Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations

Figures

• 

  Figure 1. (a) Committor probabilities for Cl− in p7 at −140 mV (red), −70 mV (green), −35 mV (black), 0 V (blue), 70 mV (cyan) and 140 mV (magenta). Error bars are shown for the N6 data sets at −35 mV and 140 mV; (b) Committor probabilities for p7 at 140 mV from the N6 data set for 1-sided forward (green) and backward (blue) trajectories, respectively, 2-sided data set in the backward direction (red lines), and average in the forward direction with error bars (red symbols). In the inset we show the number of first passage trajectories to reach z for one N6 data set in the forward (green) and backward (magenta) directions and the total (light blue).

• 

  Figure 2. (a) PMFs for K+ (lower curves) and Cl− (upper curves) in TTX from stochastic simulations with an applied voltage of 50 mV. The PMFs have been reconstructed by way of CWDM at the N6 (blue) and N7 (gold) levels or by way of CPM at the N6 (green) and N7 (magenta) levels; (b) PMF for Na+ in GLIC from stochastic simulations with applied voltage of 100 mV. The PMF has been reconstructed by way of CWDM at the N7 (blue) and N8 (gold) level or by way of CPM at the N7 (green) and N8 (magenta) level. In both panels, the underlying PMF is in red.

• 

  Figure 3. (a) PMF for Cl− in p7 from stochastic simulations with an applied voltage of 140 mV. The PMFs have been reconstructed by way of CWDM at the N6 (blue) and N7 (gold) levels or by way of CPM at the N6 (green) and N7 (magenta) levels. The input PMF (red) is shown for reference. PMFs at the N8 level are not shown, as they coincide with the underlying PMFs and statistical errors associated with this level arequite small and are poorly visible at this scale; (b) PMFs for P7 reconstructed by way of one-sided forward trajectories (green) using Equation (13) and backward trajectories (blue) using Equation (14) from stochastic simulations at the N6 level with applied voltage of 140 mV. Two-sided reconstruction (magenta) and the underlying PMF (red) are shown for comparison. Note that one-sided, but not two-sided reconstructions are burdened with large errors at the ends.

• 

  Figure 4. (a) I-V curves for K+ (green) and Cl− (blue) in TTX reconstructed from simulations at 50 mV at the N6 level. Blue and green dots are currents obtained from direct simulations at specific voltages.; (b) I-V curves for Cl− in p7 reconstructed from simulations at 140 mV at the N6 (blue), N7 (green) and N8 (red) level, and for −35 mV at the N6 level (magenta). N7 and N8 curves are not shown because they are almost identical to the N6 results. Black dots are currents obtained from direct simulations at specific voltages. All reconstructions were done using the PMFs obtained by way of CPM. The results of reconstructions using the PMFs from CWDM are not displayed because they are nearly identical.

• 

  Figure 5. I-V curves for Na+ in GLIC reconstructed from simulations at 100 mV at the N7 level with PMF from CPM (blue), at the N7 level with PMF from CWDM (magenta), and N8 with PMF from CWDM (red). N8 with CPM (not shown) is almost identical to N7 CPM. Black dots are currents obtained from direct simulations at specific voltages.

• 

  Figure 6. Reconstructions of I-V curves in TTX from individual sets of trajectories for K+ (a) and Cl− (b). The PMFs were obtained from CPM (upper panels) or CWDM (lower panels). The curves were calculated by way of Equation (20) (blue) or Equation (18) (green). All reconstructions were carried out from simulations at applied voltage of 50 mV at the N6 level. Note that blue curves, but not green curves, are tightly clustered together indicating that Equation (20) is more accurate than Equation (18).