SELECTED DEFINITIONS

TOP ABSTRACT SELECTED DEFINITIONS INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

[Ca2+]c(dia, 0.25), [Ca2+]c(dia, 2)	=	Cytosolic [Ca2+] in diastole at 0.25 or 2 Hz pacing frequency ([Ca2+]c(dia, 0.25) measured only with Indo-1, while [Ca2+]c(dia, 2) measured with Indo-1 or Rhod-2).
[Ca2+]m(0.25), [Ca2+]m(2)	=	Mitochondrial [Ca2+] at 0.25 or 2 Hz (in diastole) (depends on time-averaged [Ca2+]c; e.g. higher time-averaged [Ca2+]c with increased frequency).
R2(dia)	=	Total Rhod-2 intensity during diastole (mitochondrial + cytosolic Rhod-2).
Itot(0.25)	=	R2(dia) at 0.25 Hz steady-state pacing.
Itot(2init)	=	Initial R2(dia) following an increase from 0.25 to 2 Hz.
Itot(2SS)	=	R2(dia) at 2 Hz steady-state pacing.
R2c	=	Beat-to-beat Rhod-2 transient amplitude (mainly from cytosolic Rhod-2).
R2c(dia)	=	Amplitude of the fast increase in diastolic Rhod-2 signal with increased frequency (Itot(2init)  Itot(0.25); mainly from cytosolic Rhod-2).
R2m	=	Amplitude of the slow increase in diastolic Rhod-2 signal with increased frequency (Itot(2SS)  Itot(2init); mainly from mitochondrial Rhod-2).
	=	Time constant for the slow rise component of the Rhod-2 signal.
	=	Time constant for the slow decay component of the Rhod-2 signal.
NADH	=	Semicalibrated [NADH]m from Nratio (see Eq. 2) or nicotineamid adenine dinucleotide (reduced form).
[NADH]m	=	Mitochondrial [NADH].
NADH MIN	=	Minimum level of NADH following increased work (previously shown to depend on work level).
NADH REC	=	Amount of NADH recovery following prolonged work (hypothesized to depend on [Ca2+]m).
NADH MAX	=	Maximum level of NADH following reduced work ("overshoot"; hypothesized to depend on [Ca2+]m prior to reducing work.)
	=	Time constant for the slow rise of the NADH signal.
	=	Time constant for the slow decay of the NADH signal.

	INTRODUCTION

TOP ABSTRACT SELECTED DEFINITIONS INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

The mechanisms of regulation of oxidative phosphorylation with increased work have recently gained new interest. Evidence has suggested that increased mitochondrial [Ca²⁺], [Ca²⁺]_m, may, in addition to ADP (Jacobus et al., 1982; Koretsky et al., 1987; Unitt et al., 1989), stimulate the ATP synthesis rate by indirect action on the F₀F₁-ATPase (Wan et al., 1993; Territo et al., 2000). Such downstream regulation of the ATP synthesis rate would result in increased NADH consumption rate, and, consequently, necessitate increased NADH production rates as well. Up-regulation of the NADH production rate has also been hypothesized to be controlled by increased [Ca²⁺]_m, activating pyruvate dehydrogenase (PDH) or tricarboxylic acid cycle dehydrogenases (Hansford, 1991; Crompton, 1990; McCormack et al., 1990). Provided that the activation of the F₀F₁-ATPase and the dehydrogenases occur on different timescales and with different relative magnitudes, slow changes in mitochondrial NADH, [NADH]_m, may be observed following increased [Ca²⁺]_m. Increased [Ca²⁺]_m, in turn, is expected following increased (average) cytosolic [Ca²⁺], [Ca²⁺]_c, such as when the workload is increased by increased pacing frequency (Miyata et al., 1991).

In support of this mechanism, we have previously shown that, in intact cardiac trabeculae, [NADH]_m and average [Ca²⁺]_c increased when the workload was increased by increased pacing frequency (Brandes and Bers, 1996; Brandes et al., 1998), but [NADH]_m did not increase when the workload was increased by stretching the muscle (no expected increase in [Ca²⁺]_c) (Brandes and Bers, 1997). However, there is little direct evidence that shows that, with increased workload (e.g., by increased pacing frequency), increased [NADH]_m is correlated with increased [Ca²⁺]_m.

The primary goal of this study is therefore to test whether increased pacing frequency causes increased [Ca²⁺]_m and [NADH]_m, and to compare the kinetics of change. To more closely follow the effect of increased [Ca²⁺]_m on [NADH]_m, it is necessary to measure both simultaneously.

Previous studies have used Indo-1 to measure [Ca²⁺]_m and endogenous fluorescence to measure [NADH]_m. A problem with Ca²⁺-measurements using Indo-1, however, is that its emission spectrum overlaps with that of NADH (~400-500 nm), and changing [NADH]_m would thus affect the Indo-1 signal. In contrast, Rhod-2 fluoresces at a longer wavelength (~590 nm) than Indo-1, making it more suitable for Ca²⁺-measurements than Indo-1 when [NADH]_m is expected to change. Furthermore, because the Rhod-2 spectrum does not overlap with NADH fluorescence, [NADH]_m measurements may be performed simultaneously with Rhod-2-based Ca²⁺-measurements (although changes in [NADH]_m can be assessed in the presence of Indo-1 (Brandes et al., 1993a)).

A disadvantage of Rhod-2 versus Indo-1, however, is that the wavelength of the Rhod-2 emission maximum is independent of [Ca²⁺]_m, and Rhod-2 can therefore not be used as a ratiometric dye. It is consequently much more difficult to convert Rhod-2 intensities to explicit [Ca²⁺] values. A secondary goal of this study was therefore to develop a method whereby quantitative information about [Ca²⁺]_m, or at least relative changes in [Ca²⁺]_m, may be calculated from Rhod-2 fluorescence intensities.

	MATERIALS AND METHODS

TOP ABSTRACT SELECTED DEFINITIONS INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Trabeculae preparation

Thin band-shaped trabeculae (~200 by 500 µm) were isolated from rat right ventricles as described elsewhere (Brandes and Bers, 1996). Briefly, brown male LBN-F1 rats (370-510 g) were deeply anesthetized and anticoagulated by injecting 65 mg pentobarbital and 1000 U heparin i.p. The hearts were excised and then perfused retrograde before removing the trabeculae. The perfusion solution contained (in mM): NaCl (108), KCl (21), MgCl₂ (1.2), CaCl₂ (0.5), NaHCO₃ (24), Glucose (4), sodium pyruvate (10), insulin (20 units/L) and was equilibrated with a 95% O₂, 5% CO₂ gas mixture to produce pH = 7.40.

