Mitochondrial Inner Membrane Electrophysiology Assessed by Rhodamine-123 Transport and Fluorescence

Abstract

Rhodamine-123 is widely used to make dynamic measurements of mitochondrial membrane potential both in vitro and in situ. Yet data interpretation is difficult due to a lack of quantitative understanding of how membrane potential and measured fluorescence are related. To develop such understanding, a model for dye transport across the mitochondrial inner membrane and partition into the membrane was developed. The model accounts for experimentally measured dye self-quenching and was integrated into a model of mitochondrial electrophysiology to estimate transients in mitochondrial membrane potential from kinetic fluorescence measurements. Our analysis indicates that (i) R123 fluorescence peaks at concentrations near 50 μM due to self-quenching; (ii) measured fluorescence intensity and membrane potential are related by a non-linear calibration curve sensitive to certain experimental details, including total concentration of dye and mitochondria in suspensions; and (iii) the time courses of membrane potential and electron transport fluxes following a perturbation (i.e. addition of ADP) significantly differ from observed transients in fluorescence intensity. These findings are consistent with the model predictions that mitochondria display a characteristic time of response to changes in substrate concentration of less than 0.1 s, corresponding to the time scale over which the rate of ATP synthesis changes to meet changes in ADP concentration.

INTRODUCTION

Dyes sensitive to membrane potential are used to make noninvasive dynamic measurements of mitochondrial membrane potential (ΔΨ), a key indicator of mitochondrial energetics, in both in vitro and in vivo systems. Among them, rhodamine-123 (R123) is the first to be widely used and remains one of the most commonly used to track mitochondrial membrane potential changes in both bulk and single mitochondria measurements.^{7,12–14,17,21,28} Chen et al. first demonstrated that R123 specifically stained mitochondria in response to mitochondria energization in cultured cells, and those chemical agents that collapse membrane potential prevents uptake of R123 by mitochondria.^7,8,16 Emaus et al.¹³ extensively characterized R123 as a probe of membrane potential for suspensions of isolated mitochondria. They showed that the R123 fluorescence spectrum shifts to the red in response to mitochondria energization, and that there is an empirical linear relationship between fluorescence intensity change and membrane potential. Emaus et al. reported their method to be qualitative, yet this linear relationship has been widely used as basis to quantify membrane potential in mitochondria (see for example Ref. 22).

R123 is a fluorescent aromatic monovalent cation that accumulates in the matrix of energized mitochondria. The advantage of using R123 as an indicator of membrane potential include its availability, high sensitivity (high quantum yield), specificity (against other environmental changes), non-invasiveness, and low interference with underlying metabolic processes.¹³ Changes in accumulation produce changes in fluorescence signal, indicating changes in ΔΨ.^7,8,13 Yet the measured dye distribution (concentration in buffer vs. that in mitochondria) can deviate significantly from Nernst equilibrium. The deviation comes from (i) response time needed to reach equilibrium due to the dye’s limited permeability in measurements of transient changes, and (ii) substantial partition of the dye into the mitochondrial membranes.^5,13,24 Although several works have attempted to assess the influence of the dye binding and transport kinetics,^5,24 a quantitative treatment of the transport processes in mitochondria that may be used to analyze observed kinetic data has not been previously available. In addition, despite the apparent importance of self-quenching at the dye concentration achieved in the mitochondrial matrix, this key phenomenon has never been fully explored.^1,26

In the present study, we addressed the quantitative relationship between mitochondrial membrane potential and R123 fluorescence intensity by integrating experimental observations and computational modeling. Our existing mitochondria model² has been extended to account for the transport of R123. The model incorporates experimentally measured R123 self-quenching behavior and was parameterized and validated with kinetic and static measurements on suspensions of isolated mitochondria. The resulting model provides a method to determine membrane potential transients from florescence intensity and a means to quantify the kinetics of mitochondrial energetics under various experimental conditions. Our analysis is consistent with the model predicted time course of mitochondrial membrane potential and electron transport fluxes during state-3 respiration which indicates that mitochondrial ATP synthesis changes to meet changes in ADP concentration with a characteristic response time of less than 0.1 s.

