Calibration procedures for the quantitative determination of membrane potential in human cells using anionic dyes


Department of Dermatology and Venereology, Martin Luther University of Halle-Wittenberg, Ernst-Grube-Str. 40, D-06097 Halle (Saale), Germany. E-mail:


Quantitative determinations of the cell membrane potential of lymphocytes (Wilson et al., J Cell Physiol 1985;125:72–81) and thymocytes (Krasznai et al., J Photochem Photobiol B 1995;28:93–99) using the anionic dye DiBAC4(3) proved that dye depletion in the extracellular medium as a result of cellular uptake can be negligible over a wide range of cell densities. In contrast, most flow cytometric studies have not verified this condition but rather assumed it from the start. Consequently, the initially prepared extracellular dye concentration has usually been used for the calculation of the Nernst potential of the dye. In this study, however, external dye depletion could be observed in both large IGR-1 and small LCL-HO cells under experimental conditions, which have often been applied routinely in spectrofluorimetry and flow cytometry. The maximum cell density at which dye depletion could be virtually avoided was dependent on cell size and membrane potential and definitely needed to be taken into account to ensure reliable results. In addition, accepted calibration procedures based on the partition of sodium and potassium (Goldman-Hodgkin-Katz equation) or potassium alone (Nernst equation) were performed by flow cytometry on cell suspensions with an appropriately low cell density. The observed extensive lack of concordance between the correspondingly calculated membrane potential and the equilibrium potential of DiBAC4(3) revealed that these methods require the additional measurement of cation parameters (membrane permeability and/or intracellular concentration). In contrast, due to the linear relation between fluorescence and low DiBAC4(3) concentrations, the Nernst potential of the dye for totally depolarized cells can be reliably used for calibration with an essentially lower effort and expense. © 2013 International Society for Advancement of Cytometry

In contrast to electrophysiological methods, the quantitative determination of the plasma membrane potential V by fluorescence measurement using charged dyes requires calibration. If cell subpopulations under study differ in the number of dye-binding sites, they will exhibit an individual relation between fluorescence and V. Consequently, calibration may be necessary more than once within an experiment. Several procedures have been accepted, which, nevertheless, differ considerably in methodological complexity. A direct relation between fluorescence and V can be obtained by the microscopic imaging of cells electrophysiologically clamped at definite voltages [1-4]. As this method is quite laborious, the number of measuring values within a reasonable time is quite low. In a lot of studies using spectrofluorimetry [5-13], microscopic imaging [14-23], or flow cytometry [24, 25], calibration was usually based on applying a voltage ramp by varying concentrations of extracellular sodium or potassium with isosmolar substitution of the respective alkali ion for choline chloride or N-methyl-D-glucamine (NMDG) in the presence of gramicidin (anionic dyes) or valinomycin (cationic dyes). In spectrofluorimetric and fluorescence imaging experiments, changes in external potassium concentration were also performed by sequential additions of KCl [26-28]. In addition, external potassium was isotonically replaced by sodium [29-32]. Although successful only in cells with Ca2+-activated potassium (KCa) channels, the combination of treatment with the calcium ionophore ionomycin and varying extracellular potassium may be an alternative approach [29]. Dependent on the medium composition, V was calculated from either the Goldman-Hodgkin-Katz (GHK) equation for potassium and sodium or the equilibrium potential for potassium (EK) according to the Nernst equation. The intracellular K+ and Na+ concentrations and membrane permeabilities, however, were usually only estimated rather than measured. Results may therefore imply a methodological error of an unknown extent [33]. Compared with these methods, the calibration approach provided by Krasznai et al. [34] requires considerably less time and effort when performed at low dye concentrations [35]. It is based on the Nernst partition of the dye itself (Edye) and thus independent of the respective concentration of any other ion involved in establishing V. Although adapted to microscopic imaging [36], too, it seems to prevail in flow cytometry using the anionic oxonol DiBAC4(3) [34, 35, 37-43]. In addition to the prerequisite of avoiding artifactual and thus only apparent changes in the calculated membrane potential by interactions of dye and added compounds, dye depletion in the extracellular buffer must under no circumstances occur. Irrespective of the cell type under study, the extracellular dye concentration has generally been taken as initially prepared, assuming it remains unchanged in the course of staining. In the case of polarized mitochondria, however, cellular uptake of cationic dyes is highly likely to result in a decrease in extracellular dye concentration [44-46]. This may be compensated for if selective depolarization of mitochondria, thus leaving V unchanged, could be done successfully. It is exactly this that has been described as a result of the action of protonophores in lymphocytes with 5 μM CCCP [47], in Jurkat cells with 10 μM CCCP [48], and neurons with 250 nM FCCP [32]. Consistent with findings from lymphocytes with 1 μM CCCP [44] and the rat sarcoma cell line UMR-106 treated with 2.5 μM FCCP [49], however, a concentration of 250 nM CCCP was already sufficient for a partial but significant depolarization (with 1μM essentially stronger) of the plasma membrane of IGR-1 cells (data not shown). When a steady state V or slow changes in V are to be detected, staining with anionic oxonols seems therefore to be more reliable and simplifies the experimental conditions, as intact mitochondria virtually do not contribute to the total cell fluorescence of anionic dyes. In addition, in human peripheral lymphocytes [29] and rat thymocytes [34], stained with 150 or 50 nM DiBAC4(3), dye depletion could not be observed up to a cell density of 2 × 106 cells/mL, thus supporting the validity of the calculation of V according to Edye. Considering the very low cell diameters of about 7 μm and below for small lymphocytes [50, 51] and rat thymocytes [52, 53], however, the unconditional use of relatively high cell densities may be restricted to specific cell types. Nevertheless, studies where cell density was 0.5 × 106/mL or lower seem to be the exception [35, 38, 41].

In our view, the explanations above verify that conditions where Edye will give reliable results have thus far not been examined sufficiently. A systematic investigation by flow cytometry seemed to be reasonable to check for limitations in respect of DiBAC4(3) dye depletion. For this, IGR-1 and LCL-HO cells possessing volume equivalent sphere diameters of higher than 10 μm [35] were prepared at different cell densities. In addition, V values calculated according to Edye and obtained from cell suspensions where dye depletion was negligible were to be compared with those from alkali ion-based calibration procedures following the most popular approach to only estimate rather than measure membrane permeabilities and intracellular concentrations.

Materials and Methods


Bis(1,3-dibutylbarbituric acid)trimethine oxonol (B-438) (DiBAC4(3)) and ionomycin (I24222) were obtained from Molecular Probes (Invitrogen Detection Technologies, Eugene, OR). Gramicidin (Fluka 50845) and propidium iodide (Calbiochem 537059) were from Merck Biosciences (Schwalbach, Germany). DiBAC4[3], gramicidin, and ionomycin were dissolved in DMSO to obtain stock solutions of adequate concentrations (DiBAC4(3): 12.5, 25, 50, 100, and 1,000 μM; gramicidin: 2 mg/mL; ionomycin: 1 mM and 100 μM) and were added to cell suspensions at a ratio of 1:1,000. For dead cell discrimination, propidium iodide (PI) was dissolved in Na-buffer (stock solution 500 μg/mL) and added to cell suspensions at a final concentration of 1 or 5 μg/mL (dependent on oxonol concentration).

