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Journal of Mathematical Biology

, Volume 74, Issue 7, pp 1657–1678 | Cite as

A phenomenological model of cell–cell adhesion mediated by cadherins

  • Simona ManciniEmail author
  • René-Marc Mège
  • Benoit Sarels
  • Pierre-Olivier Strale
Article

Abstract

We present a phenomenological model intended to describe at the protein population level the formation of cell–cell junctions by the local recruitment of homophilic cadherin adhesion receptors. This modeling may have a much wider implication in biological processes since many adhesion receptors, channel proteins and other membrane-born proteins associate in clusters or oligomers at the cell surface. Mathematically, it consists in a degenerate reaction–diffusion system of two partial differential equations modeling the time-space evolution of two cadherin populations over a surface: the first one represents the diffusing cadherins and the second one concerns the fixed ones. After discussing the stability of the solutions of the model, we perform numerical simulations and show relevant analogies with experimental results. In particular, we show patterns or aggregates formation for a certain set of parameters. Moreover, perturbing the stationary solution, both density populations converge in large times to some saturation level. Finally, an exponential rate of convergence is numerically obtained and is shown to be in agreement, for a suitable set of parameters, with the one obtained in some in vitro experiments.

Keywords

Cell adhesion Cadherins Adherens junctions Protein clustering Degenerate reaction–diffusion system Patterns formation 

Mathematics Subject Classification

92C15 82B21 35J70 

Notes

Acknowledgments

POS has been supported by an ANR funding (2010 Blan 1515). BS is supported by the Labex LMH (ANR-11-IDEX-003-02) and by the FMJH (ANR-Investissements d’Avenir). The authors thank the CNRS, INRIA and INSERM for the founding of the PEPS-MBI project “MAC: Modélisation d’Adhésion des Cadhérines” the ANR 2010 Blan 1515 and Human Frontier Science Program grant RTG0040/2012, and the ANR blanche project “Kibord” (ANR-13-BS01-0004) funded by the French Ministry of Research.

References

  1. Bihr T, Seifert U, Smith AS (2012) Nucleation of ligand-receptor domains in membrane adhesion. Phys Rev Lett 109:258,101. doi: 10.1103/PhysRevLett.109.258101 CrossRefGoogle Scholar
  2. Gavard J, Lambert M, Grosheva I, Marthiens V, Irinopoulou T, Riou JF, Bershadsky A, Mège RM (2004) Lamellipodium extension and cadherin adhesion: two cell responses to cadherin activation relying on distinct signalling pathways. J Cell Sci 117(2):257–270. doi: 10.1242/jcs.00857. http://jcs.biologists.org/content/117/2/257.abstract
  3. Grillot M, Grillot P, Mancini S (2016) Study of a degenerate reaction-diffusion system arising in particle dynamics with aggregation effects. arxiv:1412.0602 (under revison)
  4. Harrison OJ, Jin X, Hong S, Bahna F, Ahlsen G, Brasch J, Wu Y, Vendome J, Felsovalyi K, Hampton CM, Troyanovsky RB, Ben-Shaul A, Frank J, Troyanovsky SM, Shapiro L, Honig B (2011) The extracellular architecture of adherens junctions revealed by crystal structures of type I cadherins. Structure 19(2):244–256. doi: 10.1016/j.str.2010.11.016. http://www.sciencedirect.com/science/article/pii/S0969212611000037
  5. Hong S, Troyanovsky RB, Troyanovsky SM (2013) Binding to f-actin guides cadherin cluster assembly, stability, and movement. J Cell Biol 201(1):131–143. doi: 10.1083/jcb.201211054. http://jcb.rupress.org/content/201/1/131.abstract
  6. Lambert M, Choquet D, Mège RM (2002) Dynamics of ligand-induced, rac1-dependent anchoring of cadherins to the actin cytoskeleton. J Cell Biol 157(3):469–479. doi: 10.1083/jcb.200107104
  7. Lambert M, Thoumine O, Brevier J, Choquet D, Riveline D, Mège RM (2007) Nucleation and growth of cadherin adhesions. Exp Cell Res 313(19):4025–4040CrossRefGoogle Scholar
  8. Mège RM, Gavard J, Lambert M (2006) Regulation of cell–cell junctions by the cytoskeleton. Curr Opin Cell Biol 18(5):541–548. doi: 10.1016/j.ceb.2006.08.004. http://www.sciencedirect.com/science/article/pii/S0955067406001141
  9. Murray JD (2003) Mathematical biology II. Spatial models and biomedical applications. Springer, Berlin. doi: 10.1007/b98869 zbMATHGoogle Scholar
  10. Strale PO, Duchesne L, Peyret G, Montel L, Nguyen T, Png E, Tampé R, Troyanovsky S, Hénon S, Ladoux B, Mège RM (2015) The formation of ordered nano-clusters controls cadherin anchoring to actin and cell–cell contact fluidity. J Cell Biol 210(2):333–346CrossRefGoogle Scholar
  11. Thoumine O, Lambert M, Mège RM, Choquet D (2006) Regulation of n-cadherin dynamics at neuronal contacts by ligand binding and cytoskeletal coupling. Mol Biol Cell 17(2):862–875. doi: 10.1091/mbc.E05-04-0335
  12. Wu Y, Honig B, Ben-Shaul A (2013) Theory and simulations of adhesion receptor dimerization on membrane surfaces. Biophys J 104(6):1221–1229. doi: 10.1016/j.bpj.2013.02.009. http://www.sciencedirect.com/science/article/pii/S000634951300194X
  13. Yamada S, Pokutta S, Drees F, Weis WI, Nelson WJ (2005) Deconstructing the cadherin-catenin-actin complex. Cell 123(5):889–901. doi: 10.1016/j.cell.2005.09.020. http://www.sciencedirect.com/science/article/pii/S0092867405009748

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire MAPMO, UMR 7349, Fédération D. PoissonUniversité of OrléansOrléansFrance
  2. 2.Institut Jacques Monod, Centre National de la Recherche ScientifiqueUniversité Paris DiderotParisFrance
  3. 3.UPMC Univ Paris 06, Laboratoire Jacques-Louis LionsSorbonne UniversitésParisFrance
  4. 4.Laboratoire de Biologie Intégrative des Modéles MarinsRoscoffFrance

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