Computer modeling of whole-cell voltage-clamp analyses to delineate guidelines for good practice of manual and automated patch-clamp

Figure 1. (A) Simplified scheme of a cell studied in voltage-clamp, illustrating how the potential clamped between the two electrodes is split between the membrane potential and a potential generated at the pipette tip. (B) Scheme of the equivalent electrical circuit. Pipette capacitance and leak current due to imperfect seal between the pipette and the cell have been omitted for the sake of clarity. Rm: cell resistance for Na+. This value depends on the Na+ channel expression level and the fraction of expressed Na+ channels that are open (the higher the value, the less active are the Na+ channels). The fraction of channels in the open state depends on voltage and time. ENa: value of the reversal potential for Na+ (determined by intra- and extracellular Na+ concentrations according to the Nernst equation); Cm: cell capacitance (the higher the value, the larger is the cell). (C) Left, representative, superimposed recordings of heterologously-expressed Nav1.5 during an activation voltage protocol (from HP = − 100 mV depolarization to steps from − 80 to + 65 mV), with no compensation. Right, recordings of the same cell with RS compensation. (D) I/V curves in the two conditions presented in…

Figure 2. Kinetic model of cardiac INa current (Nav1.5)—computed effects of increasing series resistance and current amplitude range on current recordings. (A) Expression of the Na+ current depending on the activation gate (m3), inactivation gate (j.h), the maximal conductance (Gmax) and the reversal potential for Na+ (ENa)5,16. (B) Superimposed computed INa, for increasing current amplitude range (INa, see vertical scales, top to bottom) and series resistance (RS, left to right). The activation voltage protocol shown (in inset, holding potential: − 100 mV; 50-ms pulse at the indicated potentials; one sweep every 2 s) corresponds to the potential at the membrane, not the command potential between the two electrodes. It is thus altered when (RS x I) is elevated, its maximum deflection reaching 26 mV at Vcmd = − 40 mV (cf text). (C) Superimposed computed voltage deviation for the highest amplitude (10 nA) and various Rs, as in (B).

Figure 3. Kinetic model of cardiac INa current (Nav1.5)—computed effects of increasing series resistance and current amplitude range on apparent current parameters. (A) Computed time course of INa current at the indicated command potential, for various values of RS, as indicated by colors. (B) Peak current/voltage (I/V) relationships in the three conditions. Optimal I/V curve is repeated (light green), allowing easy comparison. Straight lines are fits of the I/V curves when voltage-dependent activation is achieved. The slope of the linear function corresponds to the maximal conductance. (C) Activation curves (G/Gmax vs Vcmd) in various conditions as indicated by color and symbol size. Theoretical half-activation potential (V0.5) and slope (k) values in black. V0.5 and k for RS of 0, 2 and 5 MΩ and current range of 10 nA are indicated in colors.

Figure 4. Kinetic model of cardiac INa current (Nav1.5)—computed effects of increasing series resistance and current amplitude on apparent TTX effects. (A) Relationships between the theoretical values of peak INa (with no voltage error) and the measured values of INa for three different values of RS (0, 2 and 5 MΩ). (B) Computed recordings of the INa current at the indicated TTX concentrations, for various values of Rs, as indicated by colors. (C) Computed dose–response curves for three RS conditions (RS = 0, 2 and 5 MΩ) and two amplitude ranges (I peak = − 2.7 and − 27 nA).

Figure 5. Kinetic model of cardiac Ito current—computed effects of increasing series resistance and current amplitude on current recordings. (A) Expression of the K+ current depending on the activation gate (a), inactivation gate (i), the maximal conductance (Gmax) and the reversal potential for K+ (EK)5. (B) Computed superimposed recordings of the Ito current, for various current amplitudes and series resistances (RS), as indicated. The activation voltage protocol shown (holding potential: − 100 mV; 100-ms pulse at the indicated potentials; one sweep every 2 s) corresponds to the potential experienced by the membrane (Vm), not the potential between the two electrodes (Vcmd). It is thus altered when (Rs x I) is elevated. (C) Activation curves (G/Gmax vs Vcmd) in the three conditions represented in (B). Theoretical half-activation potentials (V0.5) and slopes (k) are indicated in black. V0.5 and k for RS of 0, 5 and 15 MΩ and I peak of 100 nA are indicated in colors.

Figure 6. Optimization of the Kinetic model presented in Fig. 2 to fit the recordings of heterologously-expressed Nav1.5. (A) Left, representative, superimposed recordings of heterologously-expressed Nav1.5 during an activation voltage protocol (same as in Fig. 2). Middle, computed recordings using the same protocol, and the equation of5. Right, computed recordings using the same protocol, and the optimized model, to fit the biophysical characteristics of heterologously-expressed Nav1.5. (B) Activation curves in the three conditions presented in (A). (C) Half-activation potentials, slopes and time constants of inactivation in the three conditions.

Figure 7. V0.5 vs. amplitude plots and slope vs. amplitude plots of heterologously-expressed Nav1.5 currents recorded in COS-7 using manual patch-clamp. (A) Symbols represent the mean ± sem of pooled experimental values of V0.5 as a function of mean ± sem values of current amplitudes. Lines correspond to fit of computed values obtained from the kinetic model that has been optimized in Fig. 6 and in which RS has been set to 0, 2 and 5 M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega$$\end{document}Ω (compensated Cm = 20 pF). (B) Pooled experimental values of the activation slope as a function of mean ± sem values of current amplitudes.

Figure 8. V0.5 vs. amplitude and slope vs. amplitude plots of INa measured from neonatal mouse ventricular cardiomyocytes using manual patch clamp. (A) Top, distribution of Ipeak amplitudes of the data set. Blue data points correspond to a subset of cells with absolute amplitudes greater than 7000 pA. Left, symbols represent V0.5 values as a function of current amplitude values. The black line corresponds to exponential fit of the data, and the orange line corresponds to fit of computed values obtained from the kinetic model that has been optimized for heterologously-expressed Nav1.5 currents in COS-7 cells and in which RS has been set to 2 M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega$$\end{document}Ω. Right, mean ± sem activation V0.5 for cells with current amplitudes smaller or greater than 7000 pA. ****, p < 0.0001, **, p < 0.01, Mann–Whitney test (Ipeak) and student’s t-test (V0.5). (B) Same as in A for the slope of the activation curve. ****, p < 0.0001, **, p < 0.01, Mann–Whitney test (Ipeak)…

Figure 9. V0.5 vs. amplitude plots and slope vs. amplitude plots for INa in HEK293 cells stably expressing Nav1.5 measured using a Nanion Syncropatch 384PE. (A) Symbols represent the mean ± sem of pooled values of V0.5 as a function of mean ± sem values of current amplitudes. Data points were pooled by 500 pA amplitudes intervals (0–500, 500–1000, etc.) (B) Pooled experimental values of the activation slope as a function of mean ± sem values of current amplitudes.