Regulation of actomyosin ATPase by a single calcium-binding site on troponin C from crayfish.

Equilibrium-binding studies at 4 degrees C show that, in the instance of crayfish, troponin C contains only one Ca-binding site with an affinity in the range of physiological free [CA2+] (K = 2 X 10(5) M-1). At physiological levels of Mg2+, this site does not bind Mg2+. In the complexes of troponin C-troponin I, troponin and troponin-tropomyosin, the regulatory Ca-specific site exhibits a 10- to 20-fold higher affinity (K = 2-4 X 10(6) M-1). The latter affinity is reduced to that of troponin C upon incorporation of the troponin-tropomyosin complex into the actin filament (regulated actin), as determined at 4 degrees C by the double isotope technique. The Ca-binding constant is again shifted to a higher value (7 X 10(6) M-1) when regulated actin is associated with nucleotide-free myosin. Both crayfish myofibrils and rabbit actomyosin regulated by crayfish troponin-tropomyosin display a steep rise in ATPase activity with [Ca2+]. Comparison of the pCa/ATPase relationship and the Ca-binding properties at 25 degrees C for the crayfish troponin-regulated actomyosin indicates that while the threshold [Ca2+] for activation corresponds to the range of [Ca2+] where the regulatory site in its low affinity state (K = 1 X 10(5) M-1) starts to bind Ca2+ significantly, full activation is reached at [Ca2+] for which the Ca-specific site in its high affinity state (K = 3 X 10(6) M-1) approaches saturation. These results suggest that, in the actomyosin ATPase cycle, there are at least two calcium-activated states of regulated actin (one low and one high), the high affinity state being induced by interactions of myosin with actin in the cycle.

three subunits of Tn in the thin filament which is composed of Tn, Tm, and F-actin in a 1:1:7 molar ratio (2). The steric blocking model has been proposed as a mechanism for the calcium-regulated control (3,4). This all-or-none model suggests that, when TnC is Ca2+-free, Tm sterically prevents the binding of the myosin heads to actin, thus relaxing the muscle.
In the presence of Ca2+, Tm does not block the binding of myosin cross-bridges. Recent data suggest that the Tn-linked regulation may be better viewed as an allosteric system (5,6).
In many invertebrate muscles, the Tn-linked regulatory system coexists with the myosin-linked system (7). Yet, in fast striated muscle of arthropods such as horseshoe crab (8) and crayfish (9), Ca2+ binding to TnC seems to be the primary trigger for contraction. Similarly to its vertebrate counterpart, Tn isolated from arthropods appears to consist of three components (10-12). The latter differ, however, from the corresponding subunits of vertebrate Tn (13) in molecular weight and amino acid composition. The smallest (Mr = 16,000 to 18,000) and medium (M, = 23,000 to 29,000) subunits are analogous in function to vertebrate TnC and TnI, respectively (11, 12). As for the TnT-like protein (Mr = 50,000 to 60,000), its involvement in troponin function has not yet been studied in detail (10-12).
Rabbit skeletal TnC contains four potential binding sites for Ca2+ (14, 15). Only two sites that bind Ca2+ specifically are thought to be functional (15). The two other sites that bind both Ca2+ and Mg2+ seem to play a structural role (16). Bovine cardiac TnC is analogous to the skeletal muscle protein, with two Ca2+-Mg2+ sites but only one Ca2+-specific site (17). There is still some doubt about the regulatory sites in vertebrate systems, since magnesium ions affect the calcium activation of myofibrillar ATPase (18) and of tension development (19). Invertebrate TnC binds less Ca2+ than does vertebrate TnC (11,20-22); arthropod TnC seems to have no more than one Ca2+-binding site (20, 21).
