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The aim of this thesis is to contribute to an understanding of the intracellular signalling network that is linked to the activation of metabotropic glutamate receptors (mGluRs) in a cerebellar Purkinje cell. In the thesis, ten different computational models of the mGluR signalling network are mathematically analysed and numerically integrated. The main result of this thesis is that the mGluR signalling network can implement an adaptive time delay between the activation of the mGluRs by glutamate and the release of calcium from intracellular stores. The adaptation of the time delay has at least three different computational functions. Based on the delay adjustment, a single Purkinje cell can learn the adaptive timing of the classically conditioned eye-blink response. A more general function of the adaptive time delay is that it enables a Purkinje cell to learn a radial basis function (RBF)-like response to temporal parallel fibre input patterns. Furthermore, different Purkinje cells in a group can discover different clusters in a temporal parallel fibre input space. The adaptation of a synaptic delay as opposed to a synaptic weight is a novel non-Hebbian learning mechanism. By systematically simplifying the original model, it is shown that the delay learning can be produced by a very limited set of intracellular processes. Two antagonistic phosphorylations can adjust the concentration of available mGluRs and implement the adaptation of the time delay. A delayed as opposed to an immediate response can be generated by the combination of calcium of dependent negative feedback and autocatalytic release of calcium from intracellular stores. |
