Ca2+ binding to troponin C in skinned skeletal muscle fibers assessed with caged Ca2+ and a Ca2+ fluorophore. Invariance of Ca2+ binding as a function of sarcomere length.

Ca2+ sensitivity of tension varies with sarcomere length in both skeletal and cardiac muscles. One possible explanation for this effect is that the Ca2+ affinity of the regulatory protein troponin C decreases when sarcomere length is reduced. To examine length dependence of Ca2+ binding to troponin C in skeletal muscle, we developed a protocol to simultaneously monitor changes in sarcomere length, tension, and Ca2+ concentration following flash photolysis of caged Ca2+. In this protocol, [Ca2+] was rapidly increased by flash photolysis of caged Ca2+, and changes in [Ca2+] due to photolysis and the subsequent binding to troponin C were assessed using a Ca2+ fluorophore. Small bundles of fibers from rabbit skinned psoas muscles were loaded with Ca2+ fluorophore (Fluo-3) and caged Ca2+ (dimethoxynitrophenamine or o-nitrophenyl-EGTA). The bundles were then transferred to silicone oil, where [Ca2+]free, tension, and sarcomere length were monitored before and after photolysis of caged Ca2+. Upon photolysis of caged Ca2+, fluorescence increased and then decayed to a new steady-state level within ∼1 s, while tension increased to a new steady-state level within ∼1.5 s. After extracting troponin C, fibers did not generate tension following the flash, but steady-state post-flash fluorescence was significantly greater than when troponin C was present. The difference in [Ca2+]free represents the amount of Ca2+ bound to troponin C. In fibers that were troponin C-replete, Ca2+ binding to troponin C did not differ at short (∼1.97 μm) and long (∼2.51 μm) sarcomere length, yet tension was ∼50% greater at the long sarcomere length. These results show that the affinity of troponin C for Ca2+ is not altered by changes in sarcomere length, indicating that length-dependent changes in Ca2+ sensitivity of tension in skeletal muscle are not related to length-dependent changes in Ca2+ binding affinity of troponin C.

The regulation of striated muscle contraction involves Ca 2ϩ activation of interactions between contractile proteins of the thick and thin filaments. The thin filament protein troponin plays an integral role in activating contraction by binding Ca 2ϩ that is released into the myoplasm during a twitch. Troponin consists of three subunits, troponin T, troponin I, and troponin C (TnC), 1 which is the cation binding subunit of the complex. In fast skeletal muscle, TnC has four divalent cation binding sites, two NH 2 -terminal sites (I and II) that specifically bind Ca 2ϩ with relatively low affinity (K a ϭ ϳ5 ϫ 10 6 M Ϫ1 ) and two COOH-terminal sites (III and IV) which have higher affinity for Ca 2ϩ (K a ϭ ϳ5 ϫ 10 8 M Ϫ1 ) but also bind Mg 2ϩ (K a ϭ ϳ5 ϫ 10 4 M Ϫ1 ) (1). In relaxed muscle at physiological concentrations of free Mg 2ϩ (ϳ1.0 mM), the high affinity binding sites are thought to be occupied by Mg 2ϩ , whereas the low affinity sites are unoccupied and available for Ca 2ϩ binding. During excitation-contraction coupling, Ca 2ϩ binding to the low affinity sites on TnC initiates a series of events within the thin filaments that ultimately allow interaction of myosin with actin (2).
In striated muscles, the apparent Ca 2ϩ sensitivity of tension changes as a function of SL, increasing as SL is increased (3)(4)(5). One potential explanation for this phenomenon is length dependence of Ca 2ϩ binding to TnC. Previous isotopic studies of Ca 2ϩ binding in skinned muscle preparations suggest that the extent of Ca 2ϩ binding to TnC changes as a function of SL in cardiac (6) but not in skeletal muscle (7). In the present study, a fluorescent Ca 2ϩ indicator (Fluo-3) and caged Ca 2ϩ (DMnitrophen or NP-EGTA) were used to examine Ca 2ϩ binding as a function of SL in bundles of fast skeletal muscle fibers and to directly assess the role of altered Ca 2ϩ binding in conferring length dependence of Ca 2ϩ sensitivity of tension.