MATERIALS AND METHODS

Mitochondria Model

Our model for mitochondrial electrophysiology and ATP synthesis successfully describes the development and consumption of both the chemical and electrical components of the proton motive force in a simulation of oxidative phosphorylation. Included in the model are the reactions at complexes I, III, and IV of the electron transport system, ATP synthesis at F₁F₀ ATPase, substrate transport at adenine nucleotide translocase (ANT) and the phosphate-hydrogen co-transporter (PiHt), and cation fluxes across the inner membrane including fluxes through K⁺/H⁺ antiporter and passive H⁺ permeation (proton leak). Details of the computation model are published elsewhere.^2,27 The model is extensively validated and parameterized based on sets of data obtained from suspensions of isolated mitochondria from the literature³ and from our laboratory. The model is implemented in MatLab (The MathWorks, Natick, MA) and available at http://www.bbc.mcw.edu/Computation.

Mitochondria Isolation

Cardiac mitochondria were isolated from ketamine-anesthesized guinea pigs (250–300 g) of either sex by differential centrifugation as outlined in Ref. 23. Briefly, ventricles were excised, rinsed in ice-cold isolation buffer (200 mM mannitol, 50 mM sucrose, 5 mM KH₂PO₄, 5 mM MOPS, 0.1% fatty acid free BSA, 1 mM EGTA, pH 7.15), minced into pieces of about 1 mm in size, then homogenized with ultrasonic homogenizer after brief treatment with protease (5 U/mL). The homogenate was centrifuged at 8000 × g for 10 min in a Sorvall RC-50B centrifuge, the pellet rinsed, resuspended and centrifuged at 750 × g for another 10 min, then supernatant collected and centrifuged at 8000 × g. The resulting pellet was resuspended in isolation buffer at a final concentration of ~10 mg/mL and kept on ice until use. All isolation procedures were carried out at 0–4 °C. The amount of mitochondrial protein was assessed using Bio-Rad protein assay⁴ with bovine serum albumin (BSA) as standard. All mitochondria samples were determined to have respiratory control index (RCI) between 9 and 15 (pyruvate as substrate, measured with polarographic oxygen electrode methods on System S 200A from Strathkelvin Instruments, Glasgow, Scotland), and were used within 8 hrs after preparation. Respiration buffer contains 130 mM KCl, 5 mM K₂HPO₄ · 3H₂O, 20 mM MOPS, 2.5 mM EGTA, 1 μM tetrasodium pyrophosphate, 0.1% BSA, pH to 7.15 with KOH. There is no significant decline in the coupling of phosphorylation to oxidation as assessed by the absence of decline in the RCI below 8 over this time period. The morphological integrity of the mitochondria sample prepared with this protocol has been confirmed by electron microscopy.²³

Fluorescence Measurements

Measurements were made at room temperature with continuous stirring of the mitochondrial suspension (0.5 mg protein mL⁻¹ in 2.5 mL volume) using PTI spectrophotometer (QM-8, Photon Technology International) equipped with a magnetic stirrer with fluorescent cation R123 as probe.¹⁵ The sample geometry employed was right-angle observation of the center of a centrally illuminated 10 × 10 mm cuvette. Excitation and emission wavelengths were 503 nm and 527 nm, respectively. The incubation medium used was the respiration buffer described above. R123 and sodium pyruvate were added to final concentrations of 50 nM and 10 mM, respectively. Isolated mitochondria maintained a steady membrane potential (±5%) throughout the duration of the recording (up to 30 min). As a positive control for ΔΨ = 0, CCCP (Carbonyl cyanide 3-chlorophenylhydrazone) was added at the end of each measurement (final concentration: 4 μM) to collapse ΔΨ by eliminating the proton motive force across mitochondrial inner membrane. Changes in membrane potential were obtained from model-based analysis of experimental data including experimental conditions and fluorescence signal (details described in Results). To account and correct for the effects of inner filtering on the fluorescent intensity we also used a dual path-length (4 × 10 mm) cuvette with a 1 mL sample volume and an average excitation light path length of 2 mm. Other than the difference in the excitation light path, all other settings remained the same for both cuvette sizes.

Materials

Rhodamine-123 was purchased from Molecular Probes (Eugene, OR) or Calbiotech (Spring Valley, CA). All other chemicals were purchased from Sigma Chemical Co. (St. Louis, MO). Double-distilled de-ionized water was used throughout.

RESULTS

Relationship between Fluorescence and Concentration of R123 in Aqueous Solution

To assess the self-quenching properties of R123 in vitro, the fluorescence signal from R123 at various concentrations in aqueous solution was determined. Shown in Fig. 1 are the titration profiles obtained using cuvettes with average incident light paths of 2 mm (for the 4 × 10 mm cuvette) and 5 mm (for the 10 × 10 mm cuvette). Both cuvettes have average emission light paths of 5 mm. For experiments with both cuvette dimensions, fluorescence intensity increases approximately linearly with concentration at concentrations lower than 5 μM. However, peaks in intensity are observed at [R123] = 11 and 20 μM for the 4 × 10 mm and 10 × 10 mm cuvettes, respectively. In both cases, intensity monotonically diminishes toward zero at high concentrations of R123.

