Ion shot noise in Hodgkin–Huxley neurons

Abstract

Ion shot noise, the noise associated to the random passage of ions across the cell membrane, is studied by means of a stochastic model based on the Hodgkin–Huxley equations, which includes gating channels for sodium and potassium cations and leakage channels through the biological membrane. Apart from shot noise, other sources such as extrinsic and channel noise are taken into account. Ion shot noise, of increasing influence for smaller membrane patch sizes S, can lead to the emergence of action potentials in the membrane voltage in the presence of sinusoidal excitation currents below the threshold for the onset of spikes. The spiking activity in the presence of noise has been analyzed in terms of the coefficient of variation CV, the inter-spike interval histogram, the spectrum of membrane voltage fluctuations and the signal-to-noise ratio SNR. CV shows improved coherence in the sequence of randomly generated spikes due to the presence of shot noise. The voltage noise spectra show a common signature of the presence of spikes under different operating conditions, even in the absence of excitation. The SNR exhibits intrinsic stochastic resonance when varying S. For a sinusoidal excitation current with amplitude 1.5 μA/cm2 and frequency 50 Hz, the SNR presents optimal values around 0.2 μm2. When considering the presence of ambient noise in the excitation current, extrinsic stochastic resonance is found for S > 0.6 μm2.