MATERIALS AND METHODS
Preparation of Skinned Fiber Bundles-Bundles of fibers from rabbit psoas muscles were tied to glass capillary tubes and kept at 4°C for 3 h in skinning solution containing 100 mM KCl, 10 mM imidazole, 1 mM MgCl 2 , 2 mM EGTA, 4 mM ATP, and 1% (v/v) Triton X-100. The bundles were subsequently transferred to skinning solution containing 50% glycerol (v/v) instead of Triton X-100 and stored at Ϫ20°C.
Experimental Techniques and Apparatus-On the day of an experiment, a bundle of skinned psoas fibers was transferred to relaxing solution, cut into 6-mm segments, and then split into smaller bundles of 3-4 fibers. One-half of each fiber bundle was transferred to SDS sample buffer for subsequent protein analysis using SDS-PAGE and scanning densitometry (8). The other half was transferred to relaxing solution in a stainless steel experimental chamber similar to the one described previously (9). The ends of the fiber bundle were attached to the arm of a motor (model 350, Cambridge Technology, Cambridge, MA) and a force transducer (model 403, Cambridge Technology, Cambridge, MA) as described by Metzger et al. (Fig. 3 in Ref. 10). The apparatus was then placed on the stage of an inverted microscope (Olympus) fitted with (a) 40 ϫ objective, (b) an optical block consisting of a dichroic mirror and excitation and emission filters, (c) a photomultiplier tube, and (d) a CCD camera (model WV-BL600, Panasonic). A schematic diagram of the recording system is shown in Fig. 1.
For simultaneous measurements of fluorescence, tension, and SL, the fiber bundle was transferred to a quartz trough containing silicone oil (see Fig. 1). Light from a halogen lamp used to illuminate the fiber bundle was first passed through a cut-off filter (F1, transmission Ͼ620 nm) in order that the emitted wavelength did not interfere with either photolysis or fluorescence. After passing through the fiber bundle and a 40 ϫ objective (Zeiss), the light (Ͼ620 nm) was transmitted through a dichroic mirror, another cut-off filter (F2, transmission Ͼ 520 nm), and then split by a beam splitter (BS1). Filtered light that continued toward the photomultiplier tube was prevented from reaching the photomultiplier tube by a band-pass filter (F3, transmission between 490 -530 nm). Filtered light that continued toward the eyepiece was split by a second beam splitter (BS2), so that one-half was directed to a CCD camera and the other half to the eyepiece. Images of the fiber bundle were stored on video tape and used for off-line SL measurements.
Ca 2ϩ fluorophore within the fiber bundle was excited by light ( ϭ 475 nm) from a fluorimeter (SLM Aminco, SLM Instruments, Inc., Urbana, IL) directed to the 80-l quartz-walled trough via a fiber optic light pipe. This light was first passed through a band-pass filter (F4, transmission between 400 -490 nm) and then reflected by a dichroic mirror toward the bundle of fibers in the quartz trough. Emitted fluorescence followed the same path as the filtered light from the halogen lamp, except that it passed through the band-pass filter F3 and reached the photomultiplier tube. The output signal from the photomultiplier tube was recorded and stored using SLM 8000C software package. Photolysis of caged Ca 2ϩ was achieved by exposing the caged Ca 2ϩ loaded fiber bundle to a single flash of UV light (ϳ360 nm) from a flash lamp (Hi-Tech). The extent of photolysis was varied by changing the intensity of the UV light. An electronic shutter (Uni-Blitz), with a built in delay of 15 ms, was placed in front of the photomultiplier tube to protect it from the high intensity UV flashes used for photolyzing caged Ca 2ϩ .
