The working stroke upon myosin–nucleotide complexes binding to actin

Abstract

For many years, it has been known that myosin binds to actin tightly, but it had not been possible to devise a muscle fiber experiment to determine whether this binding energy is directly coupled to the working stroke of the actomyosin crossbridge cycle. Addressing the question at the single-molecule level with optical tweezers allows the problem to be resolved. We have compared the working stroke on the binding of four myosin complexes (myosin, myosin-ADP, myosin-pyrophosphate, and myosin-adenyl-5′yl imidodiphosphate) with that observed while hydrolyzing ATP. None of the four was observed to give a working stroke significantly different from zero. A working stroke (5.4 nm) was observed only with ATP, which indicates that the other states bind to actin in a rigor-like conformation and that myosin products (M.ADP.P_i), the state that binds to actin during ATPase activity, binds in a different, prestroke conformation. We conclude that myosin, while dissociated from actin, must be able to take up at least two mechanical conformations and show that our results are consistent with these conformations corresponding to the two states characterized at high resolution, which are commonly referred to in terms of having open and closed nucleotide binding pockets.

Evidence from electron micrographs for different conformations of myosin led to the rowing model of actomyosin (AM) crossbridge action (1, 2) in which myosin binds to actin in one conformation, undergoes a working stroke, and detaches in a second conformation. The Lymn–Taylor scheme (3) describing the biochemical kinetics of AM provided a natural match to the mechanical model (Fig. 1). The detached myosin products (M.ADP.P_i) state bound to actin, and the working stroke occurred in association with product release. The binding of ATP facilitated dissociation of actin, and its hydrolysis took place while myosin was dissociated. The model postulated that the hydrolysis step is associated with repriming the head from the postpower-stroke structure back to the prepower-stroke form, although there was no evidence on this point at the time. Based on the observation that the detached states, myosin-ATP and M.ADP.P_i, behaved in a similar manner with respect to actin binding, Eisenberg and collaborators (4) favored a model in which there was a single detached conformation of myosin.

Fig. 1.

The Lymn–Taylor alignment of biochemical states with the crossbridge cycle. Pr = Products, ADP.P.

Measurement of the ATP binding constant (5) and the actin binding constant (6) were crucial steps in allowing the basic energetics of the AM mechanism to be elucidated. Much of the free energy of ATP hydrolysis is associated with actin binding to the M.ADP.P_i state and forming the rigor AM state (7), the part of the scheme that must encompass the working stroke. The myosin state in the absence of nucleotide binds even more tightly to actin, and if it is the energy of AM binding that powers the mechanical action, it would suggest that a working stroke would also result from myosin binding to actin. This idea is consistent with the views of Eisenberg (4) and the “3G” model of contraction (8). In the latter model all myosin states exist in a single myosin conformation and actin binding occurs in two steps, the first being the binding and formation of a weakly bound complex (A state) and the second being the conversion to a tightly bound complex (R state). It was natural to assume that the weak-to-strong (or A-to-R) transition corresponded to the working stroke.

In recent years, a scheme, closely related to that of Lymn and Taylor (3), has been developed based on the crystal structures of myosin subfragment 1 (S1). When crystallized in a variety of nucleotide states, two forms are common, which differ in a number of regions, including the nucleotide binding pocket, the switch 2 region, and the cleft between the upper and lower 50-kDa domains. The two forms generally are labeled based on the state of the nucleotide binding pocket as closed and open. The transition from the closed to the open form appears to be linked with movement of the lever arm and has been associated with the working stroke. The transition from open to closed occurs before the hydrolysis step and has been associated with repriming (9).

These models can be tested directly at the level of a single myosin molecule by using optical tweezers to hold an actin filament taut between two trapped beads and presenting it to a myosin molecule on a third fixed bead (10). Displacements of the actin beads “dumbbell” are monitored and used to detect attachment events; the difference between the mean displacements in free and bound periods gives the myosin working stroke, which under conditions of ATP turnover is ≈5–6 nm. To isolate the working stroke event in the biochemical cycle, we have investigated the binding of myosin and myosin–nucleotide complexes in the absence of ATP, where transitions are restricted to actin binding and loss of nucleotide. Although these transitions are reversible and no net work can be extracted from the dumbbell, any associated working stroke would still be detected as described in Materials and Methods. It is important to emphasize that the observed working stroke reflects the difference in orientations between the bound state and the dissociated state at the moment of attachment. If there is a mixture of different dissociated conformations, the relative rates of actin binding become important.

