Signal frequency transformation by Hodgkin-Huxley neurons
The response of a Hodgkin-Huxley neuron strongly depends on the form of input current. We study the model with a periodic postsynaptic current, where each of the current pulses has the form I(t) ~ gsyn ∑ (t/τ) exp(-t/τ) Θ(t) (Va-Vsyn), where gsyn is the synapse conductivity, τ is the time constant associated with the synapse conduction, Va is the maximum membrane potential and Vsyn is the reversal potential of the synapse. The other parameters are typical for the Hodgkin-Huxley model. There are three resonant frequencies at 57 Hz, 28.5 Hz, and 19 Hz, where the 57 Hz feature is the main resonance of the neuron. In the resonant regime the system has the tendency to mode locking with high values of k, where k=To/Ti is the ratio of the output ISI to the input ISI. Chaotic states are present in many areas of the resonant regime. The mode-locked states within the resonance may have large values of k. The incoming signal frequency may be substantially reduced when passing through such neuron. A chain of two or more neurons may decrease the signal frequency by more than an order of magnitude. Noise in the input signal lowers the response threshold and improves the signal-to-noise ratio. Network effects are also discussed. Acknowledgements: Part of the numerical computation was performed in the Computer Center of the Tri-city Academic Computer Network in Gdansk, Poland.