The aim of this work was to study the nature of the Ca2+and M$+-binding sites on crayfish TnC and their role in the regulation of actomyosin ATPase. We measured Ca2+ and Mg+ binding to crayfish TnC in a vast range of [Ca"] or [M$+] and found that in the limited range of physiological [Ca"] only a single site binds Ca2+. This site is analogous to the Ca2+-specific sites of vertebrate TnC. Hence, the Tm . Tn complex with the simplest physiologically significant Ca2+binding properties constitutes a convenient system to study Ca2+ regulation. For instance, conflicting reports exist concerning the mechanism responsible for the sharp transition in Ca2+ dependence of myofibrillar ATPase and of tension development (15,(23)(24)(25). We compared the Ca2+-binding properties of crayfish Tm . Tn-containing actin (alone or associated with myosin) with the pCa/ATPase relationship in the instance of both regulated actomyosin and myofibrils. This system has the advantage over the vertebrate one that 9017 the results are blurred neither by Ca2+ binding to the nonrelevant sites on TnC nor by the requirement for activation of multiple bound Ca2+ on the TnC molecule.

EXPERIMENTAL PROCEDURES
Materials-DEAE-Sephadex A-25 and SE (sulfoethy1)-Sephadex C-50 were obtained from Pharmacia (Uppsala, Sweden). Polyacrylamide gel electrophoresis reagents were purchased from Serva (Heidelberg, Germany). 45Ca (30 mCi/mg) and ~-[6-~H]glucose (13 Ci/ mmol) were from Amersham International pCI (Amersham, England). All other chemicals were reagent grade and were utilized without further purification, except for urea (Merck, Darmstadt, Germany) solutions which were deionized by means of a mixed bed resin (Bio-Rad). All buffers and protein solutions were prepared with bidistilled water from an all-quartz apparatus and contained inhibitors of bacterial growth and proteolysis: 0.5 mM NaN3 (Merck), 20 p~ phenylmethylsulfonyl fluoride (Sigma), and 0.2 pg/ml of pepstatin A (Protein Research Foundation, Osaka, Japan).
Preparation of Myofibrik-Myofibrils were prepared by the method of Lehman (26) from crayfish (Astacus leptodactylus) tail muscle and from rabbit hind leg and back muscle. The myofibrils were stored at Preparation of Rabbit Myosin and Actin-Myosin was prepared according to Watterson and Schaub (27) and then stored at -20 "C in 10 mM potassium phosphate, pH 6.5, 0.6 M KCI, 5 mM dithiothreitol, and 50% glycerol. Actin was purified by the procedure of Spudich and Watt (28) and stored on ice as F-actin.
Preparation of Tm.Tn Complex from Rabbit and Crayfish-Both complexes were extracted from fresh myofibrils in 15 mM 2-mercaptoethanol, 2 mM Tris/HCl buffer, p H 7.0, using a procedure similar to that described by Murray (29). The complexes were stored in the above buffer a t -20 "C.
Preparation of Crayfish Tn and Tn Subunits-Crayfish T n was obtained either from the T m . T n complex by the isoelectric precipitation of T m (30) or from myofibrils by a procedure similar to that of Ebashi et al. (31). T h e T n complex was dialyzed against 0.2 M NaCI, 5 mM EDTA, 15 mM 2-mercaptoethanol, 20 mM Tris/HCI buffer, pH 7.8. When applied to a column of DEAE-Sephadex A-25, only TnC was retained. The latter protein was eluted a t 0.4 M NaCI. The proteins not absorbed were dialyzed against 6 M urea, 5 mM 2mercaptoethanol, 50 mM sodium barbital, pH 8.0, and loaded on a column of SE-Sephadex C-50. TnT and TnI were eluted by a linear gradient of 0 to 0.3 M NaCl (at 0.08 and 0.20 M NaCI, respectively). Appraisal of purity of the preparations (Fig. 1) and determination of the apparent M, of the polypeptide chains (32) were carried out by means of an sodium dodecyl sulfate-polyacrylamide gel electrophoresis procedure (33) in 12.5% acrylamide gels. The TnI. TnC complex was obtained by mixing purified subunits using a procedure similar 0-4 "C. Preparation of Reconstituted Regulated Actin and Actomyosin-Regulated actin was prepared by polymerizing rabbit actin in the presence of an excess of the Tm .Tn complex from crayfish or rabbit, as described by Murray (29). The thin filament preparations and rabbit myosin were dialyzed against 80 mM KCI, 1 mM dithiothreitol, 0.1 mM EGTA, 40 mM imidazole, pH 7.0. The dialyzed actin and myosin were then mixed (4:l molar ratio) to produce a concentration of reconstituted regulated actomyosin of approximately 6 mg/ml.
