Abstract
The patchclamp technique and more recently the high throughput patchclamp technique have contributed to major advances in the characterization of ion channels. However, the wholecell voltageclamp technique presents certain limits that need to be considered for robust data generation. One major caveat is that increasing current amplitude profoundly impacts the accuracy of the biophysical analyses of macroscopic ion currents under study. Using mathematical kinetic models of a cardiac voltagegated sodium channel and a cardiac voltagegated potassium channel, we demonstrated how large current amplitude and series resistance artefacts induce an undetected alteration in the actual membrane potential and affect the characterization of voltagedependent activation and inactivation processes. We also computed how dose–response curves are hindered by high current amplitudes. This is of high interest since stable cell lines frequently demonstrating high current amplitudes are used for safety pharmacology using the high throughput patchclamp technique. It is therefore critical to set experimental limits for current amplitude recordings to prevent inaccuracy in the characterization of channel properties or drug activity, such limits being different from one channel type to another. Based on the predictions generated by the kinetic models, we draw simple guidelines for good practice of wholecell voltageclamp recordings.
Introduction
The patchclamp technique has contributed to major advances in the characterization of ion channel biophysical properties and pharmacology, thanks to the versatility of the readouts: (i) unitary currents allowing the study of a single channel conductance, open probability and kinetics, and (ii) wholecell currents allowing characterization of a population of channels, their pharmacology, the macroscopic properties of the gates, but also the gating kinetics^{1,2}.
As for any technique, some practical limits have to be taken into account. As schematized in Fig. 1A,B, a major caveat in the wholecell configuration of the voltageclamp technique is due to the fact that the pipette tip in manual patchclamp, or the glass perforation in planar automated patchclamp, creates a series resistance (R_{S}) in the order of the MΩ. Consequently, according to the Ohm’s law, when a current flowing through the pipette is in the order of the nA, it leads to a voltage deviation of several mV at the pipette tip or the glass perforation. The actual voltage applied to the cell membrane (V_{m}) is therefore different than the voltage clamped by the amplifier and applied between the two electrodes (pipette and bath electrodes, V_{cmd}). This leads for example to an erroneous characterization of a channel voltagedependent activation process.
This caveat was described early on when the patchclamp technique was developed^{3}. However, with the development of automated patchclamp for the industry and academia, the technique that was formerly used exclusively by specialized electrophysiologists, has been popularized to scientists that are not always aware of the limits of the technique. In that respect, we now extensively witness new publications that report ionic currents in the range of several nA, that undoubtedly have led to incorrect voltage clamp and erroneous conclusions. Early on, this problem was partially solved by the development of amplifiers with the capacity to add a potential equivalent to the lost one (V_{S}), a function which is called R_{S} compensation^{4}. Examples of Na^{+} currents generated by Na_{V}1.5 voltagegated Na^{+} channels, recorded from a transfected COS7 cell, with and without R_{S} compensation, are shown in Fig. 1C–E. These recordings illustrate the kind of errors that can be induced in evaluating activation in the absence of R_{S} compensation. However, compensation rarely reaches 100% and some highthroughput systems have limited compensation abilities, to avoid overcompensation and consequent current oscillation that can lead to seal disruption.
Here, we used a mathematical model to study in detail the impact of various levels of R_{S} and current amplitude on the steadystate activation and dose–response curves of the cardiac voltagedependent Na^{+} current I_{Na}, as well as the steadystate activation curve of the cardiac voltagedependent K^{+} current I_{to}. We then predicted the impact of various levels of R_{S} on the Na^{+} current activation parameters and compared this prediction to wholecell voltageclamp recordings obtained in manual patchclamp analyses of cells transiently expressing Na_{v}1.5 channels. Finally, we looked at the impact of R_{S} in wholecell voltageclamp recordings of Na_{v}1.5 currents obtained in automated patchclamp using the Nanion SyncroPatch 384PE. This study highlights potential incorrect interpretations of the data and allows proposing simple guidelines for the study of voltagegated channels in patchclamp, which will help in the design of experiments and in the rationalization of data analyses to avoid misinterpretations.
The aim of this study was thus to use kinetic models of specific ion currents to generate current ‘recordings’ that take into account the voltage error made using the wholecell configuration of the patchclamp technique. We then used and compared these data and experimental observations to propose simple rules for good quality patchclamp recordings.
Results
In order to calculate the current (I) recorded at a given voltage, in a cell, we used Hodgkin–Huxley models of voltagegated channels^{5}. For this calculation, we need to determine the actual membrane potential (V_{m}) but we only know the potential applied between the pipette and reference electrodes (V_{cmd}), illustrated in Fig. 1A,B. The voltage error between V_{m} and V_{cmd} is the voltage generated at the pipette tip (V_{S}), which depends on the series resistance (R_{S}) and the current.