After dissection, the muscle was mounted in a muscle chamber (Brandes and Bers, 1996), paced at 0.5 Hz and superfused at 10-15 ml/min with the solution described above except that 6 mM KCl, instead of 21 mM, was used, and initial [Ca²⁺] = 0.3 mM until force was stable, and then raised to 1.5 mM. Muscle stretch was adjusted to obtain maximum developed force, which was measured during isometric contractions (Backx and Ter Keurs, 1993; Brandes and Bers, 1997). All experiments and procedures were performed at room temperature (~25°C).

Fluorescence instrumentation

Instrumentation described in detail elsewhere (Brandes and Bers, 1996) was modified for simultaneous excitation at two wavelengths (350 and 540 nm) and emission detection at three wavelengths (see Fig. 1): 1) 385 nm: The reference signal for NADH motion correction (Brandes and Bers, 1996) or, alternatively, the lower Indo-1 emission wavelength (Grynkiewicz et al., 1985; Brandes et al., 1994); 2) 456 nm: The NADH emission or, alternatively, the higher Indo-1 emission wavelength (Grynkiewicz et al., 1985; Brandes et al., 1994); and 3) 590 nm: The Rhod-2 emission wavelength.

View larger version (28K): [in this window] [in a new window]   FIGURE 1   Instrumentation used to simultaneously measure NADH (at 385 and 456 nm) and Rhod-2 fluorescence (at 590 nm). The light from a Xenon arc lamp was divided into two paths by a 380-nm dichroic mirror (380 DRLP; Omega Optical, Brattleboro, VT), filtered at 350 nm (20-nm bandwidth) and 540 nm (25-nm bandwidth), respectively (Chroma Technologies, Brattelboro, VT) and recombined using a bifurcated fiber optic cable (Cuda Products Corp, Jacksonville, FL). The dichroic mirror in the inverted microscope (Nikon Diaphot-TMD, Nikon Corp., Melville, NY) was a specially designed mirror that reflected light at 350 and 540 nm, while transmitting light at 375-510 nm and above 560 nm (Chroma Technologies). The transmitted fluorescence passed through two dichroic mirrors (420 and 500 nm; Reynard Corp, San Clemente, CA and Omega Optical) and was subsequently filtered at three wavelengths (385, 456, and 590 nm; bandwidths 22, 10, and 20 nm; Chroma Technologies).

[NADH]_m measurements

[NADH]_m was assessed using methods described previously (Brandes and Bers, 1996). Briefly, the trabeculae were excited by light at 350 nm, and fluorescence detected at 385 and 456 nm. The use of these tissue light isosbestic wavelengths accounts for possible changes in tissue light absorbance, e.g., due to hypoxia (Brandes et al., 1994). However, as we have demonstrated, the trabeculae were not hypoxic at higher pacing rates (Brandes and Bers, 1996). The fluorescence signal at 456 nm (N456) is predominantly arising from mitochondrial NADH (Eng et al., 1989; Nuutinen, 1984) and motion artifacts. In contrast, the reference signal at 385 nm (due to auto-fluorescence and possibly a small component of back-scattered light; N385) is mainly sensitive to motion artifacts (Brandes and Bers, 1996). We therefore used our previously developed method to eliminate motion artifacts from the NADH fluorescence signal at 456 nm by dividing it with the reference signal (Brandes and Bers, 1996), thus obtaining a fluorescence ratio,

(1)

Because N385 and N456 gradually decreased during the experimental protocols, and at different rates (Brandes and Bers, 1996; Ashruf et al., 1995), N_ratio was normalized relative to its value at a pacing frequency of 0.25 Hz (control value). Occasionally, N_ratio slowly changed during the course of a protocol and, in this case, the whole trace was mathematically baseline corrected (by correcting the trace with a second order fitted polynomial so that consecutive N_ratio at 0.25 Hz was constant at unity). [NADH]_m is assessed from N_ratio by using a semicalibrated NADH defined such that NADH = 0 when NADH is maximally oxidized, corresponding to 0.49 · N_ratio (at 1 Hz steady state) (Brandes and Bers, 1996), and NADH = 1 during baseline conditions (at 0.25 Hz pacing frequency) according to

(2)

This calibration procedure causes the changes in NADH to be up to twice as large as the changes in N_ratio (e.g., a 10% change in N_ratio would result in a 15-20% change in the calibrated NADH). Changes in NADH will thus be expressed in absolute fractional or percentage units, where NADH at control is unity or 100%. (Note that, because N_ratio(0 Hz) ~ N_ratio(0.25 Hz), calibrated NADH would be similar regardless of whether 0 or 0.25 Hz were used as baseline condition.)

Mitochondrial and cytosolic [Ca²⁺] measurements in Rhod-2-loaded trabeculae

Trabeculae were loaded with Rhod-2/AM (Molecular Probes, Eugene, OR) to measure cytosolic and mitochondrial [Ca²⁺] ([Ca²⁺]_c and [Ca²⁺]_m). Rhod-2/AM was first dissolved with DMSO containing 25% (w/vol.) Pluronic to a concentration of 1 mM, and then diluted 100-fold to a final concentration of 10 µM in Tyrode Buffer containing (in mM) NaCl (140), KCl (6), MgCl₂ (1.0), CaCl₂ (0.3), Hepes (5), Glucose (10), sodium pyruvate (10), pH = 7.40. Stimulation was ceased, and the trabecula incubated for 50 min at room-temperature (~25°C). The trabecula was then superfused with normal perfusate containing [Ca²⁺] = 0.3 mM for ~5 min or until force relaxed completely, followed by [Ca²⁺]_c = 1.5 mM and pacing at the 0.25 Hz basal frequency for at least 30 min before any measurements. Rhod-2 fluorescence was excited at 540 nm and emission detected at 590 nm (myoglobin isosbestic wavelength with regard to oxygenation; Brandes et al., 1994). At 590 nm, the fluorescence intensity typically increased by 5-10 times after Rhod-2 loading, whereas the intensity at 456 nm (where NADH is detected) only increased by 2-5%.