Metal and Protein Anulyses-Calcium, magnesium, and ' T a were determined as described previously (34). Protein concentrations were determined by the Lowry method (35) with bovine serum albumin as a reference except for the purified crayfish TnC solutions which were standardized by either amino acid analysis or determination of dry weight. The concentrations of rabbit proteins were measured spectrophotometrically using the following absorption coefficients: 630 cm2/ g a t 290 nm for G-actin, 540 cm2/g a t 280 nm for myosin, and 280 cm2/g at 278 nm for Tm.Tn. The molecular weights used for rabbit actin, myosin, and Tm .Tn complex were 42,000,460,000, and 150,000, respectively. Those for crayfish proteins were: T m ' T n complex, 161,000, T n complex, 87,000; TnI .TnC complex, 42,000, TnC, 16,000. Quantification of TnC in crayfish preparations was achieved by densitometry of the Coomassie Blue-stained gels (36), using increasing amounts of pure TnC as internal standards. Extrapolation to zero concentration of added TnC gave the amount of TnC in the original solution.
Calcium-and Magnesium-binding Measurements-The binding of calcium to crayfish TnC (3 mg/ml), TnI.TnC (6 mg/ml), T n (8 mg/ ml), and T m . T n (15 mg/ml) was measured by equilibrium dialysis a t 4 "C using EGTA to regulate the free [Ca"] (34). The dialysis fluid contained 40 mM imidazole, pH 7.0,80 mM KCI, 0.1 mM EGTA, 0.1 pCi/ml of "CaCI2, and the appropriate amount of CaCI2 to achieve the desired free Ca2+ concentration. In experiments without added M e , the contaminating M F concentration was about 0.1 p~. In experiments with 1 mM MgCIz, KC1 concentration was diminished to 77 mM. For M e binding to TnC in the absence of Ca2+, EGTA concentration was increased to 1 mM, and the desired concentrations of MgCI, were used. The free Ca2+ and Mg2' concentrations were calculated by means of the computer program of Perrin and Sayce (37). The association constants for metals and H+ to EGTA were adjusted for use a t 4 'C using their enthalpy values (38). All constants involving protons were corrected for the proton activity as described by Martell and Smith (38); thus pH was used instead of [H+] in the calculations. For crayfish TnC, equilibrium dialysis experiments were also performed without EGTA, and the free [Ca'+] was regulated by appropriate amounts of Chelex (Bio-Rad) in the dialysis fluid, as described by Crouch and Klee (39).