Cell Culture

Cell lines were purchased from the Leibniz Institute German Collection of Microorganism and Cell Cultures GmbH (DSMZ, Braunschweig, Germany). Adherently growing IGR-1 melanoma cells (DSMZ ACC 236) were plated at a number of 0.8 × 106 cells in 75-cm2 culture flasks and maintained in phenol-red free DMEM at 37°C in a humidified atmosphere containing 10% CO2. On day 3 or 4 after seeding, IGR-1 cells were detached by short trypsinization (about 2 min) and transferred into a single cell suspension. B lymphoblastoid LCL-HO cells (DSMZ ACC 185) growing in suspension were cultured in 75-cm2 culture flasks in phenol-red free RPMI 1640 medium (PromoCell GmbH) at 37°C in a humidified atmosphere containing 5% CO2. At the time of processing for flow cytometry, cell density was usually about 1 × 106 cells/mL (in two cases, about 1.8 × 106 cells/mL).

Measurement of Cell Density and Cell Volume

Cell density and cell volume were determined using a Particle Analyzer Z2 (Beckman Coulter GmbH, Krefeld, Germany) accepting cells for analysis within a diameter range of 10 to 26 (IGR-1) or 6 to 16 μm (LCL-HO).

Buffer Composition

Where indicated, gramicidin was added to cell suspensions at a final concentration of 2 μg/mL (corresponds to about 1 μM) in order to set the membrane potential to zero [24]. The pH of all the media used was adjusted to 7.4.

Dye depletion experiments

Cells were suspended in HEPES buffer containing either 140 mM NaCl, 5.4 mM KCl, 1 mM CaCl2, 1 mM MgCl2, 10 mM glucose, and 10 mM HEPES (Na-buffer) to maintain the resting membrane potential (control) or in Na-buffer with gramicidin to clamp the membrane potential to 0 mV. The extent of depolarization by gramicidin, however, was found to be dependent on concentration [54] and may thus be impaired by possible gramicidin depletion at high cell densities. Therefore, some experiments were done with cells suspended in a buffer composed of 140 mM KCl, 5.4 mM NaCl, 1 mM CaCl2, 1 mM MgCl2, 10 mM glucose, and 10 mM HEPES (K-buffer), which was reported to be effective in depolarizing the cell membrane close to 0 mV [1, 35, 42].

Calibration experiments

If not indicated otherwise, the media described in the following contain 1 mM CaCl2, 1 mM MgCl2, 10 mM glucose, and 10 mM HEPES.

Method 1

Isotonic substitution of potassium for sodium (KCl: 1, 5.4, 15, 33, 66, 140; sum of sodium and potassium 145.4 mM) (K-Na media).

Method 2

Isotonic substitution of sodium for NMDG (NaCl: 1, 5.4, 15, 33, 66, 140; sum of sodium and NMDG 140 mM; KCl 5.4 mM each) (Na-NMDG media). Cells were treated with gramicidin.

Method 3

Isotonic substitution of potassium for NMDG (KCl: 1, 5.4, 15, 33, 66, 140; sum of potassium and NMDG 145.4 mM) in Na-free solution (K-NMDG media). Cells were treated with gramicidin (Method 3A) or 100 nM ionomycin (Method 3B). In Cl-free medium (only for 140 mM KCL in Method 3B), KCl was replaced by potassium DL-aspartate, CaCl2 by CaSO4, and MgCl2 by MgSO4.

For cells suspended in K-buffer (Method 1) or K-NMDG medium containing 140 mM KCl (Method 3B), extra samples were prepared with gramicidin.

Flow Cytometry

The respective cell suspensions in growth medium were washed twice in Na-buffer. Centrifugation was done at 200×g for 2 min. For calibration experiments, cell density was adjusted to 5 × 106/mL. A volume of 10 mL of the respective calibration medium was placed in glass test tubes followed by injection of 100 μL of the high-concentrated cell suspension (final cell density, 0.05 × 106 cells/mL). For dye depletion experiments, one more wash was performed followed by resuspending cells in the buffer finally used. Cell suspensions were then adjusted to a cell density of 2 × 106/mL or 1 × 106/mL (IGR-1) and 2 × 106/mL (LCL-HO) and repeatedly diluted 1:1 in order to obtain a series of definite cell densities (lowest density each: 0.0625 × 106 cells/mL). A cell suspension of the same origin and prepared under the same conditions (medium, ionophore treatment) is referred to as a subpopulation.

Staining in Dye Solutions Obtained From Equilibrated Cell Suspensions (Only IGR-1 cells)

A volume of 3.5 mL each of cell-free Na- and K-buffer (reference) or of cell suspensions in Na- and K-buffer (2 × 106 and 0.1 × 106 cells/mL each) was transferred into standard quartz cuvettes followed by addition of DiBAC4(3) (initial dye concentration 100 nM) and staining in the dark for 30 min under magnetic stirring. After dye equilibration, cuvettes were centrifuged at 1,400×g for 8min. Subsequently, 1 mL of the respective cell-free supernatant was transferred into Falcon tubes (three samples per cell subpopulation and reference) to serve once more as a staining solution possibly affected by dye depletion (cell containing cuvettes) or not affected by dye depletion (reference cuvettes). Then, unstained cells (50 μL each of the respective suspension at 2 × 106/mL) were injected. The low final cell density of 0.1 × 106/mL should largely avoid further dye depletion. Cells in K-buffer were additionally treated with gramicidin. After staining for 30 min at 37°C in the dark (tubes covered by aluminum foil), the measurement was performed.

Standard Protocol for Cell Staining

After transferring a volume of 1 mL of the respective cell subpopulation into Falcon tubes (for each experiment three samples per subpopulation), DiBAC4(3) was injected at a final concentration of 12.5, 25, 50, 100, or 1,000 nM (given in Results and figures). Then, incubation was carried out for 30min at 37°C in the dark (tubes covered by aluminum foil) followed by the measurement.


Collecting fluorescence versus time at intervals of 1 s, flow cytometry was done with a FACScan from Becton Dickinson (San Diego, CA) equipped with a 488-nm air-cooled argon laser. Samples were assigned to appropriate groups and run one after the other for about 20 s per sample. In this way, the number of files compared with steady state measurements (one histogram per sample) could be considerably reduced, thus making data processing, analysis, and graphic presentation easier. Monomeric DiBAC4(3) fluorescence was measured in the green FL1 channel (bandpass 530/30 nm) and PI in the red FL3 channel (longpass 650 nm), applying an appropriate FSC/SSC gate to exclude debris from the measurement. In most experiments with LCL-HO cells, this gate alone was sufficient to completely reject values of dead cells from the data acquired. The sample flow rate was set to “high” at 0.125 × 106 cells/mL and below (otherwise to “low”). The photomultiplier voltage of the FL1 channel was set to 400 V (12.5 to 100 nM DiBAC4(3)) or 300 V (1,000 nM DiBAC4(3)). For dead cell discrimination, PI was added 5 min before measurement.

