A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem

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Abstract
This paper examines the idea that ordered patterns of nerve connections are set up by means of markers carried by the individual cells. The case of the ordered retinotectal projection in amphibia and fishes is discussed in great detail. It is suggested that retinotectal mappings are the result of two mechanisms acting in concert. One mechanism induces a set of retinal markers into the tectum. By this means, an initially haphazard pattern of synapses is transformed into a continuous or piece-wise continuous projection. The other mechanism places the individual pieces of the map in the correct orientation. The machinery necessary for this inductive scheme has been expressed in terms of a set of differential equations, which have been solved numerically for a number of cases. Straightforward assumptions are made as to how markers are distributed in the retina; how they are induced into the tectum; and how the induced markers bring about alterations in the pattern of synaptic contacts. A detailed physiological interpretation of the model is given. The inductive mechanism has been formulated at the level of the individual synaptic interactions. Therefore, it is possible to specify, in a given situation, not only the nature of the end state of the mapping but also how the mapping develops over time. The role of the modes of growth of retina and tectum in shaping the developing projection becomes clear. Since, on this model, the tectum is initially devoid of markers, there is an important difference between the development and the regeneration of ordered mappings. In the development of duplicate maps from various types of compound-eyes, it is suggested that the tectum, rather than the retina, contains an abnormal distribution of markers. An important parameter in these experiments, and also in the regeneration experiments where part-duplication has been found, is the range of interaction amongst the retinal cells. It is suggested that the results of many of the regeneration experiments (including apparently contradictory ones) are manifestations of a conflict between the two alternative ways of specifying the orientation of the map: through the information carried by the markers previously induced into the tectum and through the orientation mechanism itself.

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