Mathematical analysis of competition between sensory ganglion cells for nerve growth factor in the skin

  • Raymond Kohli
  • Peter G. H. Clarke
Part I: Coding and Learning in Biology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1327)


We model the competition between sensory axons for nerve growth factor (NGF) produced in the periphery. Previous models predicted the loss of all but one of the axons innervating a given region, owing to the unlimited growth of the “fittest” axon. We have imposed an upper limit to axon growth, thereby introducing new equilibria, and we show by LaSalle's theorem that, several axons can then survive, depending on the rate of NGF production.


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  1. 1.
    Albers, K.M., Wright, D.E., Davis, B.M.: Overexpression of nerve growth factor in epidermis of transgenic mice causes hypertrophy of the peripheral nervous system. J.Neurosci. 14 (1994) 1422–1432.Google Scholar
  2. 2.
    Hamburger, V., Levi-Montalcini R.: Proliferation, differentiation and degeneration in the spinal ganglia of the chick embryo under normal and experimental conditions. J.Exp.Zool. 111 (1949) 457–501.Google Scholar
  3. 3.
    Jacobson, M.: Developmental Neurobiology, 3rd Edition. Plenum Press, New York. (1949)Google Scholar
  4. 4.
    Jeanprêtre, N., Clarke, P.G.H., Gabriel, J.P.: Competitive exclusion between axons dependent on a single trophic substance: A mathematical analysis. Math.Biosci. 135 (1996) 23–54.Google Scholar
  5. 5.
    LaSalle, J.P.: Some extensions of Liapunov's second method. IRE.Trans.CT 7 (1960) 520–527`Google Scholar
  6. 6.
    Rasmussen, C.E., Willshaw, D.J.: Presynaptic and postsynaptic competition in models for the development of neuromuscular connections. Biol. Cybern. 68 (1993) 409–419.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Raymond Kohli
    • 1
  • Peter G. H. Clarke
    • 2
  1. 1.Ecole Polytechnique Fédérale de LausanneDépartement de mathématiquesLausanneSwitzerland
  2. 2.Université de LausanneInstitut de biologie cellulaire et de morphologieLausanneSwitzerland

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