Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes
(A) Examples of simulated stochastic (black traces) and deterministic (red traces) currents in a membrane patch containing 50 stochastic Na+ channels with single channel conductance of 20 pS. The membrane potential is clamped at −20 mV. The expanded trace (right) shows the first 5 ms of the compressed trace (left). (B–C) Cumulative estimate of the mean (B) and variance (C) of stochastic currents measured as in (A) are plotted as a function of time. Examples from 5 separate simulations of duration 100 s are shown. Values between 100 and 1000 s are from concatenation of separate 100 s simulations. (D) Examples of 10 simulated current responses (black traces, lower plot), of the membrane patch simulated in (A–C), to a step change in membrane potential from −80 mV to +30 mV (upper plot). The mean (red trace) and variance (blue trace) are calculated from 1000 stochastic current responses. (E–F) Plot of membrane the membrane current variance as a function of the mean membrane current for the rapid activation phase (E) and slower inactivation phase (F) of the 1000 simulated current responses used to obtain the data for (D). The time window for the activation phase is 0–0.3 ms after the onset of the voltage step, whereas the time window for the deactivation phase is 0.3–10 ms after the onset of the voltage step. The number of single channels (N) and the single channel current (I) are estimated from the fit to the simulation data. The red parabola is the variance-mean relationship predicted from I and N of the model and the blue parabola is the fit to the simulation data. (G–H) Estimates for the number of channels (G) and single channel current (H), obtained by variance mean analysis of the inactivation phase of the current responses analyzed as in (D), plotted as a function of the number of simulated responses used for the analysis. Each dot corresponds to a set of data used for analysis. The continuous lines show convergence of the estimates as additional simulations are analyzed up to a maximum of 104 simulated responses. (I) The RMS error, calculated from the difference between the variance mean fit and the expected variance mean relationship, is plotted as a function of the number of simulated responses. The solid lines indicate progressive convergence up to a maximum of 104 simulated responses. For all examples the simulation time step was 10 µS.