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Analysis of a Model for the Development and Regeneration of the Retinotectal Projection
Citation key Bentzien1998
Author Bentzien, B. and Weber, C. and Obermayer, K.
Title of Book European Journal of Neuroscience
Year 1998
Volume 10
Publisher European Forum of Neuroscience ENA
Abstract We explore a computational model which describes among other experimental settings the establishment of the undisturbed topographic retinotectal projection. Retinae and tectum are each modeled as a 1d layer of cells where the retina(e) are fully connected to the tectal cells. The connections between eyes and tectum are described by effective synaptic weights and their development is governed by growth promoting and limiting interactions. Growth promoting interactions consist of a fiber-tectum interaction, fiber-fiber interactions and a constant growth term. Limiting interactions are a soft constraint on the total amount of incoming and outgoing fibers of a tectal and retinal cell, respectively, and a synaptic decay. Growth terms are constant or linear in the synaptic strength, but the synaptic strengths are constrained to be positive. \\ The shape of a receptive field in the undisturbed projection is decribed analytically as a function of the model parameters. The size of a receptive field depends only on the widths of the fiber-fiber interaction and on the synaptic decay, whereas the other terms scale all synaptic strengths uniformly. \\ The model reproduces a variety of regeneration experiments in goldfish with the same set of model parameters and describes receptive and projective fields of retinal and tectal cells. We explore parameter dependencies in detail and show the limits of the parameter ranges by the experimental observations. The mathematical framework also allows the study of ``knockout\'\'-experiments as are currently performed in the zebrafish-system.
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