Mechanochemical coupling in the myosin motor domain. I. Insights from equilibrium active-site simulations

Although the major structural transitions in molecular motors are often argued to couple to the binding of Adenosine triphosphate (ATP), the recovery stroke in the conventional myosin has been shown to be dependent on the hydrolysis of ATP. To obtain a clearer mechanistic picture for such "mechanochemical coupling" in myosin, equilibrium active-site simulations with explicit solvent have been carried out to probe the behavior of the motor domain as functions of the nucleotide chemical state and conformation of the converter/relay helix. In conjunction with previous studies of ATP hydrolysis with different active-site conformations and normal mode analysis of structural flexibility, the results help establish an energetics-based framework for understanding the mechanochemical coupling. It is proposed that the activation of hydrolysis does not require the rotation of the lever arm per se, but the two processes are tightly coordinated because both strongly couple to the open/close transition of the active site. The underlying picture involves shifts in the dominant population of different structural motifs as a consequence of changes elsewhere in the motor domain. The contribution of this work and the accompanying paper [] is to propose the actual mechanism behind these "population shifts" and residues that play important roles in the process. It is suggested that structural flexibilities at both the small and large scales inherent to the motor domain make it possible to implement tight couplings between different structural motifs while maintaining small free-energy drops for processes that occur in the detached states, which is likely a feature shared among many molecular motors. The significantly different flexibility of the active site in different X-ray structures with variable level arm orientations supports the notation that external force sensed by the lever arm may transmit into the active site and influence the chemical steps (nucleotide hydrolysis and/or binding).     

Millisecond-scale biochemical response to change in strain

Muscle fiber contraction involves the cyclical interaction of myosin cross-bridges with actin filaments, linked to hydrolysis of ATP that provides the required energy. We show here the relationship between cross-bridge states, force generation, and Pi release during ramp stretches of active mammalian skeletal muscle fibers at 20°C. The results show that force and Pi release respond quickly to the application of stretch: force rises rapidly, whereas the rate of Pi release decreases abruptly and remains low for the duration of the stretch. These measurements show that biochemical change on the millisecond timescale accompanies the mechanical and structural responses in active muscle fibers. A cross-bridge model is used to simulate the effect of stretch on the distribution of actomyosin cross-bridges, force, and Pi release, with explicit inclusion of ATP, ADP, and Pi in the biochemical states and length-dependence of transitions. In the simulation, stretch causes rapid detachment and reattachment of cross-bridges without release of Pi or ATP hydrolysis.     

How myosin motors power cellular functions: an exciting journey from structure to function: based on a lecture delivered at the 34th FEBS Congress in Prague, Czech Republic, July 2009

Molecular motors such as myosins are allosteric enzymes that power essential motility functions in the cell. Structural biology is an important tool for deciphering how these motors work. Myosins produce force upon the actin-driven conformational changes controlling the sequential release of the hydrolysis products of ATP (Pi followed by ADP). These conformational changes are amplified by a 'lever arm', which includes the region of the motor known as the converter and the adjacent elongated light chain binding region. Analysis of four structural states of the motor provides a detailed understanding of the rearrangements and pathways of communication in the motor that are necessary for detachment from the actin track and repriming of the motor. However, the important part of the cycle in which force is produced remains enigmatic and awaits new high-resolution structures. The value of a structural approach is particularly evident from clues provided by the structural states of the reverse myosin VI motor. Crystallographic structures have revealed that rearrangements within the converter subdomain occur, which explains why this myosin can produce a large stroke in the opposite direction to all other myosins, despite a very short lever arm. By providing a detailed understanding of the motor rearrangements, structural biology will continue to reveal essential information and help solve current enigma, such as how actin promotes force production, how motors are tuned for specific cellular roles or how motor/cargo interactions regulate the function of myosin in the cell.     