Data Analysis

Flow cytometric FCS data were transformed into ASCII files using WinMDI 2.8 (freeware written by Joseph Trotter). In this process, the data of large-sized debris, cell aggregates, and PI-positive dead cells were largely excluded from further analysis by computational pregating. The remaining measuring values were processed with Excel 2000 (Microsoft Corporation). As an example of the gating strategy, Figure 1 shows an appropriate gate definition for IGR-1 cells in depolarizing K-buffer at different cell densities (regions R1 and R2 joined in a logical conjunction) (Figs. 1A and 1B) and the resulting dot plot green oxonol fluorescence versus time after gating (Fig. 1C). The histograms of each subpopulation (Fig. 1D) were created by pooling the data of the respective three samples. To make a direct comparison of results possible, the fluorescence values acquired with 300 V were recalculated as if measured at 400 V [35]. Even at the low dye concentration of 25 nM DiBAC4(3), autofluorescence proved to be negligible [35]. Therefore, fluorescence values were not compensated for background (autofluorescence). The median was used as an average of fluorescence (MFI) for each of the three samples of a subpopulation (Fig. 1C, region R3). From these values and derived quantities, the arithmetic mean was calculated (data were expressed as mean ± SD). Statistical analysis was done using SigmaStat 1.0 software (Jandel Scientific, Erkrath, Germany). Tests for comparison of means are given in Results and figure legends. A P < 0.05 was considered to be statistically significant.

Figure 1.

Flow cytometric measurement collecting scatter signals, green and red fluorescence of IGR-1 cells depolarized by K-buffer (140 mM KCl, 5.4 mM NaCl) versus time at different cell densities (three samples each for 1, 0.5, 0.25, 0.125, and 0.0625 × 106/mL) and stained with 100 nM DiBAC4(3). (A) and (B) show representative region definitions (R1 and R2) to exclude large-sized debris and dead cells from further analysis by computational pregating (R1 and R2 joined in a logical conjunction); (C) the remaining values of green oxonol fluorescence after gating vs. time; and (D) derived histograms for selected cell densities approximated by lognormal distributions (R2 = 0.958 to 0.987). While the median of fluorescence distributions was separately calculated for each sample of a subpopulation (region R3), the histograms were created by pooling the data of the respective three samples (cell density: solid 1 × 106/mL, dashed 0.5 × 106/mL, dash-dot 0.25 × 106/mL, dotted 0.0625 × 106/mL; 0.125 × 106/mL omitted to avoid overlaying). It should be noted that the sample flow rate was set to “slow” for cell densities of 0.25 × 106/mL and higher and to “fast” for cell densities lower than 0.25 × 106/mL. Apparent membrane potentials for the resting cells (data not shown) calculated according to the Nernst potential of DiBAC4(3) without considering dye depletion were −41.8 ± 1.5 mV for 0.0625 × 106/mL but only −21.9 ± 2.5 mV for 1 × 106/mL. Statistics: one-way ANOVA with Bonferroni's t test (values for 0.0625 × 106/mL as a control; * P < 0.05).

Calculation of Membrane Potential and Dye Concentration

The cellular uptake of charged dyes is controlled by the membrane potential V described according to the Nernst equation:

display math(1)

where R is the universal gas constant, T the absolute temperature, Z the charge of the dye, and Ci the internal and Ce the external free dye concentrations. In image and flow cytometry, Eq. ( (1)) has been modified by substituting fluorescence values for free dye concentrations [1, 31, 35, 36, 56-59]. The fluorescence F of whole cells or cell organelles stained with charged dyes, however, usually also comprises a proportion of bound dye. Nevertheless, it is reasonable to assume that F is a single-valued function of Ci [29, 34, 35, 37]. This approach has been accepted in a lot of studies [36, 38, 39, 41-43]. Even in mitochondria stained with a cationic dye, the concentration of bound dye has been considered acceptable as a directly proportional measure of the free concentration if Ci is sufficiently low compared with the concentration of dye-binding sites [58]. In respect of the cell membrane potential and using the anionic dye DiBAC4(3), extracellular dye concentrations up to 100 nM actually proved to be linearly related to the total cell fluorescence, and the corresponding curve intersects with zero [35]. In addition, Klapperstück et al. [35] and Emri et al. [37] demonstrated for a wide range of the extracellular free dye concentration that the non-Nernstian proportion of the fluorescence of dye bound to the outer cell membrane has no influence on the values of calculated membrane potentials. Results obtained from confocal microscopy have verified that the fluorescence of the intracellular free dye also contributes only negligibly to the total cell fluorescence [35]. Still, F measured by flow cytometry is only valid as a reliable substitute for the dye concentrations Ci (F of control cells) and Ce (F of totally depolarized cells) when possible dye depletion in the external medium is negligible or the external dye concentrations for control and totally depolarized cells under study are at least approximately equal (in the ideal case identical). In accordance with Zeng et al. [12], Resendes et al. [13], and Tarnok et al. [54], the term “apparent membrane potential” (Vapp) was therefore introduced. Using a monovalent, anionic dye such as DiBAC4(3), the Nernst equation can then be modified by

display math(2)

where Fd is F of cells of the same origin (equal number of dye binding sites) when V is set to 0 mV, thus resulting in Ci = Ce. Because of the logarithmic relation between F and Ce at high dye concentrations such as 1,000 nM DiBAC4(3), the basic prerequisite of Eq. ( (2)) is violated, and Vapp calculation according to Eq.  (1) requires calibration curves [34, 35, 37]. In dye depletion experiments of this study, however, calibration was omitted, as it would have had to be done for each and every cell density used. Consequently, it was not possible to perform preparation and measurement for calibration in a series of different dye concentrations in parallel to that for control and depolarized cells within a reasonable time.

By analogy, a distinction must be made between the initial extracellular free dye concentration Ce,0 (concentration immediately after being injected) and the actual one after equilibration Ce. So far, the latter has been taken as initially prepared without considering possible dye depletion. Consequently, this value must be considered apparent as well. Proceeding from the fitted curves for fluorescence as a function of cell density for totally depolarized and resting cells obtained from flow cytometry (25, 50, or 100 nM initial dye concentration), intermediate F values were interpolated for each cell density. By setting cell density to zero, the fit functions (see below) give fluorescence values F0 not affected by dye depletion. Thus, the actual membrane potential V can be calculated, which must apply to any other cell density, too:

display math(3)

where Fd,0 is the oxonol fluorescence for gramicidin-depolarized cells in the case of no dye depletion (actual extracellular free dye concentration Ce is equal to the initial one Ce,0). From this, an array of curves for fluorescence as a function of membrane potential with cell density as a parameter can be derived. Based on the values of F at any V, the calculation of the intracellular free dye concentration Ci is then possible:

display math(4)

By applying the Nernst equation, the calculation of any actual Ce can be done:

display math(5)

It should be noted that Eqs. ( (4)) and  (5) are strictly valid only when no other effect than dye depletion will result in cell density-dependent changes in fluorescence. In this case, we can write

display math(6)

where D is dye depletion.

