Abstract
The Goodwin and Trainor model of pattern generation in calcium-regulated strain fields is studied in the case where calcium input and calcium output processes are involved. It is shown that the properties of the original model may still remain provided that the input-output processes are not unstable. In this last case, despite the eventual stabilizing effect of the calcium exchange term, perturbations of the generalized system can grow and lead to inhomogeneous solutions. Applications to cell differentiation and cell growth are discussed.
Similar content being viewed by others
References
Briére, C., Goodwin, B. C.: Geometry and dynamics of tip morphogenesis in Acetabularia. J. theor. Biol. 131, 461–475 (1988).
Goodwin, B. C., Trainor, L. E. H.: Tip and whorl morphogenesis in Acetabularia by calcium-regulated strain fields. J. theor. Biol. 117, 79–106 (1985).
Goodwin, B. C., Briere, C., O'Shea, P.: Mechanisms underlying the formation of spatial structure in cells. In: Poole, R. K, Trinci, A. P. J. (eds.) Spatial organisation in eukaryotic microbes. Spec. Publ. Soc. gen. Microbiol., vol. 23, 1–9 (1987).
Gross, J. D., Peacey, M. J., Strandmann, R. P. von: Plasma membrane proton pump inhibition and stalk cell differentiation in Dictyostelium discoideum. Differentiation 38, 91–98 (1988).
Hart, T., Trainor, L. E. H., Goodwin, B. C.: Diffusion effects in calcium-regulated strain fields. J. theor. Biol. 136(3), 327–336 (1989).
Murray, J. D.: Mathematical biology. (Biomathematics Texts), Berlin Heidelberg New York: Springer 1989.
Oster, G. F., Odell, G. M.: The mechanochemistry of cytogels. Physica 12D, 333–350 (1984).
Rushlow, C., Frasch, M., Doyle, H., Levine, M.: Maternal regulation of Zerknüllt: a homeobox gene controlling differentiation of dorsal tissues in Drosophila. Nature 330, 583–586 (1987).
Thisse, B., Stoetzel, C., El Messal, M., Pefrin-Schmidt, F.: Genes of the Drosophila maternal dorsal group control the specific expression of the zygotic gene twist in presumptive mesodermal cells. Genes and Development 1, 709–715 (1987).
Trainor, L. E. H., Goodwin B. C.: Stability analysis of a set of calcium-regulated viscoelastic equations. Physica 21D, 137–145 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brière, C., Goodwin, B.C. Effects of calcium input/output on the stability of a system for calcium-regulated viscoelastic strain fields. J. Math. Biol. 28, 585–593 (1990). https://doi.org/10.1007/BF00164164
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00164164