FIGURE 1.

Relationship between fluorescence and concentration of R123 in aqueous solution. Normalized fluorescence intensity is plotted against R123 concentration in the absence of mitochondria. Open circles correspond to data collected using a 10 × 10 mm cuvette, with mean excitation and emission path lengths of d_ex = 5 mm and d_em = 5 mm; squares correspond to data collected using a 4 × 10 mm cuvette, with mean excitation and emission path lengths of d_ex = 2 mm and d_em = 5 mm. Solid curves represent fits to Eqs. (1)–(3), which correct for the observed inner filter effect. The curve indicated for d = 0 is the prediction of Equation (3), with parameter values k₀ = 8.15 × 10⁴ M⁻¹, k₁ = 5.16 × 10⁴ M⁻¹, k₂ = 1.01 × 10⁶ M⁻², and k₃ = 3.909 × 10¹² M⁻³. Aqueous solution is identical to that used for mitochondrial respiration buffer with the exception that R123 concentration is varied.

The difference between the two profiles is due to the inner filter effect—attenuation of fluorescence intensity due to the absorption of the incident and emission light by R123 itself, which increases with light path. To separate dye self-quenching from this effect, we employ the formula¹⁹

$$I_{\text{observed}}=I_{\text{o}}\times {10}^{-(A_{\text{ex}}+A_{\text{em}})},$$ (1)

where I_observed and I_o are fluorescence intensity observed for finite path length and in the limit of a light path of zero length, respectively. The variables A_ex and A_em represent absorption at the excitation and the emission wavelength, respectively. Assuming negligible deviation from Beer–Lambert Law, as has been observed by Emaus et al.,¹³ we have

$$A_{\text{ex}}+A_{\text{em}}=({\epsilon }_{\text{ex}}{d}_{\text{ex}}+{\epsilon }_{\text{em}}{d}_{\text{em}})[\text{R}123],$$ (2)

where ε_ex and ε_em are the absorption coefficients of R123 at excitation and emission wavelength, which have values of 0.24 × 10⁴ cm⁻¹ M⁻¹ and 5.10 × 10⁴ cm⁻¹ M⁻¹, respectively.¹³ Variables d_ex and d_em are the excitation and emission light paths, which have values of 5 mm and 5 mm for the 10 × 10 mm cuvette, 2 mm and 5 mm for the 10 × 4 mm cuvette.

Both sets of the observed intensity data are well represented by a four-parameter function:

$$I_{\text{o}}([\text{R}123])=\frac{k_0[\text{R}123]}{1+k_1[\text{R}123]+k_2{[\text{R}123]}^2+k_3{[\text{R}123]}^3},$$ (3)

where I_o is the intensity at d_ex = 0 and d_em = 0; the parameters k₀, k₁, k₂, and k₃, are obtained by fitting the observed data.

The optimal fit of Eq. (1) to the data observed at the two light path lengths was obtained for k₀ = 8.15 × 10⁴ M⁻¹, k₁ = 5.16 × 10⁴ M⁻¹, k₂ = 1.01 × 10⁶ M⁻², and k₃ = 3.91 × 10¹² M⁻³ for the titration curve with zero light path length when the maximal fluorescence intensity is normalized to 1. The titration curves predicted using these parameter values for different light paths are plotted as solid lines in Fig. 1. The peak intensity of the reference curve I_o (indicated as d = 0) is predicted to occur at [R123] = 50 μM. The curves predicted for d_ex = 2 and 5 mm are shown to closely match the observed data.

Under commonly employed experimental conditions for membrane potential measurements in suspensions of isolated mitochondria, R123 concentration in the buffer falls within the linear range of the intensity curve, which is from 0 to ~5 μM (see Fig. 1). Yet for energized mitochondria (ΔΨ = 150–200 mV), the R123 concentration ratio in-to-out (aqueous phase only) calculated from Nernst equation is between 342 and 2400. Assuming self-quenching behavior inside matrix similar to that observed in vitro, the signal from the matrix may be significantly quenched at dye concentrations typically used. As observed by Duchen and Biscoe,^10,11 the fluorescent signal from the mitochondria can increase when mitochondria depolarize and the concentration of dye in the matrix decreases. For example, with initial R123 concentration of 0.05 μM, as used in our experiments, our calculations reveal that the matrix of energized mitochondria contributes less than 25% of the overall signal. At higher concentrations the contribution from the matrix is lower. At the total R123 concentration of 0.5 μM, the contribution from the matrix is less than 5%of the total signal. A similar phenomenon has been observed previously with another dye, TMRM, which is another rhodamine derivative that is commonly used as a potential-sensitive probe.²⁶

