Project 1: myosin mechanochemistry



Myosin, like all molecular motors, turns chemical energy into mechanical work.  The basics of this process are shown below (Fig. 1). 




Figure 1: Clockwise from the upper right, 1) myosin binds a molecule of ATP and rapidly unbinds from actin; 2) the ATP molecule is hydrolyzed in a reversible process, and this hydrolysis is coupled to a large conformational change in myosin; 3) myosin binds to actin, releasing phosphate and reversing the conformational change (the power stroke) in the process.  These steps cause actin to slide a distance d; and 4) myosin releases ADP.  This last step depends on force, which couples these chemical steps to myosin's mechanical environment.



Myosin is a unique molecular motor because it functions as part of a large ensemble.  For example, trillions of myosin motors work together during a typical muscle contraction.  In some ways, these large molecular groups are simple to model since random "noise" is averaged out.  This noise is a dominant effect in small molecular groups. 


The dynamics of these large ensembles are described by the following equations:


Where ni(x,t) is the probability density of finding a myosin molecule in the ith bound state (states 4 or 1 in Fig.1) at time t, and Ni(t) is the probability of finding a myosin molecule in the ith unbound state (states 2 or 3 in Fig. 1) at time t.  The variable x is the extension of the myosin molecule, and can be transformed into the force on the molecule with the expression F = \kappa_Mx, since myosin behaves like a linear spring (at least under some conditions).  The derivative of x with respect to time, v, is the velocity of actin relative to myosin.  The matrices Aij, Bij, Cij and Dij are determined by the reaction rates and their force dependence.  The goal of project 1 is to identify these matrices.


Below is a summary of our current progress toward this goal.  Details can be found in the papers (referenced below).


Publication 1: simplified conditions


Reference: Walcott, S., Warshaw, D.M. and Debold, E.P. Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements. Biophysical Journal, Volume 103, pages 501-10. 2012. PDF


In this paper, we used a large set of in vitro measurements published over the past twenty years to identify the matrices Aij, Bij, Cij and Dij in the absence of phosphate and ADP.  A model incorporating these values successfully fits measurements performed with anywhere between one and a hundred myosin molecules, both in the presence and absence of external force.  For example, Fig. 2 shows comparison between the model and measurements with ~10 myosin molecules at variable force.



Figure 2: A model describes experimental measurements with ~10 myosin molecules in the presence of variable external force.  A. The experimental set-up.  A small ensemble of myosin interacts with a bead-actin-bead assembly held in an optical trap (top).  Force, applied by controlling the position of the trap, slows the velocity of actin (bottom).  B. Simulations of this process (hollow dots) are consistent with measurements (filled dots) at two different concentrations of ATP.



This work not only represents progress toward our long-term goal of a model of myosin's mechanochemistry, but also gives insight into questions of immediate biological significance.  In particular, it had long been known that myosin, when working as part of a group, moves actin faster than would be predicted from single molecule measurements.  It had been suggested, based on thermodynamic arguments, that the force-dependent release of ADP was responsible for this discrepancy.  We were able to show that, indeed, internal forces between motors in an ensemble accelerate ADP release and are the cause of this increase in speed. 


Publication 2: phosphate


Reference:  Debold, E.P.*, Walcott, S.*, Woodward, M. and Turner, M. A., Direct observation of phosphate inhibiting the force generating capacity of a mini ensemble of myosin molecules. Biophysical Journal, Volume 105, pages 2374-2384. 2013. PDF  (*EPD and SW contributed equally)


When muscle becomes fatigued, phosphate concentration becomes elevated.  Phosphate decreases muscle's ability to generate force.  How phosphate affects myosin's interaction with actin is controversial. 


In this paper, Ned performed experiments with small ensembles of myosin (~10 molecules) in the optical trap.  As these myosins interact with actin, they generate force against the trap (Fig. 3A).  Phosphate strongly inhibits the forces generated by these small ensembles (Fig. 3B).


To model these experiments, we needed to modify our model from paper 1 to include the effects of phosphate.  Perhaps the most widely accepted model for phosphate's effect is that it reverses the power stroke and causes unbinding (a transition from state 4 to 3 in Fig. 1).  However, it has also been proposed that actin-bound myosin (state 4 in Fig. 1) can bind phosphate and subsequently detach without power stroke reversal.  Subsequently, it releases ADP and phosphate and rebinds ATP while unbound from actin.  This introduces a "branch" in myosin's mechanochemical cycle.  A model incorporating this branched pathway model fits Ned's measurements (Fig. 3B and C).


The model not only describes the average force generation of the ensemble (Fig. 3B) but also the distribution of forces (Fig. 3C), both in the presence and absence of phosphate.  Not only does this result provide strong support for the branched pathway model; but it also moves us closer to our goal of a model for myosin's mechanochemical cycle.




Figure 3:  A branched pathway model describes phosphate's effect on the force generation of ~10 myosin molecules.  A. The experimental set-up.  A small ensemble of myosin interacts with a bead-actin-bead assembly held in an optical trap (left).  As this small ensemble moves the actin filament, it generates a force against the trap (right).  B. Phosphate decreases the ability of these small ensembles to generate force and also decreases the duration of the interactions.  A branched pathway model (white) reproduces these effects.  C.  The model reproduces, not only the average force, but the distribution of forces (model in white, measurement in black; 0 phosphate top, 30 mM phosphate bottom).



Primary Collaborators


Ned Debold

Dave Warshaw