The binding of calcium to the reconstituted regulated actin and actomyosin was measured a t 4 and 25 "C by means of a double-isotope technique. Regulated actin (2 mg/ml) and regulated actomyosin (6 mg/ml) were incubated for 30 min at the chosen temperature in 1 ml of the solution described above containing also 0.3 pCi of [3H]glucose and 5 mM glucose. For measurements of Ca2+ binding to regulated actomyosin in the presence of 1 mM MgATP, 20 mM creatine phosphate and 0.2 mg of creatine phosphokinase were included, MgC12 concentration was increased to 2 mM, and KC1 concentration was diminished to keep ionic strength constant; ATP was brought to 1.3 mM (4 "C) or 1.2 mM (25 "C) just before centrifugation. The suspensions (0.15-ml fractions) were centrifuged in a Beckman Airfuge at 165,000 X g for 30 min. When measurements were carried out a t 4 "C, the centrifuge was placed in a cold room. The supernatant samples were analyzed for calcium by atomic absorption and counted for ' T a and 3H. The association constants for metals and H' to EGTA and ATP, adjusted for use at the appropriate temperature and corrected for the proton activity (38), were employed in the calculations of free [Ca2+]. The pellets were suspended in 0.1 ml of 1 M NaOH, placed in a boiling water bath for 5 min, and then neutralized by addition of 0.1 ml of 1 M HCI and 5 p1 of 0.5 M sodium phosphate, pH 7.0. Bound calcium was calculated from the "Ca/3H ratio of the dissolved pellets relative to that of the supernatant solutions and from the total concentration of calcium in supernatants. Corrections were made for calcium binding to pure actin (in the case of regulated actin) and myosin combined with pure actin (for regulated actomyosin) in the same assay conditions. ATPase Assays-One-ml reaction mixture, equilibrated a t 25 "C, contained 0.2 to 0.4 mg of regulated actomyosin or 0.1 to 0.5 mg of myofibrils, 40 mM imidazole, pH 7.0, 70 mM KCI, 0.1 mM EGTA, 2 mM MgClZ, 4 mM phospho(enol)pyruvate, 0.02 mg of pyruvate kinase, and the desired concentrations of CaCl2. Reactions were initiated by adding ATP to 1.2 mM and stopped at various times with 0.25 ml Of &-cold 25% trichloroacetic acid. The supernatant obtained following a low speed centrifugation of the precipitate was assayed for inorganic phosphate (40) and calcium. The pCa values were calculated as shown above.
Fluorescence Measurements-The tyrosyl fluorescence of crayfkh TnC was measured in 10 mM HEPES, pH 7.0, and 80 m M KCl, at 4 and 25 'C, in a Baird Atomic FC 100 spectrofluorimeter equipped with a thermostated cuvette holder. The free CaZ+ concentrations were controlled using an EGTA buffer system as described above. The TnC concentration was 20 pg/ml. Upon excitation at 280 nm, emission was monitored at 310 nm. In a first approximation, the intensity of the fluorescence was considered as directly proportional to the absolute quantum yield. Ca2+ titration of crayfish TnC results in an enhancement of tyrosine fluorescence (Fig. 5). The best fit of the titration curve was obtained with a single binding constant K = 3.9 X lo6 M-' (4 "C). The binding constant is similar to that obtained from direct Ca2+-binding measurements for the Caspecific site. M F (2 mM) in itself has no effect on the fluorescence nor does it affect the Ca2+ titration curve (not shown). These results suggest that solely the Ca-specific site participates in the structural change in crayfish TnC upon Ca2+ binding. Moreover, Fig. 5 shows that the affinity of Ca2+ for the regulatory site varies significantly between 4 and 25 "C.

Caand Mg-binding
Assuming that the enthalpy change, hH, for Ca2+ binding to the Ca-specific site is independent of temperature, our data and the van't Hoff equation (38) yield a A H ' value of -8.1 kcal/mol site. Similar enthalpy changes evaluated from calorimetry were reported for Ca-binding sites of rabbit TnC (41) and of parvalbumin (42).

Ca-binding Studies on Crayfish TnI. TnC, Tn, and T m . T n
Complexes-Formation of the TnI . TnC complex increases the affinity of the Ca-specific site of TnC approximately 10fold (Table I), irrespective of the presence of M e . In whole T n (Table I) or T m . T n (Fig. 6, Table I) complexes, this site has an affinity slightly higher than that in the TnI-TnC complex. As for the low affinity Ca-Mg sites of TnC, their affinity is hardly increased, if at all, in the TnC-containing complexes (Fig. 6). The Ca-Mg sites are clearly not physiologically significant as far as Ca2+ is concerned because of their too low affinity for this metal. Fig. 6 shows that incorporation ot the crayfish Tm.Tn complex into actin filaments diminishes the binding constant of the Ca-specific site from 4 X lo6 M" to 2 X lo5 M" (Fig. 6, Table I). On the other hand, combining regulated actin with myosin in the absence of ATP (i.e. rigor) changes again the Ca-binding properties of TnC; its regulatory site has an affinity as high as that in the Tm . T n complex without actin (    Table I). Thus, the single Ca-specific site on crayfish TnC in regulated actin may exist in two affinity states: 1) in a low affinity state which is reminiscent of that on TnC free of other proteins; 2) in a high affinity state which is induced by the binding of myosin to regulated actin and resembles that for TnC present in the Tm. Tn complex. During steady state ATP hydrolysis, regulated actomyosin displays Ca-binding properties similar to those of regulated actin without myosin (Fig. 7, Table I).