Experimental Protocol-The SL of fiber bundles was initially set to a slack length (ϳ1.97 m) in relaxing solution, and maximum tension generating capacity was then determined by activating the muscle in solution of pCa 4.5. Fiber bundles were used only if a clear striation pattern was maintained during maximal activation and SL shortened by less than 10%. To assess Ca 2ϩ binding during active force generation, fiber bundles were incubated for 4 min in pre-activating solution containing 0.05 mM EGTA and then bathed for 5 min in loading solution containing Fluo-3 and either NP-EGTA or DM-nitrophen to ensure uniform distribution of these compounds within the fiber bundle. Next, fiber bundles were transferred to a quartz chamber containing silicone oil where they were exposed to a 1-ms flash of UV light. The resulting changes in tension, fluorescence intensity, and SL were recorded, and the fiber bundles were then transferred back to relaxing solution. In some experiments, variable amounts of caged Ca 2ϩ were photolyzed using multiple intensities of UV light. Maximum tension at pCa 4.5 was determined following each UV flash, and fiber bundles were discarded if tension fell by more than 10% of its initial value. SL was then increased to a long length (ϳ2.51 m) while the bundle was in relaxing solution, and the above protocol was repeated.
Following characterization of length dependence of Ca 2ϩ binding, TnC was extracted from the fiber bundle to characterize TnC-independent Ca 2ϩ binding. TnC was extracted by first incubating the fiber bundles for 2 min in a solution containing 195 mM potassium propionate and 10 mM BES (pH 7.0) followed by 2 min in solution containing 165 mM potassium propionate, 10 mM BES, and 10 mM EDTA (pH 7.0) and finally 30 min in TnC extracting solution containing 10 mM BES, 5 mM EDTA and 0.2 mM trifluoperazine (pH 7.0, 2 ϫ solution change). This protocol completely depleted the fibers of TnC as judged by the absence of active tension at pCa 4.5 and the absence of TnC from SDS gels of the fiber bundles. After extraction of TnC, the fiber bundles were washed in relaxing solution for 30 min (2 ϫ solution change), and Ca 2ϩ binding was assayed using flash photolysis of caged Ca 2ϩ as described above. To determine [Ca 2ϩ ] free from fluorescence signals recorded before and after flash photolysis, a calibrated fluorescence-pCa relationship for each preparation was determined at both short and long SL. The protocol for this determination was the same as described above except that loading solution was replaced by a range of Ca 2ϩ standard solutions prepared by mixing stocks of pCa 9.0 and pCa 4.5. At the end of an experiment, the fiber bundle was cut at the points of attachment and placed in SDS-PAGE sample buffer for protein analysis.
Solutions-Solutions were made using the computer program of Fabiato (11) and the stability constants listed by Godt and Lindley (12). The stability constants were corrected to pH 7 and 15°C. In addition, all the solutions listed in Table I contained 100 mM BES, 15 mM creatine phosphate, and 5 mM dithiothreitol, and ionic strength was adjusted to 180 mM with potassium propionate. Loading solution also contained either 0.92 mM DM-nitrophen (Calbiochem) or 0.92 mM NP-EGTA (Molecular Probes, OR), 0.025 mM Fluo-3 (Calbiochem), and 100 units/ml creatine kinase (Calbiochem). In some experiments, loading solution also contained 0.05 mM calmodulin that was purified from bull testes using procedures described by Dedman et al. (13).
Statistical Analysis-Statistical analysis of the data was done using paired t tests. A p value of Ͻ0.05 was considered to indicate significant differences between data acquired at short and long SL. Pooled data are expressed as mean Ϯ S.E.

