INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

IN MOST STUDIES concerned with the effects of factors thought to affect the Ca²⁺ activation of contraction or ATPase activity in skinned (permeabilized) muscle fibers, the Ca²⁺ concentration has been computer estimated by solving the ionic equilibria equations and by using binding constants from the literature for the various ionic species of Ca²⁺ chelators such as EGTA and EDTA (5, 7, 18). Therefore, the effects of such factors could result from errors in calculations of the Ca²⁺ concentration caused by errors in the binding constants taken from the literature. To avoid such problems, this study directly measures the Ca²⁺ concentration in the test solutions used. Before this could be done it was necessary to develop a method, which is described in this study. The method used the fluorescent Ca²⁺ indicator calcium green-2, the fluorescence of which is shown to be activated over the range of Ca²⁺ concentration required for activation of force and actomyosin ATPase. Additionally, for this indicator to be useful, its dissociation constant (K_d) for Ca²⁺ has to be accurately determined in the test solutions used in the experiments.

Previous studies on skinned skeletal and cardiac muscle fibers have shown that Mg²⁺ shifts the relationship between Ca²⁺-activated force and Ca²⁺ to higher Ca²⁺ concentration (lower pCa) (2, 4, 5). Because the Ca²⁺ concentration used for analyzing the pCa-force relationship was computer generated on the basis of K_d values taken from the literature, this effect of Mg²⁺ shifting the pCa-force relationship to lower pCa may not have been due to Mg²⁺, but rather to inaccurate K_d values.

Because these previous data showed that Mg²⁺ shifts the pCa-force relationship, many investigators suggested that Mg²⁺ could alter the Ca²⁺ sensitivity of muscle by binding to the Ca²⁺-Mg²⁺ sites on troponin C, competing with the Ca²⁺-specific sites on troponin C (2, 5), or else binding to the Ca²⁺-Mg²⁺ sites on myosin light chains (3, 12, 14, 20). In vitro experiments using isolated contractile and regulator proteins and myofibrils showed that Ca²⁺-activated ATPase activity would not be affected by Mg²⁺. This finding was the basis for hypothesizing that only the Ca²⁺-specific sites on troponin were responsible for the activation of contraction (10, 15, 16, 17, 22). Therefore, it is important to repeat these studies under experimental conditions that accurately measure the Ca²⁺ concentration at different Mg²⁺ concentrations.

The standard biochemical measure of muscle contraction has traditionally been actomyosin ATPase activity (6), and it is generally accepted to be a measure of the rate of myosin cross-bridge cycling rate (1). In contrast, force is a measure of the average number of force-generating myosin cross bridges attached at any point in time (11). It has been assumed that Ca²⁺ activation of both actomyosin ATPase and force would occur over exactly the same concentration range of Ca²⁺. In skeletal muscle, measurements of Ca²⁺ activation of actomyosin ATPase activity and force have been shown not to coincide (13). One explanation for this dissociation of actomyosin ATPase and force is that the rate constant for the dissociation of force-generating myosin cross bridges (proportional to the ATPase-to-force ratio) is changing (decreasing) during Ca²⁺ activation. Because Mg²⁺ binds to myosin light chains in the millimolar range, it was decided that its effect on Ca²⁺ activation of actomyosin ATPase activity should be investigated. This study will show that, as in skeletal muscle, in cardiac muscle the relationship between Ca²⁺-activated actomyosin ATPase and force does not coincide and that this relationship is not altered by changes in Mg²⁺ concentration.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Removal of divalent cations from test solutions for fluorescent measurement. A Chelex 100 column was used to remove divalent cations from all test solutions used for determining the K_d of calcium green-2 for Ca²⁺. The column containing Chelex 100 was washed with ~10 volumes of H₂O, 4 volumes of 1 M HCl, 4 volumes of 1 mM EDTA, 2.5 volumes of both 1 M KOH with 10 mM EDTA, and another 10 volumes of H₂O. The column was equilibrated with the test solutions by passing 6 volumes of test solution. Three volumes of test solution were then passed through the column to remove contaminating divalent cations. The test solution that was passed through the column consisted of 140 mM potassium propionately adjusted to pH = 7.0. Once this solution had passed through the column, either 1, 4, or 8 mM Mg²⁺ was added to the solution. This solution was then used for measuring the K_d of calcium green-2 for Ca²⁺.