To assess [Ca²⁺]_m, it is necessary to determine the relative fractions of Rhod-2 that loads into the mitochondria versus the cytosol (by removing the cytosolic component with digitonin), and to obtain an independent measurement of [Ca²⁺]_c using a dye that only loads into the cytosol (free salt of Indo-1; see below). Furthermore, because Rhod-2 fluorescence intensity depends both on [Ca²⁺] and on [Rhod-2], Rhod-2 was saturated with Mn²⁺ to obtain an independent measure of [Rhod-2]. Eqs. A21, A22, and A27 in the Appendix shows the calculation of [Ca²⁺]_m (at 0.25 and 2 Hz) based on four independent measurements: the total measured Rhod-2 fluorescence (mitochondrial and cytosolic), the total Rhod-2 fluorescence after Mn²⁺ saturation, Indo-1 measured [Ca²⁺]_c, and the relative fraction of cytosolic Rhod-2 dye. Two different methods to determine [Ca²⁺]_m (2 Hz) are presented to determine whether there is a fast rising component of [Ca²⁺]_m when the pacing frequency is abruptly increased. If the two methods would produce similar results, it would suggest that [Ca²⁺]_m does not abruptly increase (see Appendix).

Another method to achieve the same conclusion would be to compare the diastolic values of [Ca²⁺]_c (2 Hz) immediately following increased pacing frequency, when measured by Rhod-2 versus Indo-1. If the values are similar, it would again suggest that [Ca²⁺]_m does not abruptly increase when the pacing frequency is abruptly increased (see Appendix). Eq. A30 in the Appendix shows the calculation of [Ca²⁺]_c (2 Hz), based on the same four independent measurements used to calculate [Ca²⁺]_m.

Cytosolic [Ca²⁺] measurements in Indo-1-loaded trabeculae

To selectively measure cytosolic [Ca²⁺], a separate group of trabeculae were iontophoretically loaded with the free acid of Indo-1 (Molecular Probes), as described elsewhere (Maier et al., 1998), because this approach eliminates Indo-1 compartmentalization (Backx and Ter Keurs, 1993). Indo-1 fluorescence was excited at 350 nm, and the emission ratio, I_ratio (intensity at 385 vs. 456 nm; I₃₈₅/I₄₅₆), was calculated after subtraction of background fluorescence (partly NADH) at each emission wavelength, and accounting for any changes in NADH during the protocol (separately measured) (Brandes et al., 1993a). The intensity of I_ratio is related to [Ca²⁺]_c by (Grynkiewicz et al., 1985)

(3)

or equivalently,

(4)

where S₄₅₆ is the ratio between the 456-nm Indo-1 emission intensity in the absence of [Ca²⁺]_c and with saturating [Ca²⁺]_c (Grynkiewicz et al., 1985). R_min and R_max are the I_ratio values in the absence of [Ca²⁺]_c and with saturating [Ca²⁺]_c, respectively. The calibration constant S₄₅₆ was determined in a protein solution that mimics intracellular conditions, whereas R_min and R_max were determined in vivo as described by Brandes et al. (1993b). In contrast, K_d was determined in aqueous solution (see section below).

Determination of Indo-1 and Rhod-2 calibration parameters, K_d,  and

Because of difficulties in reliably determining K_d in the intracellular milieu (Baker et al., 1994), the K_d of both Indo-1 and Rhod-2 were identically determined in aqueous solutions. The fluorescence intensities were measured as a function of [Ca²⁺] by successively diluting an EGTA solution with a buffered Ca²⁺-EGTA solution (Molecular Probes). The mixture contained Rhod-2 or Indo-1 (5.75 and 3 µM, respectively), Ca²⁺ (0-39.8 µM free as calculated from the dilutions), EGTA (10 mM), Mg²⁺ (1.0 mM), K⁺ (140 mM) and Hepes (40 mM). Measurements were done at room temperature and adjusting to pH = 7.20. K_d was obtained by nonlinear curve fitting (Microcal Software Inc, Northampton, MA) of the measured intensities of Rhod-2 and Indo-1 ratio versus [Ca²⁺] using Eqs. A1 and 3, respectively.

As shown in the Appendix, [Ca²⁺] may be determined from the Rhod-2 fluorescence intensity (I) by using two calibration parameters;  = I_min/I_max and  = I_Mn²⁺/I_max, where I_max is the maximum intensity (with saturating [Ca²⁺]), I_min is the minimum intensity (with [Ca²⁺] = 0) and I_Mn²⁺ is the intensity with saturating [Mn²⁺]. In contrast to R_min and R_max, it is difficult to determine  and  in vivo, and they were therefore determined from the same aqueous solution that was used to determine K_d. In fact,  was simply calculated from the fitted values of I_min and I_max using the K_d measurements. I_Mn²⁺, and subsequently , was determined by adding saturating [Mn²⁺] = 250 µM to the same aqueous solution as that used for the K_d measurements, but without EGTA and minimal Ca²⁺ ([Ca²⁺]₀ ~ 5 µM; typical of de-ionized H₂O as determined with a Ca²⁺ electrode).

Data analysis

A 0.2-Hz low-pass filter was applied to the NADH signal to obtain improved signal-to-noise ratio using software digital filtering (Origin, MicroCal Software Inc.). This filtering also removed the beat-to-beat changes in the NADH signal (Brandes and Bers, 1996). To determine the exponential time constants for changes in the Rhod-2 or NADH signal, nonlinear curve fitting was employed using the exponentially rising or decaying parts of the traces according to

(5)

where Y is the R2(dia) or NADH intensity, t₀ is the fitted (extrapolated) start time, Y₀ is the value of Y at t = t₀, A is the amplitude of change (A < 0 for the rise and A > 0 for the decay), and  is the time constant of the rise or decay of R2(dia) or NADH.

Results were reported as means ± SE. Statistical analysis was performed using Student's t test, and differences were considered significant when p < 0.05.

	RESULTS

TOP ABSTRACT SELECTED DEFINITIONS INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Effects of increased frequency on NADH and Rhod-2 fluorescence

Figure 2 shows an example of a trabecula loaded with Rhod-2/AM, and demonstrates the effects of increased pacing frequency (from 0.25 to 2 Hz) on the NADH fluorescence ratio, the total Rhod-2 fluorescence (cytosolic and mitochondrial Rhod-2), and Force. When the frequency was increased, the diastolic levels of Rhod-2, R2(dia), and Force initially increased abruptly, and [NADH]_m decreased to a minimum (MIN). During continued stimulation at 2 Hz, R2(dia) slowly increased (time constant  ~ 13 s) and reached a new steady state after ~1 min, at which point the Rhod-2 transient amplitude, R2_c, was similar to that at 0.25 Hz. The slow rise of R2(dia) was accompanied by a similar slow recovery of [NADH]_m (REC) whereas Force was unchanged. When the pacing frequency was returned to 0.25 Hz, R2(dia) and diastolic Force fell abruptly, and [NADH]_m rose to a maximum level (MAX). During continued stimulation at 0.25 Hz, R2(dia) and [NADH]_m slowly returned to control values whereas R2_c was again unchanged.

