Table 1.
Classification of channel noise models.
Figure 1.
Analysis of responses of channel noise models for a fixed voltage trajectory.
(A) Voltage trace obtained from the Markov chain model with no current input, 6,000 channels and 1,800
channels. Dynamics are characterized by a prolonged subthreshold period followed by a spontaneous, channel noise-induced spike at
. (B) Means of fraction of open
and
channels for the voltage trace shown in (A), as computed from Equations 10 and 11. (C) Variance in the fraction of open
channels. (D) Variance in the fraction of open
channels. Left insets in (C and D) show magnified views of the period preceding the spike. Right inset in (C) shows magnified view during the spike. For (C and D), exact variances (black) were computed from Equation 12 and Equation 13 and all other variances were estimated from 5,000 repeated simulations of the channel noise models.
Figure 2.
(A) Mean of ISIs for a membrane area of channels). (B) CV of ISIs for same membrane area as (A). 500 spikes were used to estimate the mean and variance, and error bars indicate standard error in the mean for ten repeated measurements for all models except the Markov chain model, for which only four repeated measurements were used.
Figure 3.
Markov chain kinetic models of the Na+ channel in squid giant axon.
(A) Kinetic scheme for the classical HH model of the Na channel. (B) Kinetic scheme for the Vandenberg and Bezanilla model of the Na channel. Arrows are labeled with transition rates that are functions of voltage, see [20] and [41] for further details. The open states are those in the bottom right: (3,1) in (A) and in (B).
Figure 4.
Analysis of responses of modified channel noise models to a step increase in current.
(A) Voltage trace obtained from the Markov chain model with channels and
channels. Input current is increased from
at
, onset time of the stimulus is marked by the gray arrow. (B) Means of fraction of open
and
channels for the voltage trace shown in (A). (C) Variance in the fraction of open
channels for the Markov chain and system size-based conductance noise models. (D) Variance in the fraction of open
channels for the Markov chain and system size-based conductance noise models. Means and variances were estimated from 5,000 repeated simulations of the channel noise models. (E) Histogram of spike times in response to the step increase in current described above. Solid lines show the mean of ten histograms computed from 500 spike times each and error bars represent the standard error in the mean. Gray arrow indicates the spike time of a deterministic version of the model.