An ionic–chemical–mechanical model for muscle contraction

The dynamic process underlying muscle contraction is the parallel sliding of thin actin filaments along an immobile thick myosin fiber powered by oar‐like movements of protruding myosin cross bridges (myosin heads). The free energy for functioning of the myosin nanomotor comes from the hydrolysis of ATP bound to the myosin heads. The unit step of translational movement is based on a mechanical‐chemical cycle involving ATP binding to myosin, hydrolysis of the bound ATP with ultimate release of the hydrolysis products, stress‐generating conformational changes in the myosin cross bridge, and relief of built‐up stress in the myosin power stroke. The cycle is regulated by a transition between weak and strong actin–myosin binding affinities. The dissociation of the weakly bound complex by addition of salt indicates the electrostatic basis for the weak affinity, while structural studies demonstrate that electrostatic interactions among negatively charged amino acid residues of actin and positively charged residues of myosin are involved in the strong binding interface. We therefore conjecture that intermediate states of increasing actin–myosin engagement during the weak‐to‐strong binding transition also involve electrostatic interactions. Methods of polymer solution physics have shown that the thin actin filament can be regarded in some of its aspects as a net negatively charged polyelectrolyte. Here we employ polyelectrolyte theory to suggest how actin–myosin electrostatic interactions might be of significance in the intermediate stages of binding, ensuring an engaged power stroke of the myosin motor that transmits force to the actin filament, and preventing the motor from getting stuck in a metastable pre‐power stroke state. We provide electrostatic force estimates that are in the pN range known to operate in the cycle.     

A new structural state of myosin

The mechanism by which motor proteins hydrolyze ATP and move along cytoskeletal filaments is still unknown. One approach to deciphering the mechanism is to correlate steps of ATP hydrolysis with structural states of the motors to determine the changes the motors undergo during the hydrolysis cycle. Unfortunately, available crystal structures represent only a few steps of the cycle and obtaining atomic structures that represent the motors bound to their filament has been difficult. Now, two new myosin crystal structures have been reported that show features expected for myosin motors bound in rigor to actin. The two new structures show changes at both the actin-binding surface and the active site that have not been observed previously.     

Myosin motor domain lever arm rotation is coupled to ATP hydrolysis

We have investigated coupling of lever arm rotation to the ATP binding and hydrolysis steps for the myosin motor domain. In several current hypotheses of the mechanism of force production by muscle, the primary mechanical feature is the rotation of a lever arm that is a subdomain of the myosin motor domain. In these models, the lever arm rotates while the myosin motor domain is free, and then reverses the rotation to produce force while it is bound to actin. These mechanical steps are coupled to steps in the ATP hydrolysis cycle. Our hypothesis is that ATP hydrolysis induces lever arm rotation to produce a more compact motor domain that has stored mechanical energy. Our approach is to use transient electric birefringence techniques to measure changes in hydrodynamic size that result from lever arm rotation when various ligands are bound to isolated skeletal muscle myosin motor domain in solution. Results for ATP and CTP, which do support force production by muscle fibers, are compared to those of ATPgammaS and GTP, which do not. Measurements are also made of conformational changes when the motor domain is bound to NDP's and PP(i) in the absence and presence of the phosphate analogue orthovanadate, to determine the roles the nucleoside moieties of the nucleotides have on lever arm rotation. The results indicate that for the substrates investigated, rotation does not occur upon substrate binding, but is coupled to the NTP hydrolysis step. The data are consistent with a model in which only substrates that produce a motor domain-NDP-P(i) complex as the steady-state intermediate make the motor domain more compact, and only those substrates support force production.     

The mechanism of muscle contraction

Knowledge of the mechanism of contraction has been obtained from studies of the interaction of actin and myosin in solution, from an elucidation of the structure of muscle fibers, and from measurements of the mechanics and energetics of fiber contraction. Many of the states and the transition rates between them have been established for the hydrolysis of ATP by actin and myosin subfragments in solution. A major goal is to now understand how the kinetics of this interaction are altered when it occurs in the organized array of the myofibril. Early work on the structure of muscle suggested that changes in the orientation of myosin cross-bridges were responsible for the generation of force. More recently, fluorescent and paramagnetic probes attached to the cross-bridges have suggested that at least some domains of the cross-bridges do not change orientation during force generation. A number of properties of active cross-bridges have been defined by measurements of steady state contractions of fibers and by the transients which follow step changes in fiber length or tension. Taken together these studies have provided firm evidence that force is generated by a cyclic interaction in which a myosin cross-bridge attaches to actin, exerts force through a "powerstroke" of 12 nm, and is then released by the binding of ATP. The mechanism of this interaction at the molecular level remains unknown.     