View larger version (49K): [in this window] [in a new window]   FIGURE 2   Example of changes in NADH fluorescence (top panel), Rhod-2 fluorescence (middle panel), and Force transients (bottom panel) when the pacing frequency is raised from 0.25 to 2 Hz (at t1 = 46 s) and then back to 0.25 Hz (at t2 = 122 s). Increased pacing frequency causes a fast rise of Rhod-2 fluorescence (Itot(0.25) to Itot(2init)), followed by a slower rise (Itot(2init) to Itot(2SS)). See text and Selected Definitions for additional explanation of symbols used.

The changes in [NADH]_m observed here are typical of those that we have reported previously under similar conditions (Brandes and Bers, 1997) and also at more physiological temperatures (37°C) (Brandes and Bers, 1999) and using alternative substrates (Brandes, 1999). The immediate rise of R2(dia) and diastolic Force with increased pacing frequency may be caused by increased diastolic levels of [Ca²⁺]_c ([Ca²⁺]_c(dia)) affecting cytosolic Rhod-2, whereas the slow rise may be largely caused by slowly increasing levels of [Ca²⁺]_m affecting mitochondrial Rhod-2. (Because the rise of diastolic Force was relatively small, the rise of [Ca²⁺]_c(dia) may be subthreshold for force development.) Thus, the parallel slow rise of [NADH]_m suggests that it may be caused by an increased NADH production rate which, in turn, may be stimulated by slowly increasing [Ca²⁺]_m.

Because R2_c and Force transients were similar at 0.25 and 2 Hz, the beat-to-beat Rhod-2 transients may be accounted for by variations in [Ca²⁺]_c. However, some investigators have proposed that small Ca²⁺ transients may also occur in the mitochondria (Sparagna et al., 1995; Buntinas et al., 2001; Trollinger et al., 2000), and such small transients may not be ruled out here based on the results of Fig. 2.

To investigate the hypothesis that the slow rise of the Rhod-2 signal is due to slowly increasing [Ca²⁺]_m, the cytosolic Rhod-2 signal component may possibly be eliminated by displacing Ca²⁺ bound to cytosolic Rhod-2 by the addition of saturating [Mn²⁺], "Mn²⁺ quenching" (Miyata et al., 1991).

Mn²⁺ quenching of Rhod-2 fluorescence

Other investigators have loaded myocytes with Indo-1/AM and obtained Indo-1 loading in both cytosol and mitochondria (Spurgeon et al., 1990; Miyata et al., 1991; Schreur et al., 1996). External Mn²⁺ was, in that case, applied to selectively saturate cytosolic Indo-1 but not mitochondrial Indo-1, so that it no longer responded to changes in [Ca²⁺]_c and only to changes in [Ca²⁺]_m.

To similarly Mn²⁺-saturate cytosolic Rhod-2 here, trabeculae were carefully titrated with Mn²⁺-containing perfusate. Figure 3 shows a typical example of an attempt to selectively saturate the cytosolic, but not the mitochondrial, Rhod-2 fluorescence. Before application of Mn²⁺, the pacing frequency was first increased from 0.25 to 2 Hz, and then returned to 0.25 Hz. The typical changes in NADH and Rhod-2 signal were similar to those shown in Fig. 2. The fast Rhod-2 components, R2_c (beat-to-beat transients) and R2_c(dia) (fast rising component of R2(dia)) are shown with gray and white arrows, respectively (gray and white bars in the bottom panel). The slower Rhod-2 component, R2_m (slow rising component of R2(dia)), is shown with a black arrow (and black bar).

View larger version (34K): [in this window] [in a new window]   FIGURE 3   Effects of Mn2+ quenching of cytosolic and mitochondrial Rhod-2 fluorescence. Application of Mn2+ is indicated with a solid bar. Pacing frequency was repeatedly increased and decreased (0.25-2-0.25 Hz) which, before Mn2+ quenching (baseline), caused changes in NADH (top panel) and Rhod-2 (middle panel) similar to those in Fig. 2. In the middle panel, the beat-to-beat Rhod-2 transients are indicated with a gray arrow, the fast Rhod-2 rise with a white arrow, and the slow rise with a black arrow. The bottom panel shows the relative magnitude (versus baseline = 100%) of the transients (gray bar), fast rise (white bar) and slow rise (black bar) as both cytosolic and mitochondrial Rhod-2 were progressively Mn2+ quenched.

The normal perfusion solution was then replaced with one containing 40 µM Mn²⁺ while pacing at 0.25 Hz. The addition of Mn²⁺ did not affect the transients until the frequency was increased to 2 Hz, resulting in a rapid decrease of the transient amplitude. This would suggest accelerated cytosolic Mn²⁺ uptake through the sarcolemma Ca²⁺ channels as the frequency was increased, and subsequent binding of Mn²⁺ to cytosolic Rhod-2. The normal perfusate was then switched back, and the frequency protocol repeated three more times. Figure 3 shows that there was a reduction, both of the Rhod-2 transients (down from 49 to 11%) and of the fast rising component of R2(dia) (down from 16 to 5%). However, the slow rising component of R2(dia) (during stimulation at 2 Hz) was also reduced from 21 to 9%, suggesting mitochondrial Mn²⁺ uptake and subsequent partial quenching of mitochondrial Rhod-2.

Additional Mn²⁺ was then added to saturate both the cytosolic and mitochondrial Rhod-2. Because no slow increase of R2(dia) was apparent when the frequency was increased to 2 Hz (at 62 and 68 min), it is likely that mitochondrial Rhod-2 was completely saturated with Mn²⁺. This level of Mn²⁺ did not seem to interfere with the Ca²⁺-dependent stimulation of NADH production or contraction, because the NADH recovery and Force transients (not shown) were similar regardless of [Mn²⁺]. Thus, the [Mn²⁺] used here did not interfere with Ca²⁺-dependent activation of the mitochondrial dehydrogenases or Force generation.