Determination of the Kd for calcium green-2. Calcium green-2 indicator (0.01 M) was added to 15 ml of the test solution in a separate tube. Then 1,980 µl of this binding solution and 20 µl of 1 M Ca²⁺ were added to a clean quartz cuvette, and the maximal fluorescence was measured. This same solution was diluted by one-half, and the fluorescence was remeasured. This diluting process was repeated until the concentration of the known amount of Ca²⁺ added became 1.56 µM. In addition, two more fluorescence measurements were taken to determine the fluorescence of the test solution without added Ca²⁺. Fluorescence was measured once with only 2 ml of the binding solution containing indicator (no added Ca²⁺) and again in the same solution with 6 µl of 7 mM EGTA to obtain a Ca²⁺-free fluorescence measurement of the indicator.

Determination of the Kd of calcium green-2 for Ca²⁺. The following method was used to determine the K_d values for calcium green-2. First, the fractional change in fluorescence (R) due to Ca²⁺ binding to the indicator was determined as defined in Eq. 1

(1)

where F is the fluorescence, F₀ is the fluorescence in the presence of EGTA and no added Ca²⁺, F_max is the fluorescence in maximal calcium, F₁ is the fluorescence measurement of the test sample, F is the submaximal change in fluorescence due to Ca²⁺ in the test solution, and F_max is the maximum change in fluorescence when the indicator is saturated with Ca²⁺

(2)

where [I_Ca] is concentration of the calcium indicator compound, [Ca²⁺] is the concentration of Ca²⁺, and [I] is the concentration of the Ca²⁺-free indicator (calcium green-2)

(3)

where [I]_tot is the total concentration of the indicator. Combining Eqs. 2 and 3 gives Eq. 4

(4)

(5)

Substituting Eq. 5 into Eq. 4 gives

(6)

(7)

where [Ca]_tot is the total concentration of calcium, [Ca]_unk is the unknown concentration of Ca²⁺ contamination, and [Ca]_add is the concentration of Ca²⁺ added to the solutions. Rearranging terms in Eq. 7, with Eq. 5 substituted for [I_Ca], gives Eq. 8

(8)

Substituting Eqs. 7 and 8 into Eq. 6 yields Eq. 9

(9)

The only unknown value in Eq. 9 is [Ca]_unk; this number was determined by a computer search for a value of [Ca]_unk that gave the best straight-line fit of Eq. 9 to the fractional change in fluorescence (R) measurements when the left-hand side of Eq. 9 was plotted against (1  R). An example of using Eq. 9 to plot the data is shown in Fig. 1. This procedure was repeated for three different Mg²⁺ concentrations (1.0, 4.0, and 8.0 mM), and the data were averaged, as shown in Table 1. This table shows that there were no significant differences among the K_d values for the three Mg²⁺ concentrations.

View larger version (12K): [in this window] [in a new window]   Fig. 1.   Determination of dissociation constant (Kd) for calcium green-2 in 8 mM Mg2+ solution, using equation described in MATERIALS AND METHODS. This figure shows relationship between two variables used to calculate Kd for Ca2+ binding to calcium green-2. Slope of line is equal to Kd. Resulting Kd values were used to find Ca2+ concentrations, expressed as pCa. R, fractional change in fluorescence; Caunk, unknown concentration of Ca2+ contamination; Caadd, concentration of Ca2+ added to solutions; IT, total concentration of indicator.

Determination of the effects of Mg²⁺ on ATPase and force. Skinned fiber strips (100 µm in diameter and 2-3 mm long) were dissected from small pieces of rat ventricular cardiac muscle in a relaxing solution containing 2 mM MgATP and 1 mM Mg²⁺. The strips of fibers were skinned (permeabilized) for 20 min, in a relaxing solution containing 1% Triton X-100. Single muscle fiber bundles were mounted in stainless steel tweezers and attached to a photo diode force transducer. The skinned cells and tweezers were inserted into a quartz capillary 1 cm long with a cross-sectional area of 1 mm² (9). The cuvette was illuminated by a mercury lamp, and a microscope photometer measured the fluorescence (NADH or calcium green-2) emitted from the incubation solution simultaneously with Ca²⁺-activated force measurements. The solution in the cuvette was changed every 20 s.