Structural characterization of weakly attached cross-bridges in the A*M*ATP state in permeabilized rabbit psoas muscle

It is well established that in a skeletal muscle under relaxing conditions, cross-bridges exist in a mixture of four weak binding states in equilibrium (A*M*ATP, A*M*ADP*P(i), M*ATP, and M*ADP*P(i)). It has been shown that these four weak binding states are in the pathway to force generation. In the past their structural, biochemical, and mechanical properties have been characterized as a group. However, it was shown that the myosin heads in the M*ATP state exhibited a disordered distribution along the thick filament, while in the M*ADP*P(i) state they were well ordered. It follows that the structures of the weakly attached states of A*M*ATP and A*M*ADP*P(i) could well be different. Individual structures of the two attached states could not be assigned because protocol for isolating the two states has not been available until recently. In the present study, muscle fibers are reacted with N-phenylmaleimide such that ATP hydrolysis is inhibited, i.e., the cross-bridge population under relaxing conditions is distributed only between the two states of M*ATP and A*M*ATP. Two-dimensional x-ray diffraction was applied to determine the structural characteristics of the attached A*M*ATP state. Because the detached state of M*ATP is disordered and does not contribute to layer line intensities, changes as a result of increasing attachment in the A*M*ATP state are attributable to that state alone. The equilibrium toward the attached state was achieved by lowering the ionic strength. The results show that upon attachment, both the myosin and the first actin associated layer lines increased intensities, while the sixth actin layer line was not significantly affected. However, the intensities remain weak despite substantial attachment. The results, together with modeling (see J. Gu, S. Xu and L. C. Yu, 2002, Biophys. J. 82:2123-2133), suggest that there is a wide range of orientation of the attached A*M*ATP cross-bridges while the myosin heads maintain some degree of helical distribution on the thick filament, suggesting a high degree of flexibility in the actomyosin complex. Furthermore, the lack of sensitivity of the sixth actin layer line suggests that the binding site on actin differs from the putative site for rigor binding. The significance of the flexibility in the A*M*ATP complex in the process of force generation is discussed.     

Detection of the swings of the lever arm of a myosin motor by fluorescence resonance energy transfer of green and blue fluorescent proteins

The "lever-arm" model of a myosin motor predicts that the lever-arm domain in the myosin head tilts and swings against the catalytic domain during ATP hydrolysis, resulting in force generation. To investigate if this "swing" of the lever arm really occurs during the hydrolysis of ATP, we employed fluorescence resonance energy transfer (FRET) between two fluorescent proteins [green (GFP) and blue (BFP)] fused to the N and C termini of the Dictyostelium myosin-motor domain. FRET measurements showed that the C-terminal BFP in the fusion protein first swings against the N-terminal GFP at the isomerization step of the ATP hydrolysis cycle and then swings back at the phosphate-release step. Because the C-terminal BFP mimics the motion of the lever arm, the result indicates that the lever arm swings at the specific steps of the ATP hydrolysis cycle, i.e., at the isomerization and phosphate-release steps. The latter swing may correspond to the power stroke of myosin, while the former may be related to the recovery stroke.     

A deterministic mechanism producing the loose coupling phenomenon observed in an actomyosin system

