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.