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How Does Cellular Contact Affect Differentiation Mediated Pattern Formation?

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Abstract

In this paper, we present a two-population continuous integro-differential model of cell differentiation, using a non-local term to describe the influence of the local environment on differentiation. We investigate three different versions of the model, with differentiation being cell autonomous, regulated via a community effect, or weakly dependent on the local cellular environment. We consider the spatial patterns that such different modes of differentiation produce, and investigate the formation of both stripes and spots by the model. We show that pattern formation only occurs when differentiation is regulated by a strong community effect. In this case, permanent spatial patterns only occur under a precise relationship between the parameters characterising cell dynamics, although transient patterns can persist for biologically relevant timescales when this condition is relaxed. In all cases, the long-lived patterns consist only of stripes, not spots.

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References

  • Armstrong, N. J., Painter, K. J., & Sherratt, J. A. (2006). A continuum approach to modelling cell-cell adhesion. J. Theor. Biol., 243, 98–113.

    Article  MathSciNet  Google Scholar 

  • Armstrong, N. J., Painter, K. J., & Sherratt, J. A. (2009). Adding adhesion to a chemical signalling model for somite formation. Bull. Math. Biol., 71(1), 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson, S., & Williams, P. (2009). Quorum sensing and social networking in the microbial world. J. R. Soc. Interf., 6, 959–978.

    Article  Google Scholar 

  • Aubin-Houzelstein, G., Bernex, F., Elbaz, C., & Panthier, J. J. (1998). Survival of patchwork melanoblasts is dependent upon their number in the hair follicle at the end of embryogenesis. Dev. Biol., 198, 266–276.

    Article  Google Scholar 

  • Bloomfield, J. M., Sherratt, J. A., Painter, K. J., & Landini, G. (2010). Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues. J. R. Soc. Interf. doi:10.1098/rsif.2010.0146.

    MATH  Google Scholar 

  • Buckingham, M. (2003). How the community effect orchestrates muscle differentiation. Bioessays, 25, 13–16.

    Article  Google Scholar 

  • Caicedo-Carvajal, C. E., & Shinbrot, T. (2008). In silico zebrafish pattern formation. Dev. Biol., 315(2), 397–403.

    Article  Google Scholar 

  • Cossu, G., Kelly, R., Di Donna, S., Vivarelli, E., & Buckingham, M. (1995). Myoblast differentiation during mammalian somitogenesis is dependent upon a community effect. Proc. Natl. Acad. Sci. USA, 92(6), 2254–2258.

    Article  Google Scholar 

  • Galli, R., Borello, U., Gritti, A., Minasi, M. G., Bjornson, C., Coletta, M., Mora, M., De Angelis, M. G., Fiocco, R., Cossu, G., & Vescovi, A. L. (2000). Skeletal myogenic potential of human and mouse neural stem cells. Nature Neurosci., 3, 986–991.

    Article  Google Scholar 

  • Gerisch, A. (2010). On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion. IMA J. Numer. Anal., 30, 173–194.

    Article  MathSciNet  MATH  Google Scholar 

  • Gerisch, A., & Chaplain, M. (2008). Mathematical modelling of cancer cell invasion of tissue, Local and non-local models and the effect of adhesion. J. Theor. Biol., 250(4), 684–704.

    Article  Google Scholar 

  • Green, J. E. F., Waters, S. L., Whiteley, J. P., Edelstein-Keshet, L., Shakesheff, K. M., & Byrne, H. M. (2010). Non-local models for the formation of hepatocyte-stellate cell aggregates. J. Theor. Biol. DOI:10.1016/j.jtbi.2010.08.013.

    Google Scholar 

  • Gurdon, J. B. (1988). A community effect in animal development. Nature, 336, 772–774.

    Article  Google Scholar 

  • Gurdon, J. B., Lemaire, P., & Kato, K. (1993a). Community effects and related phenomena in development. Cell, 75, 831–834.

    Article  Google Scholar 

  • Gurdon, J. B., Tiller, E., Roberts, J., & Kato, K. (1993b). A community effect in muscle development. Curr. Biol., 3, 1–11.

    Article  Google Scholar 

  • Hillen, T., & Painter, K. J. (2009). A user’s guide to PDE models for chemotaxis. J. Math. Biol., 58, 183–217.

    Article  MathSciNet  MATH  Google Scholar 

  • Hultman, K. A., & Johnson, S. L. (2010). Differential contribution of direct-developing and stem cell-derived melanocytes to the zebrafish larval pigment pattern. Dev. Biol., 337(2), 425–431.

    Article  Google Scholar 

  • Kaneko, T., Kojima, K., & Yasuda, K. (2007). Dependence of the community effect of cultured cardiomyocytes on the cell network pattern. Biochem. Biophys. Res. Commun., 356(2), 494–498.

    Article  Google Scholar 

  • Kato, K., & Gurdon, J. B. (1993). Single-cell transplantation determines the time when Xenopus muscle precursor cells acquire a capacity for autonomous differentiation. Proc. Natl. Acad. Sci. USA, 90, 1310–1314.

    Article  Google Scholar 

  • Kim, D., Chi, S., Lee, K. H., Rhee, S., Kwon, Y. K., Chung, C. H., Kwon, H., & Kang, M. S. (1999). Neuregulin stimulates myogenic differentiation in an autocrine manner. J. Biol. Chem., 274, 15395–15400.

    Article  Google Scholar 

  • Kojima, K., Kaneko, T., & Yasuda, K. (2006). Role of the community effect of cardiomyocyte in the entrainment and reestablishment of stable beating rhythms. Biochem. Biophys. Res. Commun., 351(1), 209–215.

