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Universität Ulm, Abteilung für Angewandte Physiologie Albert-Einstein-Allee 11, D-89069 Ulm, Germany

Address correspondence to Werner Melzer, Department of Applied Physiology, University of Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany. Fax: (49) 731-500-23260; email: werner.melzer{at}medizin.uni-ulm.de

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
The purpose of this study was to quantify the Ca²⁺ fluxes underlying Ca²⁺ transients and their voltage dependence in myotubes by using the "removal model fit" approach. Myotubes obtained from the mouse C2C12 muscle cell line were voltage-clamped and loaded with a solution containing the fluorescent indicator dye fura-2 (200 µM) and a high concentration of EGTA (15 mM). Ca²⁺ inward currents and intracellular ratiometric fluorescence transients were recorded in parallel. The decaying phases of Ca²⁺-dependent fluorescence signals after repolarization were fitted by theoretical curves obtained from a model that included the indicator dye, a slow Ca²⁺ buffer (to represent EGTA), and a sequestration mechanism as Ca²⁺ removal components. For each cell, the rate constants of slow buffer and transport and the off rate constant of fura-2 were determined in the fit. The resulting characterization of the removal properties was used to extract the Ca²⁺ input fluxes from the measured Ca²⁺ transients during depolarizing pulses. In most experiments, intracellular Ca²⁺ release dominated the Ca²⁺ input flux. In these experiments, the Ca²⁺ flux was characterized by an initial peak followed by a lower tonic phase. The voltage dependence of peak and tonic phase could be described by sigmoidal curves that reached half-maximal activation at -16 and -20 mV, respectively, compared with -2 mV for the activation of Ca²⁺ conductance. The ratio of the peak to tonic phase (flux ratio) showed a gradual increase with voltage as in rat muscle fibers indicating the similarity to EC coupling in mature mammalian muscle. In a subgroup of myotubes exhibiting small fluorescence signals and in cells treated with 30 µM of the SERCA pump inhibitor cyclopiazonic acid (CPA) and 10 mM caffeine, the calculated Ca²⁺ input flux closely resembled the L-type Ca²⁺ current, consistent with the absence of SR Ca²⁺ release under these conditions and in support of a valid determination of the time course of myoplasmic Ca²⁺ input flux based on the optical indicator measurements.

Key Words: Ca²⁺ release • myotube • mammalian muscle • excitation-contraction coupling

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Contractile activation in muscle is initiated by a massive efflux of Ca²⁺ ions from the SR. This Ca²⁺ flux is tightly controlled by the plasma membrane voltage (Melzer et al., 1995; Dirksen, 2002; see Fig. 2 A). In experiments on isolated muscle cells, SR Ca²⁺ release can be reproducibly triggered by plasma membrane depolarization. The precise synchronization with depolarization permits to study intracellular Ca²⁺ release in muscle cells in better kinetic detail than in any other cellular system. The release flux of Ca²⁺ from the SR can be derived from Ca²⁺ measurements with optical indicators. Its determination is equivalent to measuring the whole-cell currents of a plasmalemmal channel system and provides important information on the voltage-controlled gating of the Ca²⁺ release channels in the SR. The Ca²⁺ release is calculated as the time derivative of the total concentration change of Ca²⁺ in the myoplasmic water space during a depolarization, which is the sum of the changes in free, bound, and pumped Ca²⁺ (for a review see Ríos and Brum, 2002). Several methods to calculate the depolarization-controlled SR Ca²⁺ release flux have been reported. In one approach, estimates of the kinetic constants and intracellular concentrations of binding sites, necessary for the calculation, are obtained entirely from the biochemical literature (method 1). Baylor et al. (1983) used the myoplasmic Ca²⁺ transient measured with a metallochromic indicator and different sets of published values of the concentrations and rate constants. Melzer et al. (1984)(1987) used a reaction scheme to describe binding and transport and determined kinetic parameters of the scheme empirically by fitting calculated Ca²⁺ concentration changes to actually measured Ca²⁺ signals (Melzer et al., 1986a). In this "removal model fit" approach (method 2), the time course of the free Ca²⁺ concentration during the time interval after terminating a preceding depolarization is considered. It is assumed that release is turned off rapidly by repolarization and that removal can therefore be studied independently of release during this time. Once the model parameters are obtained by the fit, the release flux underlying the Ca²⁺ signal during the depolarization is calculated as in method 1. Combinations of method 1 and 2 using more complex schemes with a larger number of parameters (of which some were set to published values while others were determined by curve fitting) have subsequently been applied (González and Ríos, 1993; Shirokova et al., 1996). This general approach has also been extended to estimating flux rates of quantal Ca²⁺ release events (sparks) measured in microdomains of muscle cells using confocal laser scanning microscopy data (Ríos et al., 1999; Ríos and Brum, 2002). A different method (method 3) to estimate the time course of SR Ca²⁺ release rate based on the measurement of discrete Ca²⁺ release events has been reported by Klein et al. (1997) in a study on largely inactivated frog muscle fibers. The results were consistent with sparks being the quantal subunits of the global Ca²⁺ release (Schneider, 1999).

The Ca²⁺ release calculation can be facilitated by modifying intracellular conditions. González and Ríos (1993) introduced high concentrations of an external Ca²⁺ buffer, EGTA, into cut voltage-clamped muscle fibers to make the determination of Ca²⁺ release less dependent on intrinsic binding components. A similar approach was taken by Song et al. (1998) in isolated rat ventricular myocytes. Pape et al. (1995) likewise loaded muscle fibers with a high EGTA concentration (20 mM) and measured the protons released from EGTA in exchange for Ca²⁺ as an indirect way to track the largest fraction of Ca²⁺ release.