Solutions for skinned-fiber experiments. Only two solutions (relaxing and maximal contraction) for each Mg²⁺ concentration (1, 4, and 8 mM) were used in the skinned-fiber portion of the study. All solutions contained 85 mM K⁺, 2.0 mM MgATP², 1-8 mM Mg²⁺, 7 mM EGTA, 10⁹ or 10^3.4 M Ca²⁺, 5 mM phosphenol pyruvate (PEP), 100 U/ml pyruvate kinase (PK), and propionate as the major anion. Solutions for ATPase measurements also contained 0.4 mM NADH and 140 U/mL lactate dehydrogenase (LDH). Ionic strength was adjusted to 0.15 M, and the pH was maintained at 7.00 ± 0.02 with imidazole propionate. EGTA, imidazole (>99%), LDH, Na₂ATP, PEP, and PK were from Sigma Chemical, NADH was from Boehringer Mannheim, and proprionic acid was from Aldrich Chemical. Temperature was maintained at 21 ± 1°C. Maximal contraction solutions (~10^3.4 M Ca²⁺) gave a maximal Ca²⁺-activated tension, such that a further increase in Ca²⁺ would not increase tension further. Relaxing solutions contained no added Ca²⁺ (~10⁹ M Ca²⁺). The concentrations of the various ionic species for two gradient solutions were determined by solving ionic equilibrium equations using the binding constants established in earlier studies (2, 5, 7, 13). The sodium added as Na₂ATP was treated as K⁺ in the program.

ATP hydrolysis rate measurements. The hydrolysis of ATP was measured by the NADH fluorescence method, in which ATP is regenerated from ADP and PEP by PK (8). This reaction is coupled to the oxidation of NADH (fluorescent) to NAD (nonfluorescent), and the reduction of pyruvate to lactate by LDH (8, 21)

In this reaction, 1 mol of PEP and NADH is used to produce 1 mol of ATP and NAD. The solution surrounding the fiber in the quartz cuvette was illuminated at 340 nm, and the decrease in NADH concentration was detected by a decrease in the fluorescence signal at 470 nm. The solution in the cuvette was changed every 20 s, and the fluorescence change taking place between each solution change was converted to the rate of ATP hydrolysis by comparison to NADH standards (8).

Protocol for carrying out the force and ATPase experiments. A small cuvette, as previously described (9), enclosed the preparation and was used to perfuse the preparation with test contracting solutions pumped from a Ca²⁺ concentration gradient maker. The Ca²⁺ concentration in the cuvette perfusing the skinned preparation was varied by use of a gradient maker (Scientific Instruments, Heidelberg, Germany) to mix together two solutions (relaxing and maximal contracting solutions) of known Ca²⁺ and ionic composition. The Ca²⁺ concentration produced by the gradient maker was calibrated by using the fluorescent Ca²⁺ indicator calcium green-2 (Molecular Probes), which changes its fluorescence over the range of Ca²⁺ required for activation of contraction and ATPase activity (Fig. 2). The calcium green-2 fluorescence was excited at 480 nm, and the emission was measured at wavelengths greater than 515 nm. The fluorescence was then used to calculate the Ca²⁺ concentration associated with the force and ATPase measurement. In this manner, the pCa [log₁₀(Ca²⁺ concentration)] force and ATPase curves could be generated (Fig. 3 and Fig. 4).

View larger version (27K): [in this window] [in a new window]   Fig. 2.   Relationship between fluorescence of Ca2+ indicator calcium green-2 (Ca green-2), force, and pCa at three different Mg2+ concentrations. This figure shows that Ca2+ indicator is perfect for measuring Ca2+ concentration over range of Ca2+ required for Ca2+ activation of contraction.

View larger version (33K): [in this window] [in a new window]   Fig. 3.   Effect of Mg2+ on Ca2+-activated force and ATPase in rat ventricular skinned fibers. Mg2+ does not shift either force or ATPase along pCa axis. ATPase activity, as indicated by graph, is activated at lower concentrations of Ca2+ than force.

