Inhibition of actomyosin ATPase activity by troponin-tropomyosin without blocking the binding of myosin to actin.

Vertebrate skeletal muscle contraction is the result of a cyclic interaction of thick myosin filaments with the thin filaments, composed primarily of actin, troponin, and tropomyosin, causing these two sets of filaments to slide past each other (2, 3). This cycling is driven by the hydrolysis of ATP by myosin in a reaction which is activated by actin. When the sarcoplasmic reticulum lowers the free Ca2+ concentration from 10−5 to <10−7 m, muscle contraction ceases and the associated actin-activated myosin ATPase activity is inhibited. The proteins troponin and tropomyosin are responsible for this effect of Ca2+ on the interaction between myosin and actin (4, 5). 
 
The tropomyosin molecules lie end to end along the two grooves of the F-actin filament with each tropomyosin molecule binding to seven actin monomers (6). Troponin consists of three subunits, and one troponin molecule is bound to each tropomyosin molecule. The binding of Ca2+ to troponin determines the position of tropomyosin on the F-actin filament. At levels of Ca2+ low enough to cause relaxation, tropomyosin is positioned away from the central groove of the F-actin filament where it appears that it might interfere with the binding of the myosin cross-bridge (7–9). This structural work formed the basis of the steric blocking hypothesis which suggests that relaxation occurs when tropomyosin, in the “relaxed” position, physically blocks the binding of the myosin cross-bridge to actin. Three-dimensional reconstructions from electron micro-graphs have suggested that the myosin cross-bridge and the tropomyosin molecule may be in close contact with each other on the actin filament, a requirement for a steric blocking type model (10, 11). 
 
The steric blocking model predicts that in the absence of Ca2+ the degree of association of S-11 should be much weaker with regulated actin than with unregulated actin. In fact, Greene and Eisenberg (12) have recently demonstrated that, in the absence of Ca2+, the binding of S-1·ADP to regulated actin is strongly inhibited in a cooperative manner. At low levels of saturation of the actin filament with S-1·ADP, the binding of S-1·ADP to the regulated actin filament is about 103 weaker than at high levels of saturation. However, the fact that S-1·ADP binds weakly to regulated actin does not prove the steric blocking model since, in relaxed muscle, the cross-bridges normally exist with bound ATP (or ADP · Pi) and not bound ADP (13,14). Therefore, the steric blocking model predicts that troponin-tropomyosin should inhibit the binding of S-1·ADP·Pi as well as S-1·ADP to regulated actin in the absence of Ca2+. 
 
Using stopped flow turbidity measurements, we have previously measured the effect of Ca2+ on the association of S-1 · ATP and S-1 · ADP · Pi with regulated actin (15). Surprisingly, in the absence of Ca2+, the binding constant of S-1 · ATP or S-1 · ADP · Pi to regulated actin was only decreased to 56% of the value in the presence of Ca2+ although the rate of ATP hydolysis under the same conditions was decreased to 6% of the rate with Ca2+ present. These data suggest, in disagreement with the steric blocking model, that inhibition of the rate of ATP hydrolysis, in the absence of Ca2+, is not the result of inhibition of the binding of S-1 to regulated actin. 
 
In the present study, we have reinvestigated this problem using a different and more direct measurement of binding. Free S-1 was separated from actin-bound S-1 in the presence of ATP by rapid centrifugation in an air-driven ultracentrifuge and the free S-1 concentration was then determined by an ATPase assay. As in our earlier turbidity studies, we find very little effect of troponin-tropomyosin on the binding of S-1 to regulated actin in the presence of ATP. Similar confirmation of our turbidity results has already been reported by Wagner and Giniger (16). In the present study, we have also measured the binding at a higher ionic strength (50 mm) and here too have found no correlation between the inhibition of ATPase rate and the binding of S-1·ATP or S-1 · ADP · Pi to regulated actin. Finally, we demonstrate that the removal of Ca2+ affects the rate of regulated actin-activated S-1-ATPase activity primarily by lowering the maximum ATPase rate (Vmax) rather than the apparent binding constant of S-1 to actin (KATPase). These data imply that, in the absence of Ca2+, troponin-tropomyosin inhibits the ATPase activity by inhibiting a kinetic step in the cycle of ATP hydrolysis, perhaps Pi release.