This study considers only K+ and Na+ for the calibration methods based on monovalent membrane-permeant ions involved in establishing membrane potential. As several assumptions had been made, corresponding membrane potential calculations must be considered to be apparent as well. With K-Na media (Method 1) and Na-NMDG media (Method 2), calculation was performed according to the GHK equation:

display math(7)

where p is the ratio of the membrane permeabilities for Na+ and K+ (PNa/PK) assumed to be 0.05 in untreated cells (Method 1) or 1 in gramicidin-treated cells [6, 7, 9, 10, 13-15, 17, 19, 21, 23, 24] (Method 2). Comparable with other studies [6, 7, 9, 10, 13, 14, 16, 19, 20, 22, 24, 60, 61], the intracellular concentrations [K+]i and [Na+]i were taken as 140 and 10 mM, respectively. In calibrations using Na-free K-NMDG media (Method 3), the apparent membrane potential was calculated according to the Nernst potential for potassium (EK) as a special case of the GHK equation:

display math(8)

where [K+]i was assumed to be 140 mM as well. NMDG was considered cell membrane and ion channel impermeant [23].

Fluorescence response R (in %/mV) was defined as the ratio of the fractional change in fluorescence and the corresponding change in membrane potential:

display math(9)

where Vr is the resting membrane potential and Fr the accompanying fluorescence.

A Simple Model of the Effect of Cell Density on Dye Concentration

For simplicity, the following model is confined to the saturable and reversible interaction of oxonol molecules with a single class of intracellular, specific dye-binding sites under equilibrium conditions. In accordance with Emri et al. [37], the binding reaction derived from the law of mass action can then be described by

display math(10)

where Cb is the concentration of intracellularly bound dye, Ci the intracellular free dye concentration, Bmax the greatest attainable concentration of bound dye (also referred to as the total density of dye-binding sites), and Kd the equilibrium dissociation constant. At sufficiently low dye concentration, we can assume that Ci << Kd. The linearity between the green fluorescence of oxonol-stained cells F and the intracellular concentration of free dye Ci at low dye concentrations [35] suggests that DiBAC4(3) below 100 nM may satisfy this condition. In this case, Eq. ( (10)) can be simplified to

display math(11)

The total dye mass in a sample equals the initial external dye mass me,0:

display math(12)

where Ce is the actual extracellular free dye concentration, Ve the volume of the extracellular buffer, N the number of cells, and Vi the volume of the intracellular space of a single cell containing free dye and dye bound to cell constituents such as proteins. Rearrangement of Eq. ( (5)) results in

display math(13)

The fractional cell-associated volume Vf can be defined by

display math(14)

Dividing Eq. ( (12)) through by Ve and rearrangement and substitution of the right-hand side of Eq. ( (13)) for Ci in Eq. ( (12)) yield

display math(15)

Further rearrangement and algebraic manipulation result in

display math(16)


display math(17)

From Eq. ( (13)), it follows

display math(18)

Cell density Bc is defined by

display math(19)

By multiplying Eq. ( (19)) by Vi, we get

display math(20)


display math(21)

Considering the very low quantum yield of free dye compared with that of bound dye [35], F can be described by

display math(22)

where A is a proportionality factor including parameters such as instrument settings and quantum yield [37]. Substitution of the right-hand side of Eq. ( (21)) for Ci in Eq. ( (22)) results in

display math(23)

Curve fitting

For a given ideal cell subpopulation possessing the same Bmax, Kd, and membrane potential V for every single cell and stained at the same initial extracellular free dye concentration Ce,0, Eq. ( (23)) has only one independent variable: cell density Bc. This simple model suggests that curve fitting may be performed to a good approximation by the two-parameter rational function:

display math(24)

By dividing numerator and denominator by c1, we get

display math(25)

where a2 gives an interpolated F for the case of no dye depletion (cell density Bc set to zero).

Curve fitting was done using Sigmaplot 8.0 software (Jandel Scientific). R-square values (R2) were considered an estimate of the goodness of fit and are indicated in Results or figure legends.


Dye Depletion Experiments

Staining in dye solutions obtained from the cell-free supernatant of equilibrated cell suspensions (only IGR-1)

Compared with the reference (staining buffer obtained from cuvettes with cell-free pure dye solution), a significant decrease in the green oxonol fluorescence was only observed for samples where the staining solution originated from the supernatant of cuvettes containing cells at the high density of 2 × 106/mL (Fig. 2A). Therefore, we assume that the high cell density during the first staining had led to a significant dye loss in the extracellular buffer. In contrast, the low cell density in cuvettes had only been accompanied by negligible external dye depletion. As a result, dye concentrations of the reused staining buffer available for the cells actually measured (cell density for all samples, 0.1 × 106/mL) were obviously different. In addition, depolarized cells at the high density had depleted a higher amount of dye than cells at the resting potential. Calculation of Vapp based on Eq. ( (2)) thus resulted in significantly more positive values compared with the cells stained in the reference buffer (Fig. 2B).

Figure 2.

Fluorescence (A) and apparent membrane potential (B) of IGR-1 cells at the low cell density of 0.1 × 106/mL prepared with reused staining buffer obtained from the cell-free supernatant of cuvettes where cells had been stained at two different densities (2 × 106/mL and 0.1 × 106/mL) and at an initial dye concentration of 100 nM DiBAC4(3). Note that the x-axis indicates the density of cells in cuvettes during this first staining, where “0” indicates cuvettes with pure dye (reference). Expressed by a significant decrease in fluorescence (A), the high cell density during the first staining obviously caused external dye depletion. In this process, depolarized cells reduced the dye concentration more than cells at the resting potential resulting in an incorrect value of the calculated apparent membrane potential (B). In contrast, the low cell density in cuvettes had only been accompanied by negligible external dye depletion. As a result, the fluorescence and calculated membrane potential do not differ significantly from the reference. Statistics: one-way ANOVA with Bonferroni's t test separately for cells at rest and depolarized cells (preparations from pure dye cuvettes as a control); * or #P < 0.05, n = 3 each. Data represent one of two independent experiments with similar results.

Staining according to the standard protocol

For the measurement of resting (control in Na-buffer) and depolarized cells (gramicidin treatment or K-buffer) at different cell densities and DiBAC4(3) concentrations, seven independent experiments were performed using IGR-1 cells (gramicidin: one with 25 nM, two with 50 nM, one with 100 nM, and one with 1,000 nM; K-buffer: one with 100 nM and one with 1,000 nM) and four using LCL-HO cells (gramicidin: one with 50 nM, one with 100 nM, and two with 1,000 nM). K-buffer- and gramicidin-depolarized IGR-1 cells (Figs. 1C and 1D or Fig. 3, upper left) showed the same extent of dye depletion with increasing cell density. Thus, gramicidin depletion as a possible cause of the decrease in fluorescence with increasing cell density could be ruled out.

