The feasibility of determining localized Ca2+ influx using only wide-field fluorescence images was explored by imaging (using fluo-3) single channel Ca2+ fluorescence transients (SCCaFTs), due to Ca2+ entry through single openings of Ca2+-permeable ion channels, while recording unitary channel currents. Since the image obtained with wide-field optics is an integration of both in-focus and out-of-focus light, the total fluorescence increase (ΔFtotal or “signal mass”) associated with a SCCaFT can be measured directly from the image by adding together the fluorescence increase due to Ca2+ influx in all of the pixels. The assumptions necessary for obtaining the signal mass from confocal linescan images are not required. Two- and three-dimensional imaging was used to show that ΔFtotal is essentially independent of the position of the channel with respect to the focal plane of the microscope. The relationship between Ca2+ influx and ΔFtotal was obtained using SCCaFTs from plasma membrane caffeine-activated cation channels when Ca2+ was the only charge carrier of the inward current. This relationship was found to be linear, with the value of the slope (or converting factor) affected by the particular imaging system set-up, the experimental conditions, and the properties of the fluorescent indicator, including its binding capacity with respect to other cellular buffers. The converting factor was used to estimate the Ca2+ current passing through caffeine-activated channels in near physiological saline and to estimate the endogenous buffer binding capacity. In addition, it allowed a more accurate estimate of the Ca2+ current underlying Ca2+ sparks resulting from Ca2+ release from intracellular stores via ryanodine receptors in the same preparation.

Calcium ions play an important role in cell function, acting as effectors and/or signaling molecules for a variety of cellular biochemical and physiological processes. The development of a variety of Ca2+-sensitive fluorescent indicators and advancements in imaging technology have enhanced the ability to follow both global and localized changes in intracellular Ca2+ at ever improving temporal and spatial resolution. Ratiometric Ca2+ indicators like fura-2 permit the measurement of intracellular Ca2+ concentration (Grynkiewicz et al., 1985). But, they tend to have a limited dynamic range and a significant fluorescence background, which reduce their sensitivity to small local increases in Ca2+. On the other hand, certain nonratiometric Ca2+ indicators, such as fluo-3, although not able to give a dynamic direct read-out of the Ca2+ concentration, have very low fluorescence when not bound to Ca2+ and have a significant increase in fluorescence intensity upon binding Ca2+ (e.g., ∼200 times for fluo-3; Harkins et al., 1993). Therefore, they can be especially useful for following small, local changes in Ca2+ inside the cell.

Fluo-3 and other such Ca2+ indicators have been employed to record localized Ca2+ fluorescence transients such as “Ca2+ sparks” and “Ca2+ puffs” due to Ca2+ release from intracellular stores through ryanodine receptors or IP3 receptors, respectively (Parker and Yao, 1991; Cheng et al., 1993; Lopez-Lopez et al., 1995; Nelson et al., 1995; Klein et al., 1996; Bootman et al., 1997; Koizumi et al., 1999). In addition, Ca2+ fluorescence transients due to Ca2+ influx through a single opening of plasma membrane caffeine-activated channels (Zou et al., 1999), and later, L-type Ca2+ channels (Wang et al., 2001) and stretch-activated channels (Zou et al., 2002), have also been recorded using these indicators.

One goal of these types of studies is to relate the observed localized fluorescence transients to the underlying Ca2+ currents. This would make it possible to obtain the Ca2+ current passing through plasma membrane nonselective cation channels in physiological saline or underlying Ca2+ sparks and puffs. However, specialized methods are required to obtain this relationship with nonratiometric Ca2+ indicators. For a brief overview of some of these methods see Zou et al. (2004).

Sun et al. (1998) first introduced the insightful “signal mass” concept into fluorescence measurements of the Ca2+ flux underlying local Ca2+ events using confocal microscopy. They suggested that integrating the one-dimensional confocal linescan fluorescence signal, ΔF/F, over three dimensions would provide the signal mass due to the Ca2+ flux associated with Ca2+ puffs. The rate of rise of the signal mass, therefore, could provide an estimate of the Ca2+ current generating the fluorescence increase; and the peak, an estimate of the total Ca2+ flux (neglecting Ca2+ removal mechanisms, which are on a much slower time scale). However, to ensure the accuracy of this method requires (a) that the Ca2+ fluorescence event be in sharp focus and the scanning line pass through its center, (b) that the fluorescence profile be spatially symmetrical, which may not be the case (for examples, see Shen et al., 2004; Figs. 2 and 7 in Wellman and Nelson, 2003, and Chandler et al., 2003), and (c) that the event be separated spatially from other fluorescence events.

Following its first use by Sun et al. (1998), the idea of using signal mass measurements has been adopted by a number of investigators, using confocal microscopy, to obtain measurements of the Ca2+ current underlying Ca2+ fluorescence events and/or the number of ryanodine receptors involved in such events or to compare fluorescence events in different preparations (Gonzalez et al., 2000; Hollingworth et al., 2001; Wang et al., 2001; Chandler et al., 2003; Zhou et al., 2003). However, calculating signal mass directly from linescan images could involve significant errors even if all of the assumptions mentioned above were met. This is because the signal-to-noise ratio decreases farther away from the Ca2+ influx site and the contribution of the noisier signal to the signal mass gets amplified due to the weighting based on the distance from the influx site (Sun et al., 1998; Rios and Brum, 2002). In an attempt to solve this problem, alternative methods have been developed for calculating the signal mass using the full spatial width at half maximum amplitude of the ΔF/F signal (Shirokova et al., 1999; Hollingworth et al., 2001; Chandler et al., 2003).

Confocal microscopy is used for most studies of localized Ca2+ fluorescence events because of its small depth of field, which minimizes the collection of out-of-focus light. However, for the application of the signal mass method, there are theoretical advantages provided by wide-field microscopy, because the wide-field microscope will collect light from not only the in-focus plane but also the out-of-focus planes. Therefore, a wide-field image itself should be an integration of the fluorescence along the optical axis. At each point in time, the fluorescence signal mass could be obtained in a straightforward manner by adding together the fluorescence increase due to Ca2+ influx in all of the pixels (Zou et al., 1999; Fogarty et al., 2000; ZhuGe et al., 2000; Zou et al., 2002). As a result, the first two requirements that apply to confocal microscopy should not be necessary for wide-field imaging. Computer simulations have been used to show that the signal mass obtained this way should provide a good measure of the underlying current whether or not the fluorescence event is in focus (Zou et al., 1999; ZhuGe et al., 2000). However, there has not been a systematic experimental establishment of this point (Zou et al., 2004).

The present study was performed (a) to experimentally determine the validity of using signal mass or ΔFtotal measurements with wide-field microscopy for obtaining Ca2+ currents, especially to demonstrate that measurements of ΔFtotal are independent of the focal plane, and (b) to use the method to determine the Ca2+ current when it cannot be measured directly. In addition, some of the characteristics of fluo-3 and endogenous buffers are explored. For this purpose, we have mainly used the properties of an 80-pS, plasma membrane, Ca2+-permeable, nonselective cation channel that appears to be directly activated by caffeine (Guerrero et al., 1994a,b). The open time of the channel can be long and the channel density is low, possibly 10–15 channels per cell (scattered over the cell surface; Zou et al., 1999). These characteristics make it possible to record the unitary currents in the whole-cell recording configuration of the patch clamp. Also, as we have shown previously (Zou et al., 1999) with physiological concentrations of Ca2+ in the extracellular fluid, it is possible to record the fluorescence transient associated with Ca2+ entering the cell during a single opening of this channel (single channel Ca2+ fluorescence transient [SCCaFT]). All of the properties of this channel, especially those that enable simultaneous recording of the SCCaFT and the unitary current (without the membrane deformation associated with cell-attached patches as would be required with Ca2+ channels), make it a good choice for our present study.

Single Smooth Muscle Cell Preparation

Smooth muscle cells were enzymatically dispersed from the stomach of the toad Bufo marinus as previously described (Fay et al., 1982; Lassignal et al., 1986) and used on the same day. All experiments were performed at room temperature.

