A generative spike train model with time-structured higher order correlations

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics

Sensory integration dynamics in a hierarchical network explains choice probabilities in cortical area MT

Neuronal variability in sensory cortex predicts perceptual decisions. This relationship, termed choice probability (CP), can arise from sensory variability biasing behaviour and from top-down signals reflecting behaviour. To investigate the interaction of these mechanisms during the decision-making process, we use a hierarchical network model composed of reciprocally connected sensory and integration circuits. Consistent with monkey behaviour in a fixed-duration motion discrimination task, the model integrates sensory evidence transiently, giving rise to a decaying bottom-up CP component. However, the dynamics of the hierarchical loop recruits a concurrently rising top-down component, resulting in sustained CP. We compute the CP time-course of neurons in the medial temporal area (MT) and find an early transient component and a separate late contribution reflecting decision build-up. The stability of individual CPs and the dynamics of noise correlations further support this decomposition. Our model provides a unified understanding of the circuit dynamics linking neural and behavioural variability

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