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A universal route to pattern formation in multicellular systems

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Abstract

A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-field like ansatz which corresponds, in the biological setting, to sending to zero the size (or volume) of each individual cell. By relaxing this approximation and, provided a directionality in the flux is allowed for, we demonstrate here that instability leading to spatial pattern formation can always develop if the (discrete) system is large enough, namely, composed of sufficiently many cells, the units of spatial patchiness. The macroscopic patterns that follow the onset of the instability are robust and show oscillatory or steady state behavior.

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References

  1. S. Kondo, R. Asai, Nature 376, 765 (1995)

    Article  ADS  Google Scholar 

  2. J.D. Murray, Sci. Am. 258, 80 (1988)

    Article  Google Scholar 

  3. C. Klausmeier, Science 284, 1826 (1999)

    Article  Google Scholar 

  4. J.L. Maron, S. Harrison, Science 278, 1619 (1997)

    Article  ADS  Google Scholar 

  5. M. Rietkerk, J. van de Koppel, Trends Ecol. Evol. 23, 169 (2008)

    Article  Google Scholar 

  6. A.M. Turing, Phil. Trans. R. Soc. B 237, 37 (1952)

    ADS  Google Scholar 

  7. P. Ball,The self-made tapestry: Pattern formation in Nature, 1st edn. (Oxford University Press, Oxford, 1999)

  8. J.D. Murray,Mathematical biology II: Spatial models and biomedical applications (Springer-Verlag, Berlin, 2001)

  9. G. Nicolis, I. Prigogine,Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations (John Wiley & Sons, Chichester, 1977)

  10. A. Gierer, H. Meinhardt, Kybernetik 12, 30 (1972)

    Article  Google Scholar 

  11. H.G. Othmer, L.E. Scriven, J. Theor. Biol. 32, 507 (1971)

    Article  Google Scholar 

  12. H. Nakao, A.S. Mikhailov, Nat. Phys. 6, 544 (2010)

    Article  Google Scholar 

  13. R.S. Shaw, N. Packard, M. Schroter, H.L. Swinney, PNAS 104, 9580 (2007)

    Article  ADS  Google Scholar 

  14. K.S. Kim, I.S. Davis, P.A. Macpherson, T.J. Pedley, A.E. Hill, Proc. R. Soc. A 461, 273 (2005)

    Article  ADS  Google Scholar 

  15. J.C. Dallon, H.G. Othmer, Phil. Trans. R. Soc. Lond. B 352, 391 (1997)

    Article  ADS  Google Scholar 

  16. M. Asllani, R. Lambiotte, T. Carletti, Sci. Adv. 4, eaau9403 (2018)

    Article  ADS  Google Scholar 

  17. M. Postma, J. Roelofs, J. Goedhart, T.W.J. Gadella, A.J.W.G. Visser, P.J.M.V. Haastert, Mol. Biol. Cell 14, 5019 (2003)

    Article  Google Scholar 

  18. A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 96, 1193 (1992)

    Article  ADS  Google Scholar 

  19. A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 70, 778 (1993)

    Article  ADS  Google Scholar 

  20. M. Asllani, J.D. Challenger, F.S. Pavone, L. Sacconi, D. Fanelli, Nat. Commun. 5, 4517 (2014)

    Article  ADS  Google Scholar 

  21. R. Schnabel, M. Bischoff, A. Hintze, A.-K. Schulz, A. Hejnola, H. Meinhardt, H. Hutter, Dev. Biol. 294, 418 (2006)

    Article  Google Scholar 

  22. M. Asllani, D.M. Busiello, T. Carletti, D. Fanelli, G. Planchon, Sci. Rep. 5, 12927 (2015)

    Article  ADS  Google Scholar 

  23. P. Ciarletta, V. Balbi, E. Kuhl, Phys. Rev. Lett. 113, 248101 (2014)

    Article  ADS  Google Scholar 

  24. J.D. Murray, J. Theor. Biol. 88, 161 (1981)

    Article  Google Scholar 

  25. J.M. Pringle, A.M.H. Blakeslee, J.E. Byers, J. Roman, PNAS 108, 15288 (2011)

    Article  ADS  Google Scholar 

  26. O. Sporns,Networks of the Brain (MIT Press, Cambridge 2010)

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Authors and Affiliations

  1. MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland

    Malbor Asllani

  2. Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, rempart de la Vierge 8, 5000 Namur, Belgium

    Malbor Asllani & Timoteo Carletti

  3. Dipartimento di Fisica e Astronomia, Università di Firenze, INFN and CSDC, Via Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy

    Duccio Fanelli

  4. Mathematical Institute, University of Oxford, Woodstock Rd, OX2 6GG, Oxford, UK

    Philip K. Maini

Authors
  1. Malbor Asllani
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  2. Timoteo Carletti
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  3. Duccio Fanelli
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  4. Philip K. Maini
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Correspondence to Malbor Asllani.

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Asllani, M., Carletti, T., Fanelli, D. et al. A universal route to pattern formation in multicellular systems. Eur. Phys. J. B 93, 135 (2020). https://doi.org/10.1140/epjb/e2020-10206-3

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  • DOI: https://doi.org/10.1140/epjb/e2020-10206-3

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