These methods were applied to mature amphibian and mammalian muscle cells. On the other hand, cultured myotubes which have been successfully used in many molecular physiology studies of EC coupling (for a review see Beam and Franzini-Armstrong, 1997) have not yet been characterized regarding their Ca²⁺ release properties in comparable detail. Method 1 was recently used by our laboratory on mouse and porcine myotubes (Dietze et al., 1998, 2000; Ursu et al., 2001) and a modified version of the method of Song et al. (1998) was applied to C2C12 myotubes (Schuhmeier et al., 2003). The results indicated that the Ca²⁺ signals originated mainly from intracellular release with characteristics similar to differentiated muscle fibers. In the present study we implemented the removal model fit method (method 2) to further investigate the dynamics of the voltage-controlled Ca²⁺ fluxes in voltage-clamped myotubes. The method allowed us to discriminate the different kinetic components of the Ca²⁺ flux underlying depolarization-induced Ca²⁺ transients and to study their voltage dependence. Comparison with the voltage-dependent Ca²⁺ inward current allowed us to estimate the fractional contribution of Ca²⁺ entry to the total Ca²⁺ flux and to test the fidelity of this approach to determine flux kinetics.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Cell Culture
C2C12 myoblasts purchased from the American Type Culture Collection (CRL-1772) were grown in Dulbecco's modified eagle medium (DMEM, high glucose) containing 10% FCS. Cells were detached by trypsin (0.25%) in Ca²⁺- and Mg²⁺-free PBS. Within a day after reseeding in DMEM, FCS was replaced by 2% horse serum (HS) which led to the formation of myotubes. After one to two weeks myotubes were detached and seeded onto carbon- and collagen-coated coverslips for measurements (Schuhmeier et al., 2003). DMEM and trypsin were purchased from GIBCO BRL; FCS, HS, and PBS were from PAA Laboratories; and rat tail collagen (Type 1, C 7661) was from Sigma-Aldrich.

Solutions
The experimental solutions had the following composition (in mM): external solution, 140 tetraethylammonium hydroxide (TEAOH), 137 HCl, 10 CaCl₂, 1 MgCl₂, 10 HEPES, 2.5 4-aminopyridine (4-AP), 0.00125 tetrodotoxin (TTX); pH adjusted to 7.4 with HCl. In some experiments the external solution contained 30 µM cyclopiazonic acid (CPA) and 10 mM caffeine. Internal (pipette) solution, 145 CsOH, 110 HCl, 1.5 CaCl₂ (free: 20 nM), 10 HEPES, 15 EGTA, 4 MgATP (5.5 total Mg), 5 Na creatine phosphate, 0.2 K₅-fura-2; pH adjusted to 7.2 with CsOH.

Electrophysiology
Experiments were performed at room temperature (20–23°C). The whole-cell patch clamp configuration was used to control the membrane potential of the myotubes (amplifier LMPC, List-Medical; with range of capacitance compensation extended to 1,000 pF). Pipettes were fabricated from borosilicate glass (GC150TF-10; Clark Electromedical Instruments). Data acquisition was performed using a Digidata 1200 digitizer and the pCLAMP 7.0 software package (Axon Instruments, Inc.).

For I-V relations, the measured data points within a specified time interval (see RESULTS) were averaged. The currents I(V) were normalized by the linear capacitance to obtain current densities i(V). Plots of i(V) versus voltage were least-squares fitted with Eq. 1 and 2, which describe the total current as the sum of a linear leak current and of the voltage-gated Ca²⁺ current:

(1)

and

(2)

Here, g_leak and V_leak are normalized conductance and reversal potential of the leak component and g_Ca,max and V_Ca are maximal normalized conductance and reversal potential of the L-type Ca²⁺ current. f (V) indicates voltage dependence of activation according to a standard Boltzmann-distribution and V_0.5 and k indicate voltage of half-maximal activation and voltage sensitivity, respectively.

Leak-corrected current densities i_Ca were converted to Ca²⁺ entry flux (expressed as total concentration change in the myoplasmic volume per time) using Eq. 3:

(3)

Here, z is the valence of the Ca²⁺ ion, F the Faraday constant, V_C the total intracellular volume per membrane capacitance and f_V the fraction of the total volume that is immediately accessible to Ca²⁺. For traces shown in the figures and for the calculation of A_{i(0 mV)} in Table III (see legend for definition) f_V was arbitrarily set to its upper limit of 1. For V_C we used the value of 0.23 liter F^-1 determined by Schuhmeier et al. (2003).

Fluorimetry
We used a microfluorimeter based on an inverted microscope (Axiovert 100 and Objective "Fluar" 40x 1.30 oil; ZEISS) with a photomultiplier tube (R268, Hamamatsu) attached to its trinocular head. Myotubes were loaded with fura-2 by diffusion from the patch-pipette. Ca²⁺-dependent fluorescence changes were recorded at 515 nm while exciting at 380 nm. A measurement at 360 nm excitation (isosbestic wavelength) performed in an 800-ms interval before the 380-nm recording served to normalize for changes in the indicator concentration. Free Ca²⁺ concentration was determined using background- and bleaching-corrected fluorescence ratio signals (R = F₃₈₀/F₃₆₀) according to Eq. 4 (Klein et al., 1988):

(4)

The following values were used for R_min (fluorescence ratio at zero dye saturation), R_max (ratio at full dye saturation) and K_D,Fura (dissociation constant of the dye): 2.84, 0.68, and 276 nM, respectively (see Schuhmeier et al., 2003). The fura-2 dissociation rate constant k_off,Fura was determined in the removal model fit as described in RESULTS.