The mechanism of fluorescence self-quenching is not well understood, and may include formation of non-fluorescent aggregates (dimers, trimers, etc.), energy transition through collision, or some combinations of these effects. Our analysis shows that Eq. (3) effectively describes R123 fluorescence intensity in the aqueous phase as a function of concentration at the excitation and emission wavelengths of 503 nm and 527 nm. It is possible to include more terms in the denominators of Eq. (1); for the purpose of this study the third order polynomial denominator proved sufficient to adequately represent the observed data.

Relationship Between Fluorescence and Transient Membrane Potential

In order to establish quantitative relationship between observed fluorescence signal and transient membrane potential, we devised a model of R123 transport and partition as an extension of our detailed mitochondrial respiration model.² The dye transport model assumes that (i) the dye permeation through the inner membrane is rate-limiting compared with other processes (such as diffusion to and from the surface of the membrane, self quenching, equipment response, etc.); (ii) permeation of dye through the membrane is governed by the Nernst–Goldman expression for passive flux of an ion across a membrane; (iii) the dye partition in the membrane is described by a linear reversible process.

The flux (J) across the inner membrane is modeled using the Goldman–Hodgkin–Katz equation for passive flux of an ion through a membrane:^18,20

$$J=p\frac{zF}{RT}\mathrm{\Delta }\mathrm{\Psi }\left(\frac{{[\text{R}123]}_{\text{e}}{e}^{zF\mathrm{\Delta }\mathrm{\Psi }/RT}-{[\text{R}123]}_{\text{x}}}{e^{zF\mathrm{\Delta }\mathrm{\Psi }/RT}-1}\right)$$ (4)

where p is the permeability coefficient of the membrane, z is the valence of the dye, F is Faraday constant, R is the gas constant, T is temperature, ΔΨ is the membrane potential, and the concentrations of R123 in the buffer and matrix are denoted by [R123]_e and [R123]_x, respectively. Expressing p in units of moles (liter mitochondrial volume)⁻¹ s⁻¹ M⁻¹, the rate of change in R123 concentration in the buffer is given by

$$\frac{d}{dt}{[\text{R}123]}_{\text{e}}=-\frac{J}{V_{\text{e}}}$$ (5)

where V_e is the ratio of buffer volume to mitochondrial volume used in the experiment. In our experiment we used a mitochondrial concentration of 0.5 mg of protein per ml of buffer. Assuming a mitochondrial density of 1.09 g mL⁻¹ of mitochondria and protein fraction of 0.25 g protein per gram mitochondria,²⁵ we arrive at an estimate of 545 for V_e.

We assume that the mass of dye per unit volume of mitochondria bound to the mitochondrial membrane can be approximated by the linear relationship: α([R123]_e + [R123]_x)/2, where αis the dimensionless membrane partition coefficient for R123. This assumption is supported by Emaus et al.’s observation that the ratio between “bound” R123 (R123 inside the matrix plus those bound to the membrane) and “free” R123 (in buffer) were constant over the concentration range commonly used. This assumption can be viewed as a special case of Langmuir isotherm which has a more general applicability over a wider range of dye concentrations.⁹ With this relationship, we have a global statement of mass conservation

$$V_{\text{e}}{[\text{R}123]}_{\text{e}}+W_{\text{x}}{[\text{R}123]}_{\text{x}}+\alpha ({[\text{R}123]}_{\text{e}}+{[\text{R}123]}_{\text{x}})/2=\text{constant}$$ (6)

where W_x is the water space (liter water per liter mitochondria) of the mitochondrial matrix. W_x is estimated to be 0.65.² Differentiating Eq. (6) with respect to time, we obtain

$$\frac{d}{dt}{[\text{R}123]}_{\text{x}}=-\left[\frac{V_{\text{e}}+\alpha /2}{W_{\text{x}}+\alpha /2}\right]\frac{d{[\text{R}123]}_{\text{e}}}{dt}=\left[\frac{V_{\text{e}}+\alpha /2}{W_{\text{x}}+\alpha /2}\right]\frac{J}{V_{\text{e}}}.$$ (7)

Equations (5) and (7) are the governing equations for our model of R123 transport in mitochondria.

