Nonprocessive myosin motor moves unidirectional in cluster – the power of unite

The experiments are very clean and clear.

About the modeling, I do not quite understand. It is fine – I didn’t spend a lot of time.
Below is the methods section about image processing and simulation.

Image analysis of moving myosin VI nanospheres

A custom Matlab particle-tracking program (The MathWorks, Inc.) was used to identify and track the movement of individual nanospheres. Nanosphere centers were found by least squares fit to a 2D elliptical Gaussian function with a background (Churchman et al., 2005). To compensate for stage drift, fiducial (stuck to the coverslip surface outside the keratocyte) nanospheres were tracked and their movement was subtracted.

Simulation of nanosphere movement

Platinum replica images were digitized to obtain filament tracks using a custom Matlab program. Rotary shadowing with platinum/carbon results in progressively smaller quantities of platinum/carbon coating away from the apical surface of the keratocyte lamellipodium. This is reflected in actin filament darkness in the transmission electron microscope. Myosin VI molecules have a limited reach (~20 nm), hence we preferentially selected filaments, in the images, in the first 2–3 layers of the lamellipodium (~30 nm; Fig. 3 a). Nanosphere movement was simulated as described in the text (see the following section for details).

Nanosphere simulation algorithm

Dimer.

Movement of each dimer is considered stochastic, with a single exponential dwell time distribution having a mean of 0.2 s (derived from kinetic measurements; De La Cruz et al., 2001). Based on the geometry of the nanosphere (see Fig. S1), ~2 out of 10 myosin VI dimers coupled to a nanosphere interact with the actin network. Two independent stochastic dwell time sequences for the two dimers were created, and the order of movement was determined based on the dwell times of successive events. Distance between the dimers at the start of the simulation varies randomly from 10 to 100 nm depending on the location of actin filaments at the top of the image.

Movement of a dimer consisted of the following steps. (1) The trailing head (determined by relative “y” location) releases after a specified dwell time and samples a new binding site 32 ± 4 nm below the leading head, assuming uniform polarity from the cell periphery to the cell center. (2) A new binding site is selected such that the distance between the nanospheres attachment point (the attachment point is the midpoint between the two heads of a dimer) of the moving dimer and its coupled partner is maintained relative to its initial value at the start of the simulation. (3) Centroid of the nanosphere (halfway between the attachment points of the two myosin VI dimers) is updated. Release, stroke, and rebinding of the moving dimer are considered instantaneous, which is consistent with the high duty ratio of this motor (>0.8; De La Cruz et al., 2001).

Upon completing its dwell time, the second dimer now moves as per the first three steps outlined above. We assume that in events when a dimer undergoes two or more steps while the other remains bound, only the first step is successful and this dimer has to wait for its partner to step. This is consistent with the finite flexibility of the coupling between the two dimers and the large step size of myosin VI (~36 nm). Speed statistics from the simulation are based on movement of the centroid of the nanosphere, as observed under the microscope. We simulate the movement of ~20 nanospheres, thrice, over five separate digitized micrographs of the platinum replica network.

Monomer.

Similar to the dimer simulation, monomer movement is considered stochastic, with a single exponential dwell time distribution with a mean of 0.2 s. Based on the geometry of the nanospheres (Fig. S1), ~4 out of the 20 monomers coupled to the nanosphere are properly positioned to interact with the F-actin network. Four independent stochastic dwell time sequences were created, and the order of movements was determined based on the dwell times of successive events. The distance between the monomers at the start of the simulation varies randomly, with a minimum separation of 10 nm and a maximum separation of 100 nm for a group of four monomers. The separation distances are based on the area of the nanosphere that can access the keratocyte surface actin network.

Monomer movement consisted of the following steps. (1) The head detaches from the actin filament. Strain between the remaining myosins is now redistributed such that the forces between the remaining heads are balanced. The flexibility (effective spring constant keff) of each head is the same, hence the value of keff is not required for calculating the force balance. (2) The head rebinds below the nanosphere attachment point, assuming uniform F-actin polarity from the cell periphery to the cell center. (3) The head attempts to stroke through 30 ± 4 nm. The flexibility of all heads is identical, hence a force balance between all heads is used to calculate the net movement of each nanosphere attachment point and hence the movement of the bead centroid. (4) The strain in each head is monitored throughout the simulation. If the strain exceeds the permissible distension (variable, see Fig. 4 b), stiffness of that particular head–nanosphere attachment connection is set to infinity, and the strains in the system are calculated accordingly. This is consistent with the finite compliance in any head–nanosphere attachment being ironed out, leading to its nonlinear behavior. (5) After its stroke, the myosin head completes its subsequent dwell before releasing and continuing its stroke. (6) Unlike the two dimer case discussed above, where we assume steps between the two dimers are sequential, no explicit assumption of the order of strokes is made for the four monomers. The strain buildup in the system automatically adjusts the movement of successive strokes, either by the same myosin head stroking in succession or one head stroking after another. (7) To simplify our model, the only parameter we have introduced is the permissible distension in the heads. A stroking head that encounters a nonlinear distension of another head is assumed to complete a partial stroke and then release from the actin filament with a dwell time identical to what would occur in the absence of the load. This simplifying assumption, as stated in the text, causes differences between simulation and experimentation. However, in the absence of information on the kinetics of motors under these conditions, we have chosen no changes in kinetics as a first approximation.

After this monomer stroke, the next monomer releases, rebinds, and strokes in exactly the same sequence, and the movement is continued. The centroid of a nanosphere is the centroid of the attachment points of the four monomers. Speed statistics from the simulation are based on movement of the centroid of the nanospheres, as observed under the microscope. We simulate the movement of 35–40 nanospheres over five separate digitized micrographs of the platinum replica network.

J Cell Biol. 2009 Sep 28.

Coupled myosin VI motors facilitate unidirectional movement on an F-actin network.

Sivaramakrishnan S, Spudich JA.

Department of Biochemistry, Stanford University, Stanford, CA 94305 USA.

Unconventional myosins interact with the dense cortical actin network during processes such as membrane trafficking, cell migration, and mechanotransduction. Our understanding of unconventional myosin function is derived largely from assays that examine the interaction of a single myosin with a single actin filament. In this study, we have developed a model system to study the interaction between multiple tethered unconventional myosins and a model F-actin cortex, namely the lamellipodium of a migrating fish epidermal keratocyte. Using myosin VI, which moves toward the pointed end of actin filaments, we directly determine the polarity of the extracted keratocyte lamellipodium from the cell periphery to the cell nucleus. We use a combination of experimentation and simulation to demonstrate that multiple myosin VI molecules can coordinate to efficiently transport vesicle-size cargo over 10 microm of the dense interlaced actin network. Furthermore, several molecules of monomeric myosin VI, which are nonprocessive in single molecule assays, can coordinate to transport cargo with similar speeds as dimers.

PMID: 19786577