Abstract
Epithelial pattern formation is an important phenomenon that, for example, has roles in embryogenesis, development and wound-healing. The ligand Epithelial Growth Factor (EGF) and its receptor EGF-R, constitute a system that forms lateral induction patterns by juxtacrine signalling—binding of membrane-bound ligands to receptors on neighbouring cells. Owen et al. developed a generic ordinary differential equation model of juxtacrine lateral induction that exhibits stable patterning under some conditions. The model predicts relatively slow pattern formation. We examine here the effects of both intrinsic and extrinsic cellular noise arising from the stochastic treatment of this model, and show that this noise could have an accelerating effect on the patterning process.
Similar content being viewed by others
References
Alberts, B., 1994. Molecular Biology of the Cell. Garland, New York.
Atit, R., Conlon, R.A., Niswander, L., 2003. EGF signalling patterns the feather array by promoting the interbud fate. Dev. Cell 4, 231–240.
Blake, W.J., Kaern, M., Cantor, C.R., Collins, J.J., 2003. Noise in eukaryotic gene expression. Nature 422, 633–637.
Chen, L., Wang, R., Zhou, T., Aihara, K., 2005. Noise-induced cooperative behaviour in a multicell system. Bioinformatics 21, 2722–2739.
Clark, A.J.L., Ishii, S., Richert, N., Merlino, G.T., Pastan, I., 1985. Epidermal growth factor regulates the expression of its own receptor. Proc. Nat. Acad. Sci. USA 82, 8374–8378.
Coffey, R.J.J., Derynck, R., Wilcox, J.N., Bringman, T.S., Goustin, A.S., Moses, H.L., Pittelkow, M.P., 1987. Production and auto-induction of transforming growth factor-α in human keratinocytes. Nature 328, 817–820.
Collier, J.R., Monk, N.A.M., Maini, P.K., Lewis, J.H., 1996. Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling. J. Theor. Biol. 183, 429–446.
Gillespie, D.T., 1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. A 104, 1876–1889.
Mayerson, P.L., Fallon, J.F., 1985. The spatial pattern and temporal sequence in which feather germs arise in the white leghorn chick embryo. Dev. Biol. 109, 259–267.
McAdams, H.H., Arkin, A., 1997. Stochastic mechanisms in gene expression. Proc. Nat. Acad. Sci. USA 94, 814–819.
Owen, M.R., Sherratt, J.A., 1998. Mathematical modelling of juxtacrine cell signalling. Math. Biosci. 153, 125–150.
Owen, M.R., Sherratt, J.A., Wearing, H.J., 2000. Lateral induction by juxtacrine signalling is a new mechanism for pattern formation. Dev. Biol. 217, 54–61.
Pikovski, A.S., Kurths, J., 1997. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78, 775–778.
Ross, I.L., Browne, C.M., Hume, D.A., 1994. Transcription of individual genes in eukaryotic cells occurs randomly and infrequently. Immun. Cell Biol. 72, 177–185.
Shilo, B.-Z., 2003. Signalling by the Drosophila epidermal growth factor receptor pathway during development. Exp. Cell Res. 284, 140–149.
Tetreault, M.-P., Chailler, P., Rivard, N., Menard, D., 2005. Differential growth factor induction and modulation of human gastric epithelial regeneration. Exp. Cell Res. 306, 285–297.
Turner, T.E., Schnell, S., Burrage, K., 2004. Stochastic approaches for modelling in vivo reactions. Comput. Biol. Chem. 28, 165–178.
Walters, M.C., Feiring, S., Eidemiller, J., Magis, W., Groudine, M., Martin, D.I.K., 1995. Enhancers increase the probability but not the level of gene expression. Proc. Nat. Acad. Sci. USA 92, 7125–7129.
Wearing, H.J., Owen, M.R., Sherratt, J.A., 2000. Mathematical modelling of juxtacrine patterning. Bull. Math. Biol. 62, 293–320.
Webb, S.D., Owen, M.R., 2004. Oscillations and patterns in discrete models for developmental ligand-receptor interactions. J. Math. Biol. 48, 444–476.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rudge, T., Burrage, K. Effects of Intrinsic and Extrinsic Noise Can Accelerate Juxtacrine Pattern Formation. Bull. Math. Biol. 70, 971–991 (2008). https://doi.org/10.1007/s11538-007-9286-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-007-9286-x