Patch-clamp Recordings and Data Processing

The currents passing through caffeine-activated channels and stretch-activated channels were recorded with an Axopatch-1D amplifier (Axon Instruments, Inc.) using the whole-cell and cell-attached patch configurations, respectively. Currents were low-pass filtered at 200 Hz and sampled at 1 kHz. Brief transitions to the closed or open state could be masked by the filtering. Therefore, what we refer to as channel open time may correspond to a channel burst time. Sometimes a digitally generated 60-Hz signal was subtracted to reduce the background noise. Caffeine-activated channels were opened by applying caffeine to the cell by pressure ejection from a glass pipette using a picospritzer (General Valve Corp.), and stretch-activated channels were opened by applying suction to the patch pipette (Zou et al., 1999, 2002).

Single discrete channel openings (or short bursts) were usually selected for the measurements described below. Total charge entry during channel openings was obtained by integrating the unitary channel current over time.

Wide-Field Digital Imaging and Fluorescence Measurements

Two-dimensional Imaging

Methods for two-dimensional (2D) Ca2+ fluorescence imaging and data processing were similar to those used by Zou et al. (1999)(2002). Fluorescence images were acquired using a custom-built high-speed digital imaging microscope with fluo-3 as the Ca2+ indicator. The standard system set-up was the same as that diagramed in ZhuGe et al. (1999) except that a different oil immersion objective lens (60× magnification with a numerical aperture of 1.4) was used. We generally focused at the middle of the cell. Each image was composed of 128 × 128 pixels, each usually 0.333 μm square. At each pixel, the fluorescence at rest (F0) was subtracted from the fluorescence (F) for each image in the image set, and the difference was used to construct the images (ΔF1 = F − F0 or ΔF/F0 = [F − F0]/F0), which were then smoothed (with a 3 × 3 kernel approximating a Gaussian with σ = 1 pixel) before display.2 The resting fluorescence, F0, was usually obtained by averaging the fluorescence intensity of 10 consecutive images when there was no fluorescence transient. The pixel with the maximum fluorescence increase for the transient was taken as the location of the channel and its fluorescence time course plotted in the figures. Measurements of fluorescence are given in units of photons detected by the camera.

The outline of the cell in the fluorescence ratio images was determined by applying a fluorescence intensity threshold. Several image sets were generally obtained from the same cell. To facilitate capturing the desired transients/channel openings we usually used a circular image buffer protocol (Zou et al., 1999; software provided by K.D. Bellve, Biomedical Imaging Group, University of Massachusetts Medical School). The read-camera control signal (sampled at 1 kHz) was simultaneously recorded with the current to facilitate the temporal alignment of the fluorescence trace with the corresponding current trace.

Three-dimensional Imaging

Three-dimensional (3D) imaging was used to provide images at planes above, below, and at the location of the channel. The digital imaging microscope was equipped with a computer-controlled piezoelectric focus drive to move the microscope objective lens, thereby scanning the focal plane of the objective lens through the thickness of the cell (for a more complete description see Kirber et al., 2001). The lens was moved at a constant velocity of 0.5 μm/ms and images continuously acquired every 2 ms. There was a turnaround time of 2 ms at the top and 5 ms at the bottom when the lens stopped moving so as to change direction from upward to downward or vice versa (Fig. 2 B). The images acquired during the turnaround times were discarded. We used this protocol because the coupling of the objective lens (60× water immersion, NA = 1.2) to the coverslip through the water immersion medium prevented us from moving the objective lens quickly enough in steps. We obtained a set of six images from six 1-μm-thick planes on average every 15.5 ms. The displayed ΔF/F0 images were obtained by deconvolution to remove the out-of-focus light (Fig. 2 A) from the stacks of optical images using the image restoration algorithm developed by members of the Biomedical Imaging Group (Carrington and Fogarty, 1987; Carrington et al., 1995). This algorithm takes into account the additional blurring resulting from the movement of the objective lens during image acquisition (see Kirber et al., 2001).

Determining the Ca2+ Current from the Total Fluorescence Change (ΔFtotal) or Fluorescence Signal Mass

Signal mass measurements were obtained from an image area that was large enough to cover the entire fluorescence increase as determined from the ΔF or ΔF/F0 images (e.g., an area within a box like that shown in Fig. 1 A). Total fluorescence was measured from the raw images (not the ΔF/F0 images) by summing the fluo-3 fluorescence from all the pixels. To estimate Ca2+ entry into the cytoplasm, the change in total fluorescence (ΔFtotal) was determined by subtracting the total fluorescence before the channel opened from the total fluorescence at each time point during the opening. The charge influx (ΔQ) was calculated by integrating current during the channel opening. When there was a global background fluorescence change (e.g., due to photobleaching), a linear extrapolation obtained from the baseline change before the transient was used to correct for background changes during the transient.

When Ca2+ enters into the cytoplasm, due to either release from intracellular Ca2+ stores or influx from the extracellular fluid, it will either remain free or it will bind to endogenous cellular buffers or fluorescent indicators like fluo-3. During a channel opening, ΔFtotal can be taken as an estimate of the amount of Ca2+ that entered the cytoplasm and bound to fluo-3 at any time (Zou et al., 1999; Fogarty et al., 2000; ZhuGe et al., 2000; Zou et al., 2002). In addition, neglecting Ca2+ removal from the cytoplasm, ΔFtotal will be, as shown below, linearly related to the Ca2+ influx (ΔCa2+, the number of Ca ions entering the cytoplasm) over the same time period.

Determining the Relationship between ΔFtotal and ΔCa2+

From previous simulations, it was suggested that during the channel opening, at least for short time periods and for Ca2+ currents in the range of a few pA, there is a linear relationship between ΔFtotal and ΔCa2+ (Zou et al., 1999; ZhuGe et al., 2000). If this is the case, then ΔFtotal, in units of detected photons, and ΔCa2+ can be linked by a constant, k:

\[\mathrm{{\Delta}Ca}^{2\mathrm{+}}=k{\cdot}\mathrm{{\Delta}F}_{\mathrm{total}}\mathrm{.}\]
(1)

The value of the constant, or converting factor, is affected by two components. The first is a fluorescence factor (f), which is the measured fluorescence (in detected photons) per Ca2+-bound fluo-3 molecule. The measured change in fluorescence will be related to the change in the amount of Ca2+-bound fluo-3 molecules (ΔCaFluo-3) as follows:

\[\mathrm{{\Delta}F}_{\mathrm{total}}=f{\cdot}\mathrm{{\Delta}CaFluo-3.}\]
(2)

The value of f results not only from the intrinsic properties of fluo-3 itself, but it is also a function of the image exposure time, laser excitation power, lens properties (e.g., magnification and numerical aperture), and other properties (e.g., camera, filters, mirrors, etc.) of the specific imaging system setup. Here, we have neglected the change in fluorescence due to the change in the amount of Ca2+-free fluo-3 molecules (<∼0.5%).

The second component is a buffer adjustment factor (fb), which takes into account the amount of Ca2+ that binds to buffers other than fluo-3. Free Ca2+, which is assumed to be small under our experimental conditions, is included in fb for the analysis here. Therefore, fb is equal to the number of Ca2+ ions that entered the cell (ΔCa2+) for each Ca2+ ion that bound to fluo-3 such that

\[\mathrm{{\Delta}Ca}^{2\mathrm{+}}=f_{b}{\cdot}\mathrm{{\Delta}CaFluo-3.}\]
(3)

The value of the buffer adjustment factor is dependent on the intracellular environment and the concentration of fluo-3.

It is straightforward to see from the above that k is simply the buffer adjustment factor divided by the fluorescence factor or

\[\mathrm{{\Delta}Ca}^{2\mathrm{+}}=k{\cdot}\mathrm{{\Delta}F}_{\mathrm{total}}=\left({f_{b}}/{f}\right){\cdot}\mathrm{{\Delta}F}_{\mathrm{total}}\mathrm{.}\]
(4)

For the opening of a Ca2+-permeable nonselective cation channel, the total charge entry over time (ΔQ), which is directly proportional to ΔCa2+ (provided that the Ca2+ current is a constant fraction of the total channel current), is obtained by integrating the channel current during the opening.