Materials and Methods

Biochemistry. The regulatory light chain (RLC) of rabbit myosin S1 was exchanged for a Penta-His-, biotin-dependent transcarboxylase (BDTC)-tagged chicken gizzard RLC. The coding sequence of the BDTC-RLC fusion protein (11) was cloned into a pET16b expression vector. The expression vector was introduced into Escherichia coli, BL21 OMPT⁻ ION⁻. Protein expression was carried out by using standard techniques. The BDTC-RLC fusion protein was obtained by solubilizing the inclusion bodies in 6 M guanidine·HCl, 20 mM Tris·HCl, 150 mM NaCl, and 10 mM DTT, pH 7.5. The solubilized fusion protein was stored at −20°C. The exchange of the light chain was carried out as described (12) with a 1:2 molar ratio of myosin S1 to BDTC-RLC at 30°C for 30 min in 50 mM Hepes (pH 7.5), 500 mM NaCl, 10 mM EDTA, and 10 mM DTT. For single-molecule experiments, nitrocellulose cover slips were coated with 1 mg/ml BSA in 25 mM Hepes, pH 7.4/25 mM KCl/4 mM MgCl₂ (buffer A) for 1 min, washed with buffer A, incubated with 0.3–1 μg/ml BDTC-RLC myosin S1 for 10 min, and then washed again with buffer A before adding the (F-actin)-bead reaction mix. The reaction mix included a standard deoxygenating system (1% β-mercapto-ethanol, 0.2 mg/ml catalase, 1 mg/ml glucose oxidase, and 2 mg/ml glucose) and hexokinase [0.01–0.1 μg/ml for the experiments involving ADP and adenyl-5′yl imidodiphosphate (AMPPNP)]. Actin bead dumbbells were made by using biotinylated actin and trapped neutravidin beads as described (13). Despite extensive washing and blocking, we found that it was difficult to simultaneously use the biotin-avidin link to bind myosin S1 to a fixed bead. However, as detailed below, attachment of S1 with biotinylated light chain to a BSA-precoated surface resulted in relatively specific attachment via the light chain. The binding constants of myosin for ADP, PP_i, and AMPPNP are all sufficiently high that detached myosin was saturated with ligand even at the lowest concentrations used.

Trapping. The optical tweezers apparatus and methods of calibration, etc. have been described (14). All experiments were done at room temperature. Previously, the two quadrant detectors (QDs) used to monitor trapped bead position were illuminated by splitting the whole image, thus reducing the light intensity by a factor of 2. The field was halved with a 45° mirror so as to project the image of each bead onto a separate QD at full intensity. The separation of the QDs was matched to that of the image of the trapped beads. The sensitivities of the QDs were calibrated by using a stepper motor to flip a thin (0.5 mm) microscope slide ± 7.5° so as to give a known lateral displacement of the bead image (Fig. 2). Positive feedback was generally applied to both laser traps to extend the linear range of the force-extension curve along the actin axis (14). The positions of the beads were recorded at 10 kHz for periods of 100 s or for conditions with long interactions, at 5 kHz for periods of 400 s. Interactions were detected by the reduction in displacement variance during bound periods, using the Hidden Markov method (15).

Fig. 2.

Calibration of QD by displacement of bead image. (Insets) Illustration of the shift in optical path after flipping the microscope slide (S) ± 7.5°.

