## Abstract

We proposed and tested the use of nontraditional excitation wavelengths (λ_{1} and λ_{2}) and an emission wavelength (λ_{em}) to define conditions under which free calcium concentration and a fluorescence ratio are linearly related. Fluorescence spectra were determined for aqueous solutions that contained 25 μM fura 2, 125 mM K^{+}, and either 0 mM or 0.1 mM Ca^{2+}. Effectively linear relationships between [Ca^{2+}] and a fluorescence ratio, i.e., <5% bias when [Ca^{2+}] ≤ 5 × dissociation constant, were apparent when λ_{1} ≥ 400 nm, λ_{2} ≤ 370 nm, and λ_{em} ≥ 510 nm. Combinations with longer λ_{1}and λ_{em} and/or with shorter λ_{2} reduced this bias further. Although the method described does not obviate the complications that surround the correction for fluorescence background, choosing a nontraditional combination of excitation and emission wavelengths offers several practical advantages over more traditional fura 2 fluorescence methodologies in a variety of experimental settings.

- intracellular calcium
- cardiac myocyte

measurements of free calcium concentration ([Ca^{2+}]) through the use of fluorescence dyes have grounded much of the current understanding of intracellular Ca^{2+} handling and its importance to cell function (5, 6). Of the many intracellular calcium concentration ([Ca^{2+}]_{i}) indicators that are excited by two wavelengths (λ_{1} and λ_{2}) and monitored at a single emission wavelength (λ_{em}), fura 2 has become popular due to its favorable ion selectivity, fluorescence yield, and bleaching characteristics (2, 7).

The traditional fluorescence ratiometric method used to estimate [Ca^{2+}] with fura 2 (when changes in [Ca^{2+}] are slow) was presented by Grynkiewicz et al. (2) as
Equation 1where *K*
_{d} = the dissociation constant between fura 2 and free Ca^{2+}, R = a fluorescence ratio defined as the fluorescence intensity induced by λ_{1} (F_{1}) divided by the fluorescence intensity induced by λ_{2} (F_{2}), R_{min} = R recorded when [Ca^{2+}] = 0, R_{max}= R recorded when [Ca^{2+}] >> *K*
_{d}, S_{f2} = F_{2} when Ca^{2+} is not bound to fura 2, and S_{b2} = F_{2} when fura 2 is fully bound with Ca^{2+}.

The use of the fluorescence ratiometric method is straightforward in theory. However, determining background and the calibration constants is often difficult in practice. Background emissions due to cell autofluorescence, compartmentalization of fura 2 inside intracellular organelles, partial deestrification of fura 2-AM, and the fluorescence of fura 2-AM bound to the cell membrane can all be mistaken for the fluorescence signal of cytosolic fura 2 (7). In addition, determining values for R_{min} and R_{max} in an intact cell requires experimental conditions that are not easily prepared or maintained, and the chemical agents used to induce these conditions can unpredictably complicate the distinction between fluorescence and background intensities.

To avoid the complicated nature and intrinsic inaccuracies of a full calibration procedure, it has become an increasingly common practice to use R alone to characterize [Ca^{2+}]. This compromise is appropriate to the degree to which properties of the recorded R reflect those of the actual [Ca^{2+}]. When the traditional excitation wavelength pair of 340 nm and 380 nm is used, there exists a nonlinear relationship between [Ca^{2+}] and R. Therefore, the use of a recorded R transient to characterize [Ca^{2+}] is dubious. Specific temporal characteristics of [Ca^{2+}], such as exponential rate constants or time derivatives, and comparisons between values of [Ca^{2+}], such as minimum and maximum values, are complicated by the nonlinear relationship between [Ca^{2+}] and R. A more valid characterization of [Ca^{2+}] by a recorded fluorescence ratio would be possible if a linear relationship between [Ca^{2+}] and R or R^{−1} existed.

On examination of *Eq. 1
*, the relationship between [Ca^{2+}] and a fluorescence ratio would be linear if the value for R_{max} was forced to be zero. If R_{max}were zero, the calibration equation for fura 2 would simplify to the following
Equation 2As *Eq. 2
* indicates, a linear relationship between [Ca^{2+}] and a fluorescence ratio, namely R^{−1}, arises when R_{max} is equal to zero. Specific temporal characteristics of [Ca^{2+}] and relative changes in values of [Ca^{2+}] could then be reliably approximated with the use of R^{−1}. All that must be done now is to determine the conditions, i.e., the properties of λ_{1}, λ_{2}, and λ_{em}, under which *Eq. 2
*provides accurate estimates of [Ca^{2+}].

