The structure of myosin obtained by X-ray diffraction or electron microscopy provides a basis for associating the biochemical with the structural states of actomyosin. Three structural states are known: the ‘pre-stroke’ M.ADP.Pi state, the A.M ‘rigor’ complex generated after actin-binding and a 10 nm swing of the lever arm, and the ‘post-rigor’ M.ATP complex. These states correspond to three of the four Lymn-Taylor structures, which allows predictions about the fourth and any intermediate structures.  Thus, the working stroke is coupled to the release of Pi from the A.M.ADP.Pi complex, or possibly the subsequent release of ADP. The nucleotide pocket is closed in the ‘pre-stroke’ states and is open in the ‘post-stroke’ states. While it is established that the working stroke precedes the release of ADP, it is also widely accepted that the working stroke is inseparable from phosphate release due to rapid state transition.  However, biochemical and mechanical evidence suggests otherwise.

Two-step actin-binding.

 

Single-myosin trap experiments show that myosin heads bind only to actin sites whose orientation in the azimuthal plane is close to optimal.  This observation lies at the heart of what can be termed the ‘Brownian post’ binding model, in which Brownian forces drive longitudinal fluctuations in myosin position.144  Current accepted values to crossbridge stiffness are between 2-3 pN/nm, and they severely restrict the head axial motion to less than 1 nm which is << 5.5 nm, i.e. the distance between two neighboring actin sites. Consequently, only a few myosin heads can readily bind to actin filaments. Thus, necessary increase in binding rates can be improved by using a more realistic model of the binding reaction, for example by the two-step binding mechanism, which is based on the observation that the neck region of myosin has a flexible joint at residue P841 (chicken numbering), near the S1-S2 junction. This flexibility may allow the head to search for actin sites by thermally-driven rotational movements about the joint, similarly as in myosin V. A swing of ±7nm is sufficient to let the motor domain access up to three actin sites, which may have favourable orientations in the azimuthal plane. We then assume that the motor domain makes a flexible bond with the chosen actin monomer, so that its preferred orientation is determined by the longitudinal head-site separation x and the lateral spacing of the two filaments. Then, the motor domain is assumed to roll on actin before locking into a specific orientation, which fixes the orientation of the lever-arm relative to the actin filament. This ‘swing-roll-lock’ mechanism was proposed by Ferenczi and collaborators to account for their X-ray diffraction observations on rabbit psoas muscle.

Schematics of a ‘swing-roll-lock’ mechanism for myosin-S1 binding to F-actin. The junction of the S1 lever arm to the rod is orientationally flexible, so that Brownian forces cause the detached head (D) to swing about this pivot to explore a range of actin sites and make a flexible bond to one site (F) without bending its lever arm. The head then rolls on actin to attain a stronger stereospecific bond to the actin interface (A). If the lever-arm is initially in its pre-stroke conformation relative to the motor domain, that relationship is maintained and the final configuration is a strained pre-stroke state. The Gibbs-energy profile shows that the height of the A-state potential well is lowered by strain.

Multiple working strokes.

 

For the working stroke on bound myosin, a more rigorous derivation of kinetics is possible because the reaction pathway can be viewed as one-dimensional, the reaction coordinate being the angle    of the lever-arm relative to actin filament. In this case, the intrinsic energy function         is assumed to be flat between sharp potential wells at      and      which define stereospecific pre-stroke and post-stroke states. Closed analytic formulae for the forward and backward stroke rates        ,             , can be obtained by applying Kramer’s’ theory of unimolecular reactions, in the simplified form valid for an overdamped system. The ratio of the forward and backward rates is the equilibrium constant                                  where the exponent contains the difference in strain energies. In the limit of large strain-energy barriers,                 and the stroke rate is limited by the highest energy in the pathway. In that case, the stroke rate is expected to be proportional to this Boltzmann factor when it is less than unity, and constant otherwise.

Schematics of the working stroke on bound myosin-S1. Left: the pre-stroke and post-stroke states A and R, with a negative head-site distance x so that in the A-state the bent lever-arm carries negative strain equal to x. After the working stroke h, the lever-arm carries positive strain x + h and is bent in the opposite direction. Centre: Gibbs energy g(x,q) versus lever-arm angle             for the stroke transition, with the A and R states defined by narrow potential wells. Right: Strain-dependencies of the forward and backward stroke rates            ,            predicted from this energy profile by Kramers’ theory.