blocks the binding of the myosin cross-bridge to actin. Three-dimensional reconstructions from electron micro-graphs have suggested that the myosin cross-bridge and the tropomyosin molecule may be in close contact with each other on the actin filament, a requirement for a steric blocking type model (10,11). The steric blocking model predicts that in the absence of Ca 2+ the degree of association of S-1 1 should be much weaker with regulated actin than with unregulated actin. In fact, Greene and Eisenberg (12) have recently demonstrated that, in the absence of Ca 2+ , the binding of S-1·ADP to regulated actin is strongly inhibited in a cooperative manner. At low levels of saturation of the actin filament with S-1·ADP, the binding of S-1·ADP to the regulated actin filament is about 10 3 weaker than at high levels of saturation. However, the fact that S-1·ADP binds weakly to regulated actin does not prove the steric blocking model since, in relaxed muscle, the cross-bridges normally exist with bound ATP (or ADP · P i ) and not bound ADP (13,14). Therefore, the steric blocking model predicts that troponin-tropomyosin should inhibit the binding of S-1·ADP·P i as well as S-1·ADP to regulated actin in the absence of Ca 2+ .
Using stopped flow turbidity measurements, we have previously measured the effect of Ca 2+ on the association of S-1 · ATP and S-1 · ADP · P i with regulated actin (15). Surprisingly, in the absence of Ca 2+ , the binding constant of S-1 · ATP or S-1 · ADP · P i to regulated actin was only decreased to 56% of the value in the presence of Ca 2+ although the rate of ATP hydolysis under the same conditions was decreased to 6% of the rate with Ca 2+ present. These data suggest, in disagreement with the steric blocking model, that inhibition of the rate of ATP hydrolysis, in the absence of Ca 2+ , is not the result of inhibition of the binding of S-1 to regulated actin.
In the present study, we have reinvestigated this problem using a different and more direct measurement of binding. Free S-1 was separated from actin-bound S-1 in the presence of ATP by rapid centrifugation in an air-driven ultracentrifuge and the free S-1 concentration was then determined by an ATPase assay. As in our earlier turbidity studies, we find very little effect of troponin-tropomyosin on the binding of S-1 to regulated actin in the presence of ATP. Similar confirmation of our turbidity results has already been reported by Wagner and Giniger (16). In the present study, we have also measured the binding at a higher ionic strength (50 mM) and here too have found no correlation between the inhibition of ATPase rate and the binding of S-1·ATP or S-1 · ADP · P i to regulated actin. Finally, we demonstrate that the removal of Ca 2+ affects the rate of regulated actin-activated S-1-ATPase activity primarily by lowering the maximum ATPase rate (V max ) rather than the apparent binding constant of S-1 to actin (K ATPase ). These data imply that, in the absence of Ca 2+ , troponin-tropomyosin inhibits the ATPase activity by inhibiting a kinetic step in the cycle of ATP hydrolysis, perhaps P i release.

Actin-activated ATPase Assays
Actin-activated S-1 ATPase activities were measured at 25 °C both by measuring the rate of liberation of [ 32 P]P i from [γ-32 P]ATP (20) and by the pH-stat method (21). Assays based on [ 32 P]P i , were carried out in 1.5 ml of solution containing 1 mM ATP, 3 mM MgCl 2 , 1 mM EGTA (or 0.5 mM CaCl 2 ), 10 mM imidazole, pH 7.0, with or without 32 mM KC1, giving 18 or 50 mM ionic strength, respectively. A single assay usually consisted of four or five time points. Measurements with the pH-stat were performed in a 3.5-ml solution of similar composition except that 10 mM imidazole was replaced by 2 mM imidazole and 4 mM KC1.

Binding Assay
Measurement of binding of S-1 to actin in the presence of ATP is made difficult by the rapid hydrolysis of ATP by S-1, especially in the presence of Ca 2+ or in the absence of regulatory proteins. In an earlier paper, we had circumvented this problem by using stopped flow absorbance measurements which were completed prior to appreciable ATP hydrolysis (15). In the present study, we have directly measured the association of S-1 with actin by rapidly sedimenting the actin-bound S-1 and measuring the concentration of free S-1 in the supernatant by the NH 4 + -EDTA ATPase assay.
Binding of S-1 to actin or regulated actin at 18 mM ionic strength was measured at 25 °C in 1 mM ATP, 3 mM MgCl 2 , 1 mM EGTA or 0.5 mM CaCl 2 , 10 mM imidazole, pH 7.0, in a total volume of 1.5 ml. At 50 mM ionic strength, ATP was increased to 2 mM, MgCl 2 was increased to 4 mM and 27 mM KCl was included. The binding mixture, excluding S-1, was equilibrated with stirring in a thermostatted water jacket. S-1 was added in a volume of 50-100 μl and stirred briefly. Fractions of 0.2 ml were centrifuged in a Beckman Airfuge at 178,000 × g for 20 min. The final sample temperture was 25 ± 1 °C. The supernatant was assayed for free S-1 concentration by the NH 4 + -EDTA ATPase assay. The total time from the addition of S-1 to the binding mixture until the start of centrifugation was less than 3 min.
