Subthreshold voltage noise due to channel fluctuations in active neuronal membranes

Voltage-gated ion channels in neuronal membranes fluctuate randomly between different conformational states due to thermal agitation. Fluctuations between conducting and nonconducting states give rise to noisy membrane currents and subthreshold voltage fluctuations and may contribute to variability in spike timing. Here we study subthreshold voltage fluctuations due to active voltage-gated Na⁺ and K⁺ channels as predicted by two commonly used kinetic schemes: the Mainen et al. (1995) (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (1952) (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temperatures. We contrast the results from Monte Carlo simulations of the stochastic nonlinear kinetic schemes with analytical, closed-form expressions derived using passive and quasi-active linear approximations to the kinetic schemes. For all subthreshold voltage ranges, the quasi-active linearized approximation is accurate within 8% and may thus be used in large-scale simulations of realistic neuronal geometries.