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

Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

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

Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data.

Calcium Release Flux Underlying Ca2+ Sparks of Frog Skeletal Muscle

An algorithm for the calculation of Ca2+ release flux underlying Ca2+ sparks (Blatter, L.A., J. Hüser, and E. Ríos. 1997. Proc. Natl. Acad. Sci. USA. 94:4176–4181) was modified and applied to sparks obtained by confocal microscopy in single frog skeletal muscle fibers, which were voltage clamped in a two-Vaseline gap chamber or permeabilized and immersed in fluo-3–containing internal solution. The performance of the algorithm was characterized on sparks obtained by simulation of fluorescence due to release of Ca2+ from a spherical source, in a homogeneous three-dimensional space that contained components representing cytoplasmic molecules and Ca2+ removal processes. Total release current, as well as source diameter and noise level, was varied in the simulations. Derived release flux or current, calculated by volume integration of the derived flux density, estimated quite closely the current used in the simulation, while full width at half magnitude of the derived release flux was a good monitor of source size only at diameters >0.7 μm. On an average of 157 sparks of amplitude >2 U resting fluorescence, located automatically in a representative voltage clamp experiment, the algorithm reported a release current of 16.9 pA, coming from a source of 0.5 μm, with an open time of 6.3 ms. Fewer sparks were obtained in permeabilized fibers, so that the algorithm had to be applied to individual sparks or averages of few events, which degraded its performance in comparable tests. The average current reported for 19 large sparks obtained in permeabilized fibers was 14.4 pA. A minimum estimate, derived from the rate of change of dye-bound Ca2+ concentration, was 8 pA. Such a current would require simultaneous opening of between 8 and 60 release channels with unitary Ca2+ currents of the level recorded in bilayer experiments. Real sparks differ from simulated ones mainly in having greater width. Correspondingly, the algorithm reported greater spatial extent of the source for real sparks. This may again indicate a multichannel origin of sparks, or could reflect limitations in spatial resolution.