Myosin-5 varies its step length to carry cargo straight along the irregular F-actin track

Molecules of a myosin-5a construct labeled on the N terminus of one motor with a 20 nm gold bead were tracked by iSCAT microscopy at 100 Hz as they walked along actin filaments in the presence of 10 $\mathrm{\mu }$M ATP. For each molecule, the x, y position of the bead was determined with subnanometer precision (0.9 nm localization precision) (26) in each frame, allowing detection of the stride of the labeled motor and also the AB transition of the bead that accompanies the stride of the unlabeled motor (26) (Fig. 1 C and E). The difference between mean positions of the bead in successive B-states yields the length of each stride taken by the labeled head (Fig. 1B–D).

The histogram of measured stride lengths is strikingly multimodal, with very little overlap between adjacent peaks (Fig. 2A). This demonstrates unequivocally that myosin-5a takes strides of varying but quantized length and that iSCAT microscopy has the spatial precision to resolve these. The separation of adjacent peaks of 7 Gaussians fitted to the binned data is 5.45 $\pm$ 0.40 nm (mean $\pm$ SD), which corresponds to a separation of two actin subunits along the filament (5.5 nm), that is, it corresponds to neighboring subunits along one of the two long-pitch strands (Fig. 1B). The major peak at 71.8 nm corresponds to a distance spanning 26 actin subunits (expected value, 71.5 nm). This is the stride length expected from two canonical 13-subunit steps. The other peaks therefore correspond to strides that land on subunits nearby to the 26th along the same long-pitch actin strand. The family of peaks thus correspond to strides spanning 22, 24, 26, 28, 30, 32, and 34 actin subunits. Using the average of all the peaks, weighted by their normalized area, the spacing of subunits along F-actin is 2.758 $\pm$ 0.016 nm. Since the myosin motor binds stereo-specifically to actin (34), the width of each peak likely arises from imprecision of measurement. This is expected to be independent of stride length, and indeed, an excellent fit to the data is obtained using a single width parameter (SD = 1.195 nm) for all seven peaks (Fig. 2A).

Using iSCAT microscopy, it is therefore possible to describe any individual processive run by the precise numbers of actin subunits traversed in each of the strides. For example, the run shown in Fig. 1C–E can be described as 30, 26, 28, 28, 24.

The data indicate that all molecules behaved similarly. Thus, comparison of the trajectories of the 96 molecules (SI Appendix, Fig. S2A) shows that all molecules take a range of stride lengths, rather than some being inherently short-striders and others, long-striders. Also, the distribution of stride lengths is independent of the number of strides taken in a processive run (SI Appendix, Fig. S2B). Furthermore, a ${\chi }^2$ analysis showed that the length of each stride was independent of the length of the preceding stride. These are all features to be expected if successive strides are independent events.

The dataset of strides has an overall mean of 73.7 nm and SD of 5.66 nm. These overall values are close to those obtained in earlier studies using other methods that did not resolve the component peaks (11, 19, 21, 22). This indicates that the flexibility in stepping that we observe by iSCAT was also present in all those studies. This mean and SD can be represented by a Gaussian distribution and scaling its amplitude shows that it is a good fit to the relative amplitudes of the component peaks (Fig. 2A). This indicates that the underlying cause of variable stride length has a Gaussian character. We investigate this further below.

It is important to note that the overall mean value of stride length falls between our observed peaks, and thus does not correspond to a stride length that is ever taken. This is because binding sites for motors on F-actin are not separated by this mean value.

By using high-resolution iSCAT microscopy, we have thus revealed that molecules of myosin-5a take strides of variable length during a single processive run.

Quantitative analysis of the relative frequencies of each stride length (Fig. 2B) reveals further insights into the stepping behavior of myosin-5a. Each stride length is the sum of a forward step by the unlabeled motor followed by the labeled motor. For example, a 24-subunit stride can result from four different combinations {1st step subunits, 2nd step subunits}: {11, 13}, {13, 11}, {9, 15}, and {15, 9} actin subunits (Fig. 2B). Using the measured relative frequencies of the seven stride lengths (areas under the fitted peaks; Fig. 2 A and B), we found the least squares best-fit solution to the set of simultaneous equations containing the probabilities of the five underlying step lengths (motors spanning 9, 11, 13, 15, and 17 subunits) (Fig. 2B, Left panel). The fit was robust and excellent, with only small differences between the observed frequencies and those backcalculated from the fitted values of step probabilities (Fig. 2B, Right panel). The values of step probabilities versus step length are well fitted by a single Gaussian of mean 13.3 with SD 1.32 actin subunits (with associated fitting errors, 0.12 and 0.10 actin subunits, respectively) (Fig. 2C). These properties are strong evidence that the walking process is the result of a random and independent selection of step lengths governed by an underlying Gaussian probability distribution.