I is the resultant of the membrane resistance variations, due to channels opening or closing, R_{m}. For voltagegated channels, R_{m} varies with voltage, V_{m}, and time.
Since I is a function of V_{m}, through channels voltagedependence, and V_{m} depends on I (cf. the equation above), the value of I can only be obtained through an iterative calculation at each time step (see supplemental information with a limited number of equations, for further details).
We started to model the current conducted by cardiac voltagegated Na^{+} channels (Na_{v}1.5 for the vast majority) for a combination of series resistance (R_{S}) values and current amplitude ranges (depending on the amount of active channels in the membrane, Fig. 2A,B). First, when R_{S} is null (the ideal condition, which can almost be reached experimentally if R_{S} compensation is close to 100%), the voltage error is null and the shapes of the recordings are identical, independent of the current amplitude (in green in Fig. 2B). Consistent with the voltage error being proportional to both R_{S} and current amplitude values, we observed that combined increase in R_{S} and current amplitude leads to alteration in the current traces, due to a deviation of V_{m} from V_{cmd} (Fig. 2B). When R_{S} is equal to 2 MΩ (in orange), alterations in the shape of the currents are observed only when current amplitude reaches several nA (high expression of ion channels, bottom), with, for instance, time to peak at − 45 mV increasing from 0.9 ms (at R_{S} = 0 MΩ) to 1.15 ms (at R_{S} = 2 MΩ). When increasing R_{S} to 5 MΩ, alterations are minor in the medium range of current, but are emphasized when currents are large (middle and bottom, in red), with time to peak at 45 mV reaching 1.6 ms. As illustrated in Fig. 2B, when I and R_{S} are elevated, the voltage applied to the membrane, V_{m}, can reach − 14 mV, whereas the applied voltage command, V_{cmd}, is − 40 mV (bottom right, Vm inset). Thus, in these conditions, the voltage deviation represents 26 mV at the peak of the effect, which is not insignificant (Fig. 2C).
The impact of R_{S} on current amplitude is the highest for large amplitudes (Fig. 3A, 10nA range), e.g. at potentials between − 40 and − 20 mV. At such potentials, activation and inactivation time courses are clearly altered by high R_{S} values. Altogether, this leads to major artefactual modifications of the current–voltage and activation curves (Fig. 3B,C). Indeed, except when R_{S} is null, increasing the current amplitude range, from 1 to 10 nA, shifts the voltagedependence of activation (V_{0.5}) towards hyperpolarized potentials (Fig. 3C). For the largest currents, series resistance of 2 and 5 MΩ induces − 7 mV and − 11 mV shifts of V_{0.5}, respectively. The slope factor k is also drastically reduced by a factor of 1.5 and 1.8, respectively.
Besides impact on the characteristics of voltagedependent activation, R_{S} may also impact channel pharmacological characteristics. In order to model this impact, we established, for various values of R_{S}, the relationship between the theoretical values of the peak Na^{+} current, I_{peak} (with no voltage error) and the measured values of I_{peak}. We calculated this relationship at a potential that could be used to establish the dose–response curve, here 20 mV. First, when R_{S} is null, the voltage error is null and both values (theoretical and computed values) are the same. As R_{S} increases, the measured I_{Na} curve is inflected accordingly (Fig. 4A, middle and right).
We used this relationship to look at the impact of R_{S} on the apparent effects of a channel blocker—tetrodotoxin (TTX)—on the Na^{+} current. We started with published data on TTX^{6} to generate the theoretical (R_{S} = 0 MΩ) dose–response curve and current traces in the presence of various concentrations of TTX (Fig. 4B,C, green). Then we used the relationship between the theoretical and measured values of I_{peak} at R_{S} of 2 and 5 MΩ (established in Fig. 4A), to build the dose–response curves, for these R_{S} values (see “Methods” section for details). In the absence of TTX (Fig. 4B, left), current amplitude is high and voltageclamp is not efficient, thus there are major differences between theoretical (green) and measured (orange and red) amplitudes. When inhibitor concentration increases, remaining current amplitudes decrease and the voltageclamp improves. Hence, with higher TTX doses the theoretical and measured values become closer, independent of the R_{S} values (Fig. 4B, right). This leads to an artefactual shift of the resulting dose–response curve towards higher concentrations (Fig. 4C). For I_{peak} = − 27 nA, R_{S} of 2 and 5 MΩ induce an increase of IC_{50} by a factor of 1.7 and 1.8, respectively. For low I_{peak} (− 2.7 nA), these modifications are minimal.