Measurement of the Working Stroke. The working stroke of a myosin–nucleotide complex can be estimated from the difference in the average positions of the dumbbell in free and bound periods, provided that the averaging is carried out event by event, rather than in time (16). A nonzero difference in the time-averaged displacements would indicate that net work was done in moving in the traps, which is not consistent with the equilibrium conditions. In principle, event averaging will detect any working stroke made under equilibrium conditions. Detailed balancing requires that detachment be slower at negative strains; positive displacements in bound periods are balanced by a smaller number of negative displacements of longer duration, such that the time-averaged displacement on binding is zero. It was only possible to satisfactorily test whether these conditions were met for myosin complexes for which there were a reasonably large number of interactions (PP_i and AMPPNP), and for those cases the condition was met within experimental error.

The event-averaging method of measuring the working stroke also assumes that the actin filament binds myosin uniformly with no specific sites of interaction. We found this not to be the case (14) and that an individual displacement was the sum of a binding stroke, produced by thermal fluctuations and a working stroke, produced by the myosin crossbridge cycle. The binding stroke thus depends on the relative position of the myosin to the target zone. To average this effect to zero, it is necessary to move the actin past the myosin by an integral number of actin repeats (15). Fig. 3 shows the positions at which interactions take place during the course of the record, and it can be seen that first one target zone and then the second comes into view of the myosin and that within each target zone the individual monomers are clearly evident. Similar target zone stripes were seen for all of the myosin complexes studied, and an example is shown for PP_i (see Fig. 5). However such monomer stripes were less evident in cases where the frequency of interaction was low. All of our measurements of the working stroke were made by averaging over one or more actin repeats. The working stroke is measured relative to a baseline derived from the average position of the free dumbbell. Movement of the traps during a bound event is small, and the resulting movement of the beads is negligible because of the high ratio of myosin stiffness to trap stiffness.

Fig. 3.

(a) Plot of time versus position of myosin binding events in the presence of 5 μM ATP. In this experiment the dumbbell was moved two actin repeats (≈74 nm) past the BDTC-RLC S1-coated fixed bead during the 100-s run, which is represented by the broad light gray arrow, the width of which represents thermal noise (2 × SD). (b) The actin diagram relates the position of the monomers to the bound events. The myosin molecule can only access each monomer for a restricted period during the overall motion of the dumbbell past the myosin. During the early part of the record the interaction is with a group of monomers within one target zone (lower left), and during the latter part, with a group within the next target zone (upper right). The working stroke from this record was 5.6 nm.

Fig. 5.

Ten seconds of 1 mM PP_i trace at normal ionic condition (25 mM KCl) showing merged events (a) and 10 s at higher ionic strength (100 mM KCl) with clean events (b). For most purposes the dumbbell can be regarded as a rigid object in a single trap with a stiffness resulting from the two traps acting in parallel. The combined trap stiffness in this experiment was 0.07 pN/nm: variance ratio for best bead 12. (c) Plot of time versus position of myosin binding events similar to Fig. 3. In this case the ramp is 124 nm and three target zones are evident. The broad light gray arrow represents the motion of the dumbbell, the width being the thermal noise (2 × SD). (d) Rate of dissociation against [PP_i]. (e) Histogram of interactions all based on ramps from a single dumbbell [PP_i] at 0.5 mM.

Kinetics of Interaction of Actin, Myosin, and Ligand. Myosin ligand complexes bind to actin in two steps, followed by release of ligand. The A* represents the high fluorescence state of pyrene-labeled actin and A the quenched state after formation of a strongly bound complex (17):

[1]

For the three ligands investigated here, the kinetics have been investigated (17), and steps 1 and 3 can be regarded as fast equilibria relative to step 2, which is the most likely candidate for association with a working stroke. The minimum ligand concentration we used was much greater than the myosin dissociation constant and thus all myosin not bound to actin is in the M.L state. For each of the ligands, we used concentrations well below the dissociation constant from AM, and in this case the overall reaction monitored was A* + M.L → AM + L. In the case of ADP we were also able to use concentrations close to saturation of AM.L, which allowed separate determination of the working stroke on binding A* + M.L → AM.L and on dissociation AM.L → AM + L. For the ligands PP_i and AMPPNP the highest concentrations used probably resulted in <25% saturation, judging from the maximum rate of dissociation reported from solution studies (17).

