Abstract
In the process of organism growth and development, cell diversity increases in both metabolic (cell differentiation) and structural (morphogenesis) respects. This is related to a cell’s ability to switch between different dynamic modes of operation. The evolutions of an organism’s shape and cell metabolism are tightly interconnected. For instance, as early as the gastrula state the evolution of the shape of the cell ensemble (inner cavity appearance) and the cell functional variations (mesoderm and endoderm appearance) originate simultaneously and thus comprise the first step of differentiation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bard JB (1981) A model for generating aspects of zebra and other mammalian coat patterns. J Theor Biol 93(2):363–385
Belintsev BN, Belousov LB, Zaraisky AG (1985) Model of epithelial morphogenesis based on elastic forces and the contact cell polarization. Ontogenesis 16:5–14 (Rus)
Driesch H (1914) The history and theory of vitalism. Macmillan, London
Gierer A (1981) Generation of biological patterns and form: some physical, mathematical and logical aspects. Prog Biophys Mol Biol 37:1–47
Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetik 12(1):30–39
Gurvich AG (1944) The theory of biological field. Sov Nauka, Moscow (Rus)
Martiel J-L, Goldbeter A (1987) A model based on receptor desensitization for cyclic AMP signalling in Dictyostelium cells. Biophys J 52:807–828
Meinhardt H (1982) Models of biological pattern formation. Academic, London
Meinhardt H (1995) The algorithmic beauty of sea shells. Springer, Berlin
Meinhardt H (2000) Beyond spots and stripes: generation of more complex patterns and modifications and additions of the basic reaction. In: Maini PK, Othmer HG, Santosa F, Keel M (eds) Mathematical models for biological pattern formation. Springer, New York
Monk A, Othmer HG (1989) Cyclic AMP oscillations in suspensions of Dictyostelium discoideum. Phil Trans R Soc Lond 323:185–224
Murray JD (1981) A pre-pattern formation mechanism for animal coat marking. J Theor Biol 88(1):161–199
Murray JD (1993) Mathematical biology. Springer, Berlin
Murray JD (2002) Mathematical biology. I: Introduction. Springer, New York
Murray JD (2003) Mathematical biology. II: Spatial models and biomedical applications. Springer, Berlin
Oster GF, Murray JD, Harris AK (1983) Mechanical aspects of mesenchymal morphogenesis. J Embryol Exp Morphol 78:83–125
Polezhaev AA (2010) Mechanisms of biological morphogenesis. In: Riznichenko G, Rubin A (eds) Dynamic models of processes in cells and subcellular nanostructures. RCD-ICS, Moscow-Izhevsk (Rus)
Polezhaev AA, Zykov VS, Müller SC (1998) Destabilization of cell aggregation under nonstationary conditions. Phys Rev E 58(5):6328–6332
Polezhaev AA, Hilgardt C, Mair T et al (2005) Transition from an excitable to an oscillatory state in Dictyostelium discoideum. Syst Biol 152(2):75–79
Romanovsky YM, Stepanova NV, Chernavsky DS (2004) Mathematical modeling in biophysics. Introduction to the theoretical biophysics. ICS-RCD, Moscow-Izhevsk (Rus)
Segel LA (1984) Modeling dynamic phenomena in molecular and cellular biology. Cambridge University Press, Cambridge
Soljanik GI, Chernavskii DS (1980) Mathematical model of morphogenesis. Preprint FIAN 8 (Rus)
Thomas D (1975) Artificial enzyme membranes, transport, memory, and oscillatory phenomena. In: Thomas D, Kernevez J-P (eds) Analysis and control of immobilized enzyme systems. Springer, Berlin
Turing AM (1952) The chemical basis of morphogenesis. Phil Trans R Soc Lond B 237:37–71
Vasiljev VA, Romanovsky YM (1976) About the role of diffusion in the autocatalytic systems. In: Theoretical and experimental biophysics, vol 6. Kaliningrad (Rus)
Webster G, Wolpert L (1966) Studies on pattern regulation in hydra. J Embryol Exp Morphol 16(1):91–104
Young DA (1984) A local activator-inhibitor model of vertebrate skin patterns. Math Biosci 72:51–58
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rubin, A., Riznichenko, G. (2014). Models of Morphogenesis . In: Mathematical Biophysics. Biological and Medical Physics, Biomedical Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8702-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8702-9_6
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-8701-2
Online ISBN: 978-1-4614-8702-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)