We applied the same modeling strategy to study the impact of R_{S} on the ‘measurement’ of the voltagegated K^{+} current I_{to} , using a HodgkinHuxley model of this current^{5} (Fig. 5A). As for the Na^{+} current, we modeled the I_{to} current for a combination of values of series resistance and current amplitude. Again, when R_{S} is null, the voltage error is null and the shapes of the recordings are identical, independent of the current amplitude (in green in Fig. 5B). Consistent with voltage error being proportional to both R_{S} and current amplitude, we observed that combined increase in R_{S} and current amplitude leads to alteration in the recordings, due to a deviation of V_{m} from V_{cmd} (Fig. 5B). I_{to} current characteristics, nonetheless, are less sensitive to R_{S} and current amplitude than I_{Na}: when R_{S} is equal to 5 MΩ (in orange), alteration in the shape of the recordings is significant only when current amplitude is tenfold higher than Na^{+} currents (Fig. 5B, bottom center). However, a reduction in current amplitude is readily obtained for intermediate R_{S} and current amplitudes. When R_{S} reaches 15 MΩ and current amplitude is equal to several tens of nA, conditions routinely observed in automated patchclamp with stable cell lines^{7,8}, the model predicts a major modification of the activation curve and apparition of a delayed inactivation (Fig. 5B, bottom right). When R_{S} is not null, increasing peak current amplitude up to 100 nA leads to a major shift in voltagedependence of activation as follows: for a peak current of 100 nA, R_{S} of 5 and 15 MΩ induces − 9 mV and − 16 mV shifts of the halfactivation potential, respectively. The slope is also drastically increased by a factor of 1.8 and 2.4, respectively (Fig. 5C). Noteworthy, when Rs is 15 MΩ and amplitudes are in the order of several tens of nA, major voltage deviation occurs, decreasing the current amplitude by a factor of ten. This may falsely give the impression that the current is not high and thus that the introduced voltage error is negligible.
In order to test whether the model reproduces experimental data, we used a set of data of heterologouslyexpressed Na_{v}1.5 currents recorded in COS7 cells using manual voltageclamp (qualitatively validated or not, to include highly ‘artefacted’, erroneous data). When using transient transfection systems, recorded currents are very variable from cell to cell, with peak currents measured at − 20 mV ranging from 391 pA to 17.8 nA in the chosen cell set (52 cells). We used this variability to study the effect of current amplitude on the activation curve properties. First, in order for the model to be as close as possible to experimental data, we modified the previously published HodgkinHuxley model to match the properties of the Na_{v}1.5 current obtained in optimal experimental conditions (Fig. 6). We used as reference group, the cells presenting peak current amplitudes (measured at − 20 mV) in a range smaller than 1 nA (7 cells), and with R_{S} compensation allowing residual R_{S} of around 2 MΩ. The initial model (Fig. 3) suggests negligible alteration of V_{0.5} and k in these conditions. The model was then optimized by adjusting the HodgkinHuxley equations (Eqs. 9 and 10 in the “Methods” section) to obtain V_{0.5}, k and inactivation time constants that are similar to averaged values of the 7 reference cells (Fig. 6B,C).
We then split the 52 cells in six groups according to current amplitude range (the 7 reference cells, then four groups of 10 cells, and a last group of 5 cells with a peak I_{−20 mV} greater that 10 nA), and plotted, for each group, the mean V_{0.5} (Fig. 7A) and k values (Fig. 7B) as a function of mean current amplitude. We observed a decrease in both V_{0.5} and k when current range increases. These relationships were successfully fitted by the computer model when R_{S} was set to 2 MΩ, which is close to the experimental value, after compensation (R_{S} = 2.3 ± 0.2 MΩ). In these conditions, if we accept maximal inward peak current amplitudes up to 7 nA, the error in V_{0.5} is below 10 mV and k remains greater than 5 mV. Experimentally, current amplitudes larger than 7 nA should be prevented or discarded, to prevent larger errors in evaluating V_{0.5} and k. Nevertheless, the benefit of such a representation (Fig. 7) is obvious as a correlation can be drawn between current amplitude and V_{0.5} and k values, with a more reliable evaluation of these values at low current amplitude levels.
We then used a dataset of I_{Na} currents obtained from neonatal mouse ventricular cardiomyocytes, with values of current amplitudes that are frequently published, ranging from 1.8 to 10.3 nA, and using 80% series resistance compensation. We drew similar plots as in Fig. 7, of the experimental activation parameters, V_{0.5} and k, as a function of current amplitude in Fig. 8A,B, respectively, and we added the model of heterologouslyexpressed Na_{v}1.5 currents (in orange) generated above. The model does not fit exactly to the data, suggesting that I_{Na} properties are slightly different in cardiomyocytes and transfected COS7 cells. Interestingly, however, the exponential fits of the data follow the same trend, parallel to the COS7 model, suggesting the same effect of Rs on V_{0.5} and k. Similar to transfected COS7 cells, cardiomyocytes with currents greater than 7 nA display mean V_{0.5} ~ 5mV more negative, and mean k ~ 1mV smaller than cardiomyocytes with currents smaller than 7 nA (Fig. 8A,B), suggesting that using a 7 nA amplitude cutoff is appropriate. This comparison shows that differences in activation parameters may be blurred or exaggerated by inappropriate data pooling of cells with excessive current amplitude.