Attachment of S1 via a Biotinylated RLC. The binding of the modified S1 to the surface was tested by using a simple actin binding assay in which a nitrocellulose surface was first coated with1mg/ml BSA for 1 min. A concentration of 1 μg/ml S1 with or without biotinylated light chain was incubated for another 10 min, and finally 2 μg/ml fluorescent actin filaments were added to the flow cell for 10 min before washing and counting of bound actin filaments. About 10 times more actin filaments bound to the surface incubated with the BDTC-RLC S1 than with normal S1 (see Fig. 4), indicating that 90% of the modified S1 bound via its light chain and was thus likely to be available for interaction with actin. We found that the velocity of motion in the actin motility assay at room temperature when the S1 was bound via its light chain was ≈4–5 μm/s, two to three times greater than when S1 was bound nonspecifically to nitrocellulose. This rate is very similar to that found by Iwane et al. (11) where biotinylated S1 was bound to a streptavidin surface. The BSA protocol was used with a glass-beaded surface for the trap experiments. Extensive comparisons of biotinylated S1 attached in this manner with S1 bound directly to a nitrocellulose surface showed the former gave more consistent results. Preliminary experiments suggest that this finding is at least in part because the head is more free to rotate and thus take up its correct orientation with respect to the actin filament.

Fig. 4.

Rhodamine-phalloidin-labeled actin filaments used to test the binding of S1 (a) and Biotin RLC S1 (b) on a BSA-coated surface. (Scale bar: 20 μm.)

Results

Myosin-Pyrophosphate (M.PP_i). In solution the reported rate for M.PP_i binding to actin is 10⁷ M⁻¹·s⁻¹ (17), an order of magnitude faster than M.ADP.P_i (10⁶ M⁻¹·s⁻¹). Our initial results immediately provided evidence for this difference because periods of low variance were generated at a high frequency (Fig. 5a). Moreover, the record was not recognizable as being caused by single interactions. We interpreted this behavior as arising from rapid rebinding with a single myosin head rather than from interactions with more than one head. At a low density of myosin, typically it was necessary to search four or five fixed myosin-bearing beads thoroughly before interactions were observed. Furthermore, clean single interactions were seen at similar myosin densities with ATP. To overcome this problem we increased the KCl concentration in the buffer from 25 to 100 mM, because the rate of actin binding to all myosin states is known to be a strongly decreasing function of ionic strength. At this higher ionic strength we observed clearly defined interactions well separated in time (Fig. 5b). In these studies, the observed variance ratio, that is, the ratio of the variance of bead position when the actin filament was free and bound to myosin, was typically ≈15. The interactions were relatively long and thus easily detected. Fig. 5c shows that interactions can be associated with specific actin monomers that fall into target zones. The observed rate of PP_i-induced dissociation of AM increased linearly over our experimental range of [PP_i] (Fig. 5d) with no sign of a plateau, the second-order rate constant being 63 mM⁻¹·s⁻¹. For acto-S1 in solution (I = ≈0.015 and 20°C) the maximum rate of dissociation is 250 s⁻¹ and the half-maximal rate occurs at 0.5 mM PP_i (17). Increasing ionic strength reduces the affinity of most ligands and accounts in part for the lack of curvature up to 1 mM in Fig. 5d and the corresponding 8-fold decrease in the second-order rate constant.

Fig. 5e shows the histogram resulting from experiments in which the dumbbell was moved past the fixed myosin bead by two actin repeats to get the true working stroke. The average displacement (working stroke) of a single dumbbell (for constant actin polarity), which experienced 2,904 interactions, observed in 13 100-s data sets, from three S1 molecules, was 0.4 ± 1 nm (mean ± SEM) (Table 1). For the experiments reported here, the sign of the displacement has no significance as the polarity of the actin filament was not determined, and consequently data sets from different dumbbells could not be combined. The rate of dissociation at 0.5 mM PP_i, ≈30 s⁻¹ was very much less than the maximum value observed in solution (250 s⁻¹), so that bound myosin is mostly in the form AM rather than AM.PP_i. However, the lowest PP_i concentrations used were still sufficient to saturate free myosin, and this experiment was monitoring the working stroke for the reaction A + M.PP_i → AM + PP_i.

