Abstract
In the development of nerve connections, neurons are believed to compete for target-derived neurotrophic factors which support their survival and maintenance of their synapses. We introduce a mathematical framework for neurotrophin release and its uptake by the innervating neurons. We explore the idea that central to the action of neurotrophins is their capacity to upregulate their own receptors.
Using nerve growth factor (NGF) as the paradigm case, we show theoretically how the form of the upregulation determines the nature and outcome of the competitive process. Under some conditions, the target structure becomes singly innervated, under others, multiple innervation results, the amount of multiple innervation depending on the supply of neurotrophins. The finding that electrical activity increases the numbers of receptors means that competition for neurotrophin amongst synapses leads to the survival of the more active ones. Reduction in receptor upregulation or in the supply of neurotrophin (which may occur in ageing and disease-related neurodegeneration), can lead to a complete loss of innervation.
Our model encompasses previous models of neuronal competition during development and couples the field of neurobiology to that of population biology, where the notion of competition is better developed.
Preview
Unable to display preview. Download preview PDF.
References
Jansen, J. K. S., Fladby, T. (1990) The perinatal reorganization of the innervation of skeletal muscle in mammals. Prog. Neurobiol. 34: 39–90.
Crepel, F. (1982) Regression of functional synapses in the immature mammalian cerebellum. Trends Neurose. 5: 266–269.
Purves, D. (1988) Body and Brain: A Trophic Theory of Neural Connections, Harvard Univ. Press, Cambridge, MA.
Wiesel, T. N. (1982) Postnatal development of the visual cortex and the influence of the environment. Nature 299: 583–591.
Bothwell, M. (1995) Functional interactions of neurotrophins and neurotrophin receptors. Ann. Rev. Neurosc. 18: 223–253.
Bernd, P., Greene, L. A. (1984) Association of 1125-nerve growth factor with PC12 pheochromocytoma cells. Evidence for internalization via high affinity receptors only and for long-term regulation by nerve growth factor of both high-and lowaffinity receptors. J. Biological Chemistry 259 (24): 15509–15516.
Holtzman, D. M., Li, Y., Parada, L. F., Kinsman, S., Chen, C.-K., Valletta, J. S., Zhou, J., Long, J. B., Mobley, W. C. (1992) p140trk mRNA marks NGF-responsive forebrain neurons: evidence that trk gene expression is induced by NGF. Neuron 9: 465–478.
Verge, V. M. K., Merlio, J.-P., Grondin, J., Ernfors, P., Persson, H., Riopelle, R. J., Hokfelt, T., Richardson, P. M. (1992) Colocalization of NGF binding sites, trk mRNA, and low-affinity NGF receptor mRNA in primary sensory neurons: responses to injury and infusion of NGF. J. Neurosc. 12 (10): 4011–4022.
Zhou, J., Valletta, J. S., Grimes, M. L., MObley, W. C. (1995) Multiple levels for regulation of TrkA in PC12 cells by nerve growth factor. J. Neurochemistry 65: 1146–1156.
Wyatt, S., Shooter, E. M., Davies, A. M. (1990) Expression of the NGF receptor gene in sensory neurons and their cutaneous targets prior to and during innervation. Neuron 2: 421–427.
Black, I. B. (1993) Environmental regulation of brain trophic interactions. Int. J. Dev. Neurosc. 11: 403–410.
Rasmussen, C. E., Willshaw, D. J. (1993) Presynaptic and postsynaptic competition in models for the development of neuromuscular connections. Biol. Cybern. 68: 409–419.
Yodzis, P. (1989) Introduction to Theoretical Ecology, Harper and Row, New York.
Doherty, P., Seaton, P., Flanigan, T. P., Walsh, F. S. (1984) Factors controlling the expression of the NGF receptor in PC12 cells. Neuroscience Letters 92: 222–227.
Jeanpretre, N., Clarke, P. G. H., Gabriel, J.-P. (1996) Competitive exclusion between axons dependent on a single trophic substance: a mathematical analysis. Mathematical Biosciences 135: 233–54.]
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van Ooyen, A., Willshaw, D.J. (1997). Competition amongst neurons for neurotrophins. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020146
Download citation
DOI: https://doi.org/10.1007/BFb0020146
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63631-1
Online ISBN: 978-3-540-69620-9
eBook Packages: Springer Book Archive