This paper demonstrates that many combinations of λ_{1}, λ_{2}, and λ_{em} can be chosen such that an effectively linear relationship between [Ca^{2+}] and a fluorescence ratio, specifically R^{−1}, will arise over the range [Ca^{2+}] ≤ 5 ×*K*
_{d}. First, we present fluorescence emission spectra of fura 2 in vitro over a wide range of excitation wavelengths. We then define “an effectively linear relationship” to exist when combinations of λ_{1}, λ_{2}, and λ_{em} allow estimates of [Ca^{2+}] using the simplified *Eq. 2
* to be within 5% of the nonbiased estimate of [Ca^{2+}] using *Eq. 1
*. In reference to the recorded fura 2 fluorescence spectra, it is demonstrated that wavelength combinations, when λ_{1} ≥ 400 nm, λ_{2} ≤ 370 nm, and λ_{em} ≥ 510 nm, satisfy the effectively linear relationship criterion.

## METHODS

#### Spectrophotometric characterization of fura 2 fluorescence in vitro.

Fura 2 pentopotassium salt (Molecular Probes, Eugene, OR) was prepared to a concentration of 25 μM in two aqueous solutions, both of which contained concentrations of (in mM) 125 KCl, 5 NaCl, 20 HEPES, 2 MgCl_{2} · 6H_{2}O, and 2 ATP, pH 7.2. All chemicals were acquired from Sigma Chemical, St. Louis, MO, except where noted. One solution was termed the “zero [Ca^{2+}] solution” after the addition of 0.1 mM EGTA, which buffered excess Ca^{2+}, and the other was termed the “high [Ca^{2+}] solution” after the addition of 0.1 mM CaCl_{2}. Because *K*
_{d} in this medium has been estimated between 135 and 224 nM (2), the concentration of 0.1 mM [Ca^{2+}] in the high [Ca^{2+}] solution was considered to satisfy the condition [Ca^{2+}] >> *K*
_{d}. Respective solutions were also prepared without fura 2 for purposes of determining fluorescence background.

Fluorescence intensities were recorded at 25°C for the zero [Ca^{2+}] solution, the high [Ca^{2+}] solution, and for the respective background solutions with the use of a spectrophotometer (model LS-5; Perkin-Elmer, Norwalk, CT) with an excitation bandwidth of 3 nm and an emission bandwidth of 5 nm. Fluorescence intensity was recorded at intervals of 3 nm over the range of excitation wavelengths of 330–441 nm and at intervals of 5 nm over the range of emission wavelengths of 480–560 nm. Fluorescence intensities of the zero [Ca^{2+}] solution and high [Ca^{2+}] solution were corrected for background with the use of the respective solutions without fura 2.

The resulting fluorescence spectrum for the zero [Ca^{2+}] solution provided a map of the fluorescence intensity emitted at a specific wavelength that was due to excitation at a specific wavelength when fura 2 was totally free of Ca^{2+}. Similarly, the fluorescence spectrum for the high [Ca^{2+}] solution provided a map of the fluorescence when fura 2 was fully bound with Ca^{2+}. Figure1 demonstrates these two fluorescence spectra as contour plots. Each contour represents a level of relative fluorescence intensity that would be recorded at any specified emission and excitation wavelength that we examined.

With these spectra in hand, the relative values for F_{1} and F_{2} when fura 2 is free of Ca^{2+} (S_{f1} and S_{f2}, respectively) and when fura 2 is fully bound with Ca^{2+}(S_{b1} and S_{b2}, respectively) could then be obtained. These values for S_{f1}, S_{f2}, S_{b1}, and S_{b2} provide a means by which values for R at any [Ca^{2+}] could be calculated for any proposed combination of λ_{1}, λ_{2}, and λ_{em}(2)
Equation 3With the use of *Eq. 3
* and the recorded fura 2 fluorescence spectra displayed in Fig. 1, the values for R_{min} and R_{max} were calculated for all possible excitation wavelength pairs, namely λ_{1} = 330–441 nm and λ_{2} = 330–441 nm with bandwidths of 3 nm, when the emission wavelength λ_{em}= 510 nm with bandwidths of 5 nm. For comparison purposes, the values for R_{min} and R_{max} were also calculated for all possible excitation wavelength pairs with the λ_{1}bandwidth = 20 nm and λ_{2} bandwidth = 10 nm, and when λ_{em} = 540 nm with bandwidths of 35 nm.