Myosins are molecular motors that convert the chemical energy of ATP into mechanical work called a power stroke. Class II myosin engaged in muscle contraction is reported to show a "loose coupling phenomenon", in which the number of power strokes is greater than the number of ATP hydrolyses. This phenomenon cannot be explained by the lever-arm hypothesis, which is currently accepted as a standard theory for myosin motility. In this paper, a model is proposed to reproduce the loose coupling phenomenon. The model is based on a mechanochemical process called "Driven by Detachment (DbD)" mechanism, which assumes that the energy of the power strokes originates from the potential energy generated by the attractive force between myosin and actin. During the docking process, the potential energy is converted into an intramolecular strain in a myosin molecule, which drives the power stroke after the myosin is firmly attached to an actin filament. The energy of ATP is used to temporarily reduce the attractive force and to increase the potential energy. Therefore, it is not directly linked to the power strokes. When myosin molecules work as an aggregate, the sliding movement of a myosin filament driven by the power strokes of some myosin heads makes other myosin heads that have completed their power strokes detach from the actin without consuming ATP. Under the DbD mechanism, these passively detached myosins can be again engaged in power strokes after the next attachment to actin. As a result, the number of power strokes becomes greater than the number of ATP hydrolyses, and the loose coupling phenomenon will be observed. A theoretical analysis indicates that the efficiency of converting the potential energy into intramolecular elastic energy determines the number of power strokes per each ATP hydrolysis. Computer simulations showed that the DbD mechanism actually produced the loose coupling phenomenon. A critical requirement for this mechanism is that ATP must preferentially facilitate the detachment of myosins that have completed their power strokes, but are still strongly attached to the actin. This requirement may be fulfilled by ATP hydrolysis tightly depending on the conformation of a myosin molecule.     

Myosin light-chain domain rotates upon muscle activation but not ATP hydrolysis.

We have studied the correlation between myosin structure, myosin biochemistry, and muscle force. Two distinct orientations of the myosin light-chain domain were previously resolved using electron paramagnetic resonance (EPR) spectroscopy of spin-labeled regulatory light chains in scallop muscle fibers. In the present study, we measured isometric force during EPR spectral acquisition, in order to define how these two light-chain domain orientations are coupled to force and the myosin ATPase cycle. When muscle fibers are partially activated with increasing amounts of calcium, the distribution between the two light-chain domain orientations shifts toward the one associated with strong actin binding. This shift in distribution is linearly related to the increase in force, suggesting that rotation of the light-chain domain is coupled to strong actin binding. However, when nucleotide analogues are used to trap myosin in the pre- and posthydrolysis states of its ATPase cycle in relaxed muscle, there is no change in the distribution between light-chain domain orientations, showing that the rotation of the light-chain domain is not directly coupled to the ATP hydrolysis step. Instead, it is likely that in relaxed muscle the myosin thick filament stabilizes two light-chain domain orientations that are independent of the nucleotide analogue bound at the active site. We conclude that a large and distinct rotation of the light-chain domain of myosin is responsible for force generation and is coupled to strong actin binding but is not coupled to a specific step in the myosin ATPase reaction.     

Resolution of conformational states of spin-labeled myosin during steady-state ATP hydrolysis

We have measured the conventional electron paramagnetic resonance (EPR) spectrum of spin-labeled myosin filaments as a function of the nucleotide occupancy of the active site of the enzyme. The probe used was 4-(2-iodoacetamido)-2,2,6,6-tetramethylpiperidine-1-oxyl (IASL), which reacts specifically with sulfhydryl 1 of the myosin head. In the absence of nucleotide, the probe remains strongly immobilized (rigidly attached to the myosin head) so that no nanosecond rotational motions are detectable. When MgADP is added to IASL-labeled myosin filaments (T = 20 degrees C), the probe mobility increases slightly. During steady-state MgADP hydrolysis (T = 20 degrees C), the probe undergoes large-amplitude nanosecond rotational motion. These results are consistent with previous studies of myosin monomers, heavy meromyosin, and myosin subfragment 1. Isoclinic points observed in overlays of sequential EPR spectra recorded during ATP hydrolysis strongly suggest that the probes fall into two motional classes, separated by approximately an order of magnitude in effective rotational correlation time. Both of the observed states are distinct from the conformation of myosin in the absence of nucleotides, and the spectrum of the less mobile population is indistinguishable from that observed in the presence of MgADP. The addition of ADP and vanadate to IASL-myosin gives rise to two motional classes virtually identical with those observed in the presence of ATP, but the relative concentrations of the spin populations are significantly different. We have quantitated the percentage of myosin in each motional state during ATP hydrolysis. The result agrees well with the predicted percentages in the two predominant chemical states in the myosin ATPase cycle. Spectra obtained in the presence of nucleotide analogues permit us to assign the conformational states to specific chemical states. We propose that the two motional classes represent two distinct local conformations of myosin that are in exchange with one another during the ATP hydrolysis reaction cycle.     