The range of step sizes that is implicit in the multiple stride lengths shows that the canonical 13-subunit step is not as abundant as previously thought. Only 56% of all steps are 13-subunits long (Fig. 2B, Middle panel, and Table 1). From the calculated relative abundance of the various step lengths (Fig. 2B), the average step length is 13.469 actin subunits (= 37.04 nm) (Table 1). Likewise, only 38% of the strides are 26-subunits, and this includes combinations of 11+15 subunit steps in addition to two 13-subunit steps. Only 32% of all strides are a combination of two consecutive 13-subunit steps (Fig. 2B, Right panel).

This analysis to determine step frequencies shows that myosin-5a is a more flexible stepper than has been widely recognized, and that the widely stated 36 nm step accounts for only about half of the steps taken.

We used cryoEM to examine the structure of full-length myosin-5a during stepping on actin, to test the earlier conclusions from nsEM. In practice, it proved difficult to get these samples into the holes of the support film, but a small dataset has been obtained that delineates the structures present.

In the presence of ATP, at low calcium concentration and with no cargo adaptor molecules, myosin-5a is mainly compactly folded (35–38). These folded molecules are autoinhibited and bind only weakly to actin (38). However a small fraction of molecules is found to be active and to move processively along actin (38), so these should be present in samples flash frozen and examined by cryoEM. 55% of the myosin molecules observed were in the extended conformation and attached by both heads to the same actin filament (SI Appendix, Fig. S3). This abundance of myosin-5a molecules attached to actin is not surprising because we used a high ratio of myosin to actin (1 molecule per 2.5 actin subunits). Counts of myosin molecules per $\mathrm{\mu }$m actin suggest that less than 10% of the added myosins were attached, which is consistent with the typical $\sim$10-fold regulation of actin-activated ATPase activity in full-length myosin-5a preparations (36). The relative scarcity of detached molecules may arise from their adsorption to the carbon film.

In raw cryoEM images, the motor domains, levers and the first, coiled-coil segment of the tail are frequently identifiable (Fig. 3A). The two heads of doubly attached molecules typically show asymmetry recalling the appearance seen in negative stain (6), with the two levers pointing in opposite directions. A global average of doubly attached molecules with motor domains 13 actin subunits apart improves clarity (Fig. 3D). Both motor domains are attached on the leading side of subdomain 1 of actin (compare with the atomic model, Fig. 1A), with the N-terminal SH3-fold subdomain extending as far forward as the axial position of subdomain 1 of the next actin subunit, as in models of primed and unprimed heads on actin (Fig. 1A) (40). There is lower density between the motor and lever in the trail head than in the lead head (arrow, Fig. 3D), again in accord with the expectations from molecular models. The levers are visible throughout their length and unite at the head–tail junction without a gap, showing that the two polypeptide chains of the proximal coiled coil tail are not stretched apart by the stress within the doubly attached molecule. All these features recall those seen using nsEM (6, 33), and which can also be seen in averages from a new nsEM dataset (Fig. 3C). An exact correspondence between the cryoEM and nsEM averages should not be expected as they are fundamentally different imaging modalities, and there is flattening during drying in nsEM (41) that is avoided in cryoEM.

In the trailing head, the lever emerges from the leading side of the motor, near the SH3 domain, as expected for an unprimed head. The angle between the trailing lever and F-actin axis in the global average where the two motor domains are 13 subunits apart is 40°, as previously found by nsEM at rate-limiting, low ATP concentration (39° to 49°) (7) in which the trailing heads were largely devoid of ADP. This indicates that release of ADP from the trailing head has little effect on the overall geometry of the doubly attached myosin-5a, in contrast to the small lever swing found for single myosin-5a heads attached to actin when ADP is released (13, 34).