RESULTS
Tension-pCa Relationships at Short and Long SL-The effect of SL on Ca 2ϩ sensitivity of isometric tension in fast skeletal muscle fibers is shown in Fig. 2. The concentration of Ca 2ϩ required to produce half-maximal tension (i.e. pCa 50 ) was 5.77 Ϯ 0.02 at short SL (1.94 Ϯ 01 m) in the presence of 1   Fig. 3A shows that [Ca 2ϩ ] free within the fiber bundle was pCa 6.8 before flash photolysis of DM-nitrophen, and there was essentially no active tension, even when free Mg 2ϩ was as low as 0.1 mM. Following photolysis, the Ca 2ϩ binding affinity of DM-nitrophen changes from 2 ϫ 10 8 to 3.33 ϫ 10 2 M Ϫ1 , resulting in the rapid release of Ca 2ϩ (14). Thus, [Ca 2ϩ ] free rises rapidly following the flash, which is evident in the fluorescence signal in Fig. 3A, and then decays to a new steady-state level that is intermediate between base line and peak. Coincident with the Ca 2ϩ transient, tension increases and attains a new steady-state level (Fig. 3B). In this example, the steady-state [Ca 2ϩ ] free increased from pCa 6.80 pre-flash to a final level of pCa 6.27 post-flash, whereas tension increased from ϳ0.05 P 0 to ϳ0.75 P 0 . Mean SL was also monitored during changes in free Ca 2ϩ and tension following flash photolysis. Photomicrographs obtained before and after each flash ( Fig. 4) indicated that there was minimal sarcomere shortening in the fiber bundle following the flash; in this case, SL shortened from 2.59 to 2.38 m during the development of tension.
When this protocol was repeated after extracting TnC from the fiber bundle, the fiber bundle failed to generate tension upon photogeneration of Ca 2ϩ , and the post-flash steady-state [Ca 2ϩ ] free was elevated (pCa 5.97) relative to the pre-TnC extraction value. SDS-polyacrylamide gel electrophoresis confirmed that virtually all the TnC was extracted from the fiber bundles (Fig. 5). Based on these results we conclude that part of the Ca 2ϩ released as a result of photolysis of DM-nitrophen binds to TnC and induces activation of tension in these fiber bundles.
Similar results were obtained when NP-EGTA was used (Fig. 6) in place of DM-nitrophen. In this case, [Ca 2ϩ ] free increased from pCa 6.47 before the flash to pCa 5.96 following the flash, consistent with a decrease in the affinity of NP-EGTA for Ca 2ϩ from 1.25 ϫ 10 7 to 1.0 ϫ 10 2 M Ϫ1 (15). After TnC extraction, photolysis increased [Ca 2ϩ ] free from pCa 6.47 to 5.14 ( Fig. 6A). Corresponding to steady-state [Ca 2ϩ ] free following flash photolysis, the post-flash steady-state ten-sions were 0.6 P 0 before and 0.05 P 0 after TnC extraction (Fig. 6B).
Ca 2ϩ Binding to TnC at Short and Long SL-Figs. 7 and 8 show effects of length on flash-induced changes in Ca 2ϩ binding to TnC (Fig. 7A) and tension (Fig. 7B). Photomicrographs of the same bundle are shown in Fig. 8. At both short and long SL, [Ca 2ϩ ] free prior to the flash was approximately pCa 6.67 and tension was less than 5% of peak. Upon exposing the bundle to a flash of 40% of maximum intensity, steady-state [Ca 2ϩ ] free increased to pCa 6.13 at short SL (2.03 m) and 6.26 at long SL (2.57 m). This increase in [Ca 2ϩ ] free at short SL elicited isometric tension equivalent to 0.55 P 0 , and at long SL tension increased to 0.75 P 0 . In the same bundle, when flash intensity was reduced to 27% of maximum intensity, steady-state [Ca 2ϩ ] free and fractional tension (P/P 0 ) were pCa 6.31 and 0.25, respectively, at short SL and 6.41 and 0.50, respectively, at long SL (data not shown). When the same fiber bundle was exposed to a flash of 40% maximum intensity following TnC extraction, the fiber bundle did not generate tension (Fig. 7D), and the steady-state [Ca 2ϩ ] free increased from pCa 6.72 to 6.05 at both short length and long length. Mean values of results from several experiments are presented in Table II. At both flash intensities, [Ca 2ϩ ] free values were similar at short and long lengths, indicating that Ca 2ϩ binding by TnC does not vary with SL. In contrast, tension was significantly greater at long SL than at short SL, indicating that the SL dependence of submaximal tension does not involve a change in the extent of Ca 2ϩ binding to TnC. Also, the similarity of steady-state [Ca 2ϩ ] free values recorded at short and long length after TnC extraction indicates that there was little variation in the amount of Ca 2ϩ released when DM-nitrophen was photolyzed at the two lengths.