Figure 3.

Fluorescence (upper row) and apparent membrane potential (lower row) of resting and gramicidin-depolarized IGR-1 and LCL-HO cells stained with 50 nM DiBAC4(3) as a function of cell density. Apparent membrane potential was calculated according to the Nernst potential of DiBAC4(3) without considering dye depletion. Photomultiplier voltage and amplification for the two cell types were identical. Dependent on cell density, a significant decrease in the fluorescence of gramicidin-treated cells (in IGR-1 also to some extent for cells at the resting membrane potential) was observed resulting in apparent membrane potentials shifted to artifactually more positive values (one-way ANOVA with Bonferroni's t test (values for 0.0625 × 106/mL as a control); *P < 0.05; n = 3 each). Data represent one of five (IGR-1) or two (LCL-HO) independent experiments with similar results.

Figures 3 and 4 are representative for experiments where cells were stained with low dye concentrations. It should be noted that IGR-1 cells are considerably larger than LCL-HO cells (cell volume 2.89 ± 0.16 pL or 0.78 ± 0.06 pL; mean of six independent experiments each). Thus, the higher fluorescence of IGR-1 cells (Figs. 3-5) is clearly a result of the difference in cell size or, more exactly, in the number of dye-binding sites. With increasing cell density, the reduction in the fluorescence of depolarized cells was consistently more pronounced in IGR-1 cells (Fig. 3, upper row). Because of the lower amount of incorporated anionic dye by resting cells, this could be observed to an essentially lesser extent only in IGR-1 cells but not in LCL-HO cells (Fig. 3, upper row). Consequently, calibration based on depolarized cells using Eq. ( (2)) resulted in an apparent membrane potential shifted to artifactually less negative values as cell density increased (Fig. 3, lower row). The curves for the fluorescence F of IGR-1 and LCL-HO cells as a function of cell density could be approximated by the rational function according to Eq.  (25) (R2 higher than 0.936, except for resting LCL-HO cells with R2 = 0.363). In the observed range of cell density, the fluorescence of resting LCL-HO cells was virtually parallel to the x-axis. Hence, slight fluctuations of the measuring values may be responsible for the low R2 using a rational function. Considering the underlying physics and chemistry (no detectable dye depletion), nevertheless, this fit may still be acceptable. The curves for the resting membrane potential Vapp(Edye) as a function of cell density were also approximated according to Eq.  (25) in both IGR-1 and LCL-HO cells (R2 = 0.953 or 0.981), while the curves for the totally depolarized cells are straight lines with V = 0 mV for all cell densities by definition. By setting cell density in Eq.  (25) to zero, the actual resting membrane potential V for IGR-1 and LCL-HO cells could be interpolated [Eq.  (3)]. In the large IGR-1 cells, V at 0.0625 × 106/mL (representing real measurements) and V at 0/mL (representing the ideal case of no dye depletion) as calculated according to the respective fit function differ by only 5.4 ± 1.0% (mean of five independent experiments). Thus, dye depletion was virtually negligible at the lowest cell density used. In LCL-HO cells, this was still valid at 0.5 × 106 cells/mL. Even when the density of LCL-HO cells was 1 × 106/mL, Vapp(Edye) was only about 10% lower than the actual membrane potential (in IGR-1 cells about 43%). Fitted values of measured (only control and totally depolarized cells) and values obtained by interpolation as an estimate of intermediate fluorescences and membrane potentials were presented as an array of curves with fluorescence as a function of cell density and the actual membrane potential as a parameter (Fig. 4, upper row). Dye depletion [Eq.  (6)] as a function of cell density with the actual membrane potential as a parameter may serve as a model to estimate the external loss of dye (Fig. 4, lower row).

Figure 4.

Estimation of dye depletion mathematically derived from fitted curves for fluorescence as a function of cell density shown in Figure 3. An array of curves for DiBAC4(3) fluorescence as a function of cell density was created for measuring and, obtained by interpolation, intermediate values (upper row). The actual membrane potential as a parameter was estimated by setting cell density in the fit function Eq. ( (25)) to zero and is indicated in the legends in millivolts (legends of the lower row are also valid for the upper row). The known linear relation between fluorescence and intracellular free dye concentration allows the calculation of the corresponding extracellular free dye concentration and thus extracellular dye loss for each cell density. Resulting curves (lower row) may serve as a model of dye depletion.

At correspondingly high cell densities, staining with an initial dye concentration of 1,000 nM also led to extracellular dye depletion in the depolarized subpoplations of the two cell types. Here, calibration was omitted due to reasons given in Material and Methods. So, results are only presented as fluorescence as a function of cell density (Fig. 5). As with 50 nM DiBAC4(3), the curves were approximated by Eq.  (25) (R2 higher than 0.977 for depolarized cells, 0.848 for resting IGR-1 cells, and, similar to 50 nM, only 0.446 for resting LCL-HO cells).

Figure 5.

Fluorescence of IGR-1 (A) and LCL-HO cells (B) stained with an initial DiBAC4(3) concentration of 1,000 nM as a function of cell density [membrane potential at rest (control) or totally depolarized (gramicidin)]. Photomultiplier voltage and amplification for the two cell types were identical. The actual membrane potential, determined from cells additionally stained with 50 nM at a cell density of 0.0625 × 106/mL, was −45.3 ± 1.8 mV (IGR-1) or −48.9 ± 1.6 mV (LCL-HO). Statistics: one-way ANOVA with Bonferroni's t test (values for 0.0625 × 106/mL as a control); *P < 0.05; n = 3 each. Data represent one of two independent experiments for either cell type with similar results.

Considering all cell density experiments, the actual membrane potential of IGR-1 cells ranged from −36.2 ± 1.9 to −53.3 ± 2.9 mV and of LCL-HO cells from −43.9 ± 0.6 to −57.6 ± 0.4 mV.

Comparison of calibration methods

Except for one experiment (IGR-1, K-Na medium, 12.5 nM), cells were stained with 50 nM DiBAC4(3) to ensure a linear relation between green fluorescence and dye concentration. Because of the low cell density used (0.05 × 106/mL), Vapp(Edye) calculated according to Eq. ( (2)) was considered to be the actual membrane potential V or Edye.