The overall fluorescent signal obtained from a suspension of isolated mitochondria is assumed to be the sum of contributions from dye in the buffer, in mitochondrial matrix, and in the membrane:

$$I=(V_{\text{e}}{I}_{\text{o}}({[\text{R}123]}_{\text{e}})+W_{\text{x}}{I}_{\text{o}}({[\text{R}123]}_{\text{x}})+\beta k_0\alpha ({[\text{R}123]}_{\text{e}}+{[\text{R}123]}_{\text{x}})/2)/(V_{\text{e}}{I}_{\text{o}}({[\text{R}123]}_{\text{o}}))$$ (8)

In Eq. (8) the first two terms in the numerator correspond to volume-weighted contributions from the aqueous-phase compartments. The third term in the numerator assumes that the membrane-bound component is linearly proportional to the mass of dye bound to the membrane. The coefficient β is the ratio of fluorescence coefficients for membrane-bound R123 and R123 in aqueous phase in the linear range. The parameter k₀ is the same as appears in Eq. (3). The denominator normalizes the function to be equal to one for a solution containing no mitochondria at total dye concentration denoted by [R123]_o.

Data on R123 fluorescence measured in suspensions of isolated mitochondria in states 2–4 are used to validate and parameterize the model. States 2–4 refer to respiring mitochondria (here supported by phosphate and pyruvate substrate) before the addition of ADP (state 2), during the ATP synthesis period following addition of ADP (state 3), and in the period following the consumption of available ADP (state 4).⁶ Figure 2A shows a measurement from a typical experiment in which mitochondria are added to the buffer at time zero. The measured fluorescence decreases following the addition of mitochondria as the R123 in the buffer is taken up into the mitochondria. When ADP is added to the suspension to initiate state-3 respiration, mitochondria transiently depolarize, resulting in a transient increase in fluorescence. After CCCP is added to uncouple the respiratory chain from ATP synthesis, the membrane potential collapses which results in an increase in fluorescence intensity.

FIGURE 2.

Comparison of model-predicted and experimentally measured fluorescence time courses for state-2, -3, and -4 respiration. (A) Fluorescence measurement on suspensions of isolated mitochondria (gray circles) overlaid with model prediction (solid black line). Mitochondria isolated from guinea pig heart (described in Methods) were added at time 0 to the cuvette containing respiration buffer with R123 and pyruvate substrate. Accumulation and self-quenching of dye inside the matrix and quenching of membrane-bound dye cause a drop of fluorescence signal of over 50%. Addition of ADP results in transient and reversible activation of respiration as well as transient depolarization of the mitochondrial membrane potential. CCCP was added at the end of the experiment to collapse the membrane potential as a positive control for ΔΨ = 0. (B) A detailed view of the ADP-induced transient depolarization of the mitochondrial membrane potential is plotted. In addition to the measured and model-predicted fluorescence intensity, the model-predicted ΔΨ is plotted. Model predictions was obtained for p = 5.869 moles (liter mitochondrial volume)⁻¹ s⁻¹ M⁻¹, α = 4.727, and β = 0.3799.

The model for R123 transport (Eqs. 5 and 7) and fluorescence (Eq. 8) was combined with our model of oxidative phosphorylation and electrophysiology^2,27 to predict and analyze the data illustrated in Fig. 2. The oxidative phosphorylation model predicts ΔΨ over the time course of the experiment; the predicted ΔΨ drives the transport of R123. (Calculations reveal that the transport of R123 does not have a significant effect on the membrane potential transient.) The R123 transport model includes three unknown adjustable parameters p, α, and β; values for these parameters are estimated based on fitting the data from the experiment shown in Fig. 2. The fit illustrated in Fig. 2 is obtained with p = 5.89 moles (liter mitochondrial volume)⁻¹ s⁻¹ M⁻¹, α= 4.73, and β= 0.380. Based on 6 independent experiments, the estimated values of these parameters are p = 6.88 ± 0.39 mol (liter mitochondrial volume)⁻¹ s⁻¹ M⁻¹, α= 4.49 ± 0.21, and β= 0.33 ± 0.02.

Independent estimates of μare available based on a study by Emaus et al.,¹³ in which the concentration ratio of R123 in mitochondria versus buffer was measured to be ~4000 under state-2 conditions. According to our transport model, this ratio can be expressed as:

$$r=\left(W_{\text{x}}+\frac{\alpha }{2}\right)\frac{{[\text{R}123]}_{\text{x}}}{{[\text{R}123]}_{\text{e}}}+\frac{\alpha }{2}\approx 4000.$$ (9)

For values of ΔΨ ranging from 180 to 190 mV, the ratio [R123]_x/[R123]_e range from approximately 1121 to 1655, and Eq. (9) yields an estimate for αbetween 3.53 and 5.83. Despite the fact that the study of Emaus et al. ¹³ used mitochondria isolated from rat liver while our model parameters estimated here is based on mitochondria from guinea pig heart, the agreement between the estimates of α provides independent validation of the current study.