We also used NP-EGTA to investigate length dependence of Ca 2ϩ binding to TnC. Data from one experiment is shown in Fig. 9, and a summary of the results is presented in Table III. In the example shown, the fiber generated Ͻ5% tension both at short and long SL prior to flash photolysis of NP-EGTA. Using flashes with 90% of maximum output intensity, steady-state [Ca 2ϩ ] free at short and long SL increased from pCa 6.47 to 5.94 and 5.96, respectively, (Fig. 9A). After TnC extraction, identical flashes increased [Ca 2ϩ ] free from pCa 6.43 to 5.10 and 5.14, respectively, (Fig. 9C). Similar to the data with DM-nitrophen, the post-flash tension generated by the fiber bundle was greater at long SL (0.62 P 0 ) than at short SL (0.30 P 0 ) despite similar levels of Ca 2ϩ binding to TnC.
Calculation of the Amount of Ca 2ϩ Bound to TnC-The amounts of Ca 2ϩ bound to TnC before and after flash photolysis of caged Ca 2ϩ were calculated using Fabiato's solution program (11). We first calculated the extent of photolysis of DM-nitrophen or NP-EGTA, as appropriate. By adjusting our estimate of percent photolysis, we were able to match calculated values of [Ca 2ϩ ] free to those measured in TnC-extracted fibers both before (resting level) and after (steady-state level) photolysis of caged Ca 2ϩ chelators at the two sarcomere lengths (see Tables  II and III, respectively). As described under "Materials and Methods," the measured values of [Ca 2ϩ ] free were calibrated by recording fluorescence intensity as a function of pCa in stand-ard Ca 2ϩ solutions applied to each bundle at both long and short SL. This calculation was done with an iterative process using binding affinities listed in Table IV and assuming 1) that the concentrations of other Ca 2ϩ buffering ligands remained constant and 2) that no TnC remained in the fiber bundles following extraction. The calculated extent of photolysis of DMnitrophen averaged 28.8 and 34.8% of the total at flashes that were 27 and 40% of maximum intensity, respectively. With respect to NP-EGTA, a flash that was 90% maximum intensity resulted in 25% photolysis of total NP-EGTA.
In the second part of the calculation, TnC was included as a Ca 2ϩ buffering ligand, but all other variables that had been determined in the first part of the calculation were kept constant. The concentrations of the low and high affinity divalent cation binding sites on TnC were each assumed to be 180 M. This assumption is based on an earlier determination of TnC content (770 pmol/mg myofibril protein) in rabbit muscle (16). By adjusting the affinities of the high and low affinity sites, we matched the calculated [Ca 2ϩ ] free to the mean values of steadystate [Ca 2ϩ ] free recorded before (resting level) and after (steady-state level) photolysis reported in Tables II and III.  Table V  Additional experiments were done to verify that the changes in fluorescence intensity provided accurate reports of Ca 2ϩ binding to TnC. Similar to TnC, calmodulin also has four divalent cation binding sites. From measurements on calmodulin purified from rat testis, Dedman et al. (13) suggested that all four sites on calmodulin are Ca 2ϩ -specific and all four sites have a Ca 2ϩ binding affinity of 2.4 M (K Ca ϭ 4.5 ϫ 10 5 M Ϫ1 ). Since this binding affinity is similar to that of the low affinity sites on TnC used in the present calculations (K Ca ϭ 3.00 ϫ 10 5 M Ϫ1 ), addition of 45 M calmodulin (180 M Ca 2ϩ binding sites) to TnC-extracted fibers should decrease the post-flash fluorescence intensity to the same level as that recorded in