Abstract
This book deals with the problem of biological pattern formation. What are the mechanisms according to which individual organisms develop and biological patterns form? Biological organisms are characterized by their genomes. The letters of the genetic alphabet (the nucleotides), their precise arrangement in selected organisms (the gene sequence), and the molecular structure of a large number of encoded proteins are public today. However, analysis of single gene and protein function is not sufficient to explain complex pattern formation which results from collective behavior of interacting molecules and cells. In the beginning of embryological development , all cells are identical – equipped with basically the same set of genes. Accordingly, collective phenomena brought about by the interaction of cells with themselves and their surrounding are responsible for differentiation and pattern formation characterizing subsequent developmental stages. Mathematical modeling is strongly needed to discover the self-organization principles of interacting cell systems (Deutsch et al. 2003). Still, an open question is: what are appropriate mathematical models, how can they be analyzed, and which specific biological problems can they address? In this chapter, the motivation for the book is provided. The basic problems are introduced and the connection of biological pattern formation and mathematical modeling is emphasized. Finally, an outline introduces the book structure and specific suggestions on how to read the book depending on the reader’s background.
Things should be made as simple as possible, but not any simpler.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
A. Einstein
- 2.
So we clearly reject the following statement quoted from a review paper on the first edition of “Cellular Automaton Modeling of Biological Pattern Formation”: “…We do not believe that CA [cellular automata] should be viewed as a replacement for rigorous mathematical models. Instead, they should be considered as a first step in the modeling process. Once it has been established that the CA implementation of one’s hypothesis produces the desired results, then one must proceed toward deriving a traditional mathematical model. For then and only then is it possible to bring to bear tools from analysis such as stability theory, bifurcation theory, and perturbation methods …” (from Ermentrout and Edelstein-Keshet 1993).
Bibliography
Britton, N. F. 1986. Reaction-Diffusion Equations and their Applications to Biology. London: Academic.
Casti, J. L. 1989. Alternate Realities. New York: Wiley.
Casti, J. L. 2002. Science is a computer program. Nature 417: 381–382. book review.
Chaplain, M. A. J., G. D. Singh, and J. C. McLachlan, eds. 1999. On Growth and Form: Spatio-Temporal Pattern Formation in Biology. Chichester: Wiley.
Darwin, C. 1859. On the Origin of Species by Means of Natural Selection. London: John Murray.
Deutsch, A., M. Falcke, J. Howard, and W. Zimmermann, eds. 2003. Function and Regulation of Cellular Systems: Experiments and Models. Basel: Birkhauser.
Drasdo, D. 2003. On selected individual-based approaches to the dynamics in multicellular systems. In Models of Polymer and Cell Dynamics, eds. W. Alt, M. Chaplain, M. Griebel, and J. Lenz. Basel: Birkhäuser.
Ermentrout, G. B., and L. Edelstein-Keshet. 1993. Cellular automata approaches to biological modeling. Journal of Theoretical Biology 160: 97–133.
Frisch, U., B. Hasslacher, and Y. Pomeau. 1986. Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters 56(14): 1505–1509.
Gierer, A., and H. Meinhardt. 1972. A theory of biological pattern formation. Kybernetik 12: 30–39.
Hartsoeker N. 1694. Essay de dioptrique. Paris, J. Anisson
Hegselmann, R., and A. Flache. 1998. Understanding complex social dynamics: a plea for cellular automata based modelling. Journal of Artificial Societies and Social Simulation 1(3): 1.
Holtfreter, J. 1939. Gewebaffinität, ein Mittel der embryonalen Formbildung. Archiv für Experimentelle Zellforschung 23: 169–209.
Holtfreter, J. 1944. A study of the mechanics of gastrulation, part II. The Journal of Experimental Zoology 95: 171–212.
Kadanoff, L. P. 1986. On two levels. Physics Today Sept.: 7–9.
Maini, P. K. 1999. Mathematical models in morphogenesis. In Mathematics Inspired by Biology. eds. V. Capasso and O. Dieckmann, 151–189. Berlin: Springer.
Meinhardt, H. 1992. Pattern formation in biology: a comparison of models and experiments. Reports on Progress in Physics 55: 797–849.
Mitchell, M. 2002. Is the universe a universal computer? Science 298: 65–68. book review.
Murray, J. D. 2002. Mathematical Biology, 3rd ed. New York: Springer.
Othmer, H. G., P. K. Maini, and J. D. Murray, eds. 1993. Experimental and Theoretical Advances in Biological Pattern Formation. New York: Plenum Press.
Rueff, J. 1554. De conceptu et generatione hominis, et iis quae circa hec potissimum consysderantur, libri sex. Zurich: Christopher Froschauer.
Steinberg, M. S. 1963. Reconstruction of tissues by dissociated cells. Science 141(3579): 401–408.
Thompson, D. W. 1917. On Growth and Form. Cambridge: Cambridge University Press.
Townes, P. L., and J. Holtfreter. 1955. Directed movements and selective adhesion of embryonic amphibian cells. The Journal of Experimental Zoology 128: 53–120.
Turing, A. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B 237: 37–72.
Van Liedekerke, P., M. M. Palm, N. Jagiella, and D. Drasdo. 2015. Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Computational Particle Mechanics 2: 401–444.
von Neumann, J. 1966. Theory of Self-Reproducing Automata, ed. A. W. Burks. Urbana, IL: University of Illinois Press.
Watson, J. D., and F. H. C. Crick. 1953a. Genetical implications of the structure of deoxyribonucleic acid. Nature 171: 964–967.
Watson, J. D., and F. H. C. Crick. 1953b. Molecular structure of nucleic acids: a structure for desoxyribose nucleic acid. Nature 171: 737–738.
Wolfram, S. 1985. Twenty problems in the theory of cellular automata. Physica Scripta T9: 170–183. Proceedings of the fifty-ninth Nobel Symposium.
Wolfram, S. 2002. A New Kind of Science. Champaign: Wolfram Media, Inc.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media New York
About this chapter
Cite this chapter
Deutsch, A., Dormann, S. (2017). Introduction and Outline. In: Cellular Automaton Modeling of Biological Pattern Formation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-7980-3_1
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7980-3_1
Published:
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-7978-0
Online ISBN: 978-1-4899-7980-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)