Figure 2B shows the predicted time course of membrane potential that corresponds to the transient state 3 following addition of ADP. Note that the membrane potential depolarizes significantly more rapidly than the observed changes in fluorescence. The time for ΔΨ to reach half-maximal depolarization is less than 0.1 s, while the fluorescence intensity transient reaches its half-maximal value 5.5 s after the addition of ADP. Thus the R123 signal is predicted to have a time scale of response that is more than an order of magnitude slower than actual changes in mitochondrial membrane potential. For a fluorescent dye to effectively track the kinetics of mitochondrial depolarization in state 3, its response time would have to be significantly less than the mitochondrial response time scale of 0.1 s. Indeed, the time course of fluorescence change with another membrane potential-sensitive dye, TMRM, more closely matches the model predicted membrane potential time course than that obtained with R123.²⁴

Relationship between Fluorescence and Static Membrane Potential

The validated and parameterized model of R123 transport and fluorescence can be used to predict the relationship between static (steady-state) membrane potential and observed fluorescence. At equilibrium (J = 0), Eq. (4) reduces to Nernst relation:

$$\frac{{[\text{R}123]}_{\text{x}}}{{[\text{R}123]}_{\text{e}}}=e^{zF\mathrm{\Delta }\mathrm{\Psi }/RT}.$$ (10)

From Eqs. (6) and (10) we obtain the following expressions for [R123]_e and [R123]_x:

$$\begin{array}{l}{[\text{R}123]}_{\text{e}}=\frac{V_{\text{e}}{[\text{R}123]}_{\text{o}}}{V_{\text{e}}+\alpha /2+(W_{\text{x}}+\alpha /2)e^{zF\mathrm{\Delta }\mathrm{\Psi }/RT}}\\ {[\text{R}123]}_{\text{x}}={[\text{R}123]}_{\text{e}}·e^{zF\mathrm{\Delta }\mathrm{\Psi }/RT}\end{array}$$ (11)

Using these expressions with Eq. (8), the steady-state fluorescence intensity is predicted as a function of ΔΨ. Model predictions (based on the mean estimates of αand β) at total dye concentrations of 0.05, 0.5, and 25 μM are illustrated in Fig. 3A. The model predicts a sigmoid relationship between intensity and ΔΨ for concentrations of dye in the lower range. For total dye concentrations higher than a threshold of ~19 μM, the calibration curve is not monotonic, as illustrated for the concentration of 25 μM. Due to self-quenching, for dye concentrations in this high range, the predicted ΔΨ as a function of measured intensity is a multi-valued function.

FIGURE 3.

Predicted steady-state R123 fluorescence intensity versus ΔΨ. (A) Predicted fluorescence signal as a function of ΔΨ at total dye concentrations of [R123]_o = 0.05, 0.50, and 25 μM at the mitochondrial concentration of 0.5 mg protein mL⁻¹. Data points represented by circles are extracted from Ref. 13. (B) The predicted sensitivity $\left|\frac{\mathrm{\Delta }\mathrm{\Psi }}{I}\frac{\partial I}{\partial \mathrm{\Delta }\mathrm{\Psi }}\right|$ of the fluorescence measurement of membrane potential evaluated at ΔΨ = 180 mV is plotted as a function of the [R123]_o The sensitivity curves are plotted for three different values of mitochondrial concentration, as indicated in the figure. Model predictions for (A) and (B) are obtained for α = 4.49, and β = 0.33.

Also shown in Fig. 3A are the data published by Emaus et al.,¹³ which are based on measurements made on R123 fluorescence in suspensions of isolated rat liver mitochondria. Emaus et al. extrapolated a linear relationship based on these data and suggested a “residual membrane potential for non-energized mitochondria” of ~60 mV. This residual potential corresponds to the value of ΔΨ at which the linear relationship predicts the fluorescence intensity to be at the maximum value. Similar values of a “residual potential” were implied in other studies.²⁴ Our model predicts that the linear relationship holds approximately for membrane potential in the range of 60–180 mV for the total R123 concentration upto 5 μM at the mitochondria concentration of 0.5 mg protein mL⁻¹. The 60 mV offset associated with the linear relationship is due to the sigmoid nature of the relationship between potential and intensity. Note that a quantitative comparison between the data of Emaus et al.¹³ and the model predictions is not possible because a complete set of exact experimental conditions (including dye and mitochondria concentrations) is not available from the study of Emaus et al.¹³ (Also note that the source of mitochondria for the study of Emaus et al. was rat liver, while in this study mitochondria are obtained from guinea pig cardiac tissue.)