The converting factor, k, can be experimentally determined from the ΔFtotal that occurs when a known amount of Ca2+ enters the cell. To do this, a 90 mM Ca2+ bathing solution (see below) was used so that all of the inward current was due to Ca2+ entry when a caffeine-activated channel opened. In this case, the number of Ca ions coming into the cell (ΔCa2+) equals ΔQ divided by the charge of a Ca ion (3.2 × 10−19 C). With ΔFtotal measured over the same period of time, from Eq. 1, we have k = ΔQ /(3.2 × 10−19 · ΔFtotal). For these measurements, the values of ΔFtotal and ΔQ were usually taken from the time just before the channel opened until just after the channel closed and therefore are denoted as ΔFtotal-max and ΔQmax (see Fig. 3). ΔFtotal-max and ΔQmax can be obtained with higher accuracy by averaging through the baseline and the near steady-state plateau and this method was used to obtain the converting factor and related results.

The value of k, through its dependence on f (Eq. 4) changes if the imaging system set-up is changed and is also affected by the image exposure time. All of the images involved in determining k and related measurements were obtained in “full-frame rate” mode where images were acquired every 10 ms with a 10-ms exposure time. To apply the value of k to measurements where the image exposure time is different, the value of the measured ΔFtotal has to be normalized so that the effective exposure time is 10 ms. For example, if the k were to apply to the results shown in Fig. 1 (where images were acquired every 15 ms with a 6-ms exposure time), the value of ΔFtotal would have to be multiplied by 10/6.

On the other hand, fb is a function of the intracellular environment (particularly the concentration of fluo-3) and not the imaging system setup. Therefore, if we obtain the converting factor for one imaging system setup using a known Ca2+ current as described above and separately obtain a measure of f using the same set-up, we can then obtain the value of fb. Moreover, if we should choose to use a different set-up, with the value of fb known, we can calculate the new converting factor by merely obtaining f with this set-up. fb can also be used to estimate the equivalent binding capacity of the endogenous buffers (see discussion). Therefore, it is useful to be able to obtain values for f and fb.

Determining the Fluorescence Factor, f, for Ca2+-bound Fluo-3 Molecules and the Buffer Adjustment Factor, fb

When Ca2+ and fluo-3 are in equilibrium (as at rest):

\[\left[\mathrm{CaFluo-3}\right]=\left[\mathrm{Ca}^{2\mathrm{+}}\right]{\cdot}{\left[\mathrm{Fluo-3}\right]_{\mathrm{T}}}/{\left(\mathrm{K}_{\mathrm{d}}+\left[\mathrm{Ca}^{2\mathrm{+}}\right]\right)}\mathrm{.}\]
(5)

Here, [CaFluo-3] is the Ca2+-bound fluo-3 concentration, [Fluo-3]T is the total fluo-3 concentration, Kd is the dissociation constant for fluo-3 and Ca2+ (estimated to be 1.13 μM inside the cell; Smith et al., 1998), and [Ca2+] is the free Ca2+ concentration. Neglecting the fluorescence from Ca2+-free fluo-3, from Eqs. 2 and 5:

\begin{eqnarray*}&&f={\mathrm{F}_{\mathrm{total}}}/{\mathrm{CaFluo-3}}={\mathrm{F}_{\mathrm{total}}}/{\left(\mathrm{A}_{\mathrm{v}}{\cdot}\mathrm{V}{\cdot}\left[\mathrm{CaFluo-3}\right]\right)}\\&&\ ={\mathrm{F}_{\mathrm{total}}{\cdot}\left(\mathrm{K}_{d}+\left[\mathrm{Ca}^{2\mathrm{+}}\right]\right)}/{\left(\mathrm{A}_{\mathrm{v}}{\cdot}\mathrm{V}{\cdot}\left[\mathrm{Fluo-3}\right]_{\mathrm{T}}{\cdot}\left[\mathrm{Ca}^{2\mathrm{+}}\right]\right)}\end{eqnarray*}
(6)

Ftotal is the measured resting fluorescence in detected photons, Av is Avogadro's number, and V is the volume containing the fluo-3 molecules from which the Ftotal measurement is obtained. When [Ca2+] is saturating, [CaFluo-3] essentially equals [Fluo-3]T and, therefore, Eq. 6 reduces to

\[f={\mathrm{F}_{\mathrm{total}}}/{\left(\mathrm{A}_{\mathrm{v}}{\cdot}\mathrm{V}{\cdot}\left[\mathrm{Fluo-3}\right]_{\mathrm{T}}\right)}\mathrm{.}\]
(6a)

Experimentally, f was obtained using rectangular glass capillary tubes with a light path length of 20 μm (Vitro Dynamics Inc.). They were filled with a physiological saline solution containing 2 mM Ca2+ and 1, 5, or 10 μM fluo-3 penta-potassium salt. The same imaging system setup used for the experiments with isolated cells was used, and Ftotal was usually measured from the central 100 × 100 pixels of the image field. The volume of the segment of the tube, from which the measurements were obtained, was the area of the central image field times the light path length of the tube. From this volume, the measured Ftotal, and the total concentration of fluo-3, we could obtain f from Eq. 6a. Because other configurations of the imaging system (with different objective lenses) were also used, f could be obtained for each configuration and will be detailed in the text where appropriate. The advantage of using the glass capillary tubes to determine f instead of an estimated segment of the cell volume (see ZhuGe et al., 2000) is that the value obtained using capillary tubes is independent of the estimates of the cell volume, the resting Ca2+ concentration, and the Kd. Values of f given in the text were normalized to a 10-ms exposure time. Once f and k have been obtained, the buffer adjustment factor, fb, can be determined using Eq. 4.

Determining the Ca2+ Current Underlying a Fluorescence Transient

For a nonselective Ca2+-permeable plasma membrane cation channel, integrating the current during the channel opening will provide ΔQmax. With ΔCa2+max obtained from ΔFtotal-max using Eq. 1, the fraction of the current carried by Ca2+ is simply 3.2 × 10−19 · ΔCa2+max/ΔQmax or 3.2 × 10−19 · k · ΔFtotal-max/ΔQmax. The actual unitary Ca2+ current is determined by multiplying the total unitary channel current at the same membrane potential by this fraction.

Alternatively, the rate of rise for ΔCa2+ with time during the channel opening can be used to obtain the underlying Ca2+ current (iCa):

\[\mathrm{i}_{\mathrm{Ca}}=3.2\ \mathrm{{\times}}\ 10^{\mathrm{{-}}19}{\cdot}{\mathrm{{\Delta}Ca}^{2\mathrm{+}}}/{\mathrm{{\Delta}t}}=3.2\ \mathrm{{\times}}\ 10^{\mathrm{{-}}19}{\cdot}k{\cdot}{\mathrm{{\Delta}F}_{\mathrm{total}}}/{\mathrm{{\Delta}t}}\mathrm{.}\]
(7)

This equation is especially useful for those fluorescence transients where the underlying current cannot be recorded and/or the duration of the channel openings is not known (like for Ca2+ sparks). But there are also limitations with this method (see discussion).

For measurements of the fraction of the current carried by Ca2+ through caffeine-activated channels, there was no significant difference in ΔFtotal-max between the two groups of cells: one bathed in the 90 mM Ca2+ solution used to determine k and the other bathed in 1.8 mM Ca2+.

Criteria for Data Selection for Analysis

For most of the fluorescence transients analyzed, it was necessary that (a) the transient of interest be separated in time and space from other transients; (b) ΔFtotal measurements, though confined to a limited region of the cell, include all of the fluorescence signal associated with the transient within the field of view of the camera; (c) the transient not be so out of focus that it was hard to distinguish the transient from the noise, (d) the underlying channel opening be sufficiently long; and (e) for measuring charge influx, ΔQ, the channel current associated with the transient be free of interfering currents from other channel openings.

For two of the 3D transients where there were interfering currents, instead of plotting ΔFtotal versus ΔQ, we plotted ΔFtotal versus time. We could do this because there appeared to be no significant closures (i.e., the channel was essentially always open so ΔQ would increase linearly with time) judging from the in-focus ΔF, which clearly reflects the openings and closings of the channel (Zou et al., 1999; Video 1, available). Statistical data are expressed as the mean ± SEM.

Obtaining the Point Spread Function (PSF) of the Microscope

To help compare the results here using our custom-built microscope with what might be obtained using other (commercially available) microscopes (see discussion), the microscope PSFs were obtained using fluorescent microspheres (PS-Speck Microscope Point Source Kit). The microspheres (0.175 μm) were diluted in 90% glycerol mounting medium, applied to a No. 1.5 glass coverslip, and sealed onto a glass slide. Only isolated, individual beads lying on the coverslip surface were used. Images were acquired as optical sections by moving the objective lens over a range of ±10 μm from the microsphere.