Table 1. Working strokes for different myosin nucleotide complexes.

	ATP*	PPi, 500 μm	PPi*	AMP-PNP, 1 mM	AMP-PNP*	ADP, 50 μm	ADP*	None	None*
Working stroke, SEM	5.4 ± 0.2 nm	0.4 ± 1 nm	0.7 nm	0.1 ± 0.2 nm	0.5	0.6 ± 0.5 nm	0.8 nm	0.1 ± 0.9 nm	0.2
No. of events	5,580	2,904	14,888	3,023	3,514	800	1,670	223	359
No. of records	18 × 100 s	13 × 100 s	43 × 100 s	13 × 100 s	18 × 100 s	12 × 400 s	17 × 400 s	5 × 400 s	10 × 400 s
Rate M-1·s-1	3 × 106	NA	63,000	NA	5,200	NA	2,100	NA	NA
No. of myosins	5	3	10	5	8	2	4	1	3

For each nucleotide, data from a single dumbbell are summarized to avoid combining working strokes from actin filaments of possibly different polarities. Errors are SEM. * indicates pooled data sets (absolute values of the working stroke averaged) using different dumbbells of unknown polarity (except for the case of ATP). BDTC-RLC S1 was used throughout. NA, not applicable.

Myosin-AMPPNP (M.AMPPNP). To observe clean single interactions as in Fig. 6a, it was again necessary to use 100 mM KCl. Hexokinase was used to avoid the effect of contaminant ATP. The rate of AM dissociation is plotted against [AMPPNP] in Fig. 6b; this rate also linearly depended on concentration, consistent with the weak binding of AMPPNP to acto-S1. The second-order rate constant for dissociation was 5.2 mM⁻¹·s⁻¹, to be compared with the acto-S1 value of 11 mM⁻¹·s⁻¹ (18). Our maximum observed rate of ≈10 s⁻¹ was much less than the rate in solution at saturating [AMPPNP] [>100 s⁻¹: (17)], indicating that in our experiments the [AMPPNP] is far from saturating and that the binding sequence we observe is essentially A* + M.AMPPNP → A.M + AMPPNP. To measure the working stroke, ramped traps were used, and Fig. 6c shows a histogram of displacements based on data at 1 mM AMPPNP from a single dumbbell interacting with five S1 molecules collected during 13 ramps. The working stroke was 0.1 ± 0.2 nm (mean ± SEM, n = 3023) (Table 1).

Fig. 6.

(a) Ten seconds of 1 mM AMP-PNP trace using a buffer containing 100 mM KCl and 1 mg/ml hexokinase. Combined trap stiffness was 0.065 pN/nm: variance ratio for best bead 22. (b) Rate of dissociation as a function of [AMPPNP]. (c) Histogram of interactions all based on ramps from a single dumbbell. [AMPPNP] at 1 mM.

Myosin-ADP (M.ADP). ADP is known to dissociate AM much more slowly than ATP, PP_i, or AMPPNP and the long interactions we observed are qualitatively consistent with this fact (Fig. 7a). In this case an even higher ionic strength (500 mM KCl) was needed for clean interactions. Hexokinase was required to avoid the effect of contaminant ATP. In contrast to the previous cases, the rate of ADP-induced dissociation from actin as a function of [ADP] (Fig. 7b) comes close enough to saturation to estimate a maximum rate of ≈3s⁻¹ and an apparent binding constant of just over 1 mM. The solution value for the maximum rate of dissociation is in good agreement [2–3 s⁻¹ (17)] although the solution value for ADP binding to acto-S1 is 5–10 times tighter. Our ability to approach saturating concentrations of ADP is expected from the tighter acto-S1 binding constant of ADP relative to AMPPNP or PP_i. Because of the long lifetime of events the actin filaments were moved past the myosin at a lower velocity (≈0.2 nm/s). The working stroke was easier to measure at high [ADP] because of the shorter interaction times and at 1 mM ADP we obtained a value of 1.2 ± 0.4 nm (mean ± SEM, n = 1213). At 50 μM ADP (Fig. 7c) our value was not significantly different from zero (0.6 ± 0.5 nm, mean ± SEM, n = 800) (Table 1). At saturating [ADP] the reaction observed is primarily A* + M.ADP → AM.ADP, whereas at the lowest concentrations used the primary reaction is A* + M.ADP → A.M + ADP. Neither reaction is associated with a working stroke. It should be noted that during our M.ADP experiments we found that two of the 58 S1 molecules investigated displayed consistent behavior characterized by a rate of dissociation ≈10 times faster than the average. It is not clear whether an isoform or a degraded form of myosin is responsible but the rate does not correspond to solution values for rabbit fast myosin, and such data were discarded.