Pre-experiments (only one per media series) with IGR-1 cells suspended in selected K-Na (Method 1), Na-NMDG (Method 2), and K-NMDG (Method 3) calibration media without and with gramicidin were performed to investigate the effect of this pore-forming ionophore on membrane potential. In K-Na media, gramicidin totally depolarized cells independent of the medium composition (Fig. 6A). When it was omitted in Na-NMDG media, cells maintained the resting membrane potential (Fig. 6B). It should be noted that the difference in resting membrane potential between Figures 6A and 6B is a result of using cells at different days of culture. In addition, gramicidin had no influence in K-NMDG media (data not shown). For the calculation of Edye, however, cells in K-NMDG and K-Na media with a potassium concentration of 140 mM were treated with this ionophore to definitely set the membrane potential to zero. Apart from these special cases, gramicidin must not be added with Method 1, needs to be added with Method 2, and may or may not be added with Method 3A.

Figure 6.

Effect of gramicidin in IGR-1 cells suspended in K-Na media with isotonic substitution of potassium for sodium (sum 145.4 mM) (A) or Na-NMDG media with isotonic substitution of sodium for NMDG (sum 140 mM, 5.4 mM K+ each) (B) (filled bars: no gramicidin addition, open bars: gramicidin addition). Membrane potential was calculated according to the Nernst potential of DiBAC4(3) calibrated by gramicidin-depolarized cells in the medium with 140 mM potassium (A) or 140 mM sodium (B). In order to avoid dye depletion, cell density was 0.05 × 106/mL each. It should be noted that the experiments in (A) and (B) were performed on different days of culture resulting in different resting membrane potentials. Statistics: one-way ANOVA with Bonferroni's t test separately for untreated cells and gramicidin-treated cells (140 mM as a control each); * or # P < 0.05; n = 3 each.

Following widespread practice, membrane permeabilities and intracellular ion concentrations had only been estimated (see Material and Methods) rather than measured. Consequently, Vapp(GHK) [Eq. ( (7))] and Vapp(EK) [Eq.  (8)] gave the same calculated membrane potential for both IGR-1 and LCL-HO cells. Under the conditions assumed, there was virtually no concordance between the different alkali ion-based calculations and Edye (at least two independent experiments per calibration method each). Only in ionomycin-treated IGR-1 cells suspended in K-NMDG media were the curves for Edye and Vapp(EK) as a function of [K+]o relatively close together for [K+]o higher than 5.4 mM (Fig. 7C, Method 3B). Consistent with the activation of KCa channels, ionomycin led to a hyperpolarization of IGR-1 cells to −73.4 ± 4.1 mV in normal Na-buffer (data not shown) and -74.8 ± 5.2 mV in K-NMDG medium containing 5.4 mM KCl (mean of three independent experiments for either medium). In contrast, LCL-HO cells did not respond to ionomycin addition, thus being inappropriate for Method 3B (data not shown). Somewhat more negative than in K-buffer (Fig. 7A), IGR-1 cells in ionomycin-containing K-NMDG medium with 140 mM KCl possessed a slightly polarized cell membrane (Fig. 7C). In the case of Cl-free K-NMDG medium (140 mM potassium DL-aspartate), a significant shift to more positive values from −10.4 ± 1.8 to −5.2 ± 0.4 mV or −7 ± 0.55 to −3.53 ± 0.48 mV was observed (data not shown; two independent experiments; n = 3 per subpopulation each; Student's t test). This suggests that a Cl conductance contributes to some extent to the membrane potential of IGR-1 cells.

Figure 7.

Comparison of commonly used calibration methods in quantitative membrane potential measurement using different buffer compositions: isotonic substitution of potassium for sodium (sum 145.4 mM) (Method 1) (A); isotonic substitution of sodium for NMDG (sum 140 mM), each buffer contained 5.4 mM potassium and gramicidin (Method 2) (B); isotonic substitution of potassium for NMDG (sum 145.4 mM, Na-free) and addition of gramicidin (Method 3A) or ionomycin (Method 3B only in IGR-1 cells) (C). The alkali ion-based calculation of membrane potential was performed by the GHK equation for sodium and potassium (Methods 1 and 2) or the Nernst equation for potassium (Method 3) only assuming values for intracellular free cation concentrations ([K+]i = 140 mM, [Na+]i = 10 mM). P is the membrane permeability of the respective alkali ion (assuming PNa/PK = 0.05 in untreated cells or =1 in gramicidin-treated cells). The calculation based on the Nernst potential of DiBAC4(3) calibrated by gramicidin-depolarized cells (Edye) was considered as a reference. The presented flow cytometric data were obtained from IGR-1 and LCL-HO cells stained with 50 nM DiBAC4(3). In order to avoid dye depletion, cell density was 0.05 × 106/mL each. Note that there is virtually no concordance between the alkali ion-based calculation and Edye. Data represent one of at least two independent experiments per method (three samples per medium composition each). Except for “IGR-1 Edye (3B)” in (C) (Hill function, R2 = 0.997), the curves could be fitted to the data by a three-parameter logarithmic function (R2 = 0.995 to 0.999).

Considering all calibration experiments, the actual membrane potential of IGR-1 cells ranged from −38.4 ± 1.2 to −51.7 ± 1.4 mV and of LCL-HO cells from −42.9 ± 1.2 to −57.7 ± 3.6 mV.


Impact of Cell Density on Oxonol Dye Depletion

Cell density has thus far not been sufficiently considered to be a quantity that has essential effects on results in membrane potential measurement using anionic dyes. In a lot of flow cytometric and spectrofluorimetric studies, cell density used was between 1 and 2 × 106/mL [13, 24, 34, 37, 39, 40] and in part also indicated as a range such as 1–2 × 106/mL, 2–3 × 106/mL, or 1–3 × 106/mL [10, 29, 49]. In addition, it has not been given at all [25, 42, 43]. This study has revealed that dye depletion of DiBAC4(3) may occur in staining solutions of cell suspensions at cell densities often applied. In small gramicidin-depolarized LCL-HO cells, a cell density of 1 × 106/mL or higher significantly reduced the oxonol fluorescence after equilibration, while in the large IGR-1 cells, the quite low cell density of 0.25 × 106 /mL was already sufficient to cause this unwanted effect (Fig. 3, upper row). The extent of dye depletion was obviously different in control and depolarized cells. Consistently, membrane potential calculation according to Eq. ( (2)) resulted in incorrect values at correspondingly high cell densities when dye depletion was ignored (Fig. 3, lower row). Because of the logarithmic relation between membrane potential and fluorescence, the latter reflects the decrease in the extracellular dye concentration more sensitively (Fig. 3).

It has been assumed by others [21, 62] that dye depletion may be avoided by using a high external dye concentration. The experiments with 1,000 nM DiBAC4(3) (Fig. 5) could not confirm this view. Under this condition, formation of dye aggregates will occur to some extent resulting in a decrease in the green fluorescence by quenching [35]. Therefore, increase in cell density and thus dye depletion should be in turn accompanied by a partial dequenching of fluorescence. Actually, the corresponding fractional changes in the fluorescence of depolarized cells were smaller (Figs. 5A and 5B) than with 50 nM initial external dye concentration (Fig. 3, upper row).

