Abstract
Models based on molecular mechanisms are presented for pattern formation in developing organisms. It is assumed that there exists a diffusion governed gradient in the morphogenetic field. It is shown that cellular differentiation and the subsequent pattern formation result from the interaction of the diffusing morphogen with the genetic regulatory mechanism of cells. In a second stage it is shown that starting from a homogeneous distribution of morphogen, polarity can be generated spontaneously in the morphogenetic field giving rise to the establishment of a gradient. The stability of these gradients is demonstrated. The onset of a morphogenetic gradient and pattern formation are combined in a single coherent model. Size invariance and its biological implications are discussed.
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Literature
Auchmuty, J. F. G. 1974. Private communication.
— and G. Nicolis. 1975. “Bifurcation Analysis of Nonlinear Reaction-Diffusion Equations—I. Evolution Equations and the Steady State Solutions.”Bull. Math. Biology,37, 323–365.
Babloyantz, A. and G. Nicolis. 1972. “Chemical Instabilities and Multiple Steady State Transitions in Monod-Jacob Type Models.”J. Theor. Biology,34, 185–192.
— and M. Sanglier. 1972. “Chemical Instabilities of ‘All-or-None’ Type in β-Galactosidase Induction and Active Transport.”FEBS Letters,23, 364–366.
— and J. Hiernaux. 1974. “Models for Positional Information and Positional Differentiation.”Proc. Natn. Acad. Sci. U.S.A.,71, 1530–1533.
Britten, R. J. and E. H. Davidson. 1969. “Gene Regulation for Higher Cells: A Theory.”Science,165, 349–357.
Crick, F. 1970. “Diffusion in Embryogenesis.”Nature,225, 420–422.
Edelstein, B. B. 1972. “The Dynamics of Cellular Differentiation and Associated Pattern Formation.”J. Theor. Biology,37, 221–243.
Georgiev, G. P. 1969. “On the Structural Organization of Operon and the Regulation of RNA Synthesis in Animal Cells.”J. Theor. Biology,25, 473–490.
Gierer, A. and H. Meinhardt. 1972. “A Theory of Biological Pattern Formation.”Kybernetik,12, 30–39.
Glansdorff, P. and I. Prigogine. 1971.Thermodynamics of Structure, Stability and Fluctuations. New York: Wiley-Interscience.
Goodwin, B. C. and M. H. Cohen. 1969. “A Phase-shift Model for the Spatial and Temporal Organization of Developing Systems.”J. Theor. Biology,25, 49–107.
Hanson, M. P. 1974. “Spatial Structures in Dissipative Systems.”J. Chem. Phys.,60, 3210–3214.
Herschkowitz-Kaufman, M. and G. Nicolis. 1972. “Localized Spatial Structures and Nonlinear Chemical Waves in Dissipative Systems.”J. Chem. Phys.,56, 1890–1895.
Hicklin, J., A. Hornbruch, L. Wolpert and M. Clarke. 1973. “Positional Information and Pattern Regulation in Hydra: The Formation of Boundary Regions Following Axial Grafts.”J. Embryol. Exp. Morph.,30, 701–725.
Martinez, H. M. 1972. “Morphogenesis and Chemical Dissipative Structures: A Computer Simulated Case Study.”J. Theor. Biology,36, 479–501.
MacMahon, D. 1973. “A Cell-Contact Model for Cellular Position Determination in Development.”Proc. Nat. Acad. Sci. U.S.A. 70, 2396–2400.
Meinhardt, H. and A. Gierer. 1974. “Applications of a Theory of Biological Pattern Formation Based on Lateral Inhibition.”J. Cell Science,15, 321–346.
Monod, J. and F. Jacob. 1961. “General Conclusions: Teleonomic Mechanisms in Cellular Metabolism, Growth and Differentiation.”Cold Spring Harb. Symp. Quant. Biol.,26, 389–401.
Nicolis, G. 1971. “Stability and Dissipative Structures in Open Systems Far from Equilibrium.” InAdvances in Chemical Physics, Vol. 19. New York: John Wiley.
Nicolis, G. 1974. “Patterns of Spatio-Temporal Organization in Chemical and Biochemical Kinetics.” InProceedings of the Am. Math. Soc., Providence, Rhode Island.
— and J. F. G. Auchmuty. 1974. “Dissipative Structures, Catastrophes, and Pattern Formation: A Bifurcation Analysis.”Proc. Natn. Acad. Sci. U.S.A.,71, 2748–2751.
Prigogine, I. and R. Lefever. 1968. “Symmetry-Breaking Instabilities in Dissipative Systems.”J. Chem. Phys.,48, 1695–1700.
Sattinger, D. 1973. “Topics in Stability and Bifurcation Theory.” InLecture Notes in Mathematics, Vol. 309. Berlin: Springer.
Turing, A. M. 1952. “The Chemical Basis of Morphogenesis.”Phil. Trans. Roy. Soc.,B237, 37–72.
Wolpert, L. 1969. “Positional Information and the Spatial Pattern of Cellular Differentiation.”J. Theor. Biology,25, 1–47.
—, M. R. B. Clarke and A. Hornbruch. 1972. “Positional Signalling along Hydra.”Nature New Biology,91, 101–105.
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Babloyantz, A., Hiernaux, J. Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields. Bltn Mathcal Biology 37, 637–657 (1975). https://doi.org/10.1007/BF02459528
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DOI: https://doi.org/10.1007/BF02459528