Here we found that the mechanical characteristics of one-headed myosin-V (M5SH) were very similar to that of a two-headed myosin-V chimera (M5DH), suggesting that one-headed myosin-V like its two-headed counterpart can achieve successive steps. Various parameters determined in the present study are summarized in . Although other groups have failed to observe successive steps by one-headed myosin-V 
, we have reasoned that this is due to the one-head's successivity being dependent on the angle of the actomyosin interaction 
. We also did a single molecular motility assay in combination with total internal refraction microscope 
to investigate the single-headed myosin steps (Figure S1
). While GFP (green fluorescent protein) fused to double-headed myosin-V moved unidirectionally along an actin filament with a 250 nm travel distance, single headed myosin-V proved incapable of displacing such long distances. The single bead trapping assay 
and three beads dumbbell assay 
also failed to observe successive steps by single-headed myosin-V. The cofilament assay we performed here might create preferable conditions for such steps by constraining M5SH, most likely a consequence of myosin-V's rigid neck region and the helical structure of the actin filament. Experiments using single-headed constructs of other myosins that lack a cofilament system like myosin-VI and myosin-IX have also observed successive steps, but these myosins have much more flexible necks than myoins-V likely making the angle dependency between the myosin and actin in those circumstances negligible 
One report has suggested that the stepsize of myosin-V depends on the neck region length 
. Furthermore, successive large steps have to date been explained by a hand-over-hand model where tilting of the long neck domain of the lead head biases the Brownian motion of the rear head forward 
. The rear head detaches upon ATP binding and rapidly moves forward ~72 nm to bind to actin 
. That means the lead head generates the step direction by titling its neck such that the rear head rebinds at a forward actin binding site. According to this model, the stepsize and neck length are proportional and one-headed myosin are incapable of successive steps. However, we have previously reported that short-necked myosin-V can produce successive large steps, challenging this model 
. So too, of course, do our results here. Ultimately, an alternative model is needed to explain one-headed successivity. We assume that M5SH when in a weak binding state does not completely dissociate from actin but rather diffuses along the actin filament using Brownian energy. In the double trapping nanometry (dumbbell assay), preferred binding sites on an actin filament appear every 36-nm along the helix 
. Myosin-V binds to these preferred sites while diffusing along the filament. A change in strain on the head causes Pi release, which conforms the head into a strong binding state 
The size and kinetics (dwell time) of the M5SH steps/strokes are consistent with M5DH and myosin-V HMM 
. To confirm therefore that the M5SH results were actually due to single heads and not two heads that were within such proximity that they could not be resolved by our equipment, we examined the properties of M5DH. While the stepsize and dwell time were the same, the load dependence between M5SH and M5DH was different. If we assume that successive steps by M5SH were actually due to two adjacent heads taking non-successive strokes, then the stepsize and dwell time for M5SH should be half that of M5DH and no differences in load dependence would be observed. Therefore, the results indicate that the observed mechanical activities of M5SH were due to one myosin-V head while M5DH functioned with some level of cooperativety between the two heads to prevent the two heads from simultaneously stepping, which would result in detachment. This may also be in part a consequence of our cofilament assay system, may generate two-headed structures that are geometrically constrained when interacting with actin in a manner that reduces the likelihood of successive steps.
M5SH and M5DH showed no differences between the dwell time force dependencies () or between the energy barriers for the direction of movement (). These results lead us to think that only one of the two heads in M5DH strongly interacts with the actin filament, which would enable large steps without applying the hand-over-hand mechanism. It should be noted that M5DH was dimerized with the myosin-II S2-fragment, not the coiled-coil region of myosin-V, which may account for a different mechanism. Still, while M5DH and M5SH shared some properties, they differed in other important ones. For example, M5DH had a higher stall force () and lower probability for detachment (). This was also seen when comparing two-headed and one-head muscle myosin-II 
, suggesting that the dimerized heads in our M5DH cooperate in a manner more similar to muscle myosin-II than native myosin-V. Therefore, it is possible that the coiled-coil region and/or the long neck length of native myosin-V is critical for stepping in a hand-over-hand manner, which would achieve long travel distances. This would explain why the distance travelled as estimated from the M5DH successivity (0.5) was shorter (80 nm) than that seen in myosin-V HMM (Fig. S1
). Another point of interest is the bias between forward and backward steps, a point we discuss in more detail below, which was 3.5 kB
T and is similar to that estimated for myosin-II (2–3 kB
. This may suggest that despite different behavior, the mechanism for directional bias might be the same among different myosins.