Solutions

The bathing solution used for the experiments described here usually contained (in mM) NaCl 130, KCl 3, CaCl2 1.8, MgCl2 1, and Hepes 10 (pH adjusted to 7.4 using NaOH). The usual whole-cell pipette solution contained (in mM) KCl 137, MgCl2 3, Hepes 10, Na2ATP 3, and fluo-3 pentapotassium salt 0.05 (pH adjusted to 7.2 using KOH). At times we also used a bath solution that contained (in mM) NaCl 127, KCl 3, CaCl2 1.9, MgCl2 1, and Hepes 10 (pH adjusted to 7.4 using NaOH); and a pipette solution that contained (in mM) KCl 130, MgCl2 1, Hepes 20, Na2ATP 3, Na3GTP 1, and fluo-3 pentapotassium salt 0.05 (pH adjusted to 7.2 using KOH). A high [Ca2+] bath solution, used for calibration purposes with caffeine-activated channels so that at negative potentials the only charge carrier of the inward current would be Ca2+, contained (in mM) CaCl2 90 and Hepes 10 (pH adjusted to 7.4 using Ca[OH]2). In the text, we designate the latter as the 90 mM Ca2+ solution.

For most of the experiments described here, we wished to remove any possible contributions from intracellular Ca2+ stores, therefore thapsigargin (1 μM) was added to the bathing solutions and ryanodine (100 μM) was included in the patch pipette solution. Caffeine (20 mM in the bathing solution) was also applied to the cells before the beginning of experiments using the Picospritzer. These treatments have been previously employed to successfully block effects from the intracellular stores (ZhuGe et al., 1999; Zou et al., 1999). The stock solutions for thapsigargin (10 mM) and ryanodine (100 mM) were in DMSO and stored at −20°C.

Online Supplemental Material

The online supplemental material (Fig. S1 and Video 1) are available. Fig. S1 shows the total fluorescence of a microsphere as a function of its distance from the focus point of the microscope (for both the microscope used in the present study and one that is commercially available). This figure demonstrates that our findings concerning the signal mass method would also be valid for other wide-field imaging systems (see Discussion). Video 1 shows the sensitivity of the in-focus SCCaFT to the openings and closings of the channel.

Total Fluorescence Increase, ΔFtotal, Is Linearly Related to Charge Entry, ΔQ

When caffeine was applied to a toad stomach smooth muscle cell with the whole-cell membrane potential held at −80 mV, the inward unitary currents and the fluorescence increase associated with Ca2+ entering the cell were recorded simultaneously (Fig. 1, A and B). Temporal integration of the unitary current provided the time course of total charge entry (ΔQ) and spatial integration of the change in fluorescence at each pixel (ΔF) provided the time course of the increase in total fluorescence (ΔFtotal) associated with the channel opening (Fig. 1 B). Except when channel closures occurred, ΔQ increased linearly with time, suggesting a constant Ca2+ influx. These closures also affect the time course of ΔFtotal. However, even with the presence of brief closures, we found that there was a linear relationship between ΔFtotal and ΔQ (and therefore ΔCa2+) during a channel opening (r2 = 0.99; Fig. 1 C). Therefore, the relationship between ΔFtotal and ΔQ provides a better way of characterizing these events than the changes of ΔFtotal with time. A linear relationship between ΔQ and ΔFtotal was obtained from at least 31 transients in 16 cells with different solutions, suggesting that for our experimental conditions, the value of the converting factor (and therefore fb) does not change over the time period of a channel opening.

ΔFtotal Measurements Are Independent of the Focal Plane

Because the light detected using wide-field microscopy comes from both in- and out-of-focus planes, a 2D wide-field image is actually an integration of light throughout the depth of the cell. Therefore, theoretically, for the same Ca2+ influx, ΔFtotal should not change regardless of the location of the channel relative to the plane of focus. For example, if the transient in Fig. 1 A was not in focus, we still would have expected the relationship between the ΔFtotal and ΔQ to be the same. Although this could be predicted from computer simulations (Zou et al., 1999; ZhuGe et al., 2000), we performed two sets of experiments to determine if this was indeed the case.

In the first set of experiments, we obtained different SCCaFTs in the same cell that were either in or out of focus depending on their location. For some other cells, recordings of in- and out-of-focus SCCaFTs were obtained with the objective lens moved to different positions along its optical axis. Therefore, SCCaFTs from the same location could be recorded either close to or farther away from the focal plane. An example is shown in Fig. 1 (B and D) with a pair of SCCaFTs recorded from the same cell, one from its punctate appearance being in focus (Fig. 1 A) and the other from its diffuse appearance, out of focus (Fig. 1 E). A plot of ΔFtotal versus ΔQ showed nearly the same slope for both transients (Fig. 1 C). For the cell in Fig. 1, we obtained three in-focus transients from the same location (as shown in Fig. 1 A), one out-of-focus transient from a location close to that of the in-focus transients, and two out-of-focus transients from a third location (as shown in Fig. 1 E). The slopes from plots of ΔFtotal versus ΔQ (for approximately the first 200 ms) of the three in-focus transients were close with values of 114, 93, and 100 (or 102 ± 6) detected photons per femtoCoulomb (fC). The slopes of the three out-of-focus transients shared similar values of 96, 100, and 78 (or 91 ± 7) detected photons per fC. 13 additional transients were obtained from 4 other cells. When comparing the slopes of the more out-of-focus transients with that of the most in-focus transient in the same cell (as in Fig. 1 C), the difference on average for 12 pairs was 7.6 ± 5.5%. In general it appears that for the same charge influx, the measured total fluorescence change, ΔFtotal, is independent of the focal plane (within certain limitations, see below and discussion).

In the second set of experiments, the same Ca2+ transient was measured from six different focal planes, taking advantage of the fast 3D imaging capability of our imaging system. As shown in Fig. 2 A, the SCCaFT appeared to be located close to planes 5 and 6 (where it was most punctate in appearance). It was most out of focus in plane 1 based on its extremely diffuse appearance. From the in-focus planes, the fluorescence change (ΔF/F) in the vicinity of the channel is much greater with a more rapid rise and fall and with a steeper spatial gradient than for those planes that are more out of focus (Fig. 2 C). However, the slopes for the linear relationship between ΔFtotal, obtained from the unrestored images, and ΔQ are essentially the same for all of the six planes (Fig. 2 D). When obtained from the more out-of-focus planes, the slopes differed by −1.8 ± 0.7% compared with that from the most in-focus plane (as in Fig. 1 C). The fact that the slopes of the six linearly fitted curves are essentially the same demonstrates that the same Ca2+ current can be determined based on ΔFtotal (fluorescence signal mass) measurements from both in- and out-of-focus wide-field images. A similar result was obtained from a stretch-activated channel current in another cell where the difference of the slopes was −4.5 ± 4.9%.

There were other 3D experiments where we were able to obtain the fluorescence transient in all six planes, but because there were interfering openings in the current trace, we could not obtain the charge influx underlying the transient. Two of these transients were judged to be free of long closures using the technique described near the end of materials and methods. Since the same Ca2+ current underlies the fluorescence changes in all of the planes, we would expect the same ΔFtotal in each plane. We compared ΔFtotal versus time, instead of charge influx, for the out-of-focus planes with that of the most in-focus plane for these two transients. The difference in slopes was 10.3 ± 2.0% and −4.7 ± 5.2%. Application of this analysis to the two transients described in the previous paragraph resulted in the difference in slopes of −1.3 ± 0.7% and −3.3 ± 5.0%.

In summary, it appears that ΔFtotal is directly related to the underlying Ca2+ current; and therefore the Ca2+ current can be determined using wide-field microscopy even if the channel is not in the focal plane of the 2D image. To do this requires obtaining the converting factor between ΔFtotal and ΔCa2+.