Analysis
General analysis and nonlinear curve fitting were performed using Excel (Microsoft) and Origin (OriginLab Corporation). The program CalcV22 (Föhr et al., 1993) was used to calculate the free ion concentrations in the internal solution.

The numerical calculations to solve nonlinear differential equations and the removal fit described in RESULTS were performed using a program written in Delphi (Borland). Differential equations were solved using Euler's method. Part of the numerical calculations (simulations of the fluorescence signals) were stiff in the free Ca²⁺ component; therefore, to avoid numerical oscillations, a semi-implicit version of the Euler algorithm was implemented (see Appendix). The measured data were smoothed by using a digital filtering algorithm with variable bandwidth that depends on local signal-noise ratios (Schuhmeier et al., 2003).

The steps of the removal fit analysis were as follows:

1. The digitally filtered fluorescence ratio traces were converted to free Ca²⁺ concentration (Eq.4) which in turn was used to calculate the occupancies of the model compartments (Dye, F, S and Uptake) shown in Fig. 2 C. Unless otherwise stated, the following set of starting parameter values were used for the calculation: k_on,Dye = 164 µM^-1 s^-1_, k_off,Dye = 45.2 s^-1, [Dye]_total = 200 nM, k_on,S = 55.8 µM^-1 s^-1, k_off,S = 2.12 s^-1, [S]_total = 15 mM, k_Uptake = 1,000 s^-1. The rate constants of Dye and S are the values estimated for fura-2 and EGTA in Schuhmeier et al. (2003). [Dye]_total and [S]_total are the pipette concentrations of fura-2 and EGTA used in the experiments. Underlined parameters were further optimized by iterative least squares fitting (see Results). Note that k_on,Dye and k_off,Dye are linked by the assumed value of K_D,Fura.

2. The removal model simulations of the fluorescence ratio decay started 10 ms after the end of each depolarization to account for the time required to turn off Ca²⁺ input flux. To reduce the effect of noise on the start values we averaged the data points (occupancy of each compartment) in the interval from 5 to 15 ms after the end of the depolarization.

3. The simulated traces were fitted to the measured fluorescence ratio decays using an enhanced version of a generalized reduced gradient method (GRG2; Lasdon et al., 1978). We made use of the Small-Scale Solver Dynamic Link Library (Frontline Systems) to minimize ² (Lasdon et al., 1974), defined as the summed squares of the point-by-point differences divided by the standard deviation of the data points in a baseline immediately before the first depolarization. Iteration was stopped when ² changed less than a set convergence criterion (10^-5%) within at least 5 iterations in a row. We set all model parameters constant, for which values were available from calibration experiments. For the remaining parameters, a robust determination by least squares fitting could be obtained using the kinetic information in the measurements under the given assumptions. The usefulness of this procedure and of the choice of free parameters was confirmed by using simulated input fluxes with a large range of amplitudes to calculate artificial fluorescence ratio signals as described in Schuhmeier et al. (2003) and analyzing these signals with the present fitting algorithm.

The voltage dependence of Ca²⁺ flux was described by Eq. 5:

(5)

Here, f_R(V) and f_C(V) are Boltzmann terms (Eq. 2) for the activation of internal Ca²⁺ release and plasma membrane L-type Ca²⁺ conductance, respectively, A_R is the maximal value of the release flux term (left term in the sum of Eq. 5) and a_C a normalization factor. The term f_c(V) · g_Ca,max · (V - V_Ca) was taken from the fit of the current-voltage data (Eq. 1). Eq. 5 assumes that any deviation from a sigmoidal voltage dependence of flux activation results from a contribution of the L-type Ca²⁺ inward current. The (maximal) fractional contribution fr of the Ca²⁺ entry flux (carried by the L-type current) to the total flux was described by Eq. 6:

(6)

where A_C is the maximal value of the right term in the sum of Eq. 5.

Statistics
Data are presented and plotted as means ± SEM (n = number of experiments) for averaged values and as parameter ± SE for best fit parameters. Individual errors (SE) for fit parameters were calculated by evaluating the covariance matrix obtained at the optimum (as described in Press et al., 1992, chapter 15.6).

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Ca²⁺ Inward Current and Ca²⁺ Transient
Fig. 1 A shows leak-corrected L-type Ca²⁺ inward currents at four different test voltages in a C2C12 myotube and Fig. 1 B shows the simultaneously measured fura-2 fluorescence ratio signals R. A comparison indicates obvious differences in the voltage dependence of the two signals: At -30 mV, a clear Ca²⁺ signal can be seen while there is no current activation, and at potentials more positive than 0 mV the current declines in amplitude (Fig. 1 C) due to the decreased driving force for Ca²⁺ to enter the cell whereas Ca²⁺ signals show relatively little change. Fig. 1 D compares the voltage-dependent activation characteristics of Ca²⁺ signal (open squares) and L-type conductance (filled squares), derived from the best fit of Eqs. 1 and 2 to the data. The result shows that the Ca²⁺ transients are activated at some 15 mV more negative potentials than the L-type Ca²⁺ channels (V_0.5: -27.3 mV vs. -12.5 mV).