View larger version (34K): [in this window] [in a new window]   Fig. 4.   Effect of Mg2+ on ATPase-to-force ratio (rate constant for dissociation of force-generating myosin cross bridges; gapp) and force in rat ventricular skinned fibers. gapp decreased with increasing Ca2+ concentration or activation of force.

Calibration and calculation of pCa from the calcium green-2 fluorescence measurements. The pCa for each force and ATPase measurements was calculated from the R of calcium green-2 fluorescence associated with the data points. The Ca²⁺ concentration gradient was produced by mixing a contracting solution together with relaxing solution by using a peristaltic pump. The gradient maker consists of a flow-through solution chamber in which a fixed volume controlled by a peristaltic pump enters and leaves the chamber simultaneously. The solution entering the chamber is the contracting solution (pCa = 3.4), and the solution leaving the chamber is some mixture (Ca²⁺ gradient) of the relaxing and contracting solutions. This Ca²⁺-activating gradient solution passes through the cuvette containing the skinned muscle preparation. The gradient is calibrated by mixing the two solutions containing 1.0 µM calcium green-2 together, beginning with only the relaxing solution in the gradient maker chamber. The computer commands the peristaltic pump to make one revolution every 20 s, and the calcium green-2 fluorescence is measured in the cuvette after each pump revolution. For each pump number stored in the computer there is a corresponding fluorescence measurement. R is then used to calculate the pCa for each pump number by using the following equations
where K_d is for calcium green-2 at the three different Mg²⁺ concentrations used. Pump numbers from the calibration experiment were then used to determine the pCa for each force and ATPase measurement during the experiment. The calibration was performed at the beginning and end of each experiment to make sure that the calibration remained constant.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The K_d of calcium green-2 for Ca²⁺ was measured, as described in MATERIALS AND METHODS, for three different Mg²⁺ concentrations (1.0, 4.0, and 8.0 mM); the results are given in Table 1, which shows that there are no significant differences among the K_d values at the three different Mg²⁺ concentrations used in this study.

Figure 2 shows that the Ca²⁺ activation of fluorescence of calcium green-2 spans the range of Ca²⁺ required for activation of force at the three different Mg²⁺ concentrations, which makes it the perfect Ca²⁺ indicator for measuring Ca²⁺ concentration in skinned muscle fiber experiments. Figure 2 also shows that Ca²⁺ activation of force is not affected by Mg²⁺ concentration as evidenced by the fact that the three pCa-force curves coincide.

Figure 3 shows the relationships among force, ATPase activity, and pCa. The data show that the Ca²⁺ activation of actomyosin ATPase, like force, is not affected by Mg²⁺ concentration in the 1.0-8.0 mM range. In addition, Fig. 3 shows that Ca²⁺-activated actomyosin ATPase is activated at a lower concentration of Ca²⁺ than is force.

Figure 4 shows that ratio of ATPase to force decreases over the range of Ca²⁺ concentration required for activation of force. The ATPase-to-force ratio is assumed to be proportional to the rate constant for the dissociation of force-generating myosin cross bridges (g_app). According to this assumption, the g_app is decreasing during Ca²⁺ activation of actomyosin ATPase and force.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

This study produced three major findings. First, the fluorescent of the Ca²⁺ indicator, calcium green-2, can be used to directly measure the Ca²⁺ concentration directly in solutions used for Ca²⁺ activation of force and actomyosin ATPase activity. Second, Ca²⁺ activation of either force or actomyosin ATPase activity in skinned cardiac cells is not affected by Mg²⁺ as has been previously reported (2). Third, the Ca²⁺ activation of actomyosin ATPase is activated at a lower concentration of Ca²⁺ than force.

The method developed in this study to directly measure Ca²⁺ concentration over the range of Ca²⁺ required for activation of force in skinned (permeabilized) muscle cells overcomes the major impediment to studying the effects of different agents on the Ca²⁺ activation properties of skinned (permeabilized) muscle cells. Almost all previous studies have used the computer to solve the ionic equilibria equations for the different ionic species used in test solutions. Doing so requires knowing the K_d values for the various ligands (especially those that are used to chelate Ca²⁺, such as EGTA, EDTA, and BAPTA), but these are only available from the literature (18). Unfortunately these K_d values were determined in ionic (pH, ionic strength) and experimental (temperature) conditions different from the actual experimental conditions and therefore cannot be used to accurately predict the concentration of the ionic species, of which Ca²⁺ is one. This method avoids this problem, because the K_d for calcium green-2 was determined in ionic conditions similar to those used in this study. Additionally, this method, although only used for measuring Ca²⁺ in solutions of different Mg²⁺ concentrations, could also be used for measuring Ca²⁺ concentration directly in solutions with varying H⁺ concentration, ionic strength, inorganic phosphate, and so forth.

