Fluorescence Imaging of Cell Membrane Potential: From Relative Changes to Absolute Values

Concentration dependence of optical signals can be eliminated by a synchronous recording of two or more separable optical signals. Then one can derive a function of these signals that allows to cancel out concentration-dependence but preserve voltage-dependence at the same time. The most simple such function is the ratio of two signals possessing different voltage dependence (ratio-based approaches). A possible alternative is to record a voltage-dependent property that does not depend on sensors concentration, such as excited state lifetime.

In addition to concentration changes, detected optical signal can be altered by the changes in the local environment of sensors that occur during the experiment. These factors include the alterations in ionic strength, pH, viscosity, temperature, lipid composition [28,40,41,108,109], as well as the movement of macromolecules that bind potentiometric organic dyes [110,111,112]. Protocols that eliminate optical signal changes caused by environmental factors can be developed for some systems, but require detailed knowledge of how these factors alter the detected signal and how the potentiometric sensor works.

Finally, a source of error during membrane potential imaging experiments comes from instability in illumination intensity, the sensitivity of the detector, and other possible equipment-related measurement errors. This factor can be scaled down with the appropriate software and will not be considered here since it was described in a recent comprehensive review [40].

Ratio of two signals recorded from a single emission band. The voltage-induced shift of the emission band of electrochromic dyes results in the opposite changes of emission intensities corresponding to wavelengths at the left and right wings of the band (Figure 2a). The ratio of fluorescence intensities at two wavelengths from the left and right wings of the emission band does not depend on sensor concentration and remains voltage-dependent. The two emission wavelengths are selected to obtain the ratio with linear voltage dependence and the highest possible voltage sensitivity. The strategy allowed eliminating the effect of sensors concentration changes caused by the motion of arterioles during vascular responses [107] and the motion of epicardium during cell membrane potential imaging in isolated hearts [31]. However, the detected ratios showed baseline drifts caused by different photobleaching rates of signals from the low and high wavelength wings of emission band [31]. An alternative approach that can be used with electrochromic dyes applies the excitation of sensors at two wavelengths and the detection of total fluorescence. Voltage-induced shift of absorption band results in the opposite changes of absorption intensities at the left and right wings of the band and, therefore, opposite changes of total fluorescence excited at these two wavelengths [109,113].

Ratio of two signals recorded from two fluorophores which are parts of a single sensor. Two signals can be obtained from two fluorophores of a single sensor. This approach can be applied if two requirements are fulfilled: the emission bands of fluorophores should not overlap and they should possess different voltage-dependence. Besides, the method can provide robust results when the bleaching rates of two fluorophores are identical and environmental factors have the same effect on both fluorophores. The approach is applicable for FRET-based sensors with both donor and acceptor fluorescent. For sensors of this type, the voltage sensitivity of ratio is a sum of voltage sensitivities of donor and acceptor fluorescence. The method was applied to cancel out motion-induced changes in the detected optical signal and investigate the electrical activity of several eukaryotic cells, including astrocytoma cells and beating cardiac myocytes [51,52].

The approach was also applied for sensors constructed as the fusion of two fluorescent proteins (green and red) to the voltage-sensitive domain (Figure 2b). Voltage-induced reorganization of the domain was passed to both proteins via peptide linkers, altering the emission intensity of the green fluorescent protein, but keeping the emission intensity of the red fluorescent protein intact [106]. The ratio of green and red signals allowed the elimination of the concentration-related signal changes caused by the contraction of cardiomyocytes and the motion of cells during cell-cycle studies [28]. For HEK293 cells, the method allowed monitoring changes in resting membrane voltage caused by ectopic expression of potassium channels on the timescale of several days. However, a large cell-to-cell variation of detected signal prevented the measurement of cell membrane potential changes with single-cell resolution [106].

Ratio of two signals from different voltage-dependent distributions of sensors. Microbial rhodopsin Arch D95H demonstrates linear fluorescence response to cell membrane potential changes attributed to the voltage-dependent equilibrium between the fluorescent (F) and non-fluorescent states of the protein [114]. The fluorescence intensity of state F was supposed to be independent of the voltage, therefore, fluorescence response to membrane potential change was attributed only to the change in the concentration of state F. This concentration was estimated using the following protocol [114]. The whole population of proteins was converted into state F with blue light illumination and the corresponding fluorescence intensity Fall was measured (Figure 2c). Afterward, orange light was used to establish an equilibrium with voltage-dependent concentration of state F, and the emission intensity Feq was measured. The relative decrease of fluorescence intensity upon equilibrium establishment was shown to be a robust concentration-corrected metric for membrane potential measurements:

The method was tested on HEK cells and allowed deriving the value of resting cell membrane potential with a 10 mV resolution [114].