View larger version (24K): [in this window] [in a new window]   FIGURE 1. Ca2+ current and Ca2+ transients in a C2C12 myotube at different voltages. (A) Ca2+ inward currents for 100-ms depolarizations to different membrane potentials. (B) Calcium-dependent fluorescence ratio signals measured in parallel to the recordings of A. Note that a decrease of the ratio indicates an increase in Ca2+ concentration. (C) I-V relation showing leak-corrected inward current density versus pulse voltage (same cell as A and B). (D) Fractional activation of Ca2+ transients (open symbols) and Ca2+ conductance (filled symbols). For the plots the data points within the last 10 ms of the pulse were averaged. Continuous lines in C and D are best fit traces obtained with Eqs. 1 and 2. The fit parameters obtained for the L-type current were gCa,max = 306 ± 12 pS pF-1, VCa = 70.7 ± 4.1 mV, V0.5 = -12.5 ± 0.3 mV, k = 3.7 ± 0.3 mV. The activation parameters of the Ca2+ signals were V0.5 = -27.2 ± 1.2 mV and k = 4.2 ± 1.0 mV.

Removal Model Analysis
The Ca²⁺ input to the myoplasm during a depolarization (Fig. 2 A) is distributed to different binding and sequestration sites including troponin C, parvalbumin, the SERCA Ca²⁺ pump of the SR and ATP (Fig. 2 B; Baylor and Hollingworth, 1998). In the present experiments we used the extrinsic Ca²⁺ buffer EGTA in the intracellular solution at a concentration of 15 mM, which strongly exceeds that of any intrinsic Ca²⁺ buffer. The use of a single dominating Ca²⁺ buffer makes it possible to greatly simplify the reaction scheme for the removal of Ca²⁺ from the myoplasmic space (Pape et al., 1995; Song et al., 1998). The scheme in Fig. 2 C was used originally on mature skeletal muscle fibers of the frog (Melzer et al., 1986a, 1987; Timmer et al., 1998). It includes a saturable buffer S, in our case to represent EGTA, a simple transport mechanism (Uptake) with a rate proportional to free Ca²⁺ to account for Ca²⁺ sequestration, and an instantaneously equilibrating compartment far from saturation (i.e., binding proportional to free Ca²⁺) to account for intrinsic fast Ca²⁺ binding (F). In addition, the Ca²⁺ indicator fura-2 (Dye) is included and represents an intermediate speed saturable buffer.

View larger version (26K): [in this window] [in a new window]   FIGURE 2. Ca2+ input and removal in skeletal muscle. (A) Schematic diagram of the control of ryanodine receptor (RyR)-mediated Ca2+ release from the SR by the transverse tubular dihydropyridine receptor (DHPR). (B) Main compartments to which released Ca2+ is distributed (Baylor and Hollingworth, 1998; Jiang et al., 1999): fast binding sites on troponin C (T-sites), slow binding sites on troponin C and parvalbumin (P-sites), fast calcium binding by ATP, and binding and transport by the SR Ca2+-ATPase. (C) Simplified reaction scheme to account for binding and transport of released Ca2+ (see Eqs. 7–12): (1) Fast binding assumed to be instantaneous and linear (scaling factor F). (2) Slow binding (S, rate constants kon,S and koff,S and total concentration [S]total) dominated by EGTA in the experimental conditions. (3) Uptake assumed to be proportional to free calcium (rate constant kUptake). (4) Binding by the indicator dye (rate constants kon,Dye and koff,Dye and total concentration [Dye]total).

(7)

(8)

(9)

(10)

with the additional conditions:

(11)

and

(12)

Mass conservation is described by the following equation:

(13)

Here k_on,Dye, k_off,Dye and [Dye]_total are on- and off-rate constant and total intracellular concentration of the indicator, respectively. [S]_total, k_on,S and k_off,S are total concentration of the slow buffer S and its on- and off-rate constant, respectively. k_Uptake is the rate constant of the nonsaturating transport. F is a scaling factor to describe the component of rapidly equilibrating Ca²⁺ ([Ca²⁺]_F) as a multiple of the free Ca²⁺ concentration. A flux d[Ca²⁺]_Leak/dt was included to compensate the uptake rate at the given resting free Ca²⁺ concentration.

Fluorescence ratio signals were calculated in simulations using Eq.14:

(14)

Here, R_min and R_max are the fluorescence ratio values for Ca²⁺-free and fully Ca²⁺-saturated indicator dye. To simulate fluorescence ratio signals with this model requires to assign values to a total number of 10 parameters. Approximate values for R_max, R_min, and the dissociation constant K_D,Dye = k_off,Dye/k_on,Dye for fura-2 were obtained from previous calibration experiments (see Schuhmeier et al., 2003). [Dye]_total and [S]_total were set to the respective pipette concentrations of fura-2 and EGTA. F was found to be of negligible influence on the results (see Fig. 5) at the present high [S]_total and was arbitrarily set to 0. This leaves four free parameters (k_off,Dye, k_on,S, k_off,S, and k_Uptake) that were determined from the measured Ca²⁺ signals by using a least squares optimization procedure ("removal fit", see also MATERIALS AND METHODS).

With a first set of values for the four free model parameters (starting values), the measured fluorescence ratio signal was used to calculate free Ca²⁺ and the occupancies of the different compartments. The Ca²⁺ levels reached in each compartment at 10 ms after repolarization were then used as initial values for a theoretical prediction of the continued time course of the fluorescence ratio relaxation using Eq. 14. The predicted time course (Fig. 3 , dashed lines) was compared with the actually measured time course and the parameter values were improved by iteration until a minimum of the squared deviations between measured and calculated trace was obtained (Fig. 3 B).