Determining the Converting Factor (k), the Fluorescence Factor (f), and the Buffer Adjustment Factor (fb)

The converting factor between ΔFtotal and ΔCa2+ can be determined using the 90 mM Ca2+ bath solution such that Ca2+ is the only ion available to carry the inward current (Fig. 3). There was a linear relationship between ΔFtotal and ΔQ during the time of the channel opening (Fig. 3 C). With Ca2+ being the only charge carrier, the total charge entry, ΔQmax, directly provides the number of Ca ions that entered the cell (ΔCa2+max = ΔQmax/3.2 × 10−19). The converting factor can be obtained from the ratio of ΔCa2+max to ΔFtotal-max. A linear relationship between ΔFtotal and ΔQ was obtained for 10 transients in 7 cells, and the average ratio of ΔCa2+max to ΔFtotal-max for these transients provided a converting factor of 1.65 ± 0.12 Ca2+ ions per detected photon for a 10-ms exposure time. These results were obtained at −80 mV to increase the size of the unitary current under whole-cell current recording conditions.

To determine f, fluorescence emission was obtained using capillary tubes containing 1, 5, and 10 μM fluo-3 concentrations in the presence of 2 mM (saturating) Ca2+ as described in materials and methods. Measurements were obtained with an exposure time of 2 or 4 ms and normalized to a 10-ms time period. Using Eq. 6a and measurements with the standard setup, we found that f is equal to 2.34 detected photons per Ca2+-bound fluo-3 molecule (Fig. 4).

With the values of f and k known, fb can be determined from Eq. 4 and is equal to 3.86, i.e., on average 3.86 Ca2+ ions enter the cytoplasm for every Ca ion that binds to fluo-3. Therefore, ∼26% (=1/3.86) of the Ca2+ that entered the cytoplasm binds to fluo-3 with the rest binding to endogenous buffers except for a very small amount of free Ca2+ (see discussion). A similar value was obtained by Chandler et al. (2003) from their computer simulations of Ca2+ sparks in frog skeletal muscle using 100 μM fluo-3, and it is a little less than one half of the value that can be derived from the release flux data of Rios et al. (1999) with an average estimated fluo-3 concentration of 260 μM.

Determining the Fraction of the Current Carried by Ca2+ and the Unitary Ca2+ Current for Nonselective Cation Channels

Using the converting factor obtained with the 90 mM Ca2+ solution, we determined the fraction of the current carried by Ca2+ for the caffeine-activated channel at −80 mV using the standard solutions with the extracellular solution containing physiological levels of Ca2+. For 15 transients in 6 cells, there was a linear relationship between ΔFtotal and ΔQ over the time of the channel opening (as in Fig. 1 C). ΔCa2+max can be obtained from the ΔFtotal-max that accompanied a channel opening and the converting factor (Eq. 1). The fraction of the current carried by Ca2+ could then be calculated from 3.2 × 10−19 · ΔCa2+max/ΔQmax. In this case ΔQmax, the integral of the current during a channel opening, includes the current carried by other cations in addition to Ca2+. To use the converting factor in this way requires that the same imaging system setup and pipette (intracellular) solution (including the concentration of fluo-3) be used for both groups of cells. For the 15 transients, the fraction of the inward current carried by Ca2+ is 20.2 ± 0.8%. This makes the Ca2+ current 1.4 pA for a 7.1-pA total inward unitary current at −80 mV. The value of 20.2% is close to that (18.9%) found by Guerrero et al. (1994b) using a different methodology and somewhat different solutions (but with the same extracellular Ca2+ concentration) and is in the upper range for other nonselective cation channels where Ca2+ fluxes were obtained (Neher, 1995; Burnashev, 1998; Ohyama et al., 2000; Zou et al., 2002).

Although the openings of caffeine-activated channels tend to be long, brief openings were also examined and included in the above result. The relationship between the fraction of current carried by Ca2+ and the value of the measured ΔFtotal is independent of the duration of the channel opening (Fig. 5). Illustrated in Fig. 5 is an example of a very brief, spark-like SCCaFT recording with a channel opening lasting <12 ms. This SCCaFT resembles a Ca2+ spark in a number of characteristics: its rise time, percent change in fluorescence, t1/2, and full width at half maximum (FWHM) are all in the range of those for a Ca2+ spark in the same cell type (ZhuGe et al., 2000). More importantly, its signal mass, when corrected for differences in f (see discussion), indicates a similar increase in the number of Ca2+-bound fluo-3 molecules to that expected on average from a Ca2+ spark (∼7,000 versus 10,000, respectively). Therefore, the converting factor obtained from the present study could also be applicable for determining Ca2+ current underlying sparks in these cells (see discussion).

The results shown in this study provide experimental evidence that Ca2+ flux through a single channel can be quantitatively measured using wide-field microscopy with single wavelength fluorescent indicators (e.g., fluo-3) by measuring total fluorescence increase (ΔFtotal, or signal mass). With a known Ca2+ current for calibration, a converting factor between ΔFtotal and the underlying Ca2+ influx was obtained as a characteristic of the cell and the imaging system. The converting factor could then be applied to obtain other Ca2+ currents (e.g., that normally pass through caffeine-activated channels or that underlie Ca2+ sparks) under the same experimental conditions. Furthermore, the endogenous buffer binding capacity can also be estimated from the calibrated fluorescence measurements (see below).

A wide-field imaging microscope collects light not only from the two dimensions of the focal plane but also above and below it. The illumination intensity and the collection angle are essentially unchanged, at least within the range of the cell thickness (a few micrometers). Therefore, the same fluorescence intensity and the same fraction of the entire fluorescence emission would be collected whether the transient is in or out of focus. However, an out-of-focus transient forms an enlarged image with less intensity at each pixel. This results in a decrease in signal-to-noise ratio not only for each pixel but also for ΔFtotal. The latter occurs also because measurements have to be obtained from a larger image area in order to gather all the fluorescence from an out-of-focus transient. This decrease in overall signal-to-noise ratio may prevent the technique from being used for transients that are far out of focus. Nevertheless, this method should prove useful for channels within at least 4 μm of the focal plane, as determined from the 3D images (Fig. 2).

To determine if our findings here would also be valid for other wide-field imaging systems, we compared the total fluorescence measurements (background corrected) using our system with those of a commercially available digital imaging microscope. We did this by measuring the total fluorescence from images acquired for constructing the PSF of each microscope using a fluorescent microsphere. Each of the images was acquired with the microsphere positioned at a different distance from the focus point of the camera (see materials and methods). For our custom-built microscope, across a range of ±10 μm, the values of total fluorescence were found to be within 20% of that when the microsphere was in focus. Similar results were also obtained with the commercially available microscope (Fig. S1, available). Therefore, the independence of total fluorescence measurements with respect to the relative position of the microsphere from the focal plane is not unique to the custom-built high-speed imaging system used in the present study.

The Linear Relationship between ΔFtotal and ΔCa2+

The relationship between ΔFtotal and ΔCa2+ depends not only on the concentration of fluo-3, but also on other buffers. Moreover, the constituents are not in equilibrium during a channel opening. Nevertheless, we have previously reported from computer simulations with fluo-3 and a fixed buffer (Zou et al., 1999) that ΔFtotal increases linearly with time during the channel opening (for a constant Ca2+ current from 0.1 to at least 3 pA, a reasonable range for single channel Ca2+ currents and currents underlying Ca2+ sparks). Consistent with this simulation, our experimental results also show a linear relationship between ΔFtotal and ΔCa2+ (for stretch-activated channels in cell-attached patches see Zou et al., 2002).

A similar linear relationship can also be found in the literature for confocal microscopy. Wang et al. (2001) showed data for openings of L-type Ca2+ channels in cell-attached patches at the same potential in cardiac cells, and there appears to be a linear relationship between signal mass and total Ca2+ influx. Also, the signal mass for oocyte Ca2+ puffs and Ca2+ blips increases linearly with time, which suggests a linear relationship between signal mass and Ca2+ influx assuming a constant Ca2+ current underlying these events (Sun et al., 1998). Furthermore, simulations of the events underlying skeletal muscle Ca2+ sparks reveal a near linear relationship between signal mass and the amount of Ca2+ release with Ca2+ currents of different durations, and a near linear rise in the signal mass over time with a constant, though brief, Ca2+ current (Chandler et al., 2003). Therefore, a linear relationship, and hence a constant converting factor, between signal mass or ΔFtotal and ΔCa2+ may be more common than might be expected. The actual value of the converting factor would depend on the experimental conditions.

