Figure 5.

Spontanous action potentials in the HH model driven with Gaussian noise with varying amplitude and correlation time. (A) The impedance factor z(τ) gives the voltage fluctuations resulting from a correlated noise current as a function of the noise correlation time. It is used to ensure the voltage variance is identical as the time constant of the noise is varied. Membrane area of 1000 μm². (B) Spontaneous activity as a result of a Gaussian current noise, as a function of the correlation time of the noise. When the variance of the current is fixed, the resulting rates vary strongly depending on the correlation time (dashed curve). However, when the noise is calibrated to yield the same variance in the membrane voltage irrespective of the noise correlation time, the firing rate is much less variable even across six orders of magnitude (solid curve). (C) The firing rate vs. the impedance corrected current noise (expressed in σ_V) for various values of the noise time-constant. (D) The spontaneous firing rate vs. membrane area for K⁺ (red) and Na⁺ (blue) noise and their various approximations. Solid curve: full simulation, redrawn from Figure 1B. Thick dashed curve: approximation using Gaussian noise with identical variance and time-constant. Thin dashed curve: binomial approximation of the noise. In particular for Na⁺ noise the approximations yield rates that are substantially too low.