Stochastic resonance, coherence resonance, and spike timing reliability of Hodgkin-Huxley neurons with ion-channel noise

The random transitions of ion channels between open and closed states are a major source of noise in neurons. In this study, we investigate the stochastic dynamics of a single Hodgkin-Huxley (HH) neuron with realistic, physiological channel noise, which depends on the channel number and the voltage potential of the membrane. Without external input, the stochastic HH model can generate spontaneous spikes induced by ion-channel noise, and the variability of inter-spike intervals attains a minimum for an optimal membrane area, a phenomenon known as coherence resonance. When a subthreshold periodic input current is added, the neuron can optimally detect the input frequency for an intermediate membrane area, corresponding to the phenomenon of stochastic resonance. We also investigate spike timing reliability of neuronal responses to repeated presentations of the same stimulus with different realizations of channel noise. We show that, with increasing membrane area, the reliability of neuronal response decreases for subthreshold periodic inputs, and attains a minimum for suprathreshold inputs. Furthermore, Arnold tongues of high reliability arise in a two-dimensional plot of frequency and amplitude of the sinusoidal input current, resulting from the resonance effect of spike timing reliability.