A possible approach to avoid signal components related to the alteration of sensor concentration is to measure excited state lifetime rather than fluorescence intensity. Excited state lifetime was shown to be independent of fluorophore bleaching and illumination conditions, and largely independent of fluorophores concentration [43]. Environmental factors, including voltage, may affect excited state lifetime by changing the rate constant of non-radiative decay (knr), and for a few sensors knr and, therefore, τexc were shown to possess linear voltage-dependence:

It should be noted that due to the complex nature of non-radiative decay, voltage-dependence of fluorescence intensity does not guarantee the voltage-dependence of excited state lifetime [42,43]. Besides, the accuracy of the method largely depends on the magnitude of τexc changes caused by other environmental factors during membrane potential imaging experiments.

Linear voltage dependence of τexc was demonstrated for molecular wire-based organic dyes [41] (Figure 2d). For these dyes, knr is determined by the rate of electron transfer from the electron donor to the fluorophore molecule upon photoexcitation, which is linearly dependent on voltage. Measurement of excited state lifetime allowed monitoring slow voltage transients upon stimulation of HEK cells with growth factor providing a 5 mV voltage resolution [41]. For two sensors constructed as fluorescent proteins fused to a voltage-sensitive domain, the excited state lifetime was also found to be linearly dependent on external electric field [42], but provided limited voltage resolution due to the large contribution to τexc from environmental factors other than voltage.

Besides voltage and concentration, fluorescence intensity of potentiometric sensors can be affected by environmental factors, including the local composition of lipids and macromolecules, ionic strength, viscosity, etc. [28,40,41,108,109]. Elimination of these effects can be performed for some systems0 if the nature of the effect, as well as the principle of functioning of the sensor, is known. Here we provide two specific protocols developed for redistribution dyes.

The fluorescence intensity of redistribution dyes detected from the cell interior is determined by the intracellular dye concentration, which should be directly related to cell membrane potential value in accordance with the Nernst Equation (Equation (2)). However, a part of dye molecules are bound to intracellular interaction sites (macromolecules and organelles), and provide equal contribution to detectung fluorescence at any membrane potential value. The effect of bound dyes can be removed if the binding constant Kb is determined. The protocol to eliminate the contribution from bound molecules was developed for dyes with linear concentration dependence of fluorescence intensity, i.e., when Equation (2) can be transformed into the following relationship [115]:

where Fout and Fin are fluorescence intensities detected from dye molecules located in the extracellular medium and cell interior, respectively. Binding constant Kb was derived from the difference between Fin and Fout and 0 mV (Figure 2e):

Here, Fin0mV and Fout0mV are fluorescence intensities measured for completely depolarized cells from the cell interior and extracellular medium, respectively. Then the following corrected equation was used to derive membrane voltage from fluorescence intensity measurements:

The method was successfully applied to investigate the resting membrane potential of several cell lines [115].

Another problem associated with the application of redistribution dyes for membrane voltage imaging is associated with the cell-to-cell variation of cell size as well as changes in cell size that can occur during the target process. According to the Nernst equation, cell membrane potential can be estimated from the intracellular dye concentration, but the detected fluorescence is rather proportional to the total amount of dye molecules in the cell interior. To provide robust results the detected fluorescence has to be divided by parameters related to the cell size. The protocol to eliminate cell size dependence was developed for cationic organic dyes, which are characterized by the existence of two emission bands at high concentrations (Figure 2f). The green band is attributed to dye monomers, while the red-shifted band is attributed to dye aggregates. These two signals were detected from prokaryotic cells stained with a cationic dye at a high concentration. The green signal was emitted by dye monomers bound to intracellular interaction sites. At the saturation concentration used in the experiment (30 μM), its intensity was voltage-insensitive since all interaction sites were occupied at any membrane potential value. On the other hand, the magnitude of the red signal demonstrated voltage-dependence in agreement with the Nernst equation—the concentration of intracellular dye aggregates decreased upon membrane depolarization. Both green and red signals were proportional to cell size and their ratio was successfully applied to cancel out cell size dependence. The method was used to monitor membrane potential changes that occurred after the addition of depolarizing agents into cell medium on the timescale of several minutes [116].

However, the application of cationic dye at the high concentration required for the experiment is related to high toxicity and can affect the target biological processes.

Measurement of absolute cell membrane potential values requires the knowledge of correspondence between the magnitudes of the optical signal detected from potentiometric sensors and membrane potential values. This correspondence is obtained by measuring optical signal magnitudes for a series of determined voltage values and plotting a calibration curve. Since voltage-dependence characteristics of the optical signal of potentiometric sensors are sensitive to different factors including cell type, type of sample (cell culture, tissue, in vivo measurements), experimental conditions, calibration has to be performed for each system of interest.