    Article  Google Scholar 

  • Kondo, S., Iwashita, M., & Yamaguchi, M. (2009). How animals get their skin patterns, fish pigment pattern as a live Turing wave. Int. J. Dev. Biol., 53, 851–856.

    Article  Google Scholar 

  • Maderspacher, F., & Nusslein-Volhard, C. (2003). Formation of the adult pigment pattern in zebrafish requires leopard and obelix dependent cell interactions. Development, 130(15), 3447–3457.

    Article  Google Scholar 

  • Monk, N. (1997). The community effect and ectoderm–mesoderm interaction in Xenopus muscle differentiation. Bull. Math. Biol., 59(3), 409–425.

    MathSciNet  MATH  Google Scholar 

  • Moreira, J., & Deutsch, A. (2005). Pigment pattern formation in zebrafish during late larval stages, A model based on local interactions. Dev. Dyn., 232(1), 33–42.

    Article  Google Scholar 

  • Nagai, T., Otani, S., Saito, T., Maegawa, S., Inoue, K., Arai, K., & Yamaha, E. (2005). Germ-line chimera produced by blastoderm transplantation in zebrafish. Nippon Suisan Gakkaishi, 71(1), 1–9.

    Article  Google Scholar 

  • Nieuwkoop, P. D. (1997). Short historical survey of pattern formation in the endo-mesoderm and the neural anlage in the vertebrates, the role of vertical and planar inductive actions. Cell. Mol. Life Sci., 53, 305–318.

    Article  Google Scholar 

  • Painter, K. J., Armstrong, N. J., & Sherratt, J. A. (2010). The impact of adhesion on cellular invasion processes in cancer and development. J. Theor. Biol., 264, 1057–1067.

    Article  Google Scholar 

  • Paratore, C., Hagedorn, L., Floris, J., Hari, L., Kleber, M., Suter, U., & Sommer, L. (2002). Cell-intrinsic and cell-extrinsic cues regulating lineage decisions in multipotent neural crest-derived progenitor cells. Int. J. Dev. Biol., 46(1), 193–200. Sp. Iss. SI.

    Google Scholar 

  • Parichy, D. M. (2007). Homology and the evolution of novelty during Danio adult pigment pattern development. J. Exp. Zool. B, 308(5), 578–590.

    Article  Google Scholar 

  • Parichy, D. M., Ransom, D. G., Paw, B., Zon, L. I., & Johnson, S. L. (2000). An orthologue of the kit-related gene fms is required for development of neural crest-derived xanthophores and a subpopulation of adult melanocytes in the zebrafish, Danio rerio. Development, 127, 3031–3044.

    Google Scholar 

  • Rawls, J., & Johnson, S. (2000). Zebrafish kit mutation reveals primary and secondary regulation of melanocyte development during fin stripe regeneration. Development, 127(17), 3715–3724.

    Google Scholar 

  • Salazar-Ciudad, I., Jernvall, J., & Newman, S. A. (2003). Mechanisms of pattern formation in development and evolution. Development, 130, 2027–2037.

    Article  Google Scholar 

  • Sekimura, T., Zhu, M., Cook, J., Maini, P. K., & Murray, J. D. (1999). Pattern formation of scale cells in Lepidoptera by differential origin-dependent cell adhesion. Bull. Math. Biol., 61, 807–828.

    Article  Google Scholar 

  • Sherratt, J. A., Gourley, S. A., Armstrong, N. J., & Painter, K. J. (2009). Boundedness of solutions of a non-local reaction-diffusion model for adhesion in cell aggregation and cancer invasion. Eur. J. Appl. Math., 20(1), 123–144.

    Article  MathSciNet  MATH  Google Scholar 

  • Standley, H. J., Zorn, A. M., & Gurdon, J. B. (2001). eFGF and its mode of action in the community effect during xenopus myogenesis. Development, 128(8), 1347–1357.

    Google Scholar 

  • Watt, F. M., Lo Celso, C., & Silva-Vargas, V. (2006). Epidermal stem cells, an update. Curr. Opin. Genet. Dev., 16, 518–524.

    Article  Google Scholar 

  • Weiner, R., Schmitt, B. A., & Podhaisky, H. (1997). ROWMAP—A ROW-code with Krylov techniques for large stiff ODEs. Appl. Numer. Math., 25(2), 303–319.

    Article  MathSciNet  MATH  Google Scholar 

  • Weston, M. J. D., Kato, K., & Gurdon, J. B. (1994). A community effect is required for amphibian notochord differentiation. Dev. Genes Evol., 203(5), 250–253.

    Google Scholar 

  • Yamaguchi, M., Yoshimoto, E., & Kondo, S. (2007). Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism. Proc. Natl. Acad. Sci. USA, 104(12), 4790–4793.

    Article  Google Scholar 

  • Yang, H., Jensen, P., & Goldowitz, D. (2002). The community effect and purkinje cell migration in the cerebellar cortex, analysis of scrambler chimeric mice. J. Neurosci., 22(2), 464–470.

    Google Scholar 

  • Zhong, W. (2008). Timing cell-fate determination during asymmetric cell divisions. Curr. Opin. Neurobiol., 18, 472–478.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences, School of Mathematical and Computer Sciences, Heriot Watt University, Edinburgh, EH14 4AS, UK

    J. M. Bloomfield, K. J. Painter & J. A. Sherratt

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  1. J. M. Bloomfield
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  2. K. J. Painter
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  3. J. A. Sherratt
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Correspondence to J. M. Bloomfield.

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Bloomfield, J.M., Painter, K.J. & Sherratt, J.A. How Does Cellular Contact Affect Differentiation Mediated Pattern Formation?. Bull Math Biol 73, 1529–1558 (2011). https://doi.org/10.1007/s11538-010-9578-4

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  • DOI: https://doi.org/10.1007/s11538-010-9578-4

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