The NH 4 + -EDTA ATPase activity of S-1 was measured at 25 °C by the release of [ 32 P]P i from [γ-32 P]ATP in a solution containing 5 mM ATP, 0.4 M NH 4 C1, 35 mM EDTA (Tris salt), 25 mM Tris, pH 8.0. This condition is similar to that used by Seidel (22) except for a large increase in the EDTA concentration for chelation of 1 mM Mg 2+ which was present in the supernantant from the binding studies. This assay was linear for at least the first 25% of the reaction and was directly proportional to the S-1 concentration over the entire range investigated from 0.004 to 0.23 μM S-1 (Fig. 1). Note that for clarity several points in the range 0.004 to 0.02 μM S-1 have been omitted from Fig. 1. Addition of 8 μM actin to the assay had no effect on the rates. This is roughly five times the maximum amount of actin expected to be carried over from the binding studies.
The sedimentation time of actin was estimated by measuring the concentration of actin remaining in the supernatant, by the Lowry protein determination, after various times of centrifugation. Under our conditions, 75% of the actin was sedimented at 10 min, 95% at 15 min, and 98% at 20 min. We have observed no detectable sedimentation of 1 μM S-1 in the absence of actin after a 20-min centrifugation, as determined by NH 4 + -ATPase activity, although at 0.06 μM S-1 up to 10% of the ATPase activity was lost, probably due to slight denaturation. To avoid this problem, control experiments measuring sedimentation of S-1 in the absence of actin were carried out in the presence of either troponin-tropomyosin or 2 mg/ ml bovine serum albumin.
The S-1 concentrations used for the binding assays were 1 μ M in the presence of EGTA and 0.06 μ M in the presence of Ca 2+ . The concentration of S-1 was limited in each case by the amount of ATP hydrolysis which occurred during the centrifugation. As shown in the first three lines of Table I, these concentrations of S-1 were sufficiently low that a large fraction of the ATP remained intact at the end of the binding assay. It was particularly important in this study to avoid overestimation of the binding in the presence of EGTA. This was further tested by measuring the binding at S-1 concentrations different from the 1 μ M typically used (Table  1). Decreasing the S-1 concentration 4-fold from 1.1 to 0.23 μM had virtually no effect on the fraction bound. Increasing the concentration 3-fold significantly increased the fraction of S-1 bound as a result of excessive ATP utilization. This can be compared to the case in the absence of ATP where all of the S-1 is bound to actin. Therefore, it is likely that the binding that we are measuring at 1 μM S-1 concentration, in the presence of ATP, represents the binding of the S-1 substrate states S-1·ATP and S-1·ADP·P i to actin.

RESULTS
We first examined the relationship between the regulated actin-activated ATPase rate and the fraction of S-1 bound to regulated actin at 18 mM ionic strength, the same condition used in our earlier work. Fig. 2A is a direct plot of the actin-activated S-1 ATPase activity, in the presence of excess native tropomyosin, as a function of the concentration of regulated actin. All of the rates have been corrected for the rate of ATP hydrolysis by S-1 alone (0.09 s −1 ). Both in the presence and absence of Ca 2+ , the ATPase rates increase with regulated actin concentration although the magnitudes of the rates are much greater in the presence of Ca 2+ than in the absence of Ca 2+ . The ATPase rates for regulated actin estimated from the time to maximum turbidity rise on the stopped flow (15) are roughly twice the values reported here. This is probably because the stopped flow values are averaged over the entire reaction time although the rate of ATP hydrolysis increases with time as the ATP concentration becomes low (23). In addition, the stopped flow studies used a much higher concentration of S-1 (20-40 μM) which may have partially "turned on" the actin filament (24). In contrast to the ATPase activity which was greatly affected by Ca 2+ , the degree of association of S-1 with regulated actin is virtually the same in the presence and absence of Ca 2+ . Therefore, with ATP present in the absence of Ca 2+ , the troponin-tropomyosin complex inhibits actin activation of the S-1 ATPase rate without blocking the binding of S-1 to actin.