A physical model of ATP-induced actin-myosin movement in vitro.

The nature of the mechanism limiting the velocity of ATP-induced unidirectional movements of actin-myosin filaments in vitro is considered. In the sliding process two types of "cyclic" interactions between myosin heads and actin are involved, i.e., productive and nonproductive. In the productive interaction, myosin heads split ATP and generate a force which produces sliding between actin and myosin. In the nonproductive interaction "cycle," on the other hand, myosin heads rapidly attach to and detach from actin "reversibly," i.e., without splitting ATP or generating an active force. Such a nonproductive interaction "cycle" causes irreversible dissipation of sliding energy into heat, because the myosin cross-bridges during this interaction are passive elastic structures. This consideration has led us to postulate that such cross-bridges, in effect, exert viscous-like frictional drag on moving elements. Energetic considerations suggest that this frictional drag is much greater than the hydrodynamic viscous drag. We present a model in which the sliding velocity is limited by the balance between the force generated by myosin cross-bridges in the productive interaction and the frictional drag exerted by other myosin cross-bridges in the nonproductive interaction. The model is consistent with experimental findings of in vitro sliding, including the dependence of velocity on ATP concentration, as well as the sliding velocity of co-polymers of skeletal muscle myosin and phosphorylated and unphosphorylated smooth muscle myosins.     

Myosin dynamics on the millisecond time scale

Myosin is a motor protein associating with actin and ATP. It translates along actin filaments against a force by transduction of free energy liberated with ATP hydrolysis. Various myosin crystal structures define time points during ATPase showing the protein undergoes large conformation change during transduction over a cycle with approximately 10 ms periodicity. The protein conformation trajectory between two intermediates in the cycle is surmised by non-equilibrium Monte Carlo simulation utilizing free-energy minimization. The trajectory shows myosin transduction of free energy to mechanical work giving evidence for: (i) a causal relationship between product release and work production in the native isoform that is correctly disrupted in a chemically modified protein, (ii) the molecular basis of ATP-sensitive tryptophan fluorescence enhancement and acrylamide quenching, (iii) an actin-binding site peptide containing the free-energy barrier to ATPase product release defining the rate limiting step and, (iv) a scenario for actin-activation of myosin ATPase.     

Structural rearrangements in the active site of smooth-muscle myosin

Structural rearrangements of the myosin upper-50 kD subdomain are thought to play a key role in coordinating actin binding with nucleotide hydrolysis during the myosin ATPase cycle. Such rearrangements could open and close the active site in opposition to the actin-binding cleft, helping explain the opposing affinities of myosin for actin and nucleotide. To directly examine conformational changes across the active site during the ATPase cycle we have genetically engineered a mutant of chicken smooth-muscle myosin, F344W motor domain essential light chain, which contains a single tryptophan (344W) located on a short loop between two alpha helixes that traverse the upper-50 kD subdomain in front of the active site. Fluorescence resonance energy transfer was examined between the 344W donor probe and 2'(3')-O-(N-methylanthraniloyl) (mant)-nucleotide acceptor probes in the active site of this construct. The observed fluorescence resonance energy transfer efficiencies were 6.4% in the presence of mant ADP and 23.8% in the presence of mant ATP, corresponding to distances of 33.4 A and 24.9 A, respectively. Our results are consistent with structural rearrangements in which there is an 8.5-A closure between the 344W residue and the mant moiety during the transition from the strongly (ADP) to weakly (ATP) actin-bound states of the myosin ATPase cycle.     

Caldesmon restricts the movement of both C- and N-termini of tropomyosin on F-actin in ghost fibers during the actomyosin ATPase cycle

New data on the movements of tropomyosin singly labeled at alpha- or beta-chain during the ATP hydrolysis cycle in reconstituted ghost fibers have been obtained by using the polarized fluorescence technique which allowed us following the azimuthal movements of tropomyosin on actin filaments. Pronounced structural changes in tropomyosin evoked by myosin heads suggested the "rolling" of the tropomyosin molecule on F-actin surface during the ATP hydrolysis cycle. The movements of actin-bound tropomyosin correlated to the strength of S1 to actin binding. Weak binding of myosin to actin led to an increase in the affinity of the tropomyosin N-terminus to actin with simultaneous decrease in the affinity of the C-terminus. On the contrary, strong binding of myosin to actin resulted in the opposite changes of the affinity to actin of both ends of the tropomyosin molecule. Caldesmon inhibited the "rolling" of tropomyosin on the surface of the thin filament during the ATP hydrolysis cycle, drastically decreased the affinity of the whole tropomyosin molecule to actin, and "freezed" tropomyosin in the position characteristic of the weak binding of myosin to actin.     