7,
Calcium Dependence of Myofibrillar and Actomyosin AT-Pase-The ATPase activity of rabbit actomyosin, regulated by crayfish T m . T n complex, shows the same Ca2+ dependence as that of the crayfish myofibrillar ATPase (Fig. 81). Hence, the replacement of crayfish actin and myosin by the corre- sponding proteins from rabbit hardly changes the pCa/AT-Pase relationship. This close similarity is also reported here as evidence of the functional integrity of the reconstituted regulated actin used to characterize its Ca2+-binding properties (see also Figs. 6 and 7). As seen on Fig. 81, both actomyosin regulated by crayfish Tm.Tn complex and crayfish myofibrils display a steep rise in ATPase activity with free [Ca"]. Because there is only one Ca2+-binding site of physiological significance on crayfish TnC, such a cooperative-like behavior in calcium activation cannot be explained as a consequence of multiple sites on the TnC molecule. On rabbit skeletal TnC, there are four Ca2+-binding sites, and two of these are thought to regulate hydrolysis of MgATP (15). Therefore, it was of interest to compare, in the same experimental conditions, rabbit and crayfish myofibrils with respect to their pCa/ATPase relationship. The rabbit myofibrillar ATPase activity as a function of [Ca"'] is shown in Fig. 811. Both the position and the slope of the activation curve are not significantly different from those for crayfish myofibrils. Thus, in rabbit myofibrils also, the sharp response of ATPase to Ca2+ is controlled by factor(s) other than the requirement of more than one bound Ca2+ on TnC for activation.
The pCa/ATPase curve for crayfish myofibrils and for the crayfish Tm. Tn-regulated actomyosin was compared with the Ca-binding curves determined at the same temperature (25 "C) for crayfish Tm.Tn-containing actomyosin (Fig. 80. The relation between free [Ca"] and ATPase activity fits with neither "weak" (regulated actomyosin during steady state ATP hydrolysis) nor "strong" (regulated actomyosin, no ATP) binding of Ca2+ to TnC. The threshold [Ca"] for activation corresponds to the range of [Ca'+] where the Ca-specific site in its low affinity state starts to bind Ca" significantly. On the other hand, comparison of the activation curve and the "strong" binding of Ca2+ to TnC on regulated actomyosin (no ATP) shows that full activation is reached at [Ca"] where the regulatory site in its high affinity state approaches saturation. This suggests that during calcium activation of the actomyosin ATPase, the Ca-specific site on TnC displays at least two affinity states (one low and one high), the high affinity state being induced by interaction of myosin with regulated actin in the ATPase cycle.