#### Criterion for an effectively linear relationship.

An effectively linear relationship between [Ca^{2+}] and R^{−1} was defined to occur when estimates of [Ca^{2+}] using *Eq. 2
* were not biased by >5% compared with the actual [Ca^{2+}] over the range [Ca^{2+}] ≤ 5 × *K*
_{d}. The bias was therefore quantified as the difference between estimates using*Eq. 1
* ([Ca^{2+}]_{1}) and those made using *Eq. 2
* ([Ca^{2+}]_{2}) normalized to [Ca^{2+}]_{1}
Equation 4As *Eq. 4
* demonstrates, the value R_{max}/R conveniently quantifies the bias associated with use of the linear approximation. At this point, it was noted that the maximum bias over the range [Ca^{2+}] ≤ 5 × *K*
_{d}would always occur when [Ca^{2+}] = 5 ×*K*
_{d}. In addition, the ability to calculate the value R_{max} and the value of R when [Ca^{2+}] = 5 × *K*
_{d} has already been provided by*Eq. 3
*. Therefore, the bias associated with the linear approximation at [Ca^{2+}] = 5 ×*K*
_{d} (bias at 5 × *K*
_{d}) was calculated as follows
Equation 5With the use of *Eq. 5
* and the recorded fluorescence spectra displayed in Fig. 1, the bias at 5 ×*K*
_{d} was calculated for all possible excitation wavelength pairs, namely λ_{1} = 330–441 nm and λ_{2} = 330–441 nm with bandwidths of 3 nm, when the emission wavelength λ_{em} = 510 nm with bandwidths of 5 nm. For comparison purposes, the bias at 5 ×*K*
_{d} was also calculated for all possible excitation wavelength pairs with the bandwidths for λ_{1} = 20 nm and λ_{2} = 10 nm and when λ_{em} = 540 nm with bandwidths of 35 nm. Our task was reduced to noting those combinations of λ_{1}, λ_{2}, and λ_{em} that provided a bias at 5 × *K*
_{d} that was <0.05.

#### Demonstration of an effectively linear relationship in vivo.

Cardiac myocytes were taken from a 14-mo-old male Fisher 344 rat. Myocytes were isolated from the left ventricle and septal portions of the heart as described before (4). After dispersion, the myocytes were immediately plated onto coverslips that had been lightly laminated the day before at a density of 10 mg laminin/ml of medium 199. Myocytes were then incubated in 2 ml of medium 199 at 37°C and 5% CO_{2}-balance room air.

After 4 h of incubation, 1 μl of 1 mM fura 2-AM (Molecular Probes) was added to the media of one coverslip, thereby exposing the cells to 0.5 μM of fura 2-AM. After an additional 5 min of incubation, the coverslip served as the bottom of a custom-made flow through chamber, superfused at room temperature with normal Tyrode, that consisted of (in mM) 140 NaCl, 6 KCl, 2 MgCl_{2}, 2 CaCl_{2}, 10 glucose, 5 HEPES, and 2 pyruvate, pH 7.4. One myocyte of the coverslip was positioned in the field of view of an inverted microscope (Nikon, Melville, NY) with a ×40 epifluorescence lens with 1.3 numerical aperture.

Optical filters were chosen with wavelengths centered at 400 nm with 20-nm bandwidth and 360 nm with 10-nm bandwidth (Omega Optical, Brattleboro, VT). A spinning wheel, which held the filters, was computer controlled such that fluorescence produced by the two excitation wavelengths was interlaced and sampled at 176 Hz (C & L Instruments, Elizabethtown, PA). Ultraviolet light was supplied by a 75 W xenon arc lamp (Ushio, Los Angeles, CA). Emitted fluorescence was filtered by an optical filter centered at 510 nm with 35-nm bandwidth and detected by a photomultiplier tube (R647–04; Hamamatzu, Bridgewater, NJ), and counts were divided by 10 such that one emission count was recorded for every 10 detected (C3866; Hamamatzu).