Finally, we used a set of data from HEK293 cells stably expressing the Na_{v}1.5 channels, obtained using the automated patchclamp setup Syncropatch 384PE (Fig. 9). Cells were grouped by intervals of 500 pA: 0–500 pA, 500–1000 pA, etc. The first experimental group has a mean inward current amplitude lower than the reference group of transfected COS7 cells (− 267 ± 67 pA, n = 7 vs − 608 ± 48 pA, n = 7, respectively). It should be noticed that in this amplitude range, activation parameters are more difficult to determine. This is reflected by the large s.e.m. values for mean V_{0.5} and k. We postulate that HEK293 endogenous currents may nonspecifically affect the properties of the recorded currents when they are in the 0–500 pA range. For the following groups with larger I_{Na} amplitudes, V_{0.5} seems to be stable. Hence, a V_{0.5} value around − 25 mV appears to be reliable. When current amplitudes are lower than 3.5 nA, the V_{0.5} change is less than 10 mV and k remains greater than 5 mV. Therefore, it is essential to perform experiments in conditions in which the inward current value is comprised between 500 pA and 3.5 nA when using such an automated patchclamp system, and to exclude data with higher peak current amplitudes. These limits are more stringent than for manual patchclamp as seen above (7 nA), but this is consistent with the limited compensation capabilities of some automated patchclamp systems demonstrating slow response time for R_{S} compensation to avoid overcompensation and consequent current oscillation that can lead to seal disruption.
Discussion
Even though effects of series resistance have been described very early^{3}, a lot of published measured currents are in the range of several nA, which often leads to incorrect voltage clamp. We developed a simple model, using published kinetic models of ion currents, to simulate and describe such a caveat. We used both an inward current generated by a voltagegated Na^{+} channel and an outward current generated by a voltagegated K^{+} channel, both of them characterized by fast activation kinetics. Using these models and experimental recordings, we observed that large series resistance may give erroneous activation curves (Figs. 1,2,3,5,7,8,9) and dose–response curves (Fig. 4).
A similar mathematical model, taking into account the R_{S} impact has been used to study the causes of variability of current recordings obtained from the voltagegated K^{+} channel K_{v}11.1^{9}. Here we used such a model to provide a guideline focusing on parameters that the manipulator can easily act on: current amplitude and R_{S.}
We observed that the activation parameters of cardiac voltagegated Na^{+} current I_{Na} are much more sensitive than those of the cardiac voltagegated K^{+} current I_{to}: a current amplitude range of 10 nA combined with a R_{S} of 5 MΩ shows almost no alteration of the activation curve of the voltagegated K^{+} channel (Fig. 5B, center and Fig. 5C, middle), whereas the same condition with the voltagegated Na^{+} channel, shows a major alteration of the activation curve (Fig. 2B, bottom right and Fig. 3C, right). The simplest interpretation of this observation may be associated with the fact that, for Na^{+} channels, the increase in Na^{+} entry induced by depolarization further depolarizes the membrane and creates instability. For K^{+} channels, the increase of K^{+} outflow induced by depolarization tends to repolarize the membrane and limits instability. However, in extreme cases, repolarization prevents the occurrence of inactivation, leading to delayed inactivation (Fig. 5B, bottom right).
For the voltagegated Na^{+} channel Na_{v}1.5, we concluded that it is essential to prevent recording inward current amplitudes greater than 7 nA when residual R_{S} is around 2 MΩ to get a reasonable estimate of the activation gate characteristics in the manual patchclamp technique (Fig. 7). When using an automated patch system, the limit is lowered to 3.5 nA (Fig. 9).
In order to test for activation changes, induced, for example, by drugs, mutations or posttranslational modifications that are associated with current amplitude changes, it is advisable to generate plots of V_{0.5} or K as a function of I_{peak} in both conditions to early detect artefacts due to excessive current amplitude. This a priori caution will allow adapting experimental conditions to record currents below 7 nA.
To summarize, we suggest simple guidelines for the voltagegated Na^{+} channel Na_{v}1.5:

1.
Always compensate R_{S} as much as possible,

2.
