Abstract:
Topographic maps in the nervous system, and in particular the retinotectal map, have long been a focus of study. While there are many diverse models that explain aspects of map formation, there is as yet no general agreement on the specifics of the mechanisms at work. This thesis explores retinotectal map formation and models that have been proposed for it. Two of these are examined in detail: the Tea Trade Model and KT Model.
The Tea Trade Model was proposed 30 years ago before supporting evidence was discovered, so this thesis presents some updates to the model to bring it inline with modern understanding of the molecular cues.
The KT Model was proposed more recently and uses a probabilistic update rule that has some analytic appeal. Two avenues are explored based on this model. First, mathematical analysis leads to a new approach to model formulation based on energy surfaces; one such model reveals that while promising in theory, local minima are problematic in practice. Second, a new mechanism is incorporated into the KT Model to extend the range of experimental literature it is able to account for.