The coverslip was field stimulated with 1.5 × threshold voltage, 0.5-ms duration pulses, using platinum electrodes at a rate of 1 Hz. The myocyte was continuously exposed to the array of excitation wavelengths for 5 min, after which fura 2 bleaching no longer occurred. Fluorescence was then recorded. The superfusate was then changed to normal Tyrode with 100 μM ouabain for 10 min. Ouabain was used to suppress Na^{+}-K^{+}-ATPase activity, which in turn would induce an accumulation of Ca^{2+} in the cell (1). Fluorescence was continuously monitored until fluorescence at peak [Ca^{2+}] indicated saturation, i.e., [Ca^{2+}] > *K*
_{d}, and by definition, a high [Ca^{2+}] condition. The superfusate was then changed back to normal Tyrode, and a fluorescence recording was taken. To rid the myocyte of cytosolic fura 2, but not fura 2 compartmentalized in organelles or bound to the membrane, the coverslip was exposed for 4 min to 2 μM digitonin dissolved in Ca^{2+}-free Tyrode, which consisted of (in mM) 140 NaCl, 6 KCl, 2 MgCl_{2}, 1 EGTA, 10 glucose, 5 HEPES, and 2 pyruvate, pH 7.4. The superfusate was then switched to Ca^{2+}-free Tryode for 1 min, and a fluorescence recording was taken as the background emission. Fluorescence intensities were taken to be the recorded emissions minus the respective wavelength background emissions.

## RESULTS

#### Spectrophotometric characterization of fura 2 salt fluorescence in vitro.

The relative fluorescence intensities recorded along the 510-nm emission wavelength were plotted as excitation spectra in Fig.2. These excitation spectra demonstrated the familiar fura 2 excitation spectra with a peak fluorescence value at 376 nm for the zero [Ca^{2+}] solution and at 339 nm for the high [Ca^{2+}] solution. The isobestic wavelength was found at 359 nm. These values were comparable to those reported in Fig.3 of Grynkiewicz et al. (2).

As can be discerned in both excitation spectra illustrated in Figs. 1and 2, the fluorescence produced by fully bound fura 2 (high [Ca^{2+}] solution) at excitation wavelengths greater than ∼390 nm was negligible compared with that produced by free fura 2 (zero [Ca^{2+}] solution). This specific characteristic implied that a combination of λ_{1}, λ_{2}, and λ_{em} can be chosen, for which the value of R_{max} would be very close to zero, and the relationship between [Ca^{2+}] and R^{−1} would be effectively linear.

#### Combinations of λ_{1}, λ_{2}, and λ_{em} that satisfy linear criterion.

The calculated values for R_{min} and R_{max} when λ_{em} = 510 nm for all possible combinations of excited wavelength pairs λ_{1} and λ_{2} are plotted as contours in Fig.3
*A*. Both R_{min} and R_{max} had values of unity along the diagonal that would be expected when λ_{1} = λ_{2}. This diagonal was crossed at 376 nm by another diagonal of unity for values of R_{min} and also at 339 nm for values of R_{max}. These crossings depicted the respective fluorescence intensity peaks recorded for the zero [Ca^{2+}] solution and the high [Ca^{2+}] solution. The contours shown in Fig. 3
*A*demonstrate that values for R_{min} and R_{max} were found to lie along hyperbolas bounded asymptotically by the respective diagonals of unity.

The calculated values for bias at 5 × *K*
_{d}when λ_{em} = 510 nm for all possible combinations of excited wavelength pairs λ_{1} and λ_{2} are plotted as contours in Fig. 3
*B*. Values for the bias at 5 × *K*
_{d} that were <0.05 occurred when excitation wavelength pairs were λ_{1} ≥ 400 nm and λ_{2} ≤ 370 nm. Therefore, excitation wavelength pairs of λ_{1} ≥ 400 nm and λ_{2} ≤ 370 nm when λ_{em} = 510 nm would satisfy the criterion for producing an effectively linear relationship between [Ca^{2+}] and a fluorescence ratio.

