Coincidence detection in the Hodgkin-Huxley equations

Some of the cochlear nuclei in the auditory pathway are specialized for the sound localization. They compute the interaural time difference. The difference in sound timing is transduced by the dedicated neuronal circuit into a labeled line difference. The detector neurons along the delay line fire only when synaptic inputs reflecting signals from both cars arrive within a short time window. It was therefore called coincidence detection. We show, (1) what are the limits of coincidence detection in the leaky integrator model, which is a linear system, (2) how should the ideal coincidence detector based on the Hodkin-Huxley equations from real neurons look like, (3) what are the properties and physical limits in the real coincidence detection system. The conclusion is that the neuron with the Hodgkin Huxley dynamics has a fixed precision for the coincidence detection. The limits of the sound localization precision are set by the frequency of the sound and, therefore, by the vector strength of spike trains generated in the neuronal circuit in response to the sound.