TnCreplete fibers. We tested this prediction by recording changes in tension (Fig. 10B) and fluorescence intensity (Fig. 10A) following photolysis of NP-EGTA 1) before TnC extraction without added calmodulin and 2) after TnC extraction in both the absence and presence of 50 M calmodulin. Before TnC extraction, photolysis of NP-EGTA increased steady-state tension from 0.05 to 0.5 P 0 (0.49 Ϯ 0.02, n ϭ 6) and increased steadystate [Ca 2ϩ ] free from pCa 6.74 (6.73 Ϯ 0.05) to pCa 6.27 (6.27 Ϯ 0.06). After TnC extraction, photolysis of NP-EGTA had no effect on steady-state tension, whereas the steady-state [Ca 2ϩ ] free increased from pCa 6.69 (6.69 Ϯ 0.05) to pCa 6.05 (5.99 Ϯ 0.07) in the absence of calmodulin and from pCa 6.70 (6.70 Ϯ 0.02) to pCa 6.27 (6.22 Ϯ 0.06) in the presence of 50 M calmodulin. Using the calculation method described above, the pre-and post-flash concentrations of Ca 2ϩ bound to the Ca 2ϩspecific sites on TnC were 10.18 and 27.24 M, respectively, and to those on calmodulin were 15.07 and 37.82 M, respectively. This difference can be accounted for by the higher concentration and binding affinity of the Ca 2ϩ -specific sites used in the calculation for calmodulin as compared with those for TnC. These data corroborate our estimated values for concentration and binding affinity of Ca 2ϩ -specific sites on TnC used to calculate the amount of Ca 2ϩ bound to TnC at short and long lengths. Ca 2ϩ binding in skinned muscle fibers, particularly binding to the thin filament regulatory protein TnC. The technique was based on the premise that the Ca 2ϩ released following flash photolysis of either DM-nitrophen or NP-EGTA would be buffered to a greater extent in the presence of TnC than in its absence. This idea was confirmed in our studies, since the steady-state fluorescence intensity of Fluo-3 following flash photolysis substantially increased following near-stoichiometric extraction of TnC (Figs. 3 and 6). Additionally, similar differences in steady-state fluorescence were observed when caged Ca 2ϩ was photolyzed in the presence and absence of TnC in solution or in rigor muscle fibers before and after extraction of TnC (data not shown). These controls demonstrate that the differences in pre-and post-flash steady-state fluorescence signals in the present study were specifically due to Ca 2ϩ binding to TnC and were not artifacts due, for example, to movements of the fiber bundles during tension development.
We found that small changes in [Ca 2ϩ ] in the range of pCa between 7.0 and 5.3 produced large changes in the fluorescence intensity of Fluo-3 (fluorescence-pCa relationship not shown). Thus, to optimize resolution of small changes in steady-state [Ca 2ϩ ], the experimental conditions were designed such that steady-state [Ca 2ϩ ] free at rest and following photolysis of DM-nitrophen (0.1 mM free Mg 2ϩ ) or NP-EGTA (1.0 mM free Mg 2ϩ ), either before or after TnC extraction, fell within the range of [Ca 2ϩ ] between pCa 7.0 and 5.3. Even with this constraint, we were able to examine Ca 2ϩ binding to TnC over a wide range of tension (ϳ0.20 to ϳ0.75 P 0 ) in the presence of 0.1 mM. However, at 1.0 mM free Mg 2ϩ , the range of tensions investigated was smaller because at higher force the steady-state [Ca 2ϩ ] free determined after TnC extraction was calculated to be greater than pCa 5.3 (see Fig. 9). Since even a large change in [Ca 2ϩ ] in the pCa range between 5.3 and 4.5 produces only a small change in fluorescence intensity of Fluo-3, the [Ca 2ϩ ] free at pCa Ͻ 5.3 could not be determined with certainty.