Binding constants for the association of S-1 to unregulated or regulated actin were determined from double reciprocal plots of the fraction of S-bound versus free actin concentration (Fig.  3). The best fits to the binding data were determined using the Marquardt compromise (25). In short, both methods agree that, in the presence of ATP, S-1 binds to actin with about the same affinity whether or not native tropomyosin is present and whether or not Ca 2+ is present. Both methods also show that at 18 mM ionic strength in the absence of Ca 2+ the inhibition of the actin-activated S-1 ATPase rate by native tropomyosin is not the result of inhibition of binding of S-1 to actin.
We next repeated these experiments at 50 mM ionic strength to determine if there was a similar lack of correlation of ATPase rate with the fraction of S-1 bound at a higher ionic stength. Fig.  4 shows that, at 50 mM ionic strength, native tropomyosin remains an effective inhibitor of the actin-activated ATPase rate in the absence of Ca 2+ . The rate in the presence of EGTA is generally 2% of the rate in the presence of Ca 2+ over our working range. All rates were corrected for the rate of ATP hydrolysis by S-1 alone (0.1 s −1 ).
The association of S-1 with regulated actin in the presence of ATP at 50 mM ionic strength is shown in Fig. 5. Binding at 50 mM ionic strength was measured with 2 mM Mg-ATP rather than 1 mM Mg-ATP to compensate for a higher rate of ATP hydrolysis in the presence of Ca 2+ at 50 mM ionic strength than at 18 mM ionic strength (compare Figs. 2 and 4). The association constant in the presence of Ca 2+ is roughly 3 × 10 3 M −1 which is similar to the value of 2 × 10 3 M −1 obtained in the absence of Ca 2+ . In the absence of native tropomyosin, the binding constant is also about 3 × 10 3 M −1 (data not shown). These values of the binding constants could be slightly in error because it was not possible to work at a higher actin concentration where more binding occurs. Nevertheless, it is clear from Fig. 5 that the situation at 50 mM ionic strength is analogous to that at 18 mM ionic strength; although native tropomyosin greatly inhibits the actin-activated ATPase rate in the absence of Ca 2+ , it has little effect on the degree of association of S-1 to actin in the presence of ATP.
Our binding studies suggest that, in the absence of Ca 2+ , native tropomyosin inhibits the actinactivated S-1 ATPase rate by affecting a rate process rather than the binding of S-1 to actin at a saturating ATP concentration. On this basis, it might be expected that the effect of troponintropomyosin on the double recriprocal plot of ATPase versus actin would be to change V max rather than K ATPase . In contrast to this prediction, several previous studies (one from our laboratory) suggested that the effect of troponin-tropomyosin was on K ATPase rather than V max (26,27). However, these studies were carried out at relatively low actin concentrations and if, as is often the case, K ATPase were stronger than K binding , the actin-activated ATPase rate might be quite high, although very little binding of S-1 to actin was occurring during steady-state ATP hydrolysis. Therefore, we reinvestigated the effect of troponin-tropomyosin on the double reciprocal plot under conditions where there is considerable binding of S-1 to regulated actin in the presence of ATP.
The open symbols in Fig. 6 show that, as the ratio of troponin-tropomyosin to actin is increased, there is marked inhibition of the ATPase activity in the presence of EGTA. When the molar ratio of troponin-tropomyosin to actin is increased from 0 to 1.5/7, K ATPase increases 3-fold (from 20 to 60 μ M) but the major change is in V max which decreases to 4% of the initial value (from 22 to 0.8 s −1 ). Increasing the ratio of troponin-tropomyosin to actin from 1.5/7 to 4.7 resulted in no further inhibition. The addition of Ca 2+ to the actin fully saturated with troponintropomyosin (solid symbols) yields a double reciprocal plot very similar to the plot obtained in the absence of troponin-tropomyosin. Compared to the plot obtained in the absence of Ca 2+ , V max increases 22-fold (from 0.8 to 18 s −1 ) and K ATPase becomes about 1.5-fold stronger (60 to 40 μ M). Therefore, the inhibition of the actin-activated ATPase activity caused by troponin-tropomyosin in the absence of Ca 2+ is mainly due to an effect on V max with a much smaller effect on K ATPase .