R_{S} values around 2 MΩ after compensation allow recordings with a maximal inward current of 7 nA in manual patchclamp,

3.
Using Nanion Syncropatch 384PE, recordings with a maximal inward current of 3.5 nA can be used.
These guidelines may be extended to other Na_{V} isoforms contingent of generation of plots as in Figs. 7 and 9.
The guidelines are less stringent to record reliable K^{+} outward currents. However, one should always compensate R_{S} as much as possible. From Fig. 5B,C, for R_{S} values up to 5 MΩ after compensation, recordings with a maximal current of 10 nA will be highly reliable. With Nanion Syncropatch384PE, R_{S} values up to 15 MΩ after compensation allow recordings with a maximal current of 10 nA, but inhibitors or various transient transfection conditions should be used to make sure that the measured current amplitude is not saturating due to voltage deviation (Fig. 5B, bottom right).
For any current generated by voltagegated channels, it is judicious to draw activation slope vs. amplitude plots and activation V_{0.5} vs. amplitude plots in a preliminary study to determine adapted conditions, a prerequisite to obtain reliable data and results.
For any other ionchannel type—ligandgated, lipidgated, regulated by second messengers or else—low membrane resistance i.e. high expression of active ion channels associated with high R_{S} values will also interfere with adequate voltage command and current measurements.
Several simple adaptations can be made to reach optimal experimental conditions:

1.
R_{S} values are much lower when pipettes with low resistance (‘large’ pipettes) are used. When using amplifiers combining R_{S} and C_{m} compensation, suppression of pipette capacitance currents is of high interest since uncompensated pipette capacitance has a detrimental effect on the stability of the series resistance correction circuitry. This can be achieved by the use of borosilicate glass pipettes and wax or Sylgard coating^{10}. When using Nanion Syncropatch384PE or other automated patchclamp systems, low resistance chips are preferred.

2.
When overexpressed channels are studied, transfection has to be adapted to produce a reasonable amount of channels to generate the desired current amplitude, or, when cell lines stably expressing the channel of interest are used, the clones generating the desired current amplitude range are preferably chosen. Any current, including native currents, can also be reduced when pipette and extracellular concentrations of the carried ion are reduced. In addition, the concentration gradient can be changed to limit the electrochemical gradient. Also inhibitors, such as TTX for Na_{V} channels, may be used at low concentration to reduce the current amplitude, as long as the inhibitor does not modify the biophysics of the WT and/or mutant channels, and it does not interfere with the action of other pharmacological compounds.
Therefore, any patchclamp experiment needs to be carefully designed to reach appropriate conditions, guaranteeing rigorous analysis of the current. Finally, in native cells (excitable or nonexcitable), the current passing through an ion channel type is always recorded in combination with other currents (leak current, at the minimum), and is generally isolated pharmacologically (e.g., TTX) or through other means, all involving subtraction of currents (e.g., P/n). The voltage error caused by R_{s} also depends on these other currents. Thus, it would be interesting to also model this situation to have a more integrated view of R_{s}induced incorrect voltage clamp.
Methods
Computer models
Application to wholecell ion currents
I_{Na} and I_{to} currents were modeled using a Hodgkin–Huxley model of channel gating based on previously published models (O'Hara et al., 2011).
For cardiac I_{Na}, we did not include the slow component of h, which only represents 1% of h inactivation (O'Hara et al., 2011).
The timedependent gate values (m, h and j), were computed at every time step^{11} with an “adaptive timestep” method as:
with y being the timedependent gate value, and tstep, an adaptive time step. tstep was initialized to 0.1 µs, doubled when all the relative variations of m, h, or j were smaller than 0.5 × 10^{–5} and was halved when one of the relative variations of m, h, and j was greater than 10^{–5}. When this limit was reached, the computation went one tstep backward and repeated again with the reduced tstep value to prevent divergence.
To validate this method, we also used an "LSODE" method (cf. example in supplemental Fig. 1). m, h and j were solved as:
using R software (v3.6.3, https://www.rproject.org) and the LSODE^{12} method from deSolve package (v1.28).
In the most critical condition: with a large Na^{+} current (Gmax = 6 µS) and large series resistance (Rs = 5 MΩ), both methods gave identical Na^{+} currents (cf. supplemental Fig. 1). Therefore, the “adaptive timestep” method was used to compute m, h and j values.
I_{Na} was calculated as follows:
with \({E}_{Na}= \frac{R T}{z F}\mathrm{log}\left(\frac{\left[Na^{+}\right]out}{\left[Na^{+}\right]int}\right)\), [Na^{+}]out = 145 mM and [Na^{+}]in = 10 mM.