The leading heads show an abrupt angle between motor and lever and the lever emerges from the trailing side of the motor, indicating that the converter is in a near-primed position, despite the motor having released phosphate (7, 42) (Fig. 3D). Classification of the leading lever region shows variation in shape, with some levers convexly curved away from the actin filament and emerging from the motor at ∼120°, rather than straight and emerging from the motor at ∼140° (Fig. 3D, Right panels). The curved levers still emerge from the trailing side of the motor domain, not the leading side. Thus in these cryoEM data, the leading motor domains are in a near-primed conformation, not unprimed.

The cryoEM data demonstrate that the observations made previously using nsEM (6, 7) are not artifacts of staining and drying. In particular, the two motor domains of the doubly attached molecule are in different structural states despite being in the same biochemical state. This may underlie their different rates of ADP release (42, 43).

Myosin-5a molecules with both heads attached on the actin filaments were identified and the separation between the two motor domains of the myosin molecule was measured by an unbiased method, whereby the positions of both motors were determined independently following alignment and classification. For this analysis, it was not necessary to determine the polarity of the F-actin filament or to identify which of the two motors was the lead or trail head. In the cryoEM dataset, motors are found to be separated by 11, 13 and 15 actin subunits (Fig. 3A). 77% of molecules have motors attached 13-subunits apart, 10% have motors 11-subunits apart and 13% are 15-subunits apart (Fig. 3E). The mean separation is 13.038 actin subunits (= 35.86 nm) (Table 1).

A new dataset was also obtained using nsEM of the same myosin-5a construct as used for iSCAT and walking along phalloidin-stabilized F-actin under the same conditions as the iSCAT assay, including 10 $\mathrm{\mu }$M ATP rather than the 1 $\mathrm{\mu }$M ATP used in earlier studies (6, 33). This higher ATP concentration should produce a higher fraction of doubly attached molecules that have ADP in the trailing motor domain ($\approx$50% at 10 $\mathrm{\mu }$M ATP cf. $\approx$10% at 1 $\mathrm{\mu }$M ATP). Analysis shows 9-, 11-, 13-, 15-, and 17-subunit separations (Fig. 3 C and F). Unlike in longer steps, the global image average of molecules stepping 11 subunits shows the leading head lever emerging from the leading side of the motor domain. This indicates that the smaller separation of motor domains allows the leading motor domain converter to move to the unprimed position, as found previously (33) with concomitant distortion in the proximal lever. Like in the cryoEM data, 13-subunit steps are strongly favored (75%), with a mean step length of 13.044 actin subunits (35.87 nm) (Table 1). Suppression of CAD may account for the narrower distribution of step length in both sets of EM data: in cryoEM by physical forces in the thin aqueous film prior to freezing (44, 45), and in nsEM by phalloidin strengthening interactions between adjacent actin subunits (46). Phalloidin stabilization, which by increasing the rotation per actin subunit (46) moves the 13th subunit further from straight ahead, and brings the 15th subunit closer to straight ahead, has little effect on the step-length probabilities. The EM data complement the iSCAT data by showing the step lengths directly whereas the iSCAT data show strides, which each contain a pair of steps. Both EM methods show a reduced proportion of 15-subunit steps compared with iSCAT.

If F-actin was a perfectly regular helix, i.e., had a fixed rotation per subunit, our observation of randomly variable step length would imply that the myosin-5a molecule walks drunkenly along actin, moving left and right around the filament as well as along it (Fig. 4A). However, in our iSCAT assay, myosin-5a walks straight along actin, staying perpendicular to the plane of the microscope coverslip to which the actin is bound (as described previously (26); see also SI Appendix, Text). A possible solution to this paradox is that CAD in F-actin could force myosin-5a to vary its step length to continue walking straight. This would be equivalent to someone walking across a river using stepping stones that are spaced at variable separations along a regular lattice (Fig. 4B). Thus, the relative frequencies of stride lengths would reflect the characteristics of CAD in the F-actin used in the iSCAT assay. We have therefore tested whether CAD in F-actin could be of sufficient magnitude to account for the observed striding behavior. In doing this we have enlarged upon two methods for assessing CAD from images of F-actin (28), using recently published cryoEM images of F-actin (17), and show that CAD is indeed present (SI Appendix, Text and Figs. S4–S7).

