Examples of modulation in hearing

Many acoustic sensory organs (e.g., mammalian cochleae, reptile and bird basilar papillae, frog amphibian papillae) have a quintessential feature in common, each of them comprises an array of (band-pass) filters, each filter covering a relatively narrow frequency band and each communicating to the central nervous system through its own private channel. The incoming acoustic signal thus is decomposed into spectro-temporal components, which are translated individually into neural signals and sent over the filter's private channel. Each component (each output from an individual filter) in the lower-frequency bands is converted (by transduction) directly into a generator potential in a sensory receptor cell; and this, in turn, modulates the instantaneous firing rate of spikes being sent along one or more primary afferent axons (the private channel) to the central nervous system. Owing to low-pass filtering inherent in the structures of nerve cells, generator potentials and spike rates are incapable of being modulated directly by components (filter outputs) in higher-frequency bands (e.g., above about 500 Hz in frogs and reptiles, 5000 Hz in mammals, 10,000 Hz in birds). In those higher-frequency bands, each filter output is demodulated during the transduction process, and each generator potential and spike train follows the lower-frequency components (i.e., a smoothed version) of the amplitude envelope of the band-pass filter output rather than the filter output itself. {In the frogs and gerbils that we have studied, demodulation is accomplished by a square-law nonlinearity, and each generator potential and spike rate follows a smoothed (low-pass filtered) version of the square of the amplitude envelope of the band-pass filter output (see footnote), (see also ref 1, p. 100) and (ref2, p. 18)}. In frequency bands near the transition from low- to high-frequencies, each generator potential and spike train exhibits a component that follows the filter output itself, and a component that follows a smoothed version of the square of its amplitude envelope.


Modulation of the primary afferent axon's spike rate poses an interesting problem in reverse engineering. Spike-rate modulation by generator potentials in the basic Hodgkin-Huxley system is exceedingly nonlinear-- producing gross distortion. What we see in VIIIth-nerve axons is exceedingly linear modulation, with only mild distortion. In a modeling study, we found that dithering by a weak noise current (at amplitudes expected from known noise sources in neurons) is sufficient to linearize spike-rate modulation in the Hodgkin-Huxley system and produce results virtually identical to those we observed in the actual axons (link to 1989 paper). During my post-doctoral studies on the Hodgkin-Huxley system I had noticed a similar phenomenon. Basic control-theory analysis revealed a tendency toward subthreshold oscillation in the Hodgkin-Huxley system (link to 1965 paper, see Fig. 8); and dithering had translated the oscillations into spike trains with multimodal interval histograms (see Fig. 10 in that same 1965 paper).


Last updated 07/15/16