Abstract

Synaptic plasticity is the ability to change the influence that spiking in a presynaptic neuron has on a postsynaptic cell. Intracellular calcium elevation and relative spike timing are processes typically associated with synaptic plasticity outcomes throughout the brain. Plasticity of the parallel fibre to Purkinje cell synapse in the Cerebellum is seen as being atypical in that it is non-Hebbian, depending on an ‘error signal’ via the activation of the climbing fibre for LTD and on presynaptic NMDA receptors for LTP . Here I develop a spike based model of plasticity for this synapse, based on calcium and NO, which accurately fits a range of protocols from the literature and has been shown to have wide predictive power. I then move on to developing an analysis of a more typical, calcium-based, plasticity model for neocortical synaptic plasticity [Graupner12]. I develop analytical tools which accurately predict the behaviour of this synapse model under Poisson pre- and postsynaptic firing. Finally, I extend this theory to predict the behaviour of a large-scale recurrent network of leaky integrate-and-fire neurons under both constant and time-varying noisy external inputs. Investigation of both plasticity models reveals insights into the processes of learning and subsequent forgetting in the brain. Both models reveal the joint importance of burst frequency and relative spike timing in the induction of memory changes at the synaptic level. Adjustment of model parameters to more closely mimic in-vivo conditions extends the retention time of memories, under ongoing activity, to biologically relevant time scales. This work represents a coherent development right through from the biophysical processes of synaptic plasticity to the analytical mean-field level.