Two implications are provided by the linear relationship between ΔFtotal and ΔCa2+. First, determining an unknown Ca2+ influx using ΔFtotal requires only the value of the constant converting factor. There would be no need to develop a (nonlinear) calibration curve to relate ΔFtotal to the underlying ΔCa2+. Second, the signal mass method is demonstrated to be valid over the whole range of ΔCa2+, from near zero to at least the maximum ΔCa2+ obtained by the calibration method using the 90 mM Ca2+ solution (∼106 Ca ions from Fig. 3).

Obtaining the value for the converting factor between fluorescence events and Ca2+ influx is essential for determining the Ca2+ currents underlying fluorescence events when the currents cannot be obtained directly. The converting factor can be obtained with a known Ca2+ current through nonselective Ca2+-permeable cation channels (like stretch-activated channels or caffeine-activated channels) or with the Ca2+ current passing through Ca2+-selective channels.

A possible drawback of using Ca2+-selective channels as well as stretch-activated channels is that recordings are obtained in cell-attached patches. In cardiac cells it appears that membrane deformation during formation of the “omega-like” cell-attached patch may decrease the coupling between the L-type Ca2+ channel opening and Ca2+ spark generation (Wang et al., 2001). Furthermore, we have noticed a few ms time shift that sometimes occurs when recording the SCCaFT due to an opening of the stretch-activated channel, which may also be due to the geometry of the cell-attached patch.

There are other advantages for using channels like caffeine-activated channels instead of Ca2+-selective channels (Zou et al., 2004). The unitary current for caffeine-activated channels at −80 mV is five times larger than the Ca2+ current, making the unitary currents easier to discern. Because there are only a few caffeine-activated channels on the entire cell membrane, each of which has long openings and larger currents, recordings can be obtained in the same whole-cell patch-clamp configuration used to record Ca2+ sparks. Moreover, the cytosolic fluo-3 concentration can be approximated to be the pipette fluo-3 concentration with whole-cell recordings, making it possible to estimate the binding capacity of endogenous buffers.

The Buffer Adjustment Factor and Buffer Binding Capacity

The linear relationship between ΔFtotal and ΔCa2+ suggests that k, and therefore fb, is a constant. Computer simulations similar to those shown in Zou et al. (1999) were performed to explain this observation using parameters reported in the literature for smooth muscles. The simulations involved an endogenous fixed buffer (κ = 115 [see below], kon = 100 [μM·s]−1, koff = 100 s−1) as well as fluo-3 (50 μM, kon = 80 [μM·s]−1, koff = 90 s−1, diffusion constant = 2.5 × 10−7 cm2/s) with a resting Ca2+ level of 50 nM. Results from simulations demonstrated that fb is indeed essentially constant during a channel opening and its value is close to that at equilibrium. This conclusion remains unchanged when the on and off rates of the fixed buffer were changed by at least a factor of two, varying the concentration to keep κ the same.

Using the value of fb obtained during our experiments, we can estimate the binding capacity of an equivalent endogenous buffer, which is a reflection of the change in Ca2+ binding to a particular buffer when the Ca2+ concentration is changed (Neher and Augustine, 1992). The binding capacity (κB) of any buffer (B), at equilibrium with a given Ca2+ concentration and for small Ca2+ changes, is κB = ∂[CaB]/∂[Ca] = BT · Kd/([Ca] + Kd)2 (here, Kd is the dissociation constant of the buffer, BT is the total buffer concentration, and [CaB] is the concentration of Ca2+-bound buffer B). In the present study, the binding capacity of fluo-3 (κF) was 41 at rest, assuming a total fluo-3 concentration of 50 μM, a Kd of 1.13 μM, and a resting Ca2+ level of 50 nM. The fraction of incoming Ca2+ bound to fluo-3, equivalent to the reciprocal of our buffer adjustment factor, can be calculated from κF/(κF + κE +1) (κE is the binding capacity of endogenous buffer). Therefore, from fb = 3.86 (25.9% of the Ca2+ entered binds to fluo-3) and κF = 41, we obtained the approximate binding capacity of an equivalent endogenous buffer (an aggregate of all other buffers) under whole-cell recording conditions of 115. This value for endogenous buffer binding capacity in toad stomach smooth muscle cells is in agreement with those determined from other smooth muscle preparations (see Daub and Ganitkevich, 2000, and the references therein).

The Fluorescence Factor

We obtained the values of the fluorescence factor (f) for fluo-3 by measuring the fluorescence emission from a known amount of Ca2+-bound fluo-3 contained in glass capillary tubes. Alternatively, it can be obtained by measuring the fluo-3 florescence emission from a volume segment of a cell at rest. ZhuGe et al. (2000) obtained a calibration factor (f−1 = 2.44 Ca2+-bound fluo-3 molecules per detected photon) in the same cell type using this alternative method. For this measurement it was assumed that the volume segment was a rectangular cube with a uniform thickness of 8 μm, the resting Ca2+ concentration was 100 nM, the total fluo-3 concentration inside the cell was equal to that in the pipette (50 μM), and the Kd was 1.1 μM (see Eq. 6). Using the same imaging system, pixel size (333 × 333 nm), and lens (40× oil immersion lens with a NA = 1.3) as used for Ca2+ spark measurements, we determined f = 0.80 detected photons per Ca2+-bound fluo-3 molecule directly from rectangular glass capillary tubes without the need for the above assumptions (Fig. 4). This value is about twice that obtained by ZhuGe et al. (2000) (f = 1/2.44 = 0.41 detected photons per Ca2+-bound fluo-3 molecule). While the difference could come from the cell volume estimate, it could also be due to the estimate for the resting Ca2+ concentration. The values for f obtained using both methods would be in very good agreement (within ∼3%, see Eq. 6) if an estimate of 50 nM intracellular Ca2+ (close to the value obtained by Guerrero et al., 1994b, for toad cells with 1.8 mM extracellular Ca2+, also see Hollingworth et al., 2001, for frog skeletal muscle) was used instead of 100 nM (close to the value obtained by Drummond and Fay, 1996, with 20 mM extracellular Ca2+).

Determining the Ca2+ Currents Underlying Ca2+ Sparks

An important consequence of our measurements with the caffeine-activated channel is that it leads to an ability to obtain the Ca2+ current underlying Ca2+ fluorescence events, like Ca2+ sparks, where the current cannot be directly measured. We applied our results to Ca2+ sparks recorded previously by ZhuGe et al. (2000) who used the same cell preparation we used here.

ZhuGe et al. (2000) employed an averaging technique using the spark-induced spontaneous transient outward current (STOC) to temporally align the Ca2+ sparks and then grouped the Ca2+ sparks into quartiles according to their total fluorescence increase or signal mass. From the initial rate of rise of the averaged signal mass for each quartile, the underlying mean Ca2+ current was estimated to be 0.23, 0.66, 0.66, and 1.31 pA, respectively. These current values were minimum estimates because they were based on the assumption that all of the Ca2+ released through ryanodine receptors would bind to fluo-3 (i.e., fb = 1). If our experimentally determined values of fb (3.86) and also f (0.80) were applied, the current estimates would be increased to 0.45, 1.31, 1.31, and 2.59 pA, respectively. By doing this, we are effectively applying a converting factor of k = 3.86/0.8 = 4.83 (instead of 1/0.41 = 2.44) to the fluorescence measurements of ZhuGe et al. (2000). This accounted for the binding of the released Ca2+ to buffers other than fluo-3 and removed the assumptions involved in calculating the fluorescence factor from the cell.

There has been considerable debate as to whether the smallest of the Ca2+ sparks is due to the opening of a single receptor/channel or the concerted opening of a number of channels (Cannell and Soeller, 1999; Schneider, 1999; Shirokova et al., 1999; Gonzalez et al., 2000). Kettlun et al. (2003) estimated, based on their results from bilayer studies, that ryanodine receptors from mammalian cardiac cells and amphibian skeletal muscle have a unitary Ca2+ current of ∼0.5 pA under near physiological conditions (1 mM luminal Ca2+, symmetric 1 mM Mg2+ and 150 mM K+). The Mg2+ and K+ concentrations are similar to those used for studying Ca2+ sparks in toad stomach smooth muscle cells (ZhuGe et al., 2000). If the ryanodine receptor conductance properties are also similar, then the Ca2+ spark current estimated from the first quartile of signal mass amplitudes (0.45 pA) is possibly due to the opening of a single ryanodine receptor. Larger sparks may be generated by currents of six or more ryanodine receptors, based on the current calculated from the quartile with the largest signal mass being about six times that of the smallest quartile. If the toad cell sarcoplasmic reticulum Ca2+ concentration is closer to 0.15 mM as measured by ZhuGe et al. (1999), then the unitary Ca2+ currents from ryanodine receptors might be smaller. Therefore, an average Ca2+ spark in the first quartile might require more ryanodine receptors to open with possibly the current through one ryanodine receptor underlying the smallest detectable Ca2+ spark.