View larger version (11K): [in this window] [in a new window]   FIGURE 3. Removal model fit. Depolarization scheme (top traces) to obtain different degrees of activation of SR Ca2+ release and fluorescence ratio signals of fura-2 (bottom traces) in a voltage-clamped myotube. Note that a Ca2+ concentration increase results in a downward deflection. The pulse series produced four different Ca2+ removal phases within a single experimental sweep. (A, Start) Calculation of theoretical relaxation with the following set of start values of the free parameters: koff,Dye = 30 s-1, kon,S = 1.5 µM-1 s-1, koff,S = 0.3 s-1, and kUptake = 1,000 s-1 (Dye and S parameters from Ursu et al., 2001). (B, Fit) Result of least squares deviation minimization leading to a best simultaneous fit of the four relaxation phases with the following set of parameter values: koff,Dye = 43.2 ± 0.6 s-1, kon,S = 20.1 ± 1.3 µM-1 s-1, koff,S = 2.32 ± 0.07 s-1, and kUptake = 11,100 ± 500 s-1.

The removal analysis was successfully performed in 18 cells. The individual values obtained for the four free fit parameters (k_off,Dye, k_on,S, k_off,S, and k_Uptake) are listed in Table I . The mean values were k_off,Dye = 46.4 s^-1, k_on,S = 20.0 µM^-1 s^-1, k_off,S = 2.71 s^-1 and k_Uptake = 10,300 s^-1, respectively.

View larger version (11K): [in this window] [in a new window]   FIGURE 4. Calculation of Ca2+ input flux. (Top traces) Pulse protocol. (Middle traces) Total Ca2+ calculated as the sum of the voltage-induced changes in the different compartment occupancies (Fig. 2 C). (Bottom traces) Time derivative of total Ca2+ (Eq. 13), i.e., the total flux of Ca2+ into the myoplasm that is controlled by the depolarization. (A) Before convergence of the removal model fit (Start). (B) After convergence (Fit). Same experiment and parameter settings as in Fig. 3.

Measurements in muscle fibers indicated a significant amount of rapidly equilibrating Ca²⁺ binding sites (Melzer et al., 1984, 1986a, 1987) that likely originate predominantly from troponin C, ATP, and the Ca²⁺ pump proteins (Baylor and Hollingworth, 1998). In the model the rapidly equilibrating component of bound Ca²⁺ was represented by a multiple of free Ca²⁺ described by the parameter F (scaling factor). In previous experiments with low (submillimolar) concentrations of intracellularly applied EGTA (Melzer et al., 1984, 1987), the amplitude of the estimated release rate was critically dependent on the extent of fast Ca²⁺ binding. However, at the high (millimolar) concentrations of EGTA used in our experiments, even a rapidly equilibrating Ca²⁺ binding component many times greater than free Ca²⁺ hardly influenced the calculation result. When in Fig. 5 D the parameter F was arbitrarily set to 0 and 250, the removal model fit parameters and the release flux calculation results were almost identical (see Fig. 5 legend). Therefore, we omitted F from the present calculations (F = 0). On the other hand, the value of [S]_total (Eq. 12) had a large influence on the scale of the calculated input flux. In the model, [S]_total represents the effective concentration of EGTA in the cell. We assumed that the concentrations of both fura-2 and EGTA reached values equal to the concentrations inside the pipette (0.2 and 15 mM, respectively) at the time when the depolarizing pulses were started. In previous measurements, the intensity increase of the fura-2 fluorescence at the isosbestic excitation wavelength of 360 nm indicated that the cytoplasm was essentially in equilibrium with the pipette solution within 15 min after establishing the whole cell configuration (Schuhmeier et al., 2003). Deviations from the assumed concentration values would cause a change in scale for the flux amplitude. The effect is shown in Fig. 5 E. Here, the calculated peak flux amplitudes derived from the removal fit analysis are plotted versus the fraction of the pipette concentrations assumed to be present in the cell. The filled circles show the mean values of the peak amplitudes derived from the analysis of the 18 cells shown in Table I. In each case, the removal fit had identical quality (same ²/N values). The flux amplitudes changed in proportion to the fractional pipette concentrations. Fig. 5 F shows the superimposed time course for each of the estimates of Fig. 5 E normalized to the peak. The scaled records were identical. Thus, the total effective concentrations of fura-2 and S in the cell are required for quantifying the amplitude but not for a valid estimate of the time course of the Ca²⁺ input flux.

View larger version (17K): [in this window] [in a new window]   FIGURE 5. Ca2+ input flux calculation for different assumptions of intracellular binding. (A) Voltage pulse, (B) fluorescence ratio of fura-2, (C) calculated free Ca2+ after removal model fit, and (D) calculated Ca2+ input flux. The removal model fit was performed with two different assumptions for intrinsic fast buffering (F = 0, i.e., no intrinsic fast binding: lower trace, and F = 250: upper trace). The results are very similar. For F = 0 the best fit parameter values (koff,D, kon,S, koff,S an kUptake) were as follows: 43.2 s-1, 20.1 µM-1 s-1, 2.32 s-1, 11,100 s-1. For F = 250 the values were 44.2 s-1, 18.7 µM-1 s-1, 2.39 s-1, 10,800 s-1 (cell no. 1412). (E) Calculated Ca2+ input flux as a function of the assumption made for [Dye]total and [S]total (corresponding to intracellular concentrations of fura-2 and EGTA). The abscissa shows assumed percentage of pipette concentration present in the cell. Data points are the means of the calculated peak input fluxes of the cells in Table I. Fit quality (2/N) and estimated mean values of the parameters koff,Dye, kon,S, and koff,S, were identical. Only the mean kUptake value showed a similar proportionality to the assumed percentage of pipette concentrations. (F) Time course of Ca2+ input flux. The mean Ca2+ input fluxes obtained of each data point in E were scaled to the peak and superimposed showing that the time course is independent of the assumption made for [Dye]total and [S]total.