For comparison purposes, the values for R_{min} and R_{max} were calculated when λ_{em} = 540 nm with a bandwidth of 35 nm for all possible combinations of excited wavelength pairs λ_{1} and λ_{2} with bandwidths of 20 nm and 10 nm, respectively. The resultant contours for values of R_{min} and R_{max} are displayed in Fig.3
*C* and demonstrated again the hyperbolic patterns about the lines of λ_{1} = λ_{2} = 376 nm and λ_{1} = λ_{2} = 339 nm. It should be noted that because the bandwidth for λ_{1} was twice that for λ_{2}, values for R_{min} and R_{max}were approximately doubled compared with those in Fig. 3
*A*.

Under the same conditions used to produce Fig. 3
*C*, there existed many combinations of λ_{1} and λ_{2} for which the bias at 5 × *K*
_{d} was <0.05 (Fig.3
*D*). Again, many excitation wavelength pairs, i.e., when λ_{1} ≥ 397 nm and λ_{2} ≤ 370 nm, would satisfy the criterion for an effectively linear relationship between [Ca^{2+}] and fluorescence ratio when λ_{em}center = 540 nm with a width of 35 nm. By comparing the plot of bias at 5 × *K*
_{d} in Fig. 3, *B* and*D*, it is apparent that the emission wavelength at 540 nm provided a slightly greater number of excitation wavelength pairs that could provide an effective linear relationship between [Ca^{2+}] and fluorescence ratio.

The results presented in Fig. 3 illustrate the usefulness of three different strategies for improving fura 2 fluorescence performance when a linear relationship between [Ca^{2+}] and a fluorescence ratio is sought. First, the bandwidth of optical filters used to define the excitation and emission wavelengths may be broadened. In this way, more photon counts can be recorded, and the relative rates of fura 2 fluorescence can be determined more precisely. Second, increasing the bandwidth of λ_{1} relative to that of λ_{2}would increase the ratiometric dynamic range, R_{min}− R_{max} . For example, both values for R_{min}and R_{max} would approximately double if the bandwidth for λ_{1} were twice that of λ_{2}. If R_{max} << R_{min}, then R_{min} − R_{max} would nearly double also. It should be noted that this strategy does not improve the signal-to-noise ratio and may be warranted only when λ_{2} = the isobestic wavelength. Third, selecting a center emission wavelength >510 nm increases the range of excitation wavelengths over which R^{−1} is linearly proportional to [Ca^{2+}]. This phenomenon is evident in Fig. 3
*D* where a greater range of choices for λ_{1} and λ_{2} exists for which the bias at 5 × *K*
_{d} was <0.05.

#### Relationships between [Ca^{2+}*] and R*^{−1} using nontraditional wavelengths.

^{−1}using nontraditional wavelengths.

The actual relationships between [Ca^{2+}] and R^{−1}, as defined by *Eq. 1
*, for traditional and nontraditional combinations of excitation and emission wavelengths, were compared with the strictly linear relationship as defined by*Eq. 2
*. For the traditional combination, λ_{1} = 380 nm, λ_{2} = 340 nm, and λ_{em} = 510 nm were selected. It should be noted that, although Grynkiewicz et al. (2) defined λ_{1} = 340 nm and λ_{2} = 380 nm, the consequences of defining λ_{1} = 340 nm and λ_{2} = 380 nm on R are algebraically equivalent to those of defining λ_{1} = 380 nm and λ_{2} = 340 nm on R^{−1}, which we demonstrate here. With the traditional combination, the linear approximation given by *Eq. 2
* was found to have a 30% bias at 5 × *K*
_{d} (Fig.4
*A*). The effectively linear criterion, i.e., <5% biased, was met only over the range [Ca^{2+}] ≤ 0.84 × *K*
_{d}. Therefore, attempts to characterize [Ca^{2+}] using R^{−1}, or R with λ_{1} and λ_{2}defined by Grynkiewicz et al. (2), would be appropriate up to ∼0.84 × *K*
_{d}.