Fig. 7.

(a) Twenty-second trace of 0.5 mM ADP using a buffer containing 0.5 M KCl and 10 ng/ml hexokinase. Combined trap stiffness was 0.03 pN/nm: variance ratio for best bead 21. (b) Rate of dissociation as a function of [ADP]. (c) Histogram of ramp data set at 50 μM ADP (one dumbbell, 12 × 400-s records of S1s, 800 interactions).

Myosin. Myosin is the state that binds most tightly to actin, and high ionic strength was again necessary to raise the dissociation rate to a workable level. An experimental record is shown in Fig. 8a. At 0.5 M KCl we observed a rate of AM dissociation of the order of 0.2 s⁻¹, to be compared with a solution value of 0.27 s⁻¹ at 0.15 M KCl (17). Because of the long lifetime of the interactions, ramp experiments proved rather difficult but using slow ramps (≈0.1 nm·s⁻¹: a single actin repeat in 400 s), five data sets were obtained for one dumbbell, yielding a working stroke of 0.1 ± 0.9 nm (mean ± SEM, n = 223) (histogram, Fig. 8b and Table 1). Although this estimate is based on a small data set, two other dumbbells gave enough events to yield estimates, both of which were close to zero. A substantial amount of additional data were also consistent with a working stroke near zero.

Fig. 8.

(a) Twenty seconds of myosin–actin interaction (0.5 M KCl and 1 μg/ml apyrase). Combined trap stiffness was 0.041 pN/nm: variance ratio for best bead 18. (b) Histogram and events of a single record binned at 1 nm combined histogram of five records of 400 s with a one-actin repeat ramp binned at 5 nm (one dumbbell, 5 × 400-s records of one S1, 223 interactions).

Discussion

When considering our results, it is convenient to take the orientation of the lever arm in the rigor AM state as a datum. We observe no working stroke upon myosin binding and thus conclude that the apo form myosin binds while in the rigor position. The null strokes observed for M.ADP, M.PP_i, and M.AMPPNP at ligand concentrations well below saturation, where the end product is AM, implies that the lever arms of the forms of M.ADP, M.PP_i, and M.AMPPNP that bind to actin are also in the rigor position at the time of binding. At saturating ADP the reaction observed is A* + M.ADP → AM.ADP: we still observe no working stroke and as M.ADP has been assigned to being in a rigor conformation, so must AM.ADP. This observation is in agreement with structural studies for myosin II (19), although it must be acknowledged that fiber studies have suggested that a small lever movement could still control the rate of ADP release (20). Actin binds to M.ADP and forms a weakly bound complex that Geeves (21) labeled A-MD (an A state). Taylor (17) also characterized this state and observed that the equilibrium constant between it and AM.ADP was similar to that of the AM′.ADP state to which P_i binds (22). The equivalence of these two states has not been proven but to simplify discussion we will refer to the initial state formed upon M.ADP binding as AM′.ADP. We observe no stroke at either high or low ADP concentrations and the most likely interpretation is that the working stroke occurs in one of the steps between AM.ADP.P_i and AM′.ADP (23) and that the latter is a postworking stroke state.