This study shows that Mg²⁺ has no effect on the Ca²⁺ activation of force in rat cardiac muscle, in contrast to previous reported studies (2, 4) in which the pCa in the test solutions was predicted by computer by using K_d values taken from the literature. In addition, Mg²⁺ has been hypothesized to shift the relationship between pCa and force in skeletal muscle as well, on the basis of computer prediction of the pCa (4, 5). Therefore, it seems important that studies similar to the one reported here be carried out in skeletal muscle to determine the actual effect of Mg²⁺ on Ca²⁺ activation of skeletal muscle. In fact, many previous studies showing effects of ionic conditions on the Ca²⁺ activation of striated muscle should be repeated by using this direct calcium green-2 fluorescence measurement of Ca²⁺ concentration in test solutions.

No previous data showing the effect of Mg²⁺ on the Ca²⁺ activation of actomyosin ATPase activity in skinned striated muscle have been reported. However, there have been previous studies showing that Mg²⁺ does have an effect on the Ca²⁺ activation of actomyosin ATPase in myofibrils (19). In those studies, Mg²⁺ shifted the pCa-ATPase curve to higher Ca²⁺ concentrations. Additionally, in these studies the pCa was predicted by using a computer.

The Ca²⁺ activation of ATPase in the skinned cardiac cells was shifted to lower concentrations of Ca²⁺ than was activation of force (Fig. 4). The simplest explanation for this is that the g_app decreases during Ca²⁺ activation of force and ATPase. Using the Huxley 1957 model (Fig. 5) for muscle contraction and the assumption that, for every myosin cross bridge that cycles, one molecule of ATP is consumed, one can derive an equation (Fig. 5) for the ratio of ATPase to force that is proportional to the g_app (13). The ATPase-to-force ratio is shown in Fig. 4 to decrease and also not to be affected by Mg²⁺ concentration. Similarly, the ATPase-to-force ratio has been shown to decrease during the Ca²⁺ activation of force in skinned skeletal muscle at room temperature (13). These data show that in cardiac muscle, as in skeletal muscle, the g_app is in part responsible for the activation of muscle contraction, because it decreases with increasing activation by Ca²⁺.

View larger version (8K): [in this window] [in a new window]   Fig. 5.   Huxley 1957 model for muscle contraction. According to Huxley's (11) two-state model, force that a muscle develops can be characterized by rate constants for formation of force-generating states (fapp) and dissociation of force-generating states (gapp). Assuming that one ATP molecule is hydrolized for each cross-bridge cycle, the Huxley model predicts that the ATPase-to-force ratio is proportional to gapp as shown in the following equation (13): ATPase/F = (L · gapp) (Fav · L1/2s) where L is muscle length, Fav is force per head, and L1/2s is one-half sarcomere length. It is assumed that L, Fav, and L1/2s are constants under given experimental conditions.

In summary, calcium green-2 can be used to accurately measure Ca²⁺ concentration over the range of Ca²⁺ required for activation of force and ATPase activity in skinned cardiac muscle under widely different ionic conditions. It is only necessary to measure the K_d for calcium green-2 in ionic conditions similar to those used in the actual experiment by the method presented. By using this method to measure the Ca²⁺ concentration in the test solutions at different Mg²⁺ concentrations, it was shown that Mg²⁺ had no effect on the relationship between Ca²⁺ concentration and force, in contrast to previous reports (2, 4, 5). Additionally, Mg²⁺ had no effect on the relationship between pCa and ATPase in skinned cardiac cells. Finally, the g_app decreases during Ca²⁺ activation of contraction. These data are all consistent with the hypothesis that cardiac muscle is activated by Ca²⁺ binding to a single Ca²⁺-specific site on cardiac troponin C.