Resolving Artifacts in Voltage‐Clamp Experiments with Computational Modeling: An Application to Fast Sodium Current Recordings

Figure 1. A workflow schematic comparing our approach, which uses realistic simulations of the voltage‐clamp process, to the standard approach in which overly‐idealized assumptions are made about experimental data quality. Our mathematical model of patch‐clamp voltage clamp produces simulated experimental data that can be more accurately compared to experimental data that are affected by patch‐clamp artifacts.

Figure 2. A detailed schematic of the equivalent electrical circuit of the new detailed mathematical model for whole‐cell patch‐clamp voltage‐clamp experiments. Right shows the components of an patch‐clamp amplifier, connecting to the cell on the left. The amplifier includes the components for compensating for series resistance, supercharging, slow capacitance, fast capacitance, and liquid junction potential and voltage offset. The leak correction is modeled as a post‐processing step that is not part of the equivalent circuit.

Figure 3. Experiments to validate our mathematical model of patch clamp artifacts and compensations using a physical electrical model cell. A) A schematic of the electrical model cell (a modification of the ‘Type II’ model cell used in Lei et al.[ 17 ] with faster dynamics). B) The chosen nominal component values. C) Solid lines are experimentally measured, and dashed lines are simulated model outputs. (top) membrane voltage V m (gray line is command voltage V cmd), and (bottom) output current I out at different levels of compensation. Left: effect of series‐resistance compensation (α R ) alone. Middle: supercharging compensation (α P ) alone. Right: varying both compensation levels together (α R = α P ). The electrical circuit produces indistinguishable replications.

Figure 4. Assessing fast sodium current responses to experimental artifacts, with experimental recordings in hiPSC‐CMs. A) A schematic of the experimental setup and B) the experimental conditions for the perforated patch experiments with hiPSC‐CMs to achieve high series resistance. C) Left: Patch‐clamp voltage‐clamp in vitro experimental data measured from hiPSC‐CMs, with estimated R s = 19.5 MΩ and C m = 27.4 pF (n = 4, other repeats are shown in Supporting Information); Right: Simulations of the voltage‐clamp model (Equation (1)–(10)) using the Paci et al.[ 21 ] hiPSC‐CM model for I ion (including all of its ion currents but with traces here dominated by the NaV1.5 current). From top to bottom, it shows the command voltage (dashed lines) and the membrane voltage (solid lines), varying only the level of prediction (α P , blue), and varying only the level of series resistance compensation (α R , red), showing distinctive effects between the two. Note how the simulations reveal that the results are explained by a large loss of voltage clamp (top right panel of C), but the data can still be interpreted via the mathematical model.

Figure 5. Correction of fast sodium current experiments using the computational voltage‐clamp model. A) A schematic of the experimental setup and B) the experimental conditions for the ruptured patch experiments with HEK cells over‐expressing NaV1.5. C) i: Experimental recordings (solid lines) of the current–voltage (I–V) relationships of fast sodium current, measured with different levels of series resistance and prediction compensation (α R = α P = α), with estimated R s = 5.7 MΩ and C m = 14.1 pF (n = 3, repeats are shown in Supporting Information). ii: Simulated (dashed lines) I–V relationships. iii, iv: Membrane voltage and measured and simulated current during the step to −30 mV (iii, indicated by the vertical dotted line in panels i and ii) and −40 mV (iv, indicated by the vertical dashed line in i and ii). The figure shows the effect of increasing compensation levels simultaneously (α R = α P ). Experimental recordings are shown with solid colored lines, simulated effects shown in dashed colored lines, and ideal simulated fast sodium current shown with black dotted lines. Note how the strong deviation of the voltage clamp from the ideal V cmd (shown in (C) iii & iv) is only…

Figure 6. Consequences of averaging fast sodium current I–V curves of multiple runs of experiments demonstrated using simulated experiments. A) Comparing the average simulated I–V curve (blue with error bars showing SEM; averaged from transparent gray lines) to the artifact‐free physiological model I–V curve (red), neither the peak current, the peak voltage, nor the gradient of the curve of the average I–V matches the physiological I–V curve. Left to right shows different number of repeats, n = 5, 25, and 75, respectively. B) A simulated example of how experimental artifacts may lead to mischaracterization of mutants or drug effects. Left: The true underlying physiological I–V curves — from simulations with no artifacts — of the mutant or the drug (orange) compared to the WT or control (blue), where only current conductance was reduced by one‐third. Right: The observed I–V curves of the two conditions under one of the most stringent experimental conditions (only samples of R s < 4 MΩ were allowed). The solid lines are the mean of the individual I–V curves (n = 15) shown in transparent lines, with error bars showing the SEM. Vertical dashed lines show the voltage at which I–V curves peak,…

Figure 7. Consequences of averaging fast sodium current I–V curves of multiple runs of experiments in cell level action potential and cable simulations. A) Fitting results (dashed lines) to the average I–V curves (solid lines, error bars showing SEM with n = 50) simulated with different R s conditions; blue: 0.5 < R s < 2 MΩ, orange: 2 < R s < 5 MΩ, and red: 5 < R s < 10 MΩ, assuming measurements are done with cardiomyocytes with C m between 50 pF and 150 pF. The results show how the peak current and the peak voltage were shifted away from the physiological I–V curve (green) as R s increases, but in most literature data, R s values were between the blue and the orange cases; even the best scenario (blue) would result in a shift of the peak I–V by −13 mV and a reduction of peak current by 30 %. B) The consequences such imperfect characterizations of the fast sodium current in an action potential model, shown with a magnification of the upstroke where the sodium current took place. C) The impacts of artifact in determining the maximum upstroke velocity (dV m/dt)max, where even the best scenario (blue) was reduced by one‐third. D) Cable simulations for the action potential models in (B),…

Figure 8. The voltage‐clamp model can qualitatively capture the delayed current of fast sodium current, but this is sensitive to the details of the gating kinetics of the ionic current model. A) Experimental recordings of fast sodium current activation at different levels of compensation with NaV1.5‐expressing HEK cells and the ruptured patch technique at , where estimated R s = 4.3 MΩ and C m = 10.7 pF. It shows that near the threshold voltage of current activation (≈−30 to −40 mV), there are delays in the peak time of the current as indicated by red arrows. Inset, the voltage protocol, with holding potential at −100 mV. B) An examination of the −40 mV test step. From left to right are experimental data (true membrane voltage is unknown) and voltage‐clamp model simulations with Gray and Franz[ 24 ] and Iyer et al.[ 22 ] fast sodium models, respectively, with different levels of compensation (αR = αP = α). Note the good qualitative agreement between the compensation levels that cause large loss of voltage clamp and delayed sodium activation in the Gray and Franz[ 24 ] model and experimental recordings, but poor correspondence with the Iyer et al.[ 22 ] model.