Although the mitochondrial Rhod-2 was completely Mn²⁺ saturated, residual Rhod-2 transients were sometimes observed. These may be due to three factors. 1) Motion (and noise) artifacts: because Rhod-2 is not a ratiometric dye, its detected intensity is sensitive to motion artifacts (Brandes et al., 1992), which would manifest itself as a beat-to-beat response. 2) Cytosolic Ca²⁺ transients: even though large amounts of Mn²⁺ were added, it may not have been enough to completely saturate cytosolic Rhod-2 at maximum [Ca²⁺]_c (peak of the transient). Attempting to eliminate the transients by addition of higher [Mn²⁺]₀ resulted in reduced contraction (because of interference with the Ca²⁺-channels). 3) Mitochondrial Ca²⁺ transients: it is unlikely that any mitochondrial Ca²⁺ transients would be large enough to displace Mn²⁺ at the peak (i.e., as for cytosolic Rhod-2), because Mn²⁺ was able to eliminate the work-dependent Ca²⁺ increase, and this was larger than the transients (e.g., see Fig. 3 at 20 min immediately following partial Mn²⁺ quenching of cytosolic Rhod-2). However, we cannot exclude the unlikely possibility that there may be two fractions of mitochondrial Rhod-2: one that senses the work-dependent rise of [Ca²⁺]_m and is quenched by Mn²⁺, and another fraction that senses any mitochondrial Ca²⁺ transients, but is not quenched.

In contrast to Mn²-saturated Indo-1, where the fluorescence intensity is very weak (see cuvette experiments below), the intensity of Mn²-saturated Rhod-2 was still significant because R2(dia) only decreased by 22% in this example and, on average, decreased by 25 ± 3% (n = 5), i.e., I_Mn²⁺ = 0.75 · I_tot(0.25) or I^*_tot(0.25) = 1.33 (Eq. A12). Note that this is an upper-limit estimate. The real Mn²⁺-dependent decrease may be slightly less if some dye leaked out of the cytosol during the protocol. (A Rhod-2 leak from the mitochondria to the cytosol would, of course, not matter, because Rhod-2 would remain quenched by cytosolic Mn²⁺).

Verification of mitochondrial Rhod-2 loading

The pacing protocol above suggested that Rhod-2 was compartmentalized into (at least) two compartments; cytosol and mitochondria. To further investigate this, three different protocols were evaluated.

Fraction of mitochondrial Rhod-2

View larger version (21K): [in this window] [in a new window]   FIGURE 4   Determination of cytosolic versus mitochondrial Rhod-2 loading. Digitonin (solid bar) is expected to release cytosolic Rhod-2 while Triton-X 100 (solid bar) is expected to release the remainder, most likely in the mitochondria. Following Digitonin application, the Rhod-2 fluorescence dropped relatively fast and reached a new lower value after 8-10 min. However, this drop was sometimes followed by a slower decrease, and the level at 12 min was therefore used in all experiments.

Mitochondrial uncoupling

View larger version (18K): [in this window] [in a new window]   FIGURE 5   Validation of mitochondrial Rhod-2 loading by manipulating [Ca2+]m. [Ca2+]m (and [Ca2+]c] was first raised by switching to low Na+ perfusion (solid bar), and mitochondrial Ca2+ was subsequently released by dissipating the mitochondrial electrochemical gradient by applying a mitochondrial uncoupler, FCCP. Oligomycin (ATPase inhibitor) was simultaneously applied to prevent complete ATP hydrolysis. The resulting changes in Rhod-2 fluorescence were mirrored by changes in resting Force (bottom panel) and are further explained in the text. Note, however, the small absolute change in resting Force, which was ~20% of the typical twitch amplitude.

Inhibition of mitochondrial Na/Ca²⁺ exchanger

View larger version (18K): [in this window] [in a new window]   FIGURE 6   Validation of mitochondrial Rhod-2 loading by manipulating [Ca2+]m by blocking the mitochondrial Na+/Ca2+ exchanger with clonazepam (100 µM, solid bar). Application of clonazepam caused increased Rhod-2 fluorescence (middle panel) and increased NADH fluorescence (top panel), while Force was unaffected (bottom panel).

Effects of increased frequency on [Ca²⁺]_c using Indo-1

To verify that the fast diastolic component of the Rhod-2 signal (see Fig. 2) may be caused by alteration in diastolic [Ca²⁺]_c, a separate group of trabeculae were loaded with Indo-1 (free acid). Because Indo-1 was loaded iontophoretically, the Indo-1 ratio is expected to only be related to cytosolic [Ca²⁺]_c (Backx and Ter Keurs, 1993).

Figure 7 shows a typical example of the effects of increased followed by decreased pacing frequency (0.25-2-0.25 Hz) on the Indo-1 ratio. Within less than one second, a change in pacing frequency caused a corresponding change in diastolic levels of [Ca²⁺]_c. In contrast to the Rhod-2 signal (see Fig. 2), there was no slow rise in the Indo-1 signal after the pacing frequency was increased. These results suggest that the slow Rhod-2 component is not due to changes in [Ca²⁺]_c, and probably reflects changes in [Ca²⁺]_m.

View larger version (42K): [in this window] [in a new window]   FIGURE 7   Effect of pacing frequency (0.25-2-0.25 Hz) on cytosolic [Ca2+] and Indo-1. Top and bottom panels (expanded time scale of top panel) shows that increased frequency caused an immediate rise of Indo-1 fluorescence that was not followed by a slower rise (in contrast to Rhod-2 fluorescence; see Fig. 2).

To calibrate these signals, the Indo-1 calibration parameters R_min and R_max were determined in the trabeculae (Brandes et al., 1993b). In contrast, K_d = 247 nM was determined in aqueous solution (cuvette) as described in the Methods section. Cuvette studies also demonstrated that addition of saturating Mn²⁺ caused complete quenching of Indo-1 fluorescence (not shown), in contrast to Rhod-2 fluorescence (see below). At a pacing frequency of 0.25 Hz, [Ca²⁺]_c(dia, 0.25) = 167 ± 27 nM, and at 2 Hz, [Ca²⁺]_c(dia, 2) = 305 ± 37 nM (n = 6) (Eq. 4). Thus, increasing pacing frequency from 0.25 to 2 Hz caused [Ca²⁺]_c(dia) to increase by 138 ± 30 nM (83%; paired comparison).