Nernst potential of DiBAC4(3) as a reference for calibration

In contrast to using the Nernst potential of the charged dye [34, 35, 37-43], calibration based on the partition of K+ and Na+ [7, 8, 10, 11, 13, 24, 25, 29] or H+ [49] is in principle not dependent on dye depletion provided all the samples have the same cell density. However, conditions where dye depletion does not occur should be preferred even then. As an advantage, sample-to-sample variation of cell density must not be kept very low, and the fluorescence response is considerably higher at low cell densities (Figs. 3-5). The approach of this study was nevertheless to consider the membrane potential calculated according to Eq. ( (2)) as a well-founded reference method. First, it is generally accepted that free charged dye molecules partition between medium and cell compartments according to the Nernst potential [1, 15, 29, 31, 34, 42, 56, 57, 59, 63]. This is, however, strictly valid only for the monomeric form and thus dependent on dye concentration [57]. Second, this calibration method has been verified by comparing with results of patch clamping [1, 34, 35, 37, 43]. Third, due to the linear relation between cell-associated DiBAC4(3) fluorescence F and dye concentration up to 100 nM [35], calibration can be reduced to the measurement of the fluorescence of totally depolarized cells stained at the same dye concentration as used for the measurement of polarized cells [35, 36]. Results of confocal laser microscopic imaging revealed that the DiBAC4(3) fluorescence of intracellular free dye compared with F is negligible [35]. Consequently, pure cell volume changes were virtually not accompanied by changes in fluorescence [35]. The calculation of V according to Eq. ( (2)) will thus give reliable results provided dye depletion is negligible. Even in large cells, however, this prerequisite can be met easily by using a very low cell density from the start. For the comparison of calibration methods in this study, cell suspensions were therefore adjusted to 0.05 × 106/mL. At high extracellular oxonol concentrations [14-16, 19, 23, 53, 64, 65], the relation between cell fluorescence and dye concentration is logarithmic [34, 35, 37, 39], most probably due to increasing binding saturation and the formation of oxonol aggregates [35]. In contrast to using low dye concentrations, fluorescence and membrane potential should then be linearly related [35]. It is exactly this that could be demonstrated by microscopic imaging of voltage-clamped cells [4] stained at 2 μM DiBAC4(3). For the calculation of V according to the Nernst equation, however, this approach requires the intracellular free dye concentration, which can be calculated by the use of calibration curves established from the fluorescence of totally depolarized cells in a series of different dye concentrations [34, 35, 37, 39]. In contrast to gramicidin [66], the action of fixatives is not restricted to the cell membrane [35]. Depolarization by chemical fixation should therefore be avoided because it causes significantly enhanced fluorescence of bound dye at high dye concentrations [35]. In addition, possible activation of BKCa channels by the dye itself, which would lead to hyperpolarization, must also be taken into consideration [67]. Previous flow cytometric results in IGR-1 cells based on the Nernst potential of DiBAC4(3) at 1,600 nM and higher suggested that BKCa channels may be expressed in LCL-HO but not in IGR-1 cells [35]. Interestingly, BKCa channels could not actually be detected in the latter in a recent electrophysiological study [68], thus confirming the reliability of using Edye as a measure of membrane potential. In the last analysis, high dye concentrations may be reserved for specific questions, and low concentrations of 100 nM or less should be preferred for routine applications due to the simple calibration and to avoid side effects.

Calibration according to the Nernst equation for the dye and the GHK equation for sodium and potassium

Compared with K+, IGR-1 cells seem to have relatively small Cl and Na+ conductances when bathed in medium without ionophores. This can be concluded from the alteration of Edye by isotonic replacement of extracellular K+ for Na+ (Fig. 7A), which was not observable in red blood cells having a high chloride conductance [5], and from the lack of changes in Edye when gramicidin was omitted using Na-NMDG media (Fig. 6B). The high degree of concordance between the two cell types under study in K-Na (Method 1) and Na-NMDG (Method 2) media suggests that this may apply to LCL-HO cells, too (Figs. 7A and 7B). So, K+ gradients seem predominantly to establish V in either cell line. Unless cells have a V close to EK, as has been observed in myofibroblasts [65], calculation of membrane potential for cells in normal media according to the GHK equation will still give a better estimate than EK [32, 40] by also considering the contribution of small ion conductances.

Gramicidin treatment of cells in K-Na media will result in a voltage of zero independent of the alkali ion composition [18, 24] (Fig. 6A) by equilibrating internal and external concentrations of both sodium and potassium [18]. With Method 1, gramicidin was therefore added only for Edye calibration. In experiments where membrane permeabilities and intracellular free alkali ion concentrations had only been estimated rather than measured, considerable deviations of Vapp(GHK) from the actual membrane potential (Edye) must obviously be expected (Fig. 7). Although intracellular free alkali ion concentrations seem to remain nearly unchanged under different experimental conditions [18, 40], significant alterations in PNa/PK may still occur [40]. By setting the values for PNa/PK to 0.13 (IGR-1) or 0.12 (LCL-HO) for all K-Na media used, concordance between Edye and Vapp(GHK) could actually be achieved. In rat spermatids [11] and osteoblast-like cells [49], a PNa/PK of about 0.3 has been determined. This value is consistent with the presence of activated sodium channels, which contribute to a relatively low polarization of the cell membrane in the resting state [11, 49, 69]. In contrast to other studies using the GHK equation [29, 32, 40], Chen and Reith [18], nevertheless, preferred EK for cells in K-Na medium ([K+]o 4.2 mM, [Na+]o 130 mM, [K+]i measuring value 131 mM), leading to a calculated membrane potential of −88 mV. In this study, the resting potential of IGR-1 cells in Na-buffer ([K+]o 5.4 mM, [Na+]o 140 mM) calculated as Edye was between −36.2 and −53.3 mV (16 independent experiments), while Vapp(EK) resulted in the same value of −83.4 mV ([K+]i initially taken as 140 mM) or −74.8 mV ([K+]i taken as 100 mM). Considering the high difference between the two assumed [K+]i values, it must be questioned that Vapp(EK) can generally be taken as a reliable measure of V using Method 1, even when [K+]i has been measured. This is valid only when PNa/PK and PCl/PK are extremely low. In this case, the GHK equation will actually develop into the Nernst equation for potassium. However, this does not apply to IGR-1 and LCL-HO cells (Fig. 7A). In axons, the single-ion permeabilities and the corresponding ratios have even been dependent on [K+]o or voltage [70]. So, alkali-ion based calibration with Method 1 may require a complex approach, additionally considering variation in PNa/PK and PCl/PK especially in cells which express voltage-gated ion channels.