Two nontraditional combinations of λ_{1}, λ_{2}, and λ_{em}, which satisfied the effectively linear criterion, were compared with the strictly linear relationship. The actual relationship between [Ca^{2+}] and R^{−1}for the combination of λ_{1} = 400 nm, λ_{2} = 360 nm, and λ_{em} = 510 nm was found to be within 5% bias of the linear approximation over the range [Ca^{2+}] ≤ 5 × *K*
_{d} (Fig.4
*B*). The relationship between [Ca^{2+}] and R^{−1} for the combination of λ_{1} = 410 nm, λ_{2} = 340 nm, and λ_{em} = 540 nm was found to be <2% bias of the linear approximation over the entire range of [Ca^{2+}] ≤ 5 × *K*
_{d}(Fig. 4
*C*). These comparisons presented in Fig. 4 demonstrate that there are many combinations of λ_{1}, λ_{2}, and λ_{em}, for which an effectively linear relationship between [Ca^{2+}] and R^{−1} can be employed to better characterize [Ca^{2+}] by a fluorescence ratio.

#### Demonstration of an effectively linear relationship in vivo.

With the use of optical filters λ_{1} = 400 nm with bandwidth of 20 nm, λ_{2} = 360 nm with bandwidth of 10 nm, and λ_{em} = 510 nm with bandwidth of 35 nm, fura 2 fluorescence was recorded from a cardiac myocyte under three conditions illustrated in Fig. 5. First, fura 2 fluorescence was recorded during electrical stimulation of the cardiac myocyte. As the intracellular [Ca^{2+}] rose immediately after stimulation, fluorescence due to 400-nm excitation was diminished, and fluorescence due to 360-nm excitation remained unchanged.

Fura 2 fluorescence was then recorded after 10-min exposure to 100 μM ouabain, which was used to raise intracellular Ca^{2+}load. As demonstrated in Fig. 5
*B*, exposure to ouabain induced an increase in resting [Ca^{2+}], depicted by a lower count rate recorded for λ_{1} = 400 nm during rest. In addition, ouabain induced an increased peak [Ca^{2+}] immediately after stimulation. Because the fura 2 fluorescence values for λ_{1} = 400 nm excitation reached a saturation limit at peak [Ca^{2+}], the intracellular [Ca^{2+}] at this point was therefore much greater than *K*
_{d}.

Figure 5
*C* presents the fluorescence induced after the digitonin exposure that lysed the cell and allowed cytosolic fura 2 to escape. Fluorescence recorded during this time was taken to represent background due in part to cell autofluorescence and noncytosolic fura 2. The values of background for the two excitation wavelengths were subtracted from the respective values recorded during the saturating peak [Ca^{2+}] after ouabain exposure (Fig. 5
*B*). The value for R_{max} for this cardiac myocyte was estimated from these data to be 0.063.

The background recorded in Fig. 5
*C* also allowed the estimation of R during the normal cardiac myocyte function. On subtraction of the background from the recorded fluorescence of Fig.5
*A*, values for R were found to range from 0.84 during peak to 2.33 during rest. Therefore, the bias over the range of cytosolic [Ca^{2+}], as defined by R_{max}/R, was estimated to have ranged from 7.5% at peak [Ca^{2+}] to 2.7% during rest [Ca^{2+}]. Although the 7.5% bias during peak [Ca^{2+}] may indicate that the maximum intracellular [Ca^{2+}] was >5 × *K*
_{d}, these results indicated that an effectively linear relationship between [Ca^{2+}] and R^{−1} was achieved by this combination of λ_{1}, λ_{2}, and λ_{em} over much of the [Ca^{2+}] transient. This and other combinations of λ_{1}, λ_{2}, and λ_{em}, most notably with greater λ_{1} and λ_{em}, should prove useful in the characterization of [Ca^{2+}] by the resultant linearly related R^{−1}transient.

## DISCUSSION

The fluorescence characteristics of fura 2 are such that a carefully chosen combination of excitation and emission wavelengths can be used to produce an effectively linear relationship between [Ca^{2+}] and a fluorescence ratio. We found that a combination of λ_{1} ≥ 400 nm, λ_{2} ≤ 370 nm, and λ_{em} ≥ 510 nm satisfied the criterion to elicit an effectively linear relationship over the range [Ca^{2+}] ≤ 5 × *K*
_{d}. In addition, as demonstrated by a comparison of Fig. 3, *B* and *D*, combinations that include longer λ_{1} and λ_{em} and/or shorter λ_{2} better satisfy the linear relationship criterion.