Estimation of [Ca²⁺]_m at 0.25 Hz using Rhod-2

To estimate [Ca²⁺]_m, the Rhod-2 calibration constants K_d,  = I_Mn²⁺/I_max and  = I_min/I_max were first determined in a cuvette. Figure 8 A shows emission spectra of Rhod-2 with excess EGTA (I_min), saturating [Ca²⁺] (I_max) or saturating [Mn²⁺] (I_Mn²⁺) and for [Ca²⁺] = 150 and 225 nM. As can be seen, the Mn²⁺-saturated intensity, I_Mn²⁺, is similar to the intensity obtained with [Ca²⁺] somewhere between 150 and 225 nM. Figure 8 B shows a nonlinear fit of the Rhod-2 intensities to Eq. A1 to calculate K_d = 1344 nM, I_min and I_max. The fitted values of I_min and I_max were then used, together with I_Mn²⁺, to calculate  = 0.02274, and  = 0.1477. (Note that these values and Eq. A17 may be used to confirm that [Ca²⁺] = 197 nM would have the same intensity as I_Mn²⁺ by using I_c = I_Mn²⁺ (i.e., I^*_c = 1), f_c = 1 and the fitted Rhod-2 K_d).

View larger version (17K): [in this window] [in a new window]   FIGURE 8   Solution (cuvette) calibration of Rhod-2 dye. (A) Selected emission spectra using [Ca2+] = 0, 150, 225 nM and saturating concentration (39.8 µM). The spectra with saturating Mn2+ (IMn2+, dashed line) falls between [Ca2+] = 150 and 225 nM. (B) Nonlinear fit of the emission values at 578 nm (peak) using Eq. A1 to obtain fitted values for Imin, Imax, and Kd. The values of Imin, Imax, and IMn2+ were subsequently used to calculate  and . For comparison, the intensity IMn2+, is also shown on the fitted curve.

To calculate [Ca²⁺]_m(0.25), each trabecula was saturated with Mn²⁺ to determine I^*_tot(0.25) and then permeabilized with digitonin and TritonX-100 to determine f_c (as shown above). These data were then used together with the separately determined average value of [Ca²⁺]_c(dia, 0.25) = 167 nM to calculate [Ca²⁺]_m(0.25) = 440 ± 28 nM (n = 5) (Eq. A21).

Because  and  are calculated as ratios of Rhod-2 intensities, they are independent of [Rhod-2] (and instrumental factors), and only depend on the dye characteristics. However, it should be cautioned that they were determined in an aqueous solution, and  and  may therefore differ in the intracellular milieu. For example, we have previously shown that a protein such as albumin (0.3 mg/ml) shifts the Indo-1 isosbestic wavelength from 450 to 427 nm, similar to the in vivo value (Brandes et al., 1993b). We therefore examined the effects of albumin (0.3 mg/ml) on I_min, I_max, and I_Mn²⁺ but did not find any significant differences. Nevertheless, careful studies using various intracellular proteins (Baker et al., 1994) may reveal a larger effect on I_min, I_max, and I_Mn²⁺ and thus on  and , and this may consequently change the absolute values of [Ca²⁺]_m reported here. Similarly, the in vivo K_d for Indo-1 and Rhod-2 would most likely be different from the solution values found here and would change the absolute value of [Ca²⁺]_m(0.25). If the K_d for Indo-1 and Rhod-2 would change with similar relative amounts (e.g., both with a factor of ~2) due to dye-protein interactions, calculations using Eqs. 4 and A20 showed that [Ca²⁺]_m(0.25) would simply scale proportionally.

Effects of increased frequency on [NADH]_m, [Ca²⁺]_m, and [Ca²⁺]_c using Rhod-2

Figure 9 shows the parameters used to characterize the Rhod-2 and NADH signals. The slow changes in Rhod-2 and NADH observed when the frequency was increased from 0.25 to 2 Hz are characterized by the slow increase in R2(dia), R2_m (related to [Ca²⁺]_m), and by the slow increase in [NADH]_m (NADH), and the time constants of the slow rise of R2(dia), (related to the rise time of [Ca²⁺]_m), and of NADH, (NADH recovery-time constant). Two additional time constants related to [Ca²⁺]_m and NADH characterize the return to control after the pacing frequency was lowered back to 0.25 Hz; and . Figure 9 additionally shows the amplitude of the fast beat-to-beat Rhod-2 transients (at 0.25 and 2 Hz), R2_c and the fast rise of R2(dia), R2_c(dia).

View larger version (37K): [in this window] [in a new window]   FIGURE 9   Parameters used to characterize frequency-dependent changes in NADH (top panel, NADH, , and ) and Rhod-2 (middle and bottom panels, R2c, R2c(dia), R2m, , and ). The bottom panel shows the same data as in the middle panel but on an expanded time scale. As discussed in the text, R2c(dia) is mainly related to a fast rise in [Ca2+]c, while R2m is related to a slow rise in [Ca2+]m. The frequency was transiently increased from 0.25 to 2 Hz at t = 45-122 s.

Figure 10 shows pooled data from 11 trabeculae. When the pacing frequency was increased from 0.25 to 2 Hz, R2(dia) increased; R2_m = 18 ± 2% with a time constant  = 23 ± 5 s. After the initial decrease, [NADH]_m recovered in parallel with increasing R2(dia), NADH = 11 ± 2% with a time constant  = 28 ± 8 s. Thus, NADH increased by approximately the same relative amount as Rhod-2, and with a similar time constant (the slightly longer time constant for NADH versus R2(dia) was not significantly different). During the final phase, after the frequency was reduced back to 0.25 Hz, both R2(dia) and NADH relaxed with similar time constants;  = 53 ± 6 s and  = 78 ± 12 s (the slightly longer time constant for NADH was again not significantly different).

View larger version (37K): [in this window] [in a new window]   FIGURE 10   Relationships between changes in NADH and R2(dia) (related to [Ca2+]m). The top panel shows that increased NADH, NADH, was related to increased R2(dia), R2m. The bottom panel shows that the time constants for the rise and fall of NADH and R2(dia) were similar (no significant difference, although the observed longer time constants for NADH is consistent with a causal relation).

To calculate [Ca²⁺]_m(2) from Rhod-2 intensities, two different methods were used.

METHOD 1.  In the first method, I^*_tot(2) was approximated by using the average value of I^*_tot (0.25) = 1.33 (from a separate set of trabeculae; see Eq. A31) and combined with the average values of f_c = 0.47 and [Ca²⁺]_c(2) = 305 nM, obtained from Indo-1 measurements, and substituted into Eq. A22 to obtain [Ca²⁺]_m(2) = 582 ± 57 nM (n = 11).

