Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments

Figure 1.. Schematics of the voltage-clamp experiment: (a) idealized and (b) more realistic. (a) Only the current of interest (red) is modelled. The membrane voltage, Vm (red) is assumed to be the same as the command voltage, Vcmd (green) set by the amplifier, and the observed current, Iout (green) is assumed to be equal to the ion channel current, Iion (red). (b) Here, not only the current of interest (red) is modelled, but the patch-clamp amplifier process (green) and all of the experimental artefacts (purple) are included in the model. The differences between Vm (red) and Vcmd (green), and between Iion (red) and Iout (green), are explicitly modelled in this framework. (Online version in colour.)

Figure 2.. A more realistic voltage-clamp experiment equivalent circuit. This includes undesired factors such as voltage offset (Voff), series resistance (Rs) between the pipette electrode and the cell, cell capacitance (Cm), pipette capacitance (Cp) and leakage current (Ileak), which can introduce artefacts to the recordings. The circuit also includes the components within a typical amplifier that are designed to compensate the artefacts. The blue (a) and orange (b) components are two idealized multiplying digital-to-analogue converters that control the amount of compensation. We assume that these, and the transimpedance amplifier and differential amplifier (green), are ideal electrical components. Please refer to table 2 for a description of the symbols. (Online version in colour.)

Figure 3.. Circuit diagrams for electrical model cell experiments. (a) A circuit set-up where a model cell is connected to both a voltage-clamp amplifier and a current-clamp amplifier. The voltage-clamp imposes a command voltage, Vcmd, on the model cell and measures the current, Iout, while the current-clamp simultaneously measures its ‘membrane voltage’, Vm. (b) An equivalent circuit of the Type I Model Cell, which is identical to the commercial ‘black box’ model cells (HEKA TESC) under the ‘whole-cell’ mode. (c) An equivalent circuit for the Type II Model Cell. This model cell is designed to exhibit dynamics when stepping to different voltages, with a time constant similar to ionic currents. The circuits were built with discrete electrical components, with Cp = 4.7 pF, Rs = 30 MΩ, Cm = 22 pF, Rm = 500 MΩ, Ck = 1000 pF and Rk = 100 MΩ. (Online version in colour.)

Figure 4.. Model simulations (dashed lines) using the amplifier settings compared against the simultaneous voltage clamp-current clamp measurements of the model cells (solid lines). Measurements are shown without compensation using (a) Type I Model Cell and (b) Type II Model Cell; and measurements with automatic amplifier compensation for Voff, Cp, Cm and Rs with α = 80% using (c) Type I Model Cell and (d) Type II Model Cell. All command voltages were set to be the staircase voltage protocol [14] (top panel); here only the last 3 s of the measurement is shown, the whole trace is shown in the electronic supplementary material, figure S4. In the top panel of each subfigure, the grey lines represent the command voltage Vcmd, and the orange/red lines represent the membrane voltage Vm; the bottom panel shows the current readout via the voltage-clamp, Iout. (Online version in colour.)

Figure 5.. Inferred model simulations and predictions (dashed lines) compared with experimental data (solid lines) from a Type II Model Cell. (a) Model calibration with a staircase protocol (grey lines in the top panel), where the model was fitted to only the current recording (blue, solid line in the lower panel). The fitted model was able to predict the membrane voltage, Vm (orange, solid line) measured using current-clamp. (b) Further model validation using an independent voltage-clamp protocol, a series of action potentials (grey lines in the top panel). Again, predictions from the model fitted to the staircase protocol above (dashed lines) are excellent for both the current and the membrane voltage. (Online version in colour.)

Figure 6.. A schematic overview of the two hypotheses we explore. Hypothesis 1 assumes the collected data represent a perfect, idealized voltage-clamp experiment where any experimental artefacts have been perfectly compensated by the amplifier and leak subtraction, so all the observed variability is rooted in biological variability (varying conductance and model kinetics in every cell), we term these ‘independent kinetics models’. Hypothesis 2 assumes that the observed variability is due to differences in the voltage-clamp experimental artefacts, and that all of the cells share identical ion channel kinetics (although the maximum conductance is allowed to vary across cells), we term these ‘identical kinetics models’. (Online version in colour.)

Figure 7.. The relative root mean square error (RRMSE) histograms for six protocols, comparing the independent kinetics models from Lei et al. [14] to the identical kinetics models with voltage-clamp artefact. Each histogram represents the same 124 cells with a different protocol and RRMSE each time. Red markers indicate the best (*), median (‡) and 90th percentile (#) RRMSE values for the independent kinetics model; green markers are the same cell prediction from the identical kinetics models. The median, 10th percentile and 90th percentile of the RRMSE values are shown in the electronic supplementary material, table S3. For each protocol, the raw traces for the identical kinetics model (green), the independent kinetics model (red) and data (blue) are shown, with the voltage-clamp above. Note that the currents are shown on different scales for each cell, to reveal the details of the traces. The same analysis applied to the remaining three protocols is shown in the electronic supplementary material, figure S7. Quantitatively, the two models show a similar RRMSE distribution for each protocol, with a slightly larger error on average in the fit for the identical kinetics (a), but a slightly…

Figure 8.. The inferred voltage-clamp artefact parameters across experimental wells. Each of the parameters exhibits a Gaussian-like distribution under this choice of transformation. The artefact parameter values are within reasonable ranges: Voff†∼±5 mV and gleak†≪gKr. (Online version in colour.)