To model overexpressed Na_{v}1.5 currents, we adjusted some parameters, shown in bold, to fit the characteristics of the current when peak amplitude is less than 1 nA (cf results section and Fig. 6).
To model cardiac I_{to}, we did not include the CaMK dependent component, since at low Ca^{2+} pipette concentration (< 100 nM), this component is negligible (2%) (O'Hara et al., 2011).
a, \({i}_{fast}\) and \({i}_{slow}\) were computed at every time step^{11} using the “adaptive timestep” method (see above).
I_{to} was calculated as follows:
with \({E}_{K}= \frac{R T}{z F}\mathrm{log}\left(\frac{\left[K^{+}\right]out}{\left[K^{+}\right]int}\right)\), [K^{+}]out = 5 mM and [K^{+}]in = 145 mM.
For details on the kinetic models, please see^{5}.
Membrane potential was computed as follows at each time step:
We hypothesized that the amplifier response time was not limiting. Membrane capacitance used was 20 pF and considered electronically compensated. Errors due to poor space clamp were considered negligible in small cells like COS7 cells but it is worth mentioning that they should potentially be taken into account in bigger cells such as cardiomyocytes and in cells with complex morphologies such as neurons. Noteworthy, in some situations, specific protocols can reduce these artefacts linked to poor spaceclamp^{13}. Beyond technical issues due to the patch pipette, additional resistances, due to the narrow Ttubular lumen, are also not negligible in cardiac cell Ttubules and lead to delay in Ttubular membrane depolarization^{14}.
Application to pharmacological investigations
Before investigating the effects of TTX, we computed the incidence of peak current amplitude at − 20 mV on its measured value with various R_{s} values (Fig. 4A). TTX effects were modeled by first constructing the theoretical dose–response curve with R_{s} = 0 MΩ. Knowing the experimental IC_{50} and Hill coefficient^{6}, we calculated the TTX concentrations necessary to get 0.75 of the current (G_{Na} = 1.5 µS instead of G_{Na} = 2 µS in the absence of TTX), 0.5 (G_{Na} = 1 µS instead of G_{Na} = 2 µS in the absence of TTX), 0.3, … and 10^{–3} of the current. Then, for a given R_{s} (2 or 5 MΩ), we used the relationship between theoretical and observed measured values of peak current (Fig. 4A) to deduce the corresponding measured I_{peak} value of the residual current after TTX application. For instance, when R_{s} = 5 MΩ, for a theoretical current of − 27 nA, the measured current is about − 13 nA (see in Fig. 4A red chart). The effects of a 50% reduction of the theoretical value of − 27 nA (corresponding to the effect of 2.3 µM TTX, the IC_{50} value) results in a measured remaining current of − 8.3 nA when R_{s} = 5 MΩ (see in Fig. 4A red chart). Therefore, the apparent effect of 2.3 µM TTX on a measured current of − 13 nA is modeled by a − 8.3/− 13 ≈ 0.64 factor on G_{Na} in Eq. (8). Similar computations have been conducted for different control current amplitudes, Rs values, and TTX “doses”, and the corresponding dose–response curves have been built.
Cell culture and transfection
The African green monkey kidneyderived cell line, COS7, was obtained from the American Type Culture Collection (CRL1651) and cultured in Dulbecco’s modified Eagle’s medium (GIBCO) supplemented with 10% fetal calf serum and antibiotics (100 IU/mL penicillin and 100 µg/mL streptomycin) at 5% CO_{2} and 95% air, maintained at 37 °C in a humidified incubator. Cells were transfected in 35mm Petri dishes when the culture reached 50–60% confluence, with DNA (2 µg total DNA) complexed with jetPEI (Polyplus transfection) according to the standard protocol recommended by the manufacturer. COS7 cells were cotransfected with 200 ng of pCISCN5A (NM_000335.4), 200 ng of pRCSCN1B (NM_001037) (kind gifts of AL George, Northwestern University, Feinberg School of Medicine) and 1.6 µg pEGFPN3 plasmid (Clontech). Cells were replated onto 35mm Petri dishes the day after transfection for patchclamp experiments. HEK293 cells stably expressing hNa_{v}1.5 were cultured in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% fetal calf serum, 1 mM pyruvic acid, 2 mM glutamine, 400 µg/ml of G418 (Sigma), 100 U/mL penicillin and 100 μg/mL streptomycin (Gibco, Grand Island, NY) at 5% CO_{2} and 95% air, maintained at 37 °C in a humidified incubator.
Statement on the use of mice
All investigations conformed to directive 2010/63/EU of the European Parliament, to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 8523, revised 1985) and to local institutional guidelines.