METHOD 2.  In the second method, the rise of R2_m was analyzed by using the linear combination of intensities (See Eq. A27) to calculate [Ca²⁺]_m(2) = 676 ± 45 nM (no significant difference versus Method 1).

To investigate the possibility that R2_c(dia) is partially affected by fast mitochondrial Ca²⁺ kinetics (in addition to changes in [Ca²⁺]_c), the result of using the two approaches may be compared. As shown in the Appendix, Method 2 assumed that [Ca²⁺]_m did not initially increase when the pacing frequency was increased. If this assumption is incorrect, [Ca²⁺]_m(2) would be underestimated, e.g., [Ca²⁺]_m(2) would be lower when using Method 2 than when using Method 1. Because this was not found, the assumption is probably correct.

In addition to using Rhod-2 measurements to calculate [Ca²⁺]_m(2), it may also be used to calculate [Ca²⁺]_c(dia, 2) (using Indo-1 determined [Ca²⁺]_c(dia, 0.25); Eq. A30). With this approach, [Ca²⁺]_c(dia, 2) = 232 ± 15 nM, which is not larger than when Indo-1 alone was used to determine [Ca²⁺]_c(dia, 2) = 305 ± 37 nM (i.e., no significant difference in [Ca²⁺]_c(dia, 2) using Indo-1 versus Rhod-2). Thus, as also explained in the Appendix, Rhod-2 determination of [Ca²⁺]_c(dia, 2) does not overestimate the "true" [Ca²⁺]_c(dia, 2) (as determined by Indo-1) and the assumption of initially unchanged [Ca²⁺]_m is also confirmed by this type of measurements.

Both these results (Methods 1 versus 2, and Rhod-2 versus Indo-1 determination of [Ca²⁺]_c(dia, 2); see Table 1). suggest that, as the pacing frequency is suddenly increased, the fast rise of the diastolic Rhod-2 signal, R2_c(dia), can be accounted for by the rise of [Ca²⁺]_c alone, without an additional component due to a fast rise of [Ca²⁺]_m. However, it is possible that a concurrent small rise of [Ca²⁺]_m slightly contributes to the fast R2_c(dia) rise, but it may not be detectable with the methods used here. Nevertheless, for the purpose of this study, the main focus is the relationship between the slow recovery of NADH and increased [Ca²⁺]_m and any possible component of fast mitochondrial Ca²⁺ kinetics is therefore not important here.

The average value of [Ca²⁺]_m(2) using Methods 1 and 2 is 629 nM, and this is 43% larger than [Ca²⁺]_m(0.25) = 440 nM. As discussed above, a problem with absolute quantification is that the calculated [Ca²⁺]_c and [Ca²⁺]_m are proportional to K_d, and its in vivo value is difficult to determine. However, a change in Rhod-2 K_d alone or a similar proportional change in both Rhod-2 and Indo-1 K_d would not alter the relative increase of [Ca²⁺]_m (43%) when the pacing frequency is increased (see Eqs. 4 and A20). Furthermore, this relative increase is quite insensitive to an unproportional change in Indo-1 K_d versus Rhod-2 K_d. For example, if Indo-1 K_d is doubled from its aqueous value, while Rhod-2 K_d is unchanged, the relative increase in [Ca²⁺]_m would only change by 9% (from 43 to 52%).

	DISCUSSION

TOP ABSTRACT SELECTED DEFINITIONS INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

We have previously shown that increased work, due to increased pacing frequency, caused a slow recovery of [NADH]_m (Brandes and Bers, 1996). The primary goal of this study was to determine whether this slow recovery could be explained by slowly increasing mitochondrial [Ca²⁺] (stimulating the NADH production rate and therefore increased [NADH]_m). Our current results are consistent with this hypothesis: as the pacing frequency was increased, both [Ca²⁺]_m and [NADH]_m increased with a time constant of ~25 s. Conversely, when the pacing frequency was lowered, both [Ca²⁺]_m and [NADH]_m decreased with a time constant of ~65 s.

A secondary goal was to estimate the change in [Ca²⁺]_m when the pacing frequency was increased. It was shown that calibration of [Ca²⁺]_m was feasible using Rhod-2, without the need to obtain I_max, if, instead, the Mn²⁺-saturated Rhod-2 intensity was obtained together with separately determined [Ca²⁺]_c and the cytosolic versus mitochondrial Rhod-2 loading fraction.

Mn²⁺ quenching of Rhod-2 fluorescence

As shown here, the quenching of mitochondrial Rhod-2 occurred so fast that it was not possible to selectively exclude cytosolic Rhod-2 from mitochondrial Rhod-2 at any time after Mn²⁺ application. This appears to be in contrast to the studies using Indo-1 in hearts (Schreur et al., 1996; Griffiths et al., 1997a), where cytosolic Indo-1 was significantly quenched before mitochondrial Indo-1, but in accordance with studies using Fura-2 (Haworth and Redon, 1998). To explain the different results in the different studies, it is possible that there were differences in mitochondrial Mn²⁺ uptake rates (e.g., due to differing membrane potential) or that there were differences in the kinetics of Mn²⁺ binding to mitochondrial versus cytosolic dye.

Verification of mitochondrial Rhod-2 loading

Using Digitonin permeabilization, Miyata et al. (1991) showed that, in cardiac myocytes, loaded at 23°C, 40% of Indo-1 was localized in the mitochondria. Furthermore, because Mn²⁺ completely quenches Indo-1 (but not Rhod-2) fluorescence, Miyata et al. (1991) and Schreuer et al. (1996) used Mn²⁺ to determine the residual mitochondrial fluorescence, and similarly found that 47% and 53%, respectively, of Indo-1 was loaded in the mitochondria. These similar results, 53% for Rhod-2 here and 40-53% for Indo-1, are in contrast to the results of del Nido et al. (1998) and Trollinger et al. (2000), who found 0 and 100%, respectively, of Rhod-2 localized in the mitochondria. This large discrepancy may be due to various loading conditions and methods of evaluating mitochondrial dye loading.

Previous studies have shown that inhibition of the mitochondrial Na⁺/Ca²⁺ exchanger by clonazepam caused increased [Ca²⁺]_m (as measured by Indo-1) and [NADH]_m (Griffiths et al., 1997b), consistent with the results obtained here. Furthermore, we also found that the rise of Rhod-2 and [NADH]_m, was similar when using clonazepam or the frequency jump: Rhod-2 = 15 vs. 18% and NADH = 13 vs. 11%.

