Resolving artefacts in voltage-clamp experiments with computational modelling: an application to fast sodium current recordings

Cellular electrophysiology is the foundation of many fields, from basic science in neurology, cardiology, oncology to safety critical applications for drug safety testing, clinical phenotyping, etc. Patch-clamp voltage clamp is the gold standard technique for studying cellular electrophysiology. Yet, the quality of these experiments is not always transparent, which may lead to erroneous conclusions for studies and applications. Here, we have developed a new computational approach that allows us to explain and predict the experimental artefacts in voltage-clamp experiments. The computational model captures the experimental procedure and its inadequacies, including: voltage offset, series resistance, membrane capacitance and (imperfect) amplifier compensations, such as series resistance compensation and supercharging. The computational model was validated through a series of electrical model cell experiments. Using this computational approach, the artefacts in voltage-clamp experiments of cardiac fast sodium current, one of the most challenging currents to voltage clamp, were able to be resolved and explained through coupling the observed current and the simulated membrane voltage, including some typically observed shifts and delays in the recorded currents. We further demonstrated that the typical way of averaging data for current-voltage relationships would lead to biases in the peak current and shifts in the peak voltage, and such biases can be in the same order of magnitude as those differences reported for disease-causing mutations. Therefore, the presented new computational pipeline will provide a new standard of assessing the voltage-clamp experiments and interpreting the experimental data, which may be able to rectify and provide a better understanding of ion channel mutations and other related applications.

The derivation of the equations governing a voltage-clamp experiment without any compensation follows exactly as Lei et al. (2020), which is not repeated here.These include the equations for the effects of membrane capacitance, series resistance, leak current (seal resistance), pipette capacitance, and amplifier delays.Below shows the derivation of the mathematical model of how modern patch amplifiers typically compensate for them (Axon Instruments Inc., 1999;HEKA Elektronik GmbH, 2018), following the derivation from (Lei, 2020).Firstly, the voltage offset is usually estimated and compensated prior to adding the cell to the system, either with an automated correction estimated using software control or by applying manually a voltage offset such that it gives zero current when clamped at zero voltage, so the compensation circuit is not shown in our patch clamp equivalent circuits (Neher, 1995;Sigworth et al., 1995).The major source of voltage offset may be the liquid junction potential, a potential difference of ∼ 2 − 12 mV which develops when the pipette-filling solution is different from the bath solution (Neher, 1992).The adjustment is usually done by adding the theoretically estimated liquid junction potential offset to V * off .We can write the error in the estimate of the overall voltage offset V † off as We then simply need to replace all instances of V off in the equations above with V † off to describe the effect of imperfect voltage offset compensation, and V † off is assumed to be O(10) mV.Secondly, to compensate the effect of the parasitic capacitance at the electrode, an additional current is injected at the electrode to compensate for the current drawn by the parasitic capacitance.By analysing the fast capacitance compensation part, we obtain the compensation current as C * p dV clamp dt where C * p is the amplifier's estimate of the parasitic capacitance C p .Then we have and This is usually known as 'C-Fast' compensation.Thirdly, we need to consider compensation for the cell membrane capacitance C m .Usually the effect of C m is reduced by a hardware 'C-Slow' compensation, using a similar circuit to the 'C-Fast' compensation discussed above (Sigworth et al., 1995;Sigworth, 1995a).However, since the value of C m can reach 100 pF in some cell types, and capacitor sizes can be limited, the 'C-Slow' compensation is sometimes performed as a post-processing step by the amplifier control software rather than using built-in amplifier hardware (Weerakoon et al., 2010).In either case, the full capacitance compensation can be written as where C * m is the amplifier (or user's) estimate of the membrane capacitance C m , and V est is given below.Finally, in voltage clamp, we want V m to approach V cmd as quickly as possible.However, there are two effects introduced by R s , the first one causes V m to deviate from V cmd and the second slows down V m 's approach to V cmd .The first effect is caused by (I ion + I leak ), which can be reduced through a series resistance compensation (Sigworth et al., 1995;Sigworth, 1995a;Weerakoon et al., 2009).By analysing the series resistance compensation part, instead of clamping to V cmd , it is set to V cmd + αR * s I out , where R * s is the machine estimation of the series resistance R s , and α is the requested proportion of series resistance compensation (a machine setting, typically 70-85 %).
The second effect is caused by the product of the series resistance R s and the membrane capacitance C m , i.e. the membrane assess time constant τ a , which can be reduced through a compensation termed "supercharging" (Sigworth, 1995b).We set the clamping voltage to have a large overshoot (hence the name "supercharging") proportional to αR * s C * m dV est /dt, where according to Sigworth (1995b, Figure 18).The effect of the overshooting is to charge the membrane capacitance quickly.Including all the compensations, V clamp becomes to counterbalance the two effects caused by the series resistance.Note that the supercharging correction is particularly important when measuring big, very fast currents such as I Na which has a time-to-peak within ∼5 ms, however this correction poses almost no issue when analysing smaller, slower currents, for example I Kr .

Supplementary Figures
Voltage (mV

Figure S7 :
Figure S7: Forward sensitivity analysis of the experimental artefact of fast sodium current using Paci et al. (2020) and hiPSC-CMs (cell 2).

Figure S8 :
Figure S8: Forward sensitivity analysis of the experimental artefact of fast sodium current using Paci et al. (2020) and hiPSC-CMs (cell 3).