To study how experimental conditions affect the measurement of membrane potential, we explored the sensitivity of fluorescence to ΔΨ predicted by the model over a specified range of dye concentration. We define sensitivity as $\left|\frac{\mathrm{\Delta }\mathrm{\Psi }}{I}\frac{\partial I}{\partial \mathrm{\Delta }\mathrm{\Psi }}\right|$ evaluated at ΔΨ = 180 mV, a value within the physiologically relevant range. For example, a sensitivity of 1.1 means that a 1% change in ΔΨ at 180 mV leads to a 1.1% change in fluorescence intensity. Sensitivity curves, plotted in Fig. 3B as functions of [R123]_o for three different values of mitochondrial concentration, indicate that the sensitivity of fluorescence to change in membrane potential has a maximal value, which depends on the mitochondrial concentration. At the mitochondrial concentration of 0.5 mg protein mL⁻¹, the sensitivity is maximized near the dye concentration of 1 μM. To simultaneously maximize sensitivity and obtain a single-valued calibration curve, this analysis predicts that a total dye concentration near this value should be used at the mitochondrial concentration of 0.5 mg protein mL⁻¹. In this study we used a low total dye concentration ([R123]_o = 0.05 μM) to minimize the impact of the R123 current on the inner membrane electrophysiology. At this concentration the predicted steady-state sensitivity is 1.1, compared to the peak value of 1.74. Of course this set of sensitivity curves is different at different values of ΔΨ. Generally the sensitivity declines at both the higher and lower ends of the ΔΨ range.

Transient Behavior of Inner Membrane Currents

In response to a perturbation, such as the addition of ADP to initiate state-3 respiration in a suspension of isolated mitochondria, currents across the mitochondrial inner membrane effect changes in ΔΨ. The diagram in Fig. 4A illustrates the membrane complexes that account for the time course of membrane potential predicted using our model² during state-3 respiration. Figure 4A plots the predicted flux through complex I and ANT, normalized relative to the state-2 flux through complex I, denoted J_o. The factor of 4/10 used for normalization is the maximal ratio of steady-state complex-I flux to ANT flux (the inverse of the model-predicted P/O ratio) and is applied here for convenient comparison between the two fluxes. The nonzero flux through complex I during state 2 is necessary to balance the proton leak flux and maintain the proton motive force. Therefore the complex-I flux, J_CI, is not zero in state 2. The ANT flux, J_ANT, is zero during state 2 because there is no transport of ATP from the matrix to the buffer in state 2.

FIGURE 4.

Mitochondrial inner membrane electrophysiology. (A) Components of the electron transport chain, F₀F₁–ATPase, and adenine nucleotide translocase (ANT), which carry current across the inner membrane, are illustrated. (B) Time course of predicted fluxes through the respiratory chain and ANT are plotted for the transition from state-2 to state-3 respiration. Fluxes are normalized to J_o, the state-2 flux through complex I. Simulation is for a mitochondrial concentration of 0.5 mg protein mL⁻¹. State 3 respiration is simulated by adding 0.25 mM ADP to the buffer at time 10 s.

For the results illustrated in Fig. 4, the transient is simulated based on the addition of 0.25 mM ADP to the buffer at time 10 s to initiate state-3 respiration. The ANT flux reaches its peak value immediately following the addition of ADP, while the time for the electron transport chain fluxes to reach half their maximal value following the addition of ADP is ~0.1 s. (Predicted complex-III and -IV fluxes, which are not shown, are nearly indistinguishable from the predicted complex-I flux.)

Thus the initiation of the exchange of buffer ADP for matrix ATP occurs effectively instantaneously compared to the timescale of the changes in membrane potential and potential-sensitive dye fluorescence. However, the ANT flux immediately starts to decrease following the initial maximum. Neither ANT nor electron transport fluxes are maintained at a steady state during state 3. Thus the rate of oxygen consumption, which is the flux through complex IV, is not constant.

CONCLUSIONS

Noninvasive assays using membrane potential sensitive dyes such as R123 provide valuable tools to measure ΔΨ, a crucial variable representing the energetic state of mitochondria in both cells and suspensions of isolated mitochondria. Here we have developed a quantitative and predictive biophysical model of the transport kinetics and fluorescence quenching of R123, a widely used dye. Major findings from this study are:

1. The intensity of R123 fluorescence (at excitation and emission wavelengths of 503 nm and 527 nm, respectively) has a peak at R123 concentration of 50 μM, and decreases to zero at higher concentrations due to self-quenching.