Estimation of [Ca²⁺]_m at 0.25 Hz using Rhod-2

Other authors have assessed [Ca²⁺]_m by using Mn²⁺ to selectively quench cytosolic Indo-1 (Schreur et al., 1996; Griffiths et al., 1997a). A complication with this approach, as shown here, is that some Mn²⁺ is likely to enter the mitochondria (Hunter et al., 1980, 1981; Haworth and Redon, 1998) and thus also quench mitochondrial Indo-1. However, provided that Mn²⁺ quenches the fluorescence at both emission wavelengths identically, the fluorescence ratio should be constant. This would require, among other things, that the background fluorescence is measured prior to dye loading and then remains constant for accurate subtraction. Because the background fluorescence is, in general, not constant (Brandes and Bers, 1996; Ashruf et al., 1995), it is possible that the ratio would change after Mn²⁺ quenching, giving incorrect estimates of [Ca²⁺]_m.

In contrast to Indo-1, Rhod-2 is not a ratiometric dye, and Mn²⁺ quenching can thus not be used when Mn²⁺ enters the mitochondria. Furthermore, Mn²⁺ does not completely quench the Rhod-2 fluorescence and this complicates matters further. To solve this problem here, the fraction of mitochondrial Rhod-2 loading combined with the total Rhod-2 intensity after Mn²⁺ saturation was determined to calculate [Ca²⁺]_m = 440 ± 28 nM at 0.25 Hz. This is higher than the value obtained in isolated myocytes at 0.3 Hz; [Ca²⁺]_m = 200 nM (Griffiths et al., 1997a), and may be attributed to physiological differences (e.g., isometrically contracting trabeculae versus isolated myocytes). Alternatively, the dye calibration may be incorrect due to a [Ca²⁺]_m-insensitive component of the dye(s) (e.g., incomplete de-esterification or compartmentalization into lysosomes (Trollinger et al., 2000)), or due to differences in the K_d used to calculate [Ca²⁺]_m.

It is well established that K_d is strongly dependent on dye-protein interactions and on dye-ion interactions (Baker et al., 1994; Hove-Madsen and Bers, 1992), and the dye interactions in the intracellular milieu is not known. For example, the solution value for Rhod-2 has been reported to be K_d = 570 nM (in the absence of Mg²⁺; Molecular Probes), but K_d = 1344 nM was found here (with Mg²⁺). Thus, if K_d = 570 nM was used instead, [Ca²⁺]_m(0.25) = 187 nM and [Ca²⁺]_m(2) = 287 nM, and this is more similar to the values found in isolated myocytes (Griffiths et al., 1997a).

Effects of increased frequency on [NADH]_m, [Ca²⁺]_m, and [Ca²⁺]_c using Rhod-2

When the pacing frequency was increased from 0.25 to 2 Hz, there was an immediate fall of [NADH]_m that we have previously shown to be Ca²⁺-independent (Brandes and Bers, 1997), and may be due to increased [ADP] (Unitt et al., 1989), stimulating the oxidative phosphorylation rate and thereby the fall of [NADH]_m. There has also been some evidence suggesting that, in addition, there is a Ca²⁺-dependent stimulation of oxidative phosphorylation by indirectly activating the F₀F₁-ATPase (Wan et al., 1993; Territo et al., 2000).

With continued pacing at the higher rate, [Ca²⁺]_m and [NADH]_m rose slowly with a time constant of ~25 s. This rise of [Ca²⁺]_m is most likely mediated via Ca²⁺ uptake via the uniporter (Gunter et al., 1994), and suggests that the rise of [Ca²⁺]_m stimulates mitochondrial enzymes (PDH or the TCA cycle enzymes; -ketoglutarate or NADH-linked isocitrate dehydrogenase) to increase the NADH production rate (Hansford, 1991) and thereby [NADH]_m. The rise of [Ca²⁺]_m, with a time constant of ~25 s, is similar to that observed elsewhere (Miyata et al., 1991; Bassani et al., 1993) and predicted by simulations (Crompton, 1990). In these simulations, the mitochondria effectively act as a low-pass filter, reducing the matrix-transient amplitude versus the cytosol. If the cytosolic amplitude is increased, both the mitochondrial Ca²⁺ transients and steady-state [Ca²⁺]_m increases. Similarly, an increase of the pacing frequency would slowly (~25 s) increase [Ca²⁺]_m. Because we simultaneously measured changes in cytosolic and mitochondrial [Ca²⁺], we were not able to separately measure the relative magnitudes of cytosolic versus mitochondrial Ca²⁺ transients.

The experimental protocol used here to increase average [Ca²⁺]_c, and consequently [Ca²⁺]_m, by increased pacing frequency, differs from other studies using isolated mitochondria where [Ca²⁺]_m was increased by rapid-step increases of extra-mitochondrial Ca²⁺ (Buntinas et al., 2001; Territo et al., 2001). In the study by Territo et al., addition of 535 nM Ca²⁺ to a suspension of Ca²⁺-depleted mitochondria resulted in a very rapid rise of [Ca²⁺]_m (<100 ms) and a slower rise of [NADH]_m ( ~ 6 s). The large sudden step increase of extra-mitochondrial [Ca²⁺] apparently results in a much faster phase of mitochondrial Ca²⁺ uptake than observed here when the pacing frequency, and consequently time-averaged [Ca²⁺]_c was increased. The observed rise of [NADH]_m following stimulation depends on the NADH production rate (e.g., Ca²⁺ stimulation of the dehydrogenases) being larger than the NADH consumption rate (e.g., Ca²⁺ and ADP stimulation of the F₀F₁-ATPase). Thus, if the NADH production rate increases faster than the consumption rate, [NADH]_m will rise faster than when the NADH consumption rate also increases fast. In the case of increased work (e.g., the trabeculae studied here), the fast increase of the NADH consumption rate is expected to cause a slower rise of [NADH]_m than stimulation without increased work (e.g., isolated mitochondria). Indeed, as shown in Fig. 2, the large NADH consumption rate with increased pacing frequency even caused [NADH]_m to fall before it recovered. The difference in the Ca²⁺ protocols and the difference in [NADH]_m consumption rates could explain the differences between the kinetics of [Ca²⁺]_m and [NADH]_m in the two different types of studies.

Although increased [Ca²⁺]_m has previously been observed following increased pacing rates (Miyata et al., 1991), this has generally not been associated with increased [NADH]_m in freely contracting myocytes (White and Wittenbe