Length Dependence of Ca 2ϩ Binding-The variation in Ca 2ϩ sensitivity of tension with SL that we observed was similar to that previously reported in single psoas fibers (3). However, there was a marked difference in length dependence of Ca 2ϩ sensitivity at the two concentrations of free Mg 2ϩ used. The difference in pCa 50 at short and long SL in the presence of 0.1 mM free Mg 2ϩ was almost twice the difference recorded in the presence of 1.0 mM free Mg 2ϩ , i.e. the difference at 0.1 mM free Mg 2ϩ was 0.32 pCa unit, whereas at 1.0 mM free Mg 2ϩ the difference was 0.18 pCa unit. Previous studies on frog skinned skeletal fibers (17) and rabbit skinned psoas fibers (18) reported FIG. 7. Length dependence of fluorescence intensity and tension recorded simultaneously from a bundle of skinned psoas fibers following flash photolysis of DM-nitrophen. After incubating the bundle of psoas fibers in loading solution (0.58 mM Ca 2ϩ , 0.92 mM DM-nitrophen, 0.025 mM Fluo-3, 0.1 mM free Mg 2ϩ ) for 5 min, the bundle was transferred to a quartz trough filled with silicone oil. Fluorescence intensity (A before and C after TnC extraction) and tension (B before and D after TnC extraction) were recorded simultaneously pre-and post-photolysis of DM-nitrophen (F, 40% maximum intensity). Short SL was 2.03 m, and long SL was 2.57 m before flash photolysis. The numbers beside the fluorescence intensity traces represent [Ca 2ϩ ] free in pCa units. Tension is expressed as a fraction of the maximum tension developed by the same bundle at pCa 4.5.
that the Ca 2ϩ sensitivity of tension increased when [Mg 2ϩ ] free was reduced. The mechanism underlying the shift in Ca 2ϩ sensitivity of tension with changes in [Mg 2ϩ ] free is not yet known.
The idea that changes in Ca 2ϩ binding affinity of TnC might account for length-dependent shifts in Ca 2ϩ sensitivity of tension in fast skeletal fibers has been considered previously.  Using isotopic Ca 2ϩ binding methods, Hofmann and Fuchs (6) reported that Ca 2ϩ binding to TnC changed as a function of SL in cardiac muscle but not in either slow (6) or fast (7) skeletal muscles. Using our new approach, we also found that the extent of Ca 2ϩ buffering by TnC following flash photolysis of caged Ca 2ϩ does not change with SL in bundles of skinned psoas fibers. Despite similar Ca 2ϩ binding at long and short SL, submaximal tension was significantly greater at long SL than at short SL even when the concentration of activating Ca 2ϩ was identical. This result indicates that submaximal tension changes as a function of SL per se and is not a consequence of length-induced changes in the amount of activator Ca 2ϩ bound to TnC. One mechanism that may be involved in length dependence of submaximal tension is the decrease in lateral spacing of thick and thin filaments, i.e. interfilament lattice spacing, as fibers are stretched to longer lengths (3,19,20).  Reduced lateral spacing would increase the probability of crossbridge interaction with actin and thus the amount of tension. Increased numbers of cross-bridges would directly increase tension and also indirectly by cooperatively activating the thin filament. These mechanisms are under investigation using the approach described here. Calculated Ca 2ϩ Binding Affinity of Low Affinity Sites on TnC in Skinned Psoas Fibers-To determine the amount of Ca 2ϩ bound to low affinity site of TnC in the presence of 1 mM free Mg 2ϩ , we first assumed a concentration of 0.18 mM for the low affinity sites based on the concentration of TnC (0.09 mM) determined by Yates and Greaser (16). We also assumed a K Ca of 5.0 ϫ 10 6 M Ϫ1 for the low affinity sites and K Ca and K Mg of 5.0 ϫ 10 8 and 5.0 ϫ 10 4 M Ϫ1 for the high affinity divalent cation binding sites, as previously reported by Potter and Gergely (1). These constants were also used previously to model the time course of Ca 2ϩ binding to Ca 2ϩ binding proteins in response to trains of transient increases in the free myoplasmic [Ca 