2. Measured fluorescence intensity and membrane potential are related by a non-linear calibration curve. The previously published and widely used empirical linear calibration curve relating measured fluorescence intensity and membrane potential is valid only over limited range of ΔΨ, ranging approximately from 80 to 180 mV (see Fig. 3A).

3. The shape of the calibration curve is strongly sensitive to details of experimental protocol, including total concentration of dye used, concentration of isolated mitochondria in suspensions, etc.

4. The predicted time course of membrane potential in response to a perturbation (such as the addition of ADP to the respiration buffer) significantly differs from the observed transient in fluorescence intensity. R123 fluorescence intensity responds to rapid changes in membrane potential with a time constant of ~6 s, while the membrane potential depolarizes when ADP is added with a smaller time constant. Our model simulations predict that the mitochondrial response time constant is approximately 0.1 s.

In addition, the analysis predicts that the signal obtained from fluorescence imaging of mitochondria in cells may arise primarily from the membrane-bound component when the aqueous-phase R123 in the matrix of energized mitochondria is predicted to be highly quenched and emit no significant signal at the excitation and emission wavelengths used in this study. Our fluorescence model assumes that there is no self-quenching of membrane bound dye in this study. Therefore the membrane-bound component of Eq. (8) varies linearly with concentration. By conducting experiments described by Fig. 2 at varying dye concentrations, we found that this model reproduces observations for total dye concentrations lower than 1 μM. At higher concentrations, observations deviate from model predictions, presumably due to self-quenching of membrane-bound dye which becomes significant.

Our analysis predicts that greater than 60% of total R123 is expected to be membrane-bound for normally energized mitochondria under the experimental conditions employed here and by Emaus et al.¹³ This prediction is supported by observations on changes in fluorescence polarization due to a large degree of immobilization or binding of probe.¹³ The interaction of R123 with the membrane may be a cause for the red shift in R123 absorption and fluorescence emission spectra observed by Emaus et al.¹³

The parameterized and validated computational model for R123 kinetics developed here can be used to quantify ΔΨ from measurements of R123 fluorescence intensity. Estimates of ΔΨ from steady-state data can be made based on the steady-state equations and the associated calibration curves demonstrated in Fig. 3A. Estimation of time courses of ΔΨ from transient data on fluorescence may be obtained from model-based deconvolution of ΔΨ(t) from the intensity time course. In addition, the computational modeling approach developed here can be directly applied to other membrane potential sensitive dyes, such as the rhodamine derivatives tetramethyl rhodamine ethyl (TMRE) and tetramethyl rhodamine methyl ester (TMRM), for which self-quenching and binding to mitochondrial membrane have been reported.^24,26

To apply the methods developed here to the use of other dyes to assay membrane potential, the basic experiments to characterize the self-quenching phenomena and the transport parameters (α, β, and p) must be repeated and validated for a given dye. In addition, to apply this method to mitochondria from other tissue and/or other species, it will be necessary to determine how much these parameters vary for mitochondria obtained from different sources. Here we have shown that the partition coefficient that we estimate for guinea pig cardiac mitochondria is within the range of that reported for rat liver mitochondria.¹³ However partition coefficient is estimated from Ref. 13 to be in approximate range of ±25% the mean estimate of α from this study. Therefore it is not clear how α, or other transport parameters, vary for mitochondria from different sources. Preliminary analysis of membrane potential transient from mitochondria isolated from rat hearts (not shown) indicates that the transport parameter values for rat myocardial mitochondria are not significantly different from the estimates reported here for guinea pig heart mitochondria.

Beyond isolated mitochondria, this method may be adapted to quantify cellular membrane potential and mitochondrial membrane potential in intact cells. In intact cells the distribution of fluorescent cations such as R123 and other rhodamine derivatives throughout cytoplasmic, mitochondrial, and other cellular compartments is expected to be governed by the plasma membrane potential, the mitochondrial potential, and binding of the lipophilic ions to membranes and intracellular lipids. Thus the governing transport equations must be modified and parameterized to account for these phenomena. The next steps to extend the approach developed here to quantify the kinetics of mitochondrial membrane potential in intact cells will involve combining the transport modeling with experimental and analysis techniques that provide simultaneous measurement of plasma and mitochondrial membrane potentials. This analysis will be used to resolve the ambiguity originating from dye self-quenching in interpreting microscopic observations.