Neonatal mouse ventricular cardiomyocyte isolation and culture
Single cardiomyocytes were isolated from the ventricles of mouse neonates aged from postnatal day 0 to 3 by enzymatic and mechanical dissociation in a semiautomated procedure by using the Neonatal Heart Dissociation Kit and the GentleMACS™ Dissociator (Miltenyi Biotec). Briefly, hearts were harvested, and the ventricles were separated from the atria, and digested in the GentleMACS™ Dissociator. After termination of the program, the digestion was stopped by adding medium containing Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% horse serum, 5% fetal bovine serum and 100 U/ml penicillin and 100 μg/ml streptomycin. The cell suspension was filtered to remove undissociated tissue fragments, and centrifugated. The cell pellet was resuspended in culture medium, and the cells were plated in 60 mmdiameter Petri dishes at 37 °C for 1.5 h. The nonplated myocytes were then resuspended, plated on laminincoated dishes at a density of 50 000 cells per plate, and incubated in 37 °C, 5% CO_{2}: 95% air incubator. After 24 hplating, medium was replaced by DMEM supplemented with 1% fetal bovine serum and 100 U/mL penicillin and 100 μg/mL streptomycin, and electrophysiological experiments were performed 48 h following isolation.
Manual electrophysiology on transfected COS7 cells
One or 2 days after splitting, COS7 cells were mounted on the stage of an inverted microscope and constantly perfused by a Tyrode solution maintained at 22.0 ± 2.0 °C at a rate of 1–3 mL/min; HEPESbuffered Tyrode solution contained (in mmol/L): NaCl 145, KCl 4, MgCl_{2} 1, CaCl_{2} 1, HEPES 5, glucose 5, pH adjusted to 7.4 with NaOH. During Na^{+} current recording, the studied cell was locally superfused^{15} with a extracellular solution used to prevent endogenous K^{+} currents, containing (in mmol/L): NaCl, 145; CsCl, 4; CaCl_{2}, 1; MgCl_{2}, 1; HEPES, 5; glucose, 5; pH adjusted to 7.4 with NaOH. Patch pipettes (tip resistance: 0.8 to 1.3 MΩ) were pulled from soda lime glass capillaries (KimbleChase) and coated with dental wax to decrease pipette capacitive currents. The pipette was filled with Na^{+} intracellular medium containing (in mmol/L): CsCl, 80; gluconic acid, 45; NaCl, 10; MgCl_{2}, 1; CaCl_{2}, 2.5; EGTA, 5; HEPES, 10; pH adjusted to 7.2 with CsOH. Stimulation and data recording were performed with pClamp 10, an A/D converter (Digidata 1440A) and an Axopatch 200B (all Molecular Devices) or an Alembic amplifier (Alembic Instruments). Currents were acquired in the wholecell configuration, filtered at 10 kHz and recorded at a sampling rate of 33 kHz. Before series resistance compensation, a series of 50 25ms steps were applied from − 70 mV to − 80 mV to subsequently calculate offline C_{m} and R_{S} values from the recorded current. To generate the Na_{v}1.5 activation curve, the membrane was depolarized from a holding potential of − 100 mV to values between − 80 mV and + 50 mV (+ 5mV increment) for 50 ms, every 2 s. Activation curves were fitted by a Boltzmann equation: G = G_{max}/(1 + exp (− (V_{m} − V_{0.5})/k)), in which G is the conductance, V_{0.5} is the membrane potential of halfactivation and k is the slope factor. For Fig. 7, cells were grouped by 10, except the first group which includes the cells with a absolute peak I_{− 20 mV} of less that 1000 pA (n = 7) and the last group which includes the cells with a peak I_{− 20 mV} greater that 10 nA (n = 5).
Electrophysiology on cardiomyocytes
Wholecell Na_{v} currents were recorded at room temperature 48 h after cell isolation with pClamp 10, an A/D converter (Digidata 1440A) and an Axopatch 200B amplifier (all Molecular Devices). Current signals were filtered at 10 kHz prior to digitization at 50 kHz and storage. Patchclamp pipettes were fabricated from borosilicate glass (OD: 1.5 mm, ID: 0.86 mm, Sutter Instrument, Novato, CA) using a P97 micropipette puller (Sutter Instrument), coated with wax, and firepolished to a resistance between 0.8 and 1.5 MΩ when filled with internal solution. The internal solution contained (in mM): NaCl 5, CsF 115, CsCl 20, HEPES 10, EGTA 10 (pH 7.35 with CsOH, ~ 300 mosM). The external solution contained (in mM): NaCl 20, CsCl 103, TEACl (tetraethylammonium chloride) 25, HEPES 10, glucose 5, CaCl_{2} 1, MgCl_{2} 2 (pH 7.4 with HCl, ~ 300 mosM). All chemicals were purchased from Sigma. After establishing the wholecell configuration, stabilization of voltagedependence of activation and inactivation properties was allowed during 10 min. Before series resistance compensation, series of 25ms steps were applied from − 70 mV to − 80 mV and to − 60 mV to subsequently offline calculate C_{m} and R_{S} values from the recorded currents. After compensation of series resistance (80%), the membrane was held at a HP of − 120 mV, and the voltageclamp protocol was carried out as follows. To determine peak Na^{+} current–voltage relationships, currents were elicited by 50ms depolarizing pulses to potentials ranging from − 80 to + 40 mV (presented at 5s intervals in 5mV increments) from a HP of − 120 mV. Peak current amplitudes were defined as the maximal currents evoked at each voltage, and were subsequently leakcorrected. To analyze voltagedependence of activation properties, conductances (G) were calculated, and conductancevoltage relationships were fitted with a Boltzmann equation. Data were compiled and analyzed using ClampFit 10 (Axon Instruments), Microsoft Excel, and Prism (GraphPad Software, San Diego, CA).