Table II A summarizes the result. It shows that the best fit parameter values and the quality of the fit (²/N) depend on the values chosen for the two equilibrium constants. For each K_D,Dye a different K_D,S led to the lowest least square deviation. Even better fits (lower ²/N values) were obtained when both k_on,S and k_off,S were free parameters (data listed in Table II B).

View larger version (14K): [in this window] [in a new window]   FIGURE 6. Estimated removal parameters and Ca2+ input flux for different assumptions of intracellular fura-2 Ca2+ affinity. (A–D) Mean values of the free parameters kon,S, koff,S, kUptake, and koff,Dye, respectively, obtained in removal model fits of 18 experiments for different assumptions of intracellular KD,Dye. (E) KD,S as a function of assumed KD,Dye values calculated from data of A and B. (F) Estimated peak values of Ca2+ input flux for the same set of experiments (third voltage pulse of the pulse paradigm shown in Figs. 3 and 4. (G and H) Superimposed and normalized average traces of the calculated Ca2+ input flux corresponding to the results of Table II, B and A, respectively.

View larger version (18K): [in this window] [in a new window]   FIGURE 7. Calculated Ca2+ input flux and measured Ca2+ inward current. (A) Calculated Ca2+ input flux at different amplitudes of depolarization (100-ms pulses). (B) L-type Ca2+ inward current measured simultaneously with the signals in A. (C) Current-voltage relation derived from the data shown in B. (Continuous line) Best fit using Eq.1. The leak component is subtracted. (D) Activation curves of Ca2+ input flux (peak, circles; plateau, open squares; both measured from the baseline) and Ca2+ conductance (filled squares). Here and in Figs. 8 and 11 the means of the data values between 25 and 75 ms during the 100 ms depolarization were evaluated for the plateau and current amplitudes. The continuous lines are best fit traces using the sum of a Boltzmann-equation (Eq. 2) and a scaled and inverted version of the fit trace shown in C (see Eq. 5). For Boltzmann-parameters k and V0.5 for peak, plateau, and conductance see Table III (cell no. 1414). Same experiment as in Fig. 1.

Fig. 7 D shows the voltage dependence of peak and plateau of Ca²⁺ input flux (open circles and squares, respectively) in comparison to the voltage dependence of Ca²⁺ conductance. Both peak and plateau are measured from the baseline level. The plateau value of the flux was determined by taking the average of values between 25 and 75 ms during the 100-ms depolarization. For better comparison the same time range was used for evaluating the voltage dependence of Ca²⁺ current and conductance. The Boltzmann-fits (lines) show that conductance activation has its half-maximal value at 15 mV more positive potentials (for best fit parameter values see Table III , cell no. 1414).

View larger version (18K): [in this window] [in a new window]   FIGURE 8. Voltage dependence of input flux and inward current. Averaged data of 10 experiments as the one shown in Fig. 7 (see Table III A). (A) Current-voltage relation of the leak-corrected inward current. (B) Fractional activation of Ca2+ conductance. (C) Peak (circles) and plateau (squares) of Ca2+ input flux. (D) Flux ratio (peak/plateau) for the range from -30 to +60 mV.

Evidence for SR Depletion
The plateau component of the input flux often showed a slow decline distinct from the fast decay immediately after the peak (e.g., Fig. 5). According to the interpretation of a similar time course in adult muscle fibers (Schneider et al., 1987b), the fast decay results from inactivation whereas the slow decline results from the depletion of the SR caused by a noninactivating component of Ca²⁺ release. Following this interpretation, one can calculate a depletion-corrected rate of Ca²⁺ release that is proportional to SR-permeability (González and Ríos, 1993; Shirokova et al., 1995). This is demonstrated in Fig. 9 .

View larger version (19K): [in this window] [in a new window]   FIGURE 9. Decline in Ca2+ input flux caused by depletion of internal stores. Comparison of voltage-activated Ca2+ signals and Ca2+ entry flux through the L-type Ca2+ channels. The two columns show results obtained in the same cell with the same depolarization separated by a time interval of 8 min. (A) Scheme of the depolarizing voltage pulse. (B) Fluorescence ratio signals. (C) Calculated Ca2+ input flux. (D) SR Ca2+ content. (E) Permeability changes calculated by correction for store depletion. (Thin line) Time course before correction. (F) Ca2+ entry flux derived from the measured L-type Ca2+ current using Eq. 3. Assuming proportionality between SR content and Ca2+ release flux in the interval 30–90 ms after pulse-on, we used linear regression (sloping dashed lines) to determine amplitude A1 and slope m1 of the release flux (C) and the slope m2 of [Ca2+]SR (D). The amplitude A2 (= A1 x m2/ m1) was then used to calculate the initial SR content by adding the corresponding [Ca2+]SR value.

The initial SR content was determined as 7.2 mM in the left column of Fig. 9. It decreased by 33% during the course of the 100-ms depolarizing pulse (see Fig. 9 legend for more detail).

