Ergodicity and parameter estimates in auditory neural circuits.

This paper discusses ergodic properties and circular statistical characteristics in neuronal spike trains. Ergodicity means that the average taken over a long time period and over smaller population should equal the average in less time and larger population. The objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps find correspondence between variables and parameters. The methods used are analytical and numerical computations, numerical models of phenomenological spiking neurons and neuronal circuits. Results obtained using these methods are the following. They are: a formula to calculate vector strength of neural spike timing dependent on the spike train parameters, description of parameters of spike train variability and model of output spiking density based on assumption of the computation realized by sound localization neural circuit. Theoretical results are illustrated by references to experimental data. Examples of neurons where spike trains have and do not have the ergodic property are then discussed.

Analytical description of coincidence detection synaptic mechanisms in the auditory pathway.

Localization of sound source azimuth within horizontal plane uses interaural time differences (ITDs) between sounds arriving through the left and right ear. In mammals, ITDs are processed primarily in the medial superior olive (MSO) neurons. These are the first binaural neurons in the auditory pathway. The MSO neurons are notable because they possess high time precision in the range of tens of microseconds. Several theories and experimental studies explain how neurons are able to achieve such precision. In most theories, neuronal coincidence detection processes the ITDs and encodes azimuth in ascending neurons of the auditory pathway using modalities that are more tractable than the ITD. These modalities have been described as firing rate codes, place codes (labeled line codes) and similarly. In this theoretical model it is described how the ITD is processed by coincidence detection and converted into spikes by summing the postsynaptic potentials. Particular postsynaptic conductance functions are used in order to obtain an analytical solution in a closed form. Specifically, postsynaptic response functions are derived from the exponential decay of postsynaptic conductances and the MSO neuron is modeled as a simplified version of the Spike Response Model (SRM0) which uses linear summations of the membrane responses to synaptic inputs. For plausible ratios of time constants, an analytical solution used to describe properties of coincidence detection window is obtained. The parameter space is then explored in the vicinity of the analytical solution. The variation of parameters does not change the solution qualitatively.