transmission during signal relay and collective migration. J Cell Sci 123(10):1724–1731

    Article  CAS  Google Scholar 

  • Mombach JCM, Robert D, Graner F, Gillet G, Thomas GL, Idiart M, Rieu JP (2005) Rounding of aggregates of biological cells: experiments and simulations. Phys A 352:525–534

    Article  Google Scholar 

  • Mondal S, Phukan M, Ghatak A (2015) Estimation of solid–liquid interfacial tension using curved surface of a soft solid. PNAS 112(41):12563–12568

    Article  CAS  Google Scholar 

  • Nnetu KD, Knorr M, Kaes J, Zink M (2012) The impact of jamming on boundaries of collectively moving weak-interacting cells. New J Phys 14:115012

  • Notbohm J, Banerjee S, Utuje KJC, Gweon B, Jang H, Park Y, Shin J, Butler JP, Fredberg JJ, Marchetti MC (2016) Cellular contraction and polarization drive collective cellular motion. Biophys J 110(12):2729–2738

    Article  CAS  Google Scholar 

  • Ongenae S, Cuvelier M, Vangheel J, Ramon H, Smeets B (2021) Activity-induced fluidization and arrested coalescence in fusion of cellular aggregates. Front Phys. https://doi.org/10.3389/fphy.2021.649821

    Article  Google Scholar 

  • Oriola D, Marin-Riera M, Anlas K, Gritti N, Matsumiya M, Aalderink G, Ebisuya M, Sharpe J, Trivedi V (2020) Arrested coalescence of multicellular aggregates. https://arxiv.org/abs/2012.01455

  • Oswald L, Grosser S, Smith DM, Kaes JA (2017) Jamming transition in cancer. J Phys d: Appl Phys 50(483001):1–17

    Google Scholar 

  • Pajic-Lijakovic I. (2021) Basic concept of viscoelasticity, in Viscoelasticity and collective cell migration, eds. I. Pajic-Lijakovic and E. Barriga, Chapter 2, Elsevier, ISBN: 9780128203118.

  • Pajic-Lijakovic I, Milivojevic M (2017a) Successive relaxation cycles during long-time cell aggregate rounding after uni-axial compression. J Biol Phys 43(2):197–209

    Article  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2017b) Viscoelasticity of multicellular surfaces. J Biomech 60:1–8

    Article  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2019a) Long-time viscoelasticity of multicellular surfaces caused by collective cell migration—multi-scale modeling considerations. Sem Cell Dev Biol 93:87–96

    Article  Google Scholar 

  • Pajic-Lijakovic I. and Milivojevic M. (2019b) Functional epithelium remodeling in response to applied stress under in vitro conditions. Appl Bionics Biomech. https://doi.org/10.1155/2019/48927

  • Pajic-Lijakovic I, Milivojevic M (2019c) Jamming state transition and collective cell migration. J Biol Eng 13:73. https://doi.org/10.1186/s13036-019-0201-4

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2020a) Collective cell migration and residual stress accumulation: rheological consideration. J Biomech 108:109898. https://doi.org/10.1016/j.jbiomech.2020.109898

    Article  PubMed  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2020b) Mechanical oscillations in 2D collective cell migration: the elastic turbulence. Front Phys. https://doi.org/10.3389/fphy.2020.585681

    Article  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2021a) Multiscale nature of cell rearrangement caused by collective cell migration. Europ Biophys J 50:1–14

    Article  Google Scholar 

  • Pajic-Lijakovic I, Milivojevic M (2021b) Viscoelasticity and cell jamming state transition. https://doi.org/10.1101/2021.03.19.436195

  • Pérez-González C, Alert R, Blanch-Mercader C, Gómez-González M, Kolodziej T, Bazellieres E, Casademunt J, Trepat X (2019) Active wetting of epithelial tissues. Nature Phys 15(1):79–88

    Article  Google Scholar 

  • Petrolli V, Boudou T, Balland M, Cappello G. (2021) Oscillations in collective cell migration, in Viscoelasticity and collective cell migration, eds. I. Pajic-Lijakovic and E. Barriga, Chapter 8, Elsevier, ISBN: 9780128203118.

  • Rieu JP, Upadhyaya A, Glazier JA, Ouchi NB, Sawada Y (2000) Diffusion and Deformations of Single Hydra Cells in Cellular Aggregates. Biophys J 79:1903–1914

    Article  CAS  Google Scholar 

  • Serra-Picamal X, Conte V, Vincent R, Anon E, Tambe DT, Bazellieres E, Butler JP, Fredberg JJ, Trepat X (2012) Mechanical waves during tissue expansion. Nature Phys 8(8):628–634

    Article  CAS  Google Scholar 

  • Shafiee A, McCune M, Forgacs G, Kosztin I (2015) Post-deposition bioink self-assembly: a quantitative study. Biofabric 7:045005. https://doi.org/10.1088/1758-5090/7/4/045005

    Article  Google Scholar 

  • Tambe DT, Croutelle U, Trepat X, Park CY, Kim JH, Millet E, Butler JP, Fredberg JJ. (2013) Monolayer Stress Microscopy: Limitations, Artifacts, and Accuracy of Recovered Intercellular Stresses. PLoS ONE 8(2):e55172 1–13.

  • Tlili S, Gauquelin E, Li B, Cardoso O, Ladoux B, Delanoë-Ayari H, F Graner F. (2018) Collective cell migration without proliferation: density determines cell velocity and wave velocity. R Soc Open Sci 5:172421, https://doi.org/10.1098/rsos.172421

  • Tlili S, Durande M, Gay C, Ladoux B, Graner F, Delanoë-Ayari H. (2020) Migrating Epithelial Monolayer Flows Like a Maxwell Viscoelastic Liquid. Phys Rev Lett 125:088102.

  • Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, Fredberg JJ (2009) Physical forces during collective cell migration. Nature Phys 5:426–430

    Article  CAS  Google Scholar 

  • Tschoegl NW, Knauss WG, Emri I (2002) Poisson’s ratio in linear viscoelasticity—a critical review. Mech Time-Depend Mat 6:3–51

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Contract No. 451-03-9/2021-14/200135).

Author information

Authors and Affiliations

  1. Faculty of Technology and Metallurgy, Belgrade University, Belgrade, Serbia

    Ivana Pajic-Lijakovic & Milan Milivojevic

Authors
  1. Ivana Pajic-Lijakovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Milan Milivojevic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivana Pajic-Lijakovic.

Ethics declarations

Conflict of interest

We have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pajic-Lijakovic, I., Milivojevic, M. Mechanical waves caused by collective cell migration: generation. Eur Biophys J 51, 1–13 (2022). https://doi.org/10.1007/s00249-021-01581-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00249-021-01581-x

Keywords

Search

Navigation