Force generation in single conventional actomyosin complexes under high dynamic load

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel 'isometric' optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.     

Structural dissection of ATP turnover in the prototypical GHL ATPase TopoVI

GHL proteins are functionally diverse enzymes defined by the presence of a conserved ATPase domain that self-associates to trap substrate upon nucleotide binding. The structural states adopted by these enzymes during nucleotide hydrolysis and product release, and their consequences for enzyme catalysis, have remained unclear. Here, we have determined a complete structural map of the ATP turnover cycle for topoVI-B, the ATPase subunit of the archaeal GHL enzyme topoisomerase VI. With this ensemble of structures, we show that significant conformational changes in the subunit occur first upon ATP binding, and subsequently upon release of hydrolyzed P(i). Together, these data provide a structural framework for understanding the role of ATP hydrolysis in the type II topoisomerase reaction. Our results also suggest that the GHL ATPase module is a molecular switch in which ATP hydrolysis serves as a prerequisite but not a driving force for substrate-dependent structural transitions in the enzyme.     

C-terminal sites of caldesmon drive ATP hydrolysis cycle by shifting actomyosin itermediates from strong to weak binding of myosin and actin

Polarized fluorimetry technique and ghost muscle fibers containing tropomyosin were used to study effects of caldesmon (CaD) and recombinant peptides CaDH1 (residues 506-793), CaDH2 (residues 683-767), CaDH12 (residues 506-708) and 658C (residues 658-793) on the orientation and mobility of fluorescent label 1.5-IAEDANS specifically bound to Cys-707 of myosin subfragment-1 (S1) in the absence of nucleotide, and in the presence of MgADP, MgAMP-PNP, MgATPgammaS or MgATP. It was shown that at modelling different intermediates of actomyosin ATPase, the orientation and mobility of dye dipoles changed discretely, suggesting a multi-step changing of the myosin head structural state in ATP hydrolysis cycle. The maximum difference in orientation and mobility of the oscillator (4 degrees and 30%, respectively) was observed between actomyosin in the presence of MgATP, and actomyosin in the presence of MgADP. Caldesmon actin-binding sites C and B' inhibit formation of actomyosin strong binding states, while site B activates it. It is suggested that actin-myosin interaction in ATP hydrolysis cycle initiates nucleotide-dependent rotation of myosin motor domain, or that of its site for dye binding as well as the change in myosin head mobility. Caldesmon drives ATP hydrolysis cycle by shifting the equilibrium between strong and weak forms of actin-myosin binding.     

Solution structure of heavy meromyosin by small-angle scattering

Elucidation of x-ray crystal structures for the S1 subfragment of myosin afforded atomic resolution of the nucleotide and actin binding sites of the enzyme. The structures have led to more detailed hypotheses regarding the mechanisms by which force generation is coupled to ATP hydrolysis. However, the three-dimensional structure of double-headed myosin consisting of two S1 subfragments has not yet been solved. Therefore, to investigate the overall shape and relative orientations of the two heads of myosin, we performed small-angle x-ray and neutron scattering measurements of heavy meromyosin containing all three light chains (LC(1-3)) in solution. The resulting small-angle scattering intensity profiles were best fit by models of the heavy meromyosin head-tail junction in which the angular separation between heads was less than 180 degrees. The S1 heads of the best fit models are not related by an axis of symmetry, and one of the two S1 heads is bent back along the rod. These results provide new information on the structure of the head-tail junction of myosin and indicate that combining scattering measurements with high resolution structural modeling is a feasible approach for investigating myosin head-head interactions in solution.