The process for M5SH steps following the strong binding state is thought to be ATP binding dependent, as there were no differences in the stepping kinetics for non-successive strokes, first strokes and successive steps (). Since the cofilament assay constrains the geometry of the acto-myosin interaction, it is possible that an observed successive step was actually a quick detachment and reattachment by the myosin-V head. Even if this is the case, for a second successive to be the same, the probability of a second reattachment 36 nm from the previous spot was estimated to be approximately 38% by using the trap stiffness (0.02 pN/nm) and Gaussian distribution of the trapped bead position. Moreover, for a third step successive step, the probability would be 3.8%, one-tenth the experimental value (30%). Therefore, successive M5SH steps are not the result of a quick detachment and reattachment. Assuming a myosin-V head diffuses along an actin filament when weakly bound, if the myosin-head finds an adjacent actin binding site during this diffusion period, it can release Pi and step forward; if not, it detaches. Under this assumption, M5SH can bind to 3 sites: forward, backward and the same position. Since the bias between forward and backward steps was 3.5 kB
T, the probabilities of the three bindings are 83.0% (forward), 14.6% (same position) and 2.4% (backward). Taking into consideration successivity (), the probabilities that second forward or backward steps occur are 25% (
0.3×83%) and 0.7% (
0.3×2.4%), respectively. The remaining 74.3%, including the probability for binding to the same position (4.3%
0.3×14.6%), is the probability of nonsuccessive strokes.
A possible model for explaining how M5SH develops its successive large steps is shown in supplemental Fig. S2
. M5SH in the ADP.Pi state diffuses back and forth over the actin filament via thermal stretching of its neck region and repeated dissociations and associations to an actin filament. When releasing Pi to take a strong binding state, the head tilts its long neck forward (23 nm stroke) and then releases ADP. When a subsequent ATP binds to the head, the head again diffuses along the actin filament. This time, should the head completely dissociate from actin, a non-successive stroke is observed. If, however, the head diffuses to a favorable binding site (13 nm forward), the head strains backward and thus accelerates strong binding in the forward target region based on the search-and-catch model 
. After rebinding, another 23 nm stroke occurs, enabling successive steps to be observed.
The behavior of M5DH can be explained by a similar model shown in supplemental Fig. S3
. One head strongly interacts with actin while the other weakly interacts. Therefore, only one head waiting for ATP binding senses a load, which explains why we saw no difference in the force dependency on dwell time between M5SH and M5DH (). After ATP binding, both heads take the ADP.Pi state and diffuse on the actin filament. The two heads alternate strong binding and swing their respective necks. At this time, load is exerted on both heads, resulting in force dependencies on successivity and unidirectionality that decreased two-fold compared to M5SH ( and ).
The geometry of the acto-myosin interaction is very important for the successive steps taken by myosin-V, as it influences the search-catch behavior made by the myosin-V head. In cells, myosin-V transports cargo toward the pointed end of actin filament, which is the direction of the membrane. Since actin filaments make up a meshwork that regularly overlays filaments on top of one another, myosin-V often switches filaments during its motility. However, such switching is likely inefficient for transport. Assuming the successivity of the myosin-V head depends on the acto-myosin geometry, myosin-V can preferentially select an actin filament without switching. The hand-over-hand mechanism, along with regulating movement, may also regulate the geometry in order to optimize transport.