During our experiments, we observed a variable "run-down" of the Ca²⁺ input flux that was not accompanied by a corresponding change of the L-type inward current. It was therefore likely caused by alterations in intracellular Ca²⁺ release, possibly resulting from a decline in the responsiveness of the release channels to depolarization or from a reduced driving force for Ca²⁺ release during SR depletion. The example of Fig. 9 indicates Ca²⁺ depletion of the SR as a main cause for the "run-down". The depolarizing voltage step (Fig. 9 A, left column) was repeated after a time interval of 8 min (right column) in which different depolarizing pulses, as shown in Fig. 7 A, were applied. The amplitudes of the fluorescence ratio signal Fig. 9 B and of the calculated Ca²⁺ input flux (Fig. 9 C) were considerably smaller than during the first depolarization. In the second pulse the initial SR Ca²⁺ was estimated as 3.6 mM, indicating a reduction in SR Ca²⁺ load by 50%. During the course of this pulse SR content decreased by 40% of the initial value. Correcting the Ca²⁺ input flux traces for depletion, i.e., converting Ca²⁺ release rates to permeability changes (in the units % ms^-1) led to very similar amplitudes and time courses for both pulses (compare left and right record in panel E). It has been suggested that the loading state of the SR also affects permeability (e.g., Pape and Carrier, 1998). We cannot rule out this possibility, but the result of Fig. 9 is not in conflict with a change in driving force alone causing the observed decrease in flux amplitude.

Estimation of Ca²⁺ Entry Flux
The total myoplasmic Ca²⁺ input flux is a compound signal consisting of internal Ca²⁺ release and Ca²⁺ entry from the extracellular space. Ca²⁺ entry flux in isolation can be determined from the Ca²⁺ inward current using Eq. 3 (see MATERIALS AND METHODS). This allows us to estimate the relative contribution of entry and release. Fig. 9 F shows the Ca²⁺ entry flux calculated from the current recordings and expressed in the same dimensions (concentration per time) as the input flux in Fig. 9 C. We compared the size of the optically determined flux signal with the Ca²⁺ entry flux carried by the Ca²⁺ current. Considering the different scaling in Fig. 9, C and F, the calculated total Ca²⁺ input flux is much larger than the entry flux of Ca²⁺. Also its time course is utterly different. The absence of a component resembling the Ca²⁺ entry flux in this and the previous examples suggests little contribution of the Ca²⁺ current to the fluorescence signal.

In the set of experiments illustrated in Fig. 10 we applied two depolarizing pulses separated by a 10-ms time interval. The optically determined Ca²⁺ input flux is shown on the left, the electrically determined Ca²⁺ entry flux on the right, calculated with Eq. 3 as described above. Fig. 10 B shows the result from a cell comparable to the one in Fig. 9, i.e., with an estimated input flux much larger than the entry flux (note the difference in scale between the left and right panel). In the input flux (left), the peak seen in the first pulse is missing in the second one, whereas in the entry flux (right) both responses are almost identical. Fig. 10 C shows a measurement from a cell that exhibited very small fluorescence transients. The calculated Ca²⁺ input flux (left) is considerably smaller than in Fig. 10 B, whereas Ca²⁺ entry flux (right) has similar size. In this cell, the input flux shows amplitude and kinetic characteristics similar to the entry flux and practically no change in kinetics induced by the prepulse. The observations indicate that a large part, if not all, of the optical signals in Fig. 10 C results from Ca²⁺ entry (see also DISCUSSION).

View larger version (14K): [in this window] [in a new window]   FIGURE 10. Comparison of calculated Ca2+ input flux and transmembrane Ca2+ entry flux. (A) Scheme of double pulse paradigm to activate Ca2+ inward current and intracellular Ca2+ release. (B, left) calculated Ca2+ input flux. (Right) Ca2+ entry flux derived from the electrically recorded leak corrected inward current using Eq. 3. Note the differences in scale. Cell no. 1426. (C) Same as in B but recorded from a cell (no. 1444) that showed very small fluorescence transients. Ca2+ input flux was calculated using the mean parameter values of Table I. Vertical scales of left and right panel are similar and time course and double pulse response are comparable, indicating that the input flux results mainly from Ca2+ entry from the extracellular space.

View larger version (18K): [in this window] [in a new window]   FIGURE 11. Voltage dependence of Ca2+ input flux and Ca2+ inward current in a cell with low fluorescence response. (A) Calculated Ca2+ input flux for 100-ms pulses of variable amplitude. (B) Simultaneously measured Ca2+ inward currents. (C) I-V relation obtained from the data shown in B. (D) Voltage dependence of Ca2+ input flux (open squares) and Ca2+ entry flux (closed squares) derived from B displayed as fraction of the maximal data values. For Boltzmann-parameters k and V0.5 for peak, plateau, and conductance see Table III (cell no. 1415).

Evaluating the voltage dependence of Ca²⁺ input flux for all our measurements, we also found cells with responses intermediate between the examples of Figs. 7 and 11. Their peak and plateau values showed various degrees of reduction at large depolarization. To account for the decrease of flux amplitude at large depolarizations we fitted the Ca²⁺ input flux-voltage relations with the sum of a Boltzmann relation and a scaled version of the best fit curve describing the current-voltage relation of the leak-corrected Ca²⁺ inward current (see Eq. 5, MATERIALS AND METHODS). This description would be physically adequate if the deviations from a sigmoidal voltage activation curve resulted exclusively from Ca²⁺ inward current. Because of the additional contribution of run down, the fit serves to estimate the maximal contribution of Ca²⁺ entry to the total flux.