Highthroughput electrophysiology
Automated patchclamp recordings were performed using the SyncroPatch 384PE from Nanion (München, Germany). Singlehole, 384well recording chips with medium resistance (4.77 ± 0.01 MΩ, n = 384) were used for recordings of HEK293 cells stably expressing human Na_{v}1.5 channel (300 000 cells/mL) in wholecell configuration. Pulse generation and data collection were performed with the PatchControl384 v1.5.2 software (Nanion) and the Biomek v1.0 interface (Beckman Coulter). Wholecell recordings were conducted according to the recommended procedures of Nanion. Cells were stored in a cell hotel reservoir at 10 °C with shaking speed at 60 RPM. After initiating the experiment, cell catching, sealing, wholecell formation, buffer exchanges, recording, and data acquisition were all performed sequentially and automatically. The intracellular solution contained (in mM): 10 CsCl, 110 CsF, 10 NaCl, 10 EGTA and 10 HEPES (pH 7.2, osmolarity 280 mOsm), and the extracellular solution contained (in mM): 60 NaCl, 4 KCl, 100 NMDG, 2 CaCl_{2}, 1 MgCl_{2}, 5 glucose and 10 HEPES (pH 7.4, osmolarity 298 mOsm). Wholecell experiments were performed at a holding potential of − 100 mV at room temperature (18–22 °C). Currents were sampled at 20 kHz. Activation curves were built by 50 mslasting depolarization from − 80 mV to 70 mV (+ 5 mV increment), every 5 s. Activation curves were fitted by Boltzmann equation. Stringent criteria were used to include individual cell recordings for data analysis (seal resistance > 0.5 GΩ and estimated series resistance < 10 MΩ).
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Acknowledgements
We are indebted to Dr. Massimo Mantegazza for providing the stable cell line expressing human Na_{v}1.5. The authors wish to thank Drs Massimo Mantegazza and Flavien Charpentier for their critical reading of the manuscript. M. De Waard thanks the Agence Nationale de la Recherche for its financial support to the laboratory of excellence “Ion Channels, Science and Therapeutics” (Grant no. ANR11LABX0015). This work was supported by a grant from the Fédération Française de Cardiologie and by the Fondation Leducq in the frame of its program of ERPT equipment support (purchase of an automated patchclamp system), by a grant “New Team” of the Région Pays de la Loire to M. De Waard, and by a European FEDER grant in support of the automated patchclamp system of Nanion. The salary of S. Nicolas is supported by the Fondation Leducq, while the fellowship of J. Montnach is provided by a National Research Agency Grant to M. De Waard entitled OptChemCom (Grant no. ANR18CE19002401). C. Marionneau thanks the Agence Nationale de la Recherche [ANR15CE14000601 and ANR16CE92001301]. M. Lorenzini was supported by a Groupe de Réflexion sur la Recherche CardiovasculaireSociété Française de Cardiologie predoctoral fellowship [SFC/GRRC2018]. We thank Marja Steenman for proofreading of the manuscript.
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J.M. and S.N. carried out automated patchclamp experiments on Na_{v}1.5, under the supervision of M.D.W. M.L. and A.L. carried out the patchclamp experiments on mouse cardiomyocytes, under the supervision of C.M. I.S. and E.M. carried out the manual patchclamp experiments on transfected COS7 cells, under the supervision of I.B. J.M. carried out the model computation in R.G.L. carried out the model computation in C++ and wrote the manuscript.
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Montnach, J., Lorenzini, M., Lesage, A. et al. Computer modeling of wholecell voltageclamp analyses to delineate guidelines for good practice of manual and automated patchclamp. Sci Rep 11, 3282 (2021). https://doi.org/10.1038/s41598021820778
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