DISCUSSION
Our Ca2+-and M$+-binding studies on crayfish TnC show that this protein has one Ca2+-binding site with an affinity in the range of physiological free [Ca"] and a high selectivity for this metal as compared to M$+ (regulatory Ca2+-specific site). TnC is thought to have evolved from a four-domain ancestor which was common to many intracellular calciumbinding proteins; each domain contained a calcium-binding site (43). In skeletal TnC, domains I and I1 include the two Ca2+-specific sites, whereas domains I11 and IV correspond to the two high affinity Ca2+-binding sites that bind Mg2+ competitively (Ca2+-Mg2+ sites); domains I1 and 111 contain each a distinct TnI-binding site (13, 44). Bovine cardiac TnC is analogous to the skeletal muscle protein but its domain I not longer binds Ca2+ (17, 44). In contrast, during invertebrate evolution, as many as three of the four putative domains of TnC have lost their calcium affinity of physiological significance. The presence of a single Ca-specific site on crayfish TnC is reminiscent of the situation prevailling in cardiac TnC where only domain 11 binds Ca2+ specifically. It is tempting, therefore, to postulate that the regulatory Ca2+-specific site of crayfish TnC is located in domain 11. However, a more precise relation between structure and function cannot be predicted before amino acid sequence data for crayfish TnC become available.
The Ca2+-binding properties of crayfish TnC again raise the question of the role played by domains I11 and IV on TnC. A structural role for the Ca2+-MP sites on skeletal TnC has been postulated, since these sites would always contain either Ca2+ or M P in vivo, and their occupancy by either metal is required for attachment of TnC to TnI in intact myofibrils (16). Crayfish TnC possesses about five sites with the same low affinity ( K = 1-2 X lo3 M-') for Ca2+ and M$+. If some of these Ca2+-MP sites were the mutated sites in domains I11 and IV, then one could postulate that their occupancy by M$+ in vivo is required for maintaining the integrity of the Tn complex; however, this turns out not to be the case. Unpublished results of ours indicate that removal of metal ions from whole crayfish myofibrils by extractions with metal chelators does not cause a dissociation of TnC from the myofibrils. This suggests that in crayfish TnC, there is a region that binds TnI irrespective of Ca2+ or Mg+. The fourdomain ancestor of calcium-binding proteins probably possessed only sites specific for Ca" as in calmodulin (43). Therefore, it is likely that evolution of domains I11 and IV in TnC proceeded in two ways, toward either the loss of ionbinding capacity (invertebrates) or the acquisition of high affinity Ca2+-Mp2+ sites (vertebrates). In both cases, these two domains maintain the structure of the Tn complex intact independently of the cytosolic levels of Ca2+, thus allowing the Ca2+-specific site(s) to function in the regulation of Ca2+ activation.
We have taken advantage of the simplicity of Ca2+ binding in crayfish TnC to study those features that are more difficult to discern in the vertebrate Tn-linked regulatory system because of the presence of multiple and diverse sites which bind Ca2+ in the range of its physiological concentrations. Previous studies on the TnI.TnC and whole Tn complexes from skeletal (15) and cardiac (17) muscle indicated tht the interaction of TnI and TnC results in a 10-to 20-fold increase in the affinities of both the Ca-Mg sites and the Ca-specific sites. This is also the case for TnC from crayfish with respect to its single Ca2+-specific site. Moreover, our Ca-binding studies reveal that while the regulatory site displays essentially the same affinity ( K = 4 X lo6 M-') in the crayfish Tm .
Tn complex as in the Tn complex, in regulated actin the Caspecific site exhibits a markedly lower affinity (K = 2 x lo5 "l).
As reported in our earlier studies (l), these data show that the actin filament affects the Ca-binding properties of TnC. Similar results have recently been reported by Zot et al. (45) for the rabbit system, where an effect of similar magnitude was found exclusively for the Ca-specific sites. Interestingly, the reduced affinity approaches the level of that of TnC in its isolated state; this suggests that the effect of actin, mediated through TnI and (or) transmitted via Tm to TnT and to TnI, depresses those interactions between TnI and TnC which increase the affinity of the Ca-specific site on TnC in the absence of actin. This is in agreement with studies showing that the binding of Tm-Tn to F-actin appears to be weaker in the presence of Ca" than in its absence (46). Indeed, it follows from thermodynamic reasoning that, if the binding of Ca2+ to TnC decreases the binding constant of Tm.Tn to F-actin, the binding of the Tm. Tn complex to actin filament decreases the binding constant of Ca2+ to TnC.