The cells whose complete voltage dependence of optical and electrical signals could be determined were divided into three groups depending on the relative contribution of the nonsigmoidal component (Table III). Group A (10 cells) represents the experiments in which the maximum contribution of inward current was <30% during the plateau phase (factor fr_plateau <0.3, see Eq.6). Group B (5 cells) contains experiments in which the contribution was between 30 and 60%, in group C (2 cells) it was >90%. The calculated time course of the input flux in these two cells showed no initial peak, a slow rise, and a rapid drop, sometimes accompanied by a peak at the end of the pulse, i.e., characteristics of the Ca²⁺ entry flux mediated by the L-type Ca²⁺ channels. The experiment shown in Fig. 7 is a representative of group A, the one in Fig. 11 belongs to group C. Considering their input flux properties, it seems likely that the cells of group C were deficient in SR Ca²⁺ release.

Time Course of Ca²⁺ Entry Flux Measured Optically and Electrically
In myotubes that show no SR release, Ca²⁺ input flux equals Ca²⁺ entry flux. This condition provides the interesting possibility to test the fidelity of the optical approach to reconstruct the time course of Ca²⁺ input flux because the flux derived from the electrically measured Ca²⁺ inward current (Eq. 3) should show the temporally undistorted entry flux. Because it is possible that even the cells of group C had a residual component of SR Ca²⁺ release, we applied a protocol designed to completely deplete the SR of releasable Ca²⁺. 30 µM of the SR Ca²⁺ pump blocker cyclopiazonic acid (CPA) and 10 mM caffeine were applied to myotubes with initially normal SR release as shown in Fig. 12 A. CPA caused a strong rapid decline in the calculated flux amplitude. Caffeine led to a further small and slow progressive decrease.

View larger version (16K): [in this window] [in a new window]   FIGURE 12. Alteration of calculated Ca2+ input flux on SR store depletion. A 100-ms pulse to +20 mV was repeated every 30 s and Ca2+ input and entry flux were estimated. Parameter values determined in the removal model fit analysis: koff,D = 43.4 ± 0.9 s-1, kon,S = 19.0 ± 1.2 µM-1 ms-1, koff,S = 2.92 ± 0.14 s-1, kUptake = 3,910 ± 264 s-1. (A) Ca2+ input flux amplitude, averaged over the interval 25–75 ms after pulse on. 30 µM CPA was applied to bath solution after the fifth voltage pulse leading to a strong decrease in flux amplitude and a rise in the resting free Ca2+ concentration (not depicted). The application of 10 mM caffeine five minutes later led only to a small further amplitude decrease. (B) Ca2+ input flux plotted against entry flux during the experiment. After drug application both signals showed a linear dependence; the mean ratio of input to entry flux after adding caffeine was 5.4 ± 2.2 (n = 3). (C) Ca2+ input flux before application of CPA and caffeine (mean of the first five recordings). (D) Ca2+ input flux after drug application (mean recordings within the time interval 10–20 min; note the 10-fold smaller scale). (E) Ca2+-entry flux derived from the inward current corrected for leak and capacitive components and scaled to the same amplitude as D.

Fig. 12, C and D, show the time course of the calculated Ca²⁺ input flux before and after application of CPA and caffeine, respectively. Note that the vertical scale is 10-fold smaller in D compared with C. The time course was markedly changed after the drug application and closely resembled the time course of the flux derived from the Ca²⁺ inward current using Eq. 3, which is shown in Fig. 12 E. This is consistent with the suggestion that Ca²⁺ entry is the only source of Ca²⁺ under these conditions. In addition it is a very reassuring result regarding the quality of determining the time course of Ca²⁺ input flux with this method.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Removal Model Fit for Myotubes
In muscle cells, plasma membrane depolarization causes the activation of Ca²⁺ channels in both the plasma membrane and in the SR, leading to rapidly rising intracellular Ca²⁺ transients. In this study, we investigated depolarization-controlled Ca²⁺ transients in cultured myotubes, which are a preferred preparation for structure-function analyses in EC coupling. For the first time we applied the "removal model fit" approach to this preparation. This allowed us to extract, using fluorimetric Ca²⁺ signals, the flow of Ca²⁺ to the cytoplasm, termed "Ca²⁺ input flux", which consists of Ca²⁺ release from the SR and Ca²⁺ entry from the extracellular space. We determined the voltage dependence of the Ca²⁺ input flux and the relative contribution of the two different flux components.

The decay of the voltage-activated Ca²⁺ transient after turning off input flux by repolarization provides information on the voltage-independent Ca²⁺ removal processes (binding and transport) that act in parallel to Ca²⁺ input during the depolarization. The "removal model fit" analysis makes use of fitting model-generated traces to measured Ca²⁺ transient decays (Melzer et al., 1986a; Timmer et al., 1998; Ríos and Brum, 2002). The result is a characterization of global removal properties that allows us to separate the unknown voltage-dependent flux from the removal activity during a period of depolarization.

The high intracellular concentration of the Ca²⁺ chelator EGTA in our experiments permitted us to choose a removal model with a simple structure and a small number of kinetic parameters. The reaction kinetics of any intrinsic Ca²⁺ binding site can be neglected for the removal calculation, because EGTA is in large excess of such sites. In particular, Fig. 5 shows that the influence of a fast binding component even 250 times greater than free Ca²⁺ will be negligible.

As in previous work on muscle f