Our estimates of the Ca2+ currents underlying Ca2+ sparks in gastric smooth muscle cells are in the range of the studies of Wang et al. (2001)(2004), who also used a calibration standard. They estimated the Ca2+ current underlying Ca2+ sparks in cardiac cells from the time course of the rising phase of the fluorescence transients obtained with confocal linescan imaging. The fluorescence associated with Ca2+ influx through L-type Ca2+ channels (which they called “sparklets”) was used as a calibration standard. Their spark currents varied from ∼1 to 10 pA. If the fluorescence transients were recorded in focus, they were able to detect a fine structure in the current amplitude distribution corresponding to a unitary spark current of ∼1.2 pA, which they attributed to the current due to a single ryanodine receptor.

Estimating the Underlying Unitary Ca2+ Current from ΔFtotal Measurements Alone

Without simultaneous patch-clamp recordings, it is not that straightforward to obtain the unitary Ca2+ current from the rate of rise of ΔFtotal using Eq. 7, even with the assumption that a single channel opening underlies the fluorescence transient. Although Ca2+ influx can be determined from the converting factor and ΔFtotal, it may provide only the average unitary Ca2+ current during the transient. This could happen when continuous rapid closings and reopenings of the channel occur and any discontinuities in ΔFtotal are not detected. In this case, ΔFtotal will have a slower rate of rise and, therefore, lead to an underestimate of the open channel unitary Ca2+ current (Fig. 1 D).

When the transient is a result of openings of more than one channel, it becomes impossible to estimate the unitary Ca2+ current even if the openings and closings are synchronized, although it may be possible to estimate the total underlying Ca2+ current. Moreover, nonsynchronous openings and closings of the channels may cause ΔFtotal to deviate from linearity over time. For example, the rate of rise of ΔFtotal will decrease when some of the open channels close at different times. However, if all the channels opened synchronously (as suggested by the results of Wang et al., 2004), then measuring the initial rate of rise of ΔFtotal may provide an estimate of the Ca2+ current.

Moreover, the rise time of ΔFtotal is not the best measure of the channel open time because the spatial integration reduces the contribution from the fluorescence obtained from the location of the channel. On the other hand, when in focus, the localized fluorescence change at the channel (ΔF/F0 or ΔF) is much more sensitive to the kinetics of its opening and closing (Video 1, available). Therefore, the ΔF/F0 signal can be used as a reference for channel open and closed states (Zou et al., 1999). Even the out-of-focus ΔF/F0 or ΔF, although not as sensitive to brief closures as those in focus, can provide a good measure of the single channel open duration. As a result, the combined measurements of the in-focus fluorescence at the channel and ΔFtotal would provide a good means for determining the Ca2+ current. When measuring brief fluorescence events (such as Ca2+ sparks with the rise time of ΔF/F0 usually <20 ms), however, a much faster imaging rate is required to determine accurately the channel open time and distinguish brief closures and reopenings. Unfortunately, higher time resolution (e.g., 2-ms exposure times) also engenders a noisier fluorescence signal.

In conclusion, the calibrated signal mass measurement is a valid method for determining Ca2+ influx underlying a fluorescence transient using single wavelength dyes such as fluo-3. A wide-field microscope has advantages over a confocal microscope for such measurements because fewer assumptions are required. Once a system is calibrated with a known Ca2+ current (i.e., the converting factor is obtained), it can be used to determine the unknown Ca2+ influxes or releases underlying various fluorescence transients when ΔFtotal can be directly measured.

We thank Stephen Baker for help with the statistical analysis; Agustin Guerrero-Hernández, Michael Kirber, and Michael Sanderson for their comments on an earlier version of the manuscript; and Jeff Carmichael, the late Rebecca McKinney, Brian Packard, Paul Tilander, and Yu Yan for their excellent technical assistance. Jeff Carmichael also helped with the PSF measurements for the commercial microscope.

This work was supported by National Institutes of Health grant AR47067.

Olaf S. Andersen served as editor.

Abbreviations used in this paper: 3D, three-dimensional; fC, femtoCoulomb; PSF, point spread function; SCCaFT, single channel Ca2+ fluorescence transient.

1

To simplify the notation, all of the variables with a “Δ” prefix are time dependent except when denoted with “max” in the subscript.

2

The construction of fluorescence images from either confocal or wide-field microscopy usually involves normalizing the fluorescence at each pixel to the resting fluorescence as ΔF/F0 or F/F0. For wide-field fluorescence imaging of a macro fluorescence event occurring throughout the cell as would occur by activation of whole-cell Ca2+ current in a spherical or cylindrical cell, this procedure is appropriate in order to normalize for the effect of indicator concentration and/or cell depth. It might also be appropriate for confocal imaging of localized fluorescence events to normalize for the effect of indicator concentration where the fluorescence from each pixel is theoretically from a thin slice of the cell. However, the normalization of localized fluorescence events obtained with wide-field imaging can be misleading. This occurs because the same event (ΔF) occurring near the center of the spherical or cylindrical cell (the thicker part of the cell) would produce a smaller percent increase in fluorescence than at the edge (the thinner part of the cell) (Zou et al., 1999). Therefore, we chose to display most of our images without normalization by the resting fluorescence and used only the increase in fluorescence, ΔF, instead.