Bremel and Weber (14) first reported a slight increase in affinity of skeletal TnC for Ca2+ when regulated actin and myosin form complexes in the absence of ATP hydrolysis, i.e. under equilibrium conditions. Our studies on actomyosin, regulated by crayfish Tm . Tn, indicate that in the absence of ATP the interaction of myosin and regulated actin results in a 20-to 30-fold increase in the affinity of the Ca2+-specific site on TnC. The affinity of regulated actomyosin for Ca2+ (K = 7 X lo6 M-') is similar to that of the Tm .Tn complex.
Hence, in the rigor state where the Tm .Tn complex is "pushed" into the groove of the actin helix by myosin heads, the effect of actin on the Ca-specific site is suppressed. The rigor state can be assumed to correspond only to the final step of an actomyosin ATPase cycle. The affinity of actin to myosin-nucleotide intermediates of the cycle is lower than in the rigor state and varies over four orders of magnitude depending on the state of the nucleotide bound to myosin. Therefore, the effect of myosin intermediates on binding of Ca" to regulated actin is difficult to measure directly.
The steep pCa/ATPase curve of rabbit skeletal myofibrils has been attributed to the requirement that all four sites (23) or both Ca-specific sites (15) on TnC must be filled by Ca2+ for activation to occur. However, experimental data have been recently obtained that do not support such an explanation. First, as monitored by tension development of rabbit psoas fibers (25) and by ATPase of rabbit skeletal myofibrils (16, 24), the responses to Ca2+ are much too steep to be explained solely by a requirement for 2 or even 4 calcium ions bound on TnC. Second, the pCa/ATPase curve of cardiac myofibrils is sloping as sharply as that of skeletal myofibrils despite the suggestion that among three Ca-binding sites on cardiac TnC, only the site which is specific for Ca2+ is regulatory (17). Similarly, our studies show that crayfish myofibrils and rabbit actomyosin, regulated by crayfish Tm . Tn complex, display a steep rise of ATPase activity with [Ca"]. Moreover, we observe a close similarity in the Ca2+ dependence of ATPase activity with rabbit and crayfish myofibrils as well as with actomyosin regulated by rabbit and crayfish Tm . Tn complex.
Thus, in Tn-linked regulation of actomyosin ATPase, the requirement of more than one site occupied by Ca" on TnC does not play any role in the steep responses to Caz+.
The Ca-binding measurements carried out on the crayfish Tm. Tn-containing actomyosin during steady state ATP hydrolysis reflect essentially the noncooperative Ca-binding properties of regulated actin which is dissociated from myosin. With the simplest kinetic models, the increase in ATPase rate would be expected to be proportional to the fractional occupancy of the Ca-specific site in its low affinity state (K = 1-2 X lo5 M-') over the entire range of [Ca"]. However, this is not the case. When comparing the overall "weak" binding of Ca2+ with the ATPase activity as a function of [Ca2+], it appears that the only common range of [Ca'+] for both curves is the one where the Ca-specific site begins to bind Ca2+ significantly and activation starts (Fig. 8).
In order to explain the sensitive activation of isometric muscle contraction by Ca2+, Hill (47) has developed a model with two major ingredients in the regulation of contraction: (a) Ca2+ binds much more strongly on TnC if myosin is already attached to actin; (b) there is positive cooperativity in the system because of nearest neighbor Tm-Tm interactions which are responsible for the steep response to Caz+. The increased calcium affinity of myofilaments as a result of crossbridge interaction has recently been shown for muscle fibers in the isometric state (48). In considering the application of the model of Hill (47) to the regulation of actomyosin ATPase, we note that under the conditions used in our experiments (where the actomyosin or myofibrillar preparations are under no tension) the fraction of myosin bridges attached to actin at any instant is too small to alter the overall Ca2+ affinity of TnC in regulated actin (Fig. 7, Table I). This, of course, does not mean that the cross-bridge-induced increase in the cal-