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 . 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+  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 . 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 , 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 . Consequently, pure cell volume changes were virtually not accompanied by changes in fluorescence . 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 . In contrast to using low dye concentrations, fluorescence and membrane potential should then be linearly related . It is exactly this that could be demonstrated by microscopic imaging of voltage-clamped cells  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 , the action of fixatives is not restricted to the cell membrane . Depolarization by chemical fixation should therefore be avoided because it causes significantly enhanced fluorescence of bound dye at high dye concentrations . In addition, possible activation of BKCa channels by the dye itself, which would lead to hyperpolarization, must also be taken into consideration . 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 . Interestingly, BKCa channels could not actually be detected in the latter in a recent electrophysiological study , 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 , 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 , 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 . 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 . 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  and osteoblast-like cells , 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 , 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 . 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  (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  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 . In rat spermatids and cardiac myocytes, it was 0.62  or 0.64 . Grinstein et al.  explained the action of gramicidin in whole cells by a rapid exchange of potassium for sodium based on comparable permeabilities for either ion . 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  or 0.64  even increased the difference between the two curves (data not shown). Results of intracellular ion concentration measurements provided by Chen and Reith  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  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  (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.  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  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 . 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 . In addition, KCa channels may contribute only slightly to the total K+ conductance . 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  and prostatic cancer cells . 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 .
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 , and microscopic imaging of the fluorescence of the K- or Na-selective probes PBFI and SBFI . 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 . In mouse and bovine sperms, it proved to be even unsuitable for the detection of cytosolic [K+] . 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 . 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)).