There are at least three advantages that would arise from the use of such a combination of λ_{1}, λ_{2}, and λ_{em}. *1*) Time characteristics of the fluorescence ratio reliably reflect time characteristics of the [Ca^{2+}] transient. Specifically, time to peak, relative rates of [Ca^{2+}] rise and decay, and exponential time constants used to characterize a [Ca^{2+}] transient rise and decay could all be determined from the fluorescence ratio.*2*) Relative changes in the fluorescence ratio would correspond directly to those in [Ca^{2+}]. The limit of accuracy, with which temporal characteristics and relative changes in [Ca^{2+}] could be made with the use of the fluorescence ratio, was comparable to 5%. And because full calibration was not necessary to attain these characteristics, the constants*K*
_{d}, (S_{f2}/S_{b2}), R_{min}, and R_{max} must not be determined.*3*) In cases when a full calibration is warranted, only the constants (S_{f2}/S_{b2}) and R_{min} would be necessary, because the value of R_{max} could be estimated to be zero. The only constant that must be assumed or arduously determined is *K*
_{d}, whose value does not affect the shape or temporal characteristics of the estimated [Ca^{2+}] transient.

There is at least one practical disadvantage associated with the use of a combination λ_{1} ≥ 400 nm, λ_{2} ≤ 370 nm, and λ_{em} ≥ 510 nm proposed here. As illustrated in Figs.1 and 2, an excitation wavelength λ_{1} > 400 nm produces less free fura 2 fluorescence intensity than many other wavelengths. Therefore, fluorescence signals elicited by wavelengths >380 nm would possess a lower signal-to-noise ratio. However, a broad bandwidth emission filter may be used to recover some of these losses in signal quality. In addition, some nontraditional excitation wavelength pairs may result in a lower ratiometric dynamic range, as illustrated in Fig. 4
*B*. Nevertheless, if the application permits, dynamic range may be recovered by a careful selection of wavelength pairs, particularly a shorter λ_{2} as presented in Fig. 4
*C*.

One limitation of the mathematical development presented here lies in the assumption that the rate of change in [Ca^{2+}] is relatively low. This assumption is not unique to this study and applies to all conditions under which fura 2 is used. The relationships between [Ca^{2+}] and R of both *Eqs. 1
* and *
2
*are accurate only when the temporal changes in [Ca^{2+}] are relatively slow, specifically when d[fura-Ca^{2+}]/d*t* <<*k*
_{off}[fura-Ca^{2+}] (3). Under other circumstances, the fluorescence ratio would no longer be effectively linearly related to [Ca^{2+}].

Another limitation not unique to this study lies in the problem of accurately accounting for background emissions. When cells of any type are loaded with fura 2-AM, there is, unfortunately, a significant percentage that is trapped in noncytosolic compartments, such as in intracellular organelles (7). In the present study, we demonstrated that digitonin could be used to lyse a cardiac myocyte membrane and therefore provide a route for cytosolic fura 2 to exit. There is, however, no guarantee that this method was not complicated by some fraction of cytosolic fura 2 that did not exit before background emission was recorded. Other methods, such as recording background before dialysis of fura 2 via a patch pipette, may be more accurate in determining background emissions.

In summary, this report described conditions under which combinations of excitation and emission wavelengths can be chosen to yield a linear relationship between [Ca^{2+}] and a fura 2 fluorescence ratio. Under these conditions, the fluorescence ratio can be used to provide reliable estimates of the temporal characteristics of intracellular [Ca^{2+}], as well as relative changes in [Ca^{2+}]. The reliability of these estimates, particularly of temporal characteristics, would be uninfluenced by errors in the assignment of fura 2 *K*
_{d} values. In a variety of experimental settings, these represent advantages over the use of traditional excitation and emission wavelength combinations.

## Acknowledgments

This work was supported in part by National Institutes of Health grants HL-40306 and AG-13981.

## Footnotes

Address for reprint requests and other correspondence: R. L. Moore, Dept. of Kinesiology and Applied Physiology, Univ. of Colorado, Boulder, CO 80309 (E-mail: rmoore{at}spot.colorado.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

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- Copyright © 2000 the American Physiological Society