DISCUSSION
The results of this study suggest that inhibition of the actin-activated S-1 ATP hydrolysis by native tropomyosin, in the absence of Ca 2+ , is not due to a steric blocking of the association of S-1 to actin. We have found, in agreement with our earlier work (15), that, in the presence of ATP, the affinity of S-1 for regulated actin is relatively Ca 2+ insensitive. In contrast, the ATPase rate in the absence of Ca 2+ is decreased to about 4% of the rate in the presence of Ca 2+ . The lack of correlation between binding in the presence of ATP and the ATPase rate occurs both at low (18 mM) and moderate (50 mM) ionic strengths. Since the regulatory proteins troponin and tropomyosin have little effect on the binding of S-1 to actin in the presence of ATP, it is likely that these regulatory proteins affect a rate process in the pathway of ATP hydrolysis. This conclusion is supported by our steady state kinetic measurements. Fig. 6 shows that, for the most part, native tropomyosin acts as a noncompetitive inhibitor of ATP hydrolysis in the absence of Ca 2+ . These kinetic results strongly indicate that native tropomyosin and S-1-ATP do not compete for the same site on actin. Inhibition of the ATPase rate is primarily the result of a large decrease in the maximum velocity which suggests that a kinetic step is being affected. In considering which kinetic step is affected by troponin-tropomyosin, we will refer to the model of Stein et al. (17) since it includes all of the proposed kinetic steps (Fig. 7).
The work of Greene et al. (12), confirmed by Trybus and Taylor (28) and Murray et al. (29), has shown that troponin-tropomyosin has a major effect on the binding of M and MD (for abbreviations, see kinetic model in Fig. 7) to actin. Troponin-tropomyosin greatly inhibits this binding at low ratios of M or MD to actin while at high ratios the binding becomes even stronger than in the absence of troponin-tropomyosin. Hill et al. (30) have modeled this cooperative response in terms of two states of the actin filament: a weak binding state and a strong binding state. Ca 2+ affects the binding of S-1 and S-1 · ADP by changing the equilibrium constant between these two states.
Although the cooperative binding of S-1 induced by troponin-tropomyosin is of great interest, it cannot explain the ability of troponin-tropomyosin to inhibit the acto-S-1 ATPase activity; how strongly M or MD bind to actin will not directly affect the rate of ATP hydrolysis. Of course, if troponin-tropomyosin were to affect the binding constant of M · D · P iN , to actin (K 14 ), it would affect the actin-activated ATPase activity since K ATPase ≈ K 14 k −7 /( k −8 + k 10 ) (17). However, this effect would manifest itself as an effect on -K ATpase , not on V max , i.e. increasing the actin concentration would overcome the inhibitory effect of the troponintropomyosin. In fact, Fig. 6 shows that the major effect of troponin-tropomyosin is on V max . Therefore, it seems very unlikely that tropomyosin acts by weakening K 14 . Our data clearly show that the binding constants of MT (K 3 ) and M·D·P iR (K 13 ) to actin are essentially unaffected by troponin-tropomyosin. Therefore, troponin-tropomyosin must be affecting a step other than the binding of one of the S-1 states to actin; it must be affecting a kinetic step which occurs when S-1 is attached to actin.
Troponin-tropomyosin cannot inhibit the acto-S-1 ATPase activity by affecting the rate of the ATP hydrolysis step or the rate of transition from the refractory to the nonrefractory state when the S-1 is bound to actin because these steps occur at almost the same rate when the S-1 is detached from actin (17,31). Since S-1·ATP and S-1·ADP·P iR are in rapid equilibrium with acto-S-1. ATP and acto-S-1 · ADP · P iR , respectively, inhibition of these steps would not inhibit the acto-S-1 ATPase activity at moderate actin concentrations. Release of ADP cannot be the rate-limiting step because then the major species present in the inhibited system would be MD which binds tightly to actin; we find that S-1 binds weakly to actin in the inhibited system. Therefore, it seems most likely that the step which is inhibited by troponin-tropomyosin is the conformational change associated with P i release from A·M·D·P iN . P i release is, of course, very slow in the absence of actin. Strong inhibition of P s release, in the presence of actin, would greatly decrease the value of V max obtained from the double reciprocal plot of ATPase activity versus actin. At the same time, decreasing the rate of Pi release (k 10 ) would make K ATPase ≈ K 13 since K ATPase ≈ K 14 k −7 /( k −8 + k 10 ) ≃ K 13 k −8 /( k −8 + k 10 ) (17). This would explain why troponin-tropomyosin has a small effect on K ATPase as well as a large effect on V max .
It is of interest to consider how the inhibitory effect of troponin-tropomyosin on P i release is related to its effect on the binding of S-1·ADP to actin. One of the most striking features of troponin-tropomyosin action is the marked difference between its effect on the binding of S-1·ATP (or S-1·ADP·P i ) to actin compared with its effect on S-1 and S-1·ADP binding.