The only intermediate known to give a working stroke is M.ADP.P_i and the end result of the binding is the rigor state AM. The final product of the states myosin, M.ADP, M.PP_i, and M.AMPPNP binding to actin is also AM, but no working stroke results. The natural interpretation is that M.ADP.P_i binds in a different form from the other myosin states, consistent with the original Lymn–Taylor scheme (3).

Our observations are consistent with current interpretations of crystal structures (for review see ref. 9) in which the working stroke is aligned with the transition between crystal structures with closed and open nucleotide binding pockets. In the absence of actin, the fluorescence of myosin tryptophan residues, either native (24) or engineered (25), has been correlated with the proportions of open and closed state forms of myosin–nucleotide complexes. Myosin and M.ADP are open and M.PP_i is ≈90% open, whereas M.AMPPNP (26) is only ≈50% open and M.ADP.P_i is almost entirely closed (at least at 20°C). Support for the association of the transition from open to closed states with the mechanical conformation of the myosin head comes from studies of the helical order of myosin filaments in muscle fibers, relaxed under a range of conditions (27). Changes in temperature, which alter the ratio of open to closed states deduced from fluorescence measurements, were found to affect the helical order in the predicted manner.

Our data can be interpreted in terms of myosin binding to actin in the open form, leading to the rigor state without a working stroke. M.ADP and M.PP_i are in the same conformation as myosin and behave in a similar manner (Fig. 9). The state M.ADP.P_i is in the closed form, binds as such to actin, and gives a working stroke upon forming the open AM state. For M.AMPPNP, the open and closed states are equally populated and our observation of a working stroke close to zero carries implications about the relative rates of the open and closed states binding to actin and releasing ligand. It has been reported that myosin, M.ADP, and M.PP_i, which are primarily in the open form, bind at least an order of magnitude faster (10⁸, 10⁷, and 10⁷ M⁻¹·s⁻¹) than M.ADP.P_i, the closed form state (10⁶ M⁻¹·s⁻¹). As it happens AMPPNP, the 50/50 form, binds at half the rate of PP_i (5 × 10⁶ M⁻¹·s⁻¹). Ligands bind to the open form and consequently must also dissociate from this form. The lack of a working stroke can readily be accounted for if, as appears to be the case, the open form of M.AMPPNP binds much more rapidly than the closed form.

Fig. 9.

A model for myosin and myosin–nucleotide complexes, where the myosin lever arm can exist in either of two discrete orientations (open and closed) when free or bound to actin. Myosin in the closed state binds to actin before changing to the open state with an associated swing in the lever arm.

Our observation that no measurable working stroke is associated with the binding of nucleotide-free myosin or M.ADP is in conflict with a direct correlation between the formation of a rigor bond and a working stroke. This is implied in a simple interpretation of the 3G's model in which all myosin–nucleotide complexes on binding to actin go through a weak-to-strong or A-to-R conformational change (8). We show here that such transitions are not necessarily associated with a working stroke. If the importance of the open-to-closed transition is substantiated, the open or closed label may prove to be more significant than weak or strong or A or R labels.

Work by Kuhn (28) on the effect of the binding of AMPPNP to fibers suggested that it at least partially reverses the working stroke. This result is not immediately consistent with our observations but the filament lattice and the double-headed nature of myosin both may contribute to the effect (29).

We would like to have measured the working stroke of closed forms of myosin other than M.ADP.P_i, notably M.ADP.vanadate or . However, the kinetics of ligand interaction is unfavorable. The rate of vanadate or binding to AM.ADP (1 min⁻¹ at low ionic strength) is so slow that it would be difficult to build up a statistically meaningful description of the interaction, and the acceleration in the rate of dissociation of AM.ADP by vanadate is sufficiently slight, that it would be difficult to separate the actin binding events of M.ADP and M.ADP.vanadate.

In summary, the only state we found to give a working stroke was M.ADP.P_i, and we conclude that this binds in a different preworking-stroke form from the other states and thus that there must be at least two mechanical conformation of myosin when dissociated from actin. We show that our observations are consistent with the two states corresponding to the crystal states referred to as having open and closed nucleotide binding pockets.