In contrast to Method 1, calibration in Na-NMDG media will only work with gramicidin addition [24] (Fig. 6B). So, in addition to K+ and Na+ concentrations, the membrane permeabilities through the gramicidin pore must be known to obtain reliable results based on the GHK equation. Using artificial membranes, Andersen [71] observed that PNa/PK for gramicidin channels is dependent on the composition of the lipid bilayer. At electrophysiologically clamped voltages between 0 and 100 mV, PNa/PK was 0.4 to 0.5 in diphytanoylphosphatidylcholine but only 0.3 in glycerolmonooleate membranes [71]. In rat spermatids and cardiac myocytes, it was 0.62 [11] or 0.64 [72]. Grinstein et al. [6] explained the action of gramicidin in whole cells by a rapid exchange of potassium for sodium based on comparable permeabilities for either ion [73]. Consequently, PNa/PK has usually been set to 1, and the sum of [K+]i and [Na+]i has consistently been assumed to be constant for all medium compositions [7, 9, 10, 13-15, 17, 19, 23, 24]. Following this approach, however, Vapp(GHK) showed considerable deviations from Edye (Fig. 7B). Setting PNa/PK to 0.29 [18] or 0.64 [72] even increased the difference between the two curves (data not shown). Results of intracellular ion concentration measurements provided by Chen and Reith [18] suggest that not only may both [K+]i and [Na+]i actually change upon alterations in the extracellular medium composition but their sum may vary as well. Thus, usually assumed values for quantities involved in the GHK equation should be inappropriate to fulfill the demand for accurate calibration.

Calibration according to the Nernst equation for the dye and for potassium

Li and White [74] observed in synaptosomes that gramicidin was able to reduce [K+]i only when Na+ was present in the medium. It also seems not to alter the membrane potential in whole cells in Na-free K-NMDG media [18] (this study, data not shown). Still, the commonly used approach of Method 3A has been to add gramicidin [8, 12, 16, 20, 22, 26]. In addition, it has been assumed that [K+]i stays constant irrespective of changes in [K+]o and that EK reflects membrane potential [8, 12, 16, 20, 22, 26]. Steinberg et al. [21] modified this method by media containing a residual [Na+]o of 5 mM and calculated the membrane potential according to the GHK equation. They pointed to the fact that the independent determination of intracellular alkali ion concentration is required for calibration and gave an explanation why PNa/PK = 1 may apply to the gramicidin pore. In K-NMDG media used in this study, removal of external Na+ should lead to complete depletion of intracellular free Na+ [6, 75, 76]. Even then, external sodium concentration remains virtually zero as the total volume of cells is negligible to that of the surrounding medium. This suggests to consider EK a reliable estimate of membrane potential. At least, when based on constant [K+]i values, however, the comparison of Vapp(EK) with Edye could not confirm this view (Fig. 7C).

In accordance with Wilson and Chused [29] but using Na-free K-NMDG media, Method 3B was based on the activation of KCa channels mediated by the Ca2+-ionophore ionomycin. Of all comparisons, Vapp(EK) of ionomycin-treated IGR-1 cells at least revealed the lowest deviation from Edye over a wide range of [K+]o (Fig. 7C). As with Method 3A, intracellular free Na+ should be zero and thus did not contribute to changes in V. The lack of response to [Ca2+]i-enhancing treatment in LCL-HO cells has been found in other cell lines, too [29, 49, 77, 78]. However, this may not necessarily be a result of lacking KCa channels [76]. In lymphoblastoid and normal B cells, it has been demonstrated that a rapid elevation in [Ca2+]i was followed by an immediate return to the basal level [75, 79, 80]. The latter was probably caused by an especially high activity of the Ca2+ pump [77]. In addition, KCa channels may contribute only slightly to the total K+ conductance [79]. In IGR-1 cells suspended in Na-buffer (data not shown) or K-NMDG media containing 5.4 mM potassium (Fig. 7C, Method 3B), the strongly hyperpolarized membrane potential upon 100 nM ionomycin treatment determined as Edye was comparable with that observed in other studies by electrophysiological measurement [81, 82]. Thus, the approach of this study to use Edye as a reference has been further backed up. It should be noted that a high ionomycin concentration of 1 μM resulted in a large proportion of depolarized IGR-1 cells (data not shown). This is in line with findings in human B and T cells [29] and prostatic cancer cells [83]. An explanation may be that low ionomycin concentrations only trigger the release of Ca2+ from intracellular stores, while high concentrations cause a cell-damaging [Ca2+]i increase via Ca2+ entry from the extracellular medium [83].

Measurement of intracellular sodium and potassium concentration and corresponding membrane permeabilities complicates determination of membrane potential

In this study, establishing a millivolt-scale based on the Nernst equation for potassium or the GHK equation for sodium and potassium by merely assuming values for intracellular ion concentrations and membrane permeabilities has not proved to be a satisfactory approach. It must therefore be concluded that these alkali ion parameters have to be determined in order to achieve reliable calibration. Several attempts have actually been made to measure [K+]i and [Na+]i for membrane potential assessment, for example, by flame photometry [5, 21], atomic absorption spectrophotometry [11], and microscopic imaging of the fluorescence of the K- or Na-selective probes PBFI and SBFI [18]. The photometric methods additionally require the cytosolic volume to be determined. Still, it is hardly possible to evaluate how exactly the ratio of ion content and volume measuring values then reflects the respective cytosolic free ion concentration. The fluorescent probes could in principle be measured with the same technique as used for the potentiometric dye provided two excitation wavelengths are available. Nevertheless, it must be considered that PBFI is only 1.5-fold more sensitive for K+ than for Na+ (product information from Molecular Probes) and shows saturation of fluorescence at [K+] higher than 100 nM [84]. In mouse and bovine sperms, it proved to be even unsuitable for the detection of cytosolic [K+] [12]. Using cationic dyes, the null-point detection of the fluorescence of valinomycin-treated cells in media with varying [K+] can be used as an alternative [12]. Because of its known complex formation with valinomycin, this is, however, not possible with DiBAC4(3). If ion permeabilities have to be measured in addition to ion concentrations, for example, by means of electrophysiological current-voltage recordings [71, 72], the methodological complexity and expense is correspondingly higher. This suggests that the reason for replacing measurements by apparently well-founded assumptions in the majority of studies has been in the interest of ensuring practicability. In the last analysis, the need for the determination of cell-associated cation parameters [18, 21] considerably complicates alkali-ion-based calibration compared with using the Nernst partition of the anionic DiBAC4(3) according to Eq. ( (3)).


In summary, calibration methods based on the partition of membrane permeant monovalent cations involved in establishing membrane potential require the quantitative determination of intracellular concentrations and, dependent on the method, membrane permeabilities. In contrast, the equilibrium potential of anionic oxonols has proved to be a tool for reliable membrane potential calculation without any additional quantity needing to be measured. The prerequisite that dye depletion must not occur can be ensured by appropriate cell densities. In addition, at low DiBAC4(3) concentrations terms of ion concentration in the Nernst equation can be replaced by those of corresponding fluorescence, thus allowing cell membrane potential measurement using anionic dyes with the smallest effort and expense possible.


The authors thank Karin Hölsken, Ursula Schramm, Claudia Bruhne, Sylke Faßhauer (Department of Dermatology and Venereology), and Monika Schmidt (Julius Bernstein Institute of Physiology) for technical assistance.