Eisenberg and Greene have suggested that the S-1 states with bound P i (M·T and M·O·P i ) bind to actin at a ~90° angle while states without bound P i (M·D and M) bind at a ~45° angle (13). This hypothesis provides a natural explanation for the differential effect of troponintropomyosin on the two groups of states. Troponin-tropomyosin would cooperatively inhibit the binding of states which attach at a 45° angle but would have no effect on states which bind at a 90° angle.
This hypothesis also provides a natural explanation for the inhibitory effect of troponintropomyosin on the rate of P i release; the troponin-tropomyosin would interfere with the rotation of the S-1 from the 90° state to the 45° state and thus inhibit the release of P i from the acto-S-1. Of course, if there were sufficient AMD complexes occurring along the regulated actin filament to push the troponin-tropomyosin complex over to the strong form, troponintropomyosin would no longer interfere with the rotation of the 90° state to the 45° state and thus P i release would not be inhibitied.
This hypothesis suggests that, although troponin-tropomyosin is not acting by sterically blocking the binding of S-1 · ADP·P i to actin, it may act, in a sense, by "sterically blocking" the rotation of S-1 and the associated P i release. Of course, this interference of rotation of the S-1 would not be an all or none effect. Rather the activation energy associated with S-1 rotation would be increased because movement of the troponin-tropomyosin as well as S-1 would be required during P i release. Therefore, the rate constant for P i release would be decreased. On this basis, the role of Ca 2+ might be either to partially shift the weak form of actin to the strong form or to shift the position of the tropomyosin on the actin so that rotation of the S-1 is not associated with as high an activation energy and thus the rate of P i release is increased. We therefore conclude from out data that troponin-tropomyosin does not sterically block the binding of S-1·ATP and S-1·ADP·P, to actin. However, it may interfere with the rotation of the S-1 on the actin, thus increasing the activation energy for this step and decreasing the rate of P i release. This interference may be a direct steric effect or an indirect conformational change in the actin.
Our finding that Ca 2+ has little effect on the binding of S-1 · ADP or S-1·ADP·P i to regulated actin in vitro opens up the possibility that some fraction of the myosin cross-bridges is attached to actin in relaxed muscle. In fact, three possibilities arise. First, cross-bridges in state M·T or M·D·P i may not be attached to actin in either active or relaxed muscle. Whether they are attached depends on the rate of attachment of the cross-bridges to actin in vivo, i.e. on the "effective actin concentration." An experimental value for the rate of attachment of the crossbridge is not yet available, but calculations based on the rate of diffusion of the cross-bridge suggest that M· T and M·D·P i might well be attached to actin in vivo (32). A second possibility is that although M·T and M·D·P i bind to actin in active muscle, something other than troponintropomyosin prevents their binding in relaxed muscle. For example, the structure of the myosin filament in relaxed muscle may prevent cross-bridge attachment. But when Ca 2+ binds to troponin, it may allow force-producing (45° state) bridges to form which in turn may cooperatively change the structure of the myosin filament so that more cross-bridges can attach.
The third possibility, of course, is that cross-bridges are attached to actin in relaxed muscle. Relaxed muscle may be easily extensible because the attached cross-bridges are in rapid equilibrium with detached cross-bridges. Slipping of the attached cross-bridges along actin may result in only a small viscosity effect. 2 Data from recent x-ray diffraction (33) and ESR studies (34) seem to argue against attached cross-bridges in relaxed muscle. However, x-ray studies may not detect the attached cross-bridges because it is possible that less than half of the myosin molecules are attached by one head so that the mass of attached cross-bridges in active muscle is ¼ of the mass of attached cross-bridges in rigor. This would lead to an x-ray pattern in active muscle which is less than 1/16 as strong as in rigor muscle, making it rather difficult to detect. As for physical methods like ESR, it is possible that cross-bridges attached at a 90° angle are somewhat flexible both at their point of attachment to actin and in the neck region of the S-1 molecule near S-2. This could mean that cross-bridges attached to actin in relaxed muscle are somewhat more flexible than cross-bridges in rigor muscle. This is one of the possibilities suggested by Thomas et al. (35).
Further work will be required to determine which of the three possibilities discussed above is correct. We can conclude from our work that, whether or not cross-bridges are attached to actin in relaxed muscle, troponin-tropomyosin certainly does not act by simply blocking the binding of cross-bridges to actin. Troponin-tropomyosin inhibits a kinetic step in the ATPase cycle.