2ϩ ] (21). Using these values, our calculated concentrations of free Ca 2ϩ at rest (pre-flash) and following 25% photolysis (post-flash) of NP-EGTA were pCa 6.86 and pCa 6.61, respectively, which significantly underestimated the actual [Ca 2ϩ ] free as determined from our calibration of fluorescence intensity. In order to achieve the measured values of [Ca 2ϩ ] free using the computer simulation, K Ca for the low affinity sites on TnC had to be adjusted from 5.0 ϫ 10 6 to 3 ϫ 10 5 M Ϫ1 and the K Ca for the high affinity sites from 5 ϫ 10 8 to 1 ϫ 10 6 M Ϫ1 , while keeping K Mg and the concentration of TnC constant. Alternatively, the measured and calculated values of steady-state [Ca 2ϩ ] free could be matched by assuming the binding affinities previously reported by Potter and Gergely (1) but a concentration of TnC of 0.02 mM rather than 0.09 mM. In the present study we were unable to measure the concentration of TnC in our fiber bun-dles using SDS-PAGE, primarily because we could not precisely determine the diameter of each fiber in the fiber bundles. Even so, it is highly unlikely that the concentration of TnC in the fiber bundles was as low as 0.02 mM, since this is much lower than the concentration of TnC determined accurately by Yates and Greaser (16) and the concentration determined by Fuchs and Black (22) by SDS-PAGE of single fibers. Furthermore, by adding calmodulin to our assay system, we have demonstrated that both the concentration and the Ca 2ϩ binding affinity of low affinity sites on TnC assumed in our calculations are reasonable. Using the Ca 2ϩ binding affinity for the Ca 2ϩ -specific site on calmodulin determined in solution by Dedman et al. (13), we found close agreement between calculated and measured values of pre-and post-flash steady-state [Ca 2ϩ ] free . This finding with calmodulin in solution suggests that the difference between the binding affinity of TnC required in our calculations and that determined in solution by Potter and Gergely (1) is likely due to differences in Ca 2ϩ binding by TnC in solution as compared with TnC in the intact myofilament. Zot and Potter (23) have also suggested that TnC in the regulated thin filament has a lower affinity for Ca 2ϩ than that in whole troponin alone. Such a mechanism would also explain why we were able to use the same constants to calculate the steady-state [Ca 2ϩ ] free in the presence of 0.1 and 1.0 mM free Mg 2ϩ .
When using NP-EGTA, an apparently greater amount of Ca 2ϩ must be bound to TnC in order to increase tension above 0.5 P 0 . This can be seen in Table V by comparing the amount of Ca 2ϩ bound post-flash; using DM-nitrophen, a relative tension of 0.75 P 0 is achieved when a calculated 26 -27 M Ca 2ϩ is bound, but to achieve a relative tension of 0.59 P 0 when NP-EGTA is used, 56 M Ca 2ϩ must be bound. Such differences are most likely due to a shift in the tension-pCa relationship to  (14) 2.0 ϫ 10 8 M Ϫ1 3.333 ϫ 10 2 M Ϫ1 K Mg for DM-nitrophen (14) 4   (24). Because of this change in Ca 2ϩ sensitivity of tension, more Ca 2ϩ would be required at 1.0 mM free Mg 2ϩ than at 0.1 mM free Mg 2ϩ to achieve a given level of sub-maximal tension. It is evident from examination of the data with NP-EGTA ( Table V) that disproportionately more [Ca 2ϩ ] must be bound to achieve a tension of 0.59 P 0 (56 M Ca 2ϩ ) than is required to achieve a tension of 0.49 P 0 (27 M Ca 2ϩ ). Although the mechanism for this effect is not known for certain, activation of tension at low Ca 2ϩ has been shown to involve significant cooperative activation of the thin filament due to strong binding of cross-bridges, but at tensions greater than half-maximal, such cooperativity is much reduced (25). Thus, when the level of sub-maximal activation is relatively high, more Ca 2ϩ would be required to achieve a given increment in isometric tension. Firm conclusions about the mechanisms of effects on bound Ca 2ϩ due to [Mg 2ϩ ] and level of activation will require additional work.