Temporal and spatial factors affecting synaptic transmission in cortex

Synaptic transmission in cortex depends on both the history of synaptic activity and the location of individual anatomical contacts within the dendritic tree. This thesis analyses key aspects of the roles of both these factors and, in particular, extends many of the results for deterministic synaptic transmission to a more naturalistic stochastic framework. Firstly, I consider how correlations in neurotransmitter vesicle occupancy arising from synchronous activity in a presynaptic population interact with the number of independent release sites, a parameter recently shown to be modified during long-term plasticity. I study a model of multiple-release-site short-term plasticity and derive exact results for the postsynaptic voltage variance. Using approximate results for the postsynaptic firing rate in the limits of low and high correlations, I demonstrate that short-term depression leads to a maximum response for an intermediate number of presynaptic release sites, and that this in turn leads to a tuning-curve response peaked at an optimal presynaptic synchrony set by the number of neurotransmitter release sites per presynaptic neuron. As the nervous system operates under constraints of efficient metabolism it is likely that this phenomenon provides an activity-dependent constraint on network architecture. Secondly, I consider how synapses exhibiting short-term plasticity transmit spike trains when spike times are autocorrelated. I derive exact results for vesicle occupancy and postsynaptic voltage variance in the case that spiking is a renewal process, with uncorrelated interspike intervals (ISIs). The vesicle occupancy predictions are tested experimentally and shown to be in good agreement with the theory. I demonstrate that neurotransmitter is released at a higher rate when the presynaptic spike train is more regular, but that positively autocorrelated spike trains are better drivers of the postsynaptic voltage when the vesicle release probability is low. I provide accurate approximations to the postsynaptic firing rate, allowing future studies of neuronal circuits and networks with dynamic synapses to incorporate physiologically relevant spiking statistics. Thirdly, I develop a Bayesian inference method for synaptic parameters. This expands on recent Bayesian approaches in that the likelihood function is exact for both the quantal and dynamic synaptic parameters. This means that it can be used to directly estimate parameters for common synaptic models with few release sites. I apply the method to simulated and real data; demonstrating a substantial improvement over analysis techniques that are based around the mean and variance. Finally, I consider a spatially extended neuron model where the dendrites taper away from the soma. I derive an accurate asymptotic solution for the voltage profile in a dendritic cable of arbitrary radius profile and use this to determine the profile that optimally transfers voltages to the soma. I find a precise quadratic form that matches results from non-parametric numerical optimisation. The equation predicts diameter profiles from reconstructed cells, suggesting that dendritic diameters optimise passive transfer of synaptic currents