Bootman, M., E. Niggli, M. Berridge, and P. Lipp.
1997
. Imaging the hierarchical Ca2+ signalling system in HeLa cells.
J. Physiol.
499
:
307
–314.
Burnashev, N.
1998
. Calcium permeability of ligand-gated channels.
Cell Calcium.
24
:
325
–332.
Cannell, M.B., and C. Soeller.
1999
. Mechanisms underlying calcium sparks in cardiac muscle.
J. Gen. Physiol.
113
:
373
–376.
Carrington, W.A., and K.E. Fogarty. 1987. 3D molecular distribution if living cells by deconvolution of optical sectioning using light microscopy. Proceedings of the Thirteenth Annual Northeast Bioengineering Conference, IEEE, New York. 1:108–110.
Carrington, W.A., R.M. Lynch, E.D. Moore, G. Isenberg, K.E. Fogarty, and F.S. Fay.
1995
. Superresolution three-dimensional images of fluorescence in cells with minimal light exposure.
Science.
268
:
1483
–1487.
Chandler, W.K., S. Hollingworth, and S.M. Baylor.
2003
. Simulation of calcium sparks in cut skeletal muscle fibers of the frog.
J. Gen. Physiol.
121
:
311
–324.
Cheng, H., W.J. Lederer, and M.B. Cannell.
1993
. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle.
Science.
262
:
740
–744.
Daub, B., and V. Ganitkevich.
2000
. An estimate of rapid cytoplasmic calcium buffering in a single smooth muscle cell.
Cell Calcium.
27
:
3
–13.
Drummond, R.M., and F.S. Fay.
1996
. Mitochondria contribute to Ca2+ removal in smooth muscle cells.
Pflugers Arch.
431
:
473
–482.
Fay, F.S., R. Hoffmann, S. Leclair, and P. Merriam.
1982
. Preparation of individual smooth muscle cells from the stomach of Bufo marinus.
Methods Enzymol.
85
:
284
-292.
Fogarty, K.E., J.F. Kidd, R.A. Tuft, and P. Thorn.
2000
. A bimodal pattern of InsP3-evoked elementary Ca2+ signals in pancreatic acinar cells.
Biophys. J.
78
:
2298
–2306.
Gonzalez, A., W.G. Kirsch, N. Shirokova, G. Pizarro, G. Brum, I.N. Pessah, M.D. Stern, H. Cheng, and E. Rios.
2000
. Involvement of multiple intracellular release channels in calcium sparks of skeletal muscle.
Proc. Natl. Acad. Sci. USA.
97
:
4380
–4385.
Grynkiewicz, G., M. Poenie, and R.Y. Tsien.
1985
. A new generation of Ca2+ indicators with greatly improved fluorescence properties.
J. Biol. Chem.
260
:
3440
–3450.
Guerrero, A., F.S. Fay, and J.J. Singer.
1994
a. Caffeine activates a Ca2+-permeable, nonselective cation channel in smooth muscle cells.
J. Gen. Physiol.
104
:
375
–394.
Guerrero, A., J.J. Singer, and F.S. Fay.
1994
b. Simultaneous measurement of Ca2+ release and influx into smooth muscle cells in response to caffeine. A novel approach for calculating the fraction of current carried by calcium.
J. Gen. Physiol.
104
:
395
–422.
Harkins, A.B., N. Kurebayashi, and S.M. Baylor.
1993
. Resting myoplasmic free calcium in frog skeletal muscle fibers estimated with fluo-3.
Biophys. J.
65
:
865
–881.
Hollingworth, S., J. Peet, W.K. Chandler, and S.M. Baylor.
2001
. Calcium sparks in intact skeletal muscle fibers of the frog.
J. Gen. Physiol.
118
:
653
–678.
Kettlun, C., A. Gonzalez, E. Rios, and M. Fill.
2003
. Unitary Ca2+ current through mammalian cardiac and amphibian skeletal muscle ryanodine receptor channels under near-physiological ionic conditions.
J. Gen. Physiol.
122
:
407
–417.
Kirber, M.T., E.F. Etter, K.A. Bellve, L.M. Lifshitz, R.A. Tuft, F.S. Fay, J.V. Walsh, and K.E. Fogarty.
2001
. Relationship of Ca2+ sparks to STOCs studied with 2D and 3D imaging in feline oesophageal smooth muscle cells.
J. Physiol.
531
:
315
–327.
Klein, M.G., H. Cheng, L.F. Santana, Y.H. Jiang, W.J. Lederer, and M.F. Schneider.
1996
. Two mechanisms of quantized calcium release in skeletal muscle.
Nature.
379
:
455
–458.
Koizumi, S., M.D. Bootman, L.K. Bobanovic, M.J. Schell, M.J. Berridge, and P. Lipp.
1999
. Characterization of elementary Ca2+ release signals in NGF-differentiated PC12 cells and hippocampal neurons.
Neuron.
22
:
125
–137.
Lassignal, N.L., J.J. Singer, and J.V. Walsh Jr.
1986
. Multiple neuropeptides exert a direct effect on the same isolated single smooth muscle cell.
Am. J. Physiol.
250
:
C792
–C798.
Lopez-Lopez, J.R., P.S. Shacklock, C.W. Balke, and W.G. Wier.
1995
. Local calcium transients triggered by single L-type calcium channel currents in cardiac cells.
Science.
268
:
1042
–1045.
Neher, E.
1995
. The use of fura-2 for estimating Ca buffers and Ca fluxes.
Neuropharmacology.
34
:
1423
–1442.
Neher, E., and G.J. Augustine.
1992
. Calcium gradients and buffers in bovine chromaffin cells.
J. Physiol.
450
:
273
–301.
Nelson, M.T., H. Cheng, M. Rubart, L.F. Santana, A.D. Bonev, H.J. Knot, and W.J. Lederer.
1995
. Relaxation of arterial smooth muscle by calcium sparks.
Science.
270
:
633
–637.
Ohyama, T., D.H. Hackos, S. Frings, V. Hagen, U.B. Kaupp, and J.I. Korenbrot.
2000
. Fraction of the dark current carried by Ca2+ through cGMP-gated ion channels of intact rod and cone photoreceptors.
J. Gen. Physiol.
116
:
735
–754.
Parker, I., and Y. Yao.
1991
. Regenerative release of calcium from functionally discrete subcellular stores by inositol trisphosphate.
Proc. R. Soc. Lond. B. Biol. Sci.
246
:
269
–274.
Rios, E., and G. Brum.
2002
. Ca2+ release flux underlying Ca2+ transients and Ca2+ sparks in skeletal muscle.
Front. Biosci.
7
:
d1195
–d1211.
Rios, E., M.D. Stern, A. Gonzalez, G. Pizarro, and N. Shirokova.
1999
. Calcium release flux underlying Ca2+ sparks of frog skeletal muscle.
J. Gen. Physiol.
114
:
31
–48.
Schneider, M.F.
1999
. Ca2+ sparks in frog skeletal muscle: generation by one, some, or many SR Ca2+ release channels?
J. Gen. Physiol.
113
:
365
–372.
Shen, J.X., S. Wang, L.S. Song, T. Han, and H. Cheng.
2004
. Polymorphism of Ca2+ sparks evoked from in-focus Ca2+ release units in cardiac myocytes.
Biophys. J.
86
:
182
–190.
Shirokova, N., A. Gonzalez, W.G. Kirsch, E. Rios, G. Pizarro, M.D. Stern, and H. Cheng.
1999
. Calcium sparks: release packets of uncertain origin and fundamental role.
J. Gen. Physiol.
113
:
377
–384.
Smith, G.D., J.E. Keizer, M.D. Stern, W.J. Lederer, and H. Cheng.
1998
. A simple numerical model of calcium spark formation and detection in cardiac myocytes.
Biophys. J.
75
:
15
–32.
Sun, X.P., N. Callamaras, J.S. Marchant, and I. Parker.
1998
. A continuum of InsP3-mediated elementary Ca2+ signalling events in Xenopus oocytes.
J. Physiol.
509
:
67
–80.
Wang, S.Q., L.S. Song, E.G. Lakatta, and H. Cheng.
2001
. Ca2+ signalling between single L-type Ca2+ channels and ryanodine receptors in heart cells.
Nature.
410
:
592
–596.
Wang, S.Q., M.D. Stern, E. Rios, and H. Cheng.
2004
. The quantal nature of Ca2+ sparks and in situ operation of the ryanodine receptor array in cardiac cells.
Proc. Natl. Acad. Sci. USA.
101
:
3979
–3984.
Wellman, G.C., and M.T. Nelson.
2003
. Signaling between SR and plasmalemma in smooth muscle: sparks and the activation of Ca2+-sensitive ion channels.
Cell Calcium.
34
:
211
–229.
Zhou, J., G. Brum, A. Gonzalez, B.S. Launikonis, M.D. Stern, and E. Rios.
2003
. Ca2+ sparks and embers of mammalian muscle. Properties of the sources.
J. Gen. Physiol.
122
:
95
–114.
ZhuGe, R., K.E. Fogarty, R.A. Tuft, L.M. Lifshitz, K. Sayar, and J.V. Walsh Jr.
2000
. Dynamics of signaling between Ca2+ sparks and Ca2+- activated K+ channels studied with a novel image-based method for direct intracellular measurement of ryanodine receptor Ca2+ current.
J. Gen. Physiol.
116
:
845
–864.
ZhuGe, R., R.A. Tuft, K.E. Fogarty, K. Bellve, F.S. Fay, and J.V. Walsh Jr.
1999
. The influence of sarcoplasmic reticulum Ca2+ concentration on Ca2+ sparks and spontaneous transient outward currents in single smooth muscle cells.
J. Gen. Physiol.
113
:
215
–228.
Zou, H., L.M. Lifshitz, R.A. Tuft, K.E. Fogarty, and J.J. Singer.
1999
. Imaging Ca2+ entering the cytoplasm through a single opening of a plasma membrane cation channel.
J. Gen. Physiol.
114
:
575
–588. (published erratum appears in J. Gen. Physiol. 1999. 114:839)
Zou, H., L.M. Lifshitz, R.A. Tuft, K.E. Fogarty, and J.J. Singer.
2002
. Visualization of Ca2+ entry through single stretch-activated cation channels.
Proc. Natl. Acad. Sci. USA.
99
:
6404
–6409.
Zou, H., L.M. Lifshitz, R.A. Tuft, K.E. Fogarty, and J.J. Singer.
2004
. Imaging calcium entering the cytosol through a single opening of plasma membrane ion channels: SCCaFTs - fundamental calcium events.
Cell Calcium.
35
:
523
–533.