The most direct way to establish desired membrane voltage value is to use a patch-clamp device (Figure 3a). Actual cell membrane voltage is measured as the voltage difference between the recording electrode patched to the cell membrane and the reference electrode placed into an electrolyte or extracellular medium [117]. The recorded value is provided as input for the feedback module, which compares it with the desired value set by the signal generator. To compensate for the difference between actual and desired membrane potential values, electric current is injected into the cell via the third, current-passing electrode. To obtain the calibration curve, optical signal is recorded for a series of voltage values, usually in the −100 mV to +100 mV range.

Cells can be placed between microelectrodes [118] or in specific chambers [119] that generate a uniform electric field (Figure 3b). For a single spherical cell, membrane voltage changes induced by the field demonstrate angular distribution in accordance with Schwan’s Equation [120,121]:

Here, a is the cell radius, E is the magnitude of the electric field, and θ is the angle between the electric field and the membrane surface. For groups of cells or non-spherical cells, the electric field induces a more complex distribution of membrane voltage changes [119]. However, the application of an external electric field was shown to cause non-negligible pore formation, and the observed voltage changes were smaller than those derived from Equation (8) [118].

In a normal state the resting membrane potential of a cell is determined by unequal intracellular/extracellular concentrations and permeability of different ions in accordance with Goldman-Hodgkin-Katz Equation [122]:

Here, R is the universal gas constant, T is the absolute temperature, F is the Faraday constant, PX is the permeability of ion X, [X]in and [X]out are the intracellular and extracellular concentrations of ion X, respectively. The addition of specific ionophores makes the cell membrane predominantly permeable to a single ion type, therefore, resting membrane voltage can be estimated with the Nernst Equation (Equation (2)). Usually, valinomycin ionophore is applied to make membrane voltage determined solely by the extracellular concentration of potassium ions [71,123,124]:

If the intracellular potassium concentration is known or estimated, then calibration can be performed by measuring signal values for a series of extracellular ion concentrations, which are directly related to membrane voltage values in accordance with Equation (10) (Figure 3c). The protocol cannot be used for dyes that interact with ionophore [113,125,126], and the accuracy of calibration plot depends on the error in the estimation of intracellular concentration of potassium ions [113,127,128,129].

For charged dyes, membrane voltage can be derived from the ratio of intracellular and extracellular concentrations in accordance with the Nernst Equation (Equation (2)). The calibration plot, i.e., the relationship between detected fluorescence intensity and dye concentration, can be obtained by the measurement of fluorescence intensity for a set of dye concentrations using cells depolarized to 0 mV, i.e., when intracellular and extracellular dye concentrations are equal [70,71]. After the calibration procedure, intracellular concentration [Dye]in can be obtained from the calibration curve as a value corresponding to fluorescence intensity detected from the cell interior of intact cells. Extracellular concentration [Dye]out can be obtained as a value corresponding to fluorescence intensity detected from the interior of completely depolarized cells (Figure 3d). The obtained values are taken to calculate membrane potential using the Nernst Equation [69,72].

Membrane potential imaging in combination with optogenetic and photopharmacological techniques [130,131,132,133,134,135,136,137,138,139,140,141,142] has been already successfully applied for the investigation of fast processes involving electrically excitable cells, such as neurons and cardiomyocytes. Further progress in the investigation of excitable cells and an effective extrapolation of the approach to other cell types requires improvement of both corresponding tools and techniques. One direction for improvement is the development of new potentiometric sensors with optimized properties—bright and photostable fluorescence, red-shifted absorption and emission bands, fast fluorescence response to voltage changes, a high magnitude of fractional fluorescence changes in response to voltage, etc. Another direction, which is especially important for the investigation of long-term processes and in vivo studies, is the further development of methodologies to eliminate optical signal changes related to factors other than voltage and methodologies to derive absolute cell membrane potential values. Examples of successful applications of such methodologies are still limited. Their further development can substantially increase the number of biological systems and processes that can be investigated with membrane potential imaging techniques and open a new dimension in various areas of biology and biomedicine.

Conceptualization, M.S.P. and M.N.R.; data curation, D.M.N., V.N.M., A.A.S., I.D.K., A.S.M., A.V.V., M.S.P. and M.N.R.; writing—original draft preparation, D.M.N., V.N.M., A.A.S., I.D.K., A.S.M., A.V.V., M.S.P. and M.N.R.; writing—review and editing, D.M.N., A.V.V., M.S.P. and M.N.R.; project administration, M.S.P. and M.N.R.; funding acquisition, A.V.V. and M.N.R. All authors have read and agreed to the published version of the manuscript.

This study was supported by Russian Science Foundation (project No 20-13-00303). The study was partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program “Priority 2030” (Agreement 075-15-2021-1333 dated 30 September 2021).