Abstract
The formation of neuronal networks requires axonal growth towards target neutons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is descrbed by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.
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Literature
Cajal, S. R. 1928.Degeneration and Regeneration in the Nervous System (translated by Raoul, M. May 1959). New York: Hafner Press MacMillan.
Kuffler, D. P. 1986. Isolated satellite cells of a peripheral nerve direct the growth of regenerating frog axons.J. Comp. Neurol. 249, 57–64.
Letourneau, P. C. 1975. Cell-to-substratum adhesion and guidance of axonal elongation.Dev. Biol. 44, 92–101.
Levi-Montalcine, R. 1982. Developmental neurobiology and the natural history of nerve growth factor.Ann Rev. Neurosci. 5, 341–362.
Levi-Montalcine, R. and P. U. Angeletti. 1968. Nerve growth factor.Physiol. Rev. 48, 543–569.
Lindenmayer, A. 1987. Models for multicellular development: characterization, inference and complexity ofl-systems. InTrends, Techniques and Problems in Theoretical Computer Science, A. Kelmenova and J. Kelmen (Eds), (Lecture Notes in Computer Science282), pp. 138–168. Berlin: Springer-Verlag.
Meinhardt, H. 1982.Models of Biological Pattern Formation. London: Academic Press.
Politis, M. J., K. Ederle and P. S. Spencer. 1982. Trophism in nerve regenerationin vivo Attraction of regenerating axons by diffusible factors derived from cells in distal nerve stumps of transected peripheral nerves.Brain Res. 253, 1–12.
Prusinkiewicz, P. and A. Lindenmayer. 1990.The Algorithmic Beauty of Plants. New York: Springer-Verlag.
Richardson, P. M. and S. t. Abendal. 1982. Nerve growth activities in rat peripheral nerve.Brain Res. 246, 57–64.
Rozenberg, G. and A. Salomaa. 1980.The Mathematical Theory of L Systems. New York: Academic Press.
Rozenberg, G. and A. Salomaa. 1986.The Book of L. Berlin: Springer-Verlag.
Rozenberg, G. and A. Salomaa. 1974.L Systems (Lecture Notes in Computer Science15) Berlin: Springer-Verlag.
Wood, D. 1980.Grammar and L Forms: An Introduction (Lecture Notes in Computer Science91). Berlin: Springer-Verlag.
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Kalay, A., Parnas, H. & Shamir, E. Neuronal growth via hybrid system of self-growing and diffusion based grammar rules: I. Bltn Mathcal Biology 57, 205–227 (1995). https://doi.org/10.1007/BF02460616
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DOI: https://doi.org/10.1007/BF02460616