The implication of CAD for myosin-5a walking is as follows. The mean azimuth (μ_n) of the nth actin subunit, in degrees, relative to that of a starting subunit having an azimuth (${\mathrm{\mu }}_0$) of 0° is given by

where $\varphi$ is the mean rotation per subunit in the filament. The SD (${\sigma }_{\mathit{n}}$) of that azimuth depends on the RMSD disorder value, $d$, and the number of subunits through:

Thus, for any pair of values of $\varphi$ and $d$, one can estimate the probabilities of the 9th, 11th, 13th, 15th, and 17th subunits being closest to an azimuth of 0° and thus the preferred target for straight walking (Fig. 5A). It is important to appreciate that on the rare occasions when the 17th subunit is optimally positioned, the 13th will be at $\mathrm{\mu }$$\approx -{55}^{°}$, requiring a significant reach around the actin. We now apply these principles to test whether CAD can account for the relative frequencies of each step and stride length.

If the variable step lengths in the iSCAT data were solely a response to CAD in actin, then our estimates of the relative frequencies of 9, 11, 13, 15 and 17-subunit steps should closely match the relative probabilities of those subunits being correctly positioned for straight walking due to CAD. We therefore used our five stepping frequencies to constrain least squares best-fit estimates of $\varphi$ and $d$ in the set of five pairs of equations for μ_n and σ_n to test whether the resulting values agree with current estimates. A robust fit was found, yielding $\varphi =-166.{39}^{°}\pm 0.{11}^{°}$ and $d=5.{28}^{°}\pm 0.{26}^{°}$. Both these values are close to previous estimates, and there is an excellent match between the measured and fitted probabilities of the five step lengths (Fig. 5B). Radial plots of the probability distribution illustrate the range of azimuth that each target actin subunit occupies, as viewed along the actin filament axis (Fig. 5C). The enlarged segment around $\mathrm{\mu }=0^{°}$ shows the azimuthal dependence of probability for straight walking (Fig. 5D). For the 17th subunit, the shallow slope of this dependence accounts for the relatively narrow error limits. We conclude that the presence of CAD in F-actin is sufficient to quantitatively account for the variable step lengths taken by myosin-5a.

If CAD is indeed the origin of variable step lengths in the iSCAT assay, then it should also account for the variable stride lengths. The $\varphi$ and $d$ parameters of the actin filament derived from stepping probabilities were therefore used to predict the relative probabilities of the 22nd to 34th subunit positions that are the target sites for the striding motor. These also give a very good match with the observed frequencies (Fig. 5E). The radial plots of probability distribution for strides (Fig. 5 F and G) are noticeably broader than those for the steps, demonstrating the progressive reduction of the correlation with the starting azimuth that is a feature of cumulative (liquid-like) disorder. This good fit to the striding data indicates that CAD in actin does indeed account fully for the spread and relative frequencies of strides observed in the iSCAT data.

Our analysis demonstrates that typical amounts of CAD in F-actin are sufficient to dictate a widely varying stepping pattern for a myosin-5a molecule walking straight.

The EM data give a complementary view of myosin-5a stepping to that of iSCAT, in that the myosin is walking along F-actin that is free in solution, rather than apposed to a surface, at the point of EM grid preparation. This is similar to previous data on myosin-5 twirling around single actin filaments suspended between supports, and these showed a net left-handed rotation during stepping (30–32). For the cryoEM dataset, longer steps are rarer than in iSCAT, indicating that myosin-5a prefers to take 13-subunit steps even when CAD means that it must move left-handed around the F-actin axis to do so. The average step length 13.038 actin subunits) is therefore shorter than the average iSCAT step length (13.469 subunits). As a result, using the value of $-$166.39° for mean actin rotation per subunit, derived above from the iSCAT data, together with the proportion of each step length in the data, yields an average azimuthal movement that is left-handed of $-$2.55° per step. This value implies that on average, myosin-5a would take 141 steps to complete a left-handed rotation around the filament, while moving 5.1 $\mathrm{\mu }$m along it. The nsEM dataset is very similar, yielding an average step length of 13.044 subunits. Since the nsEM data were obtained using phalloidin-stabilized F-actin that has a rotation per subunit of $-$167° (46), the mean rotation per step is $-$10.43°, so a complete left-handed rotation would require only 36 steps covering a distance of 1.3 $\mathrm{\mu }$m.

When myosin-5a takes a long step, the levers necessarily lie at a smaller angle to the actin filament than when it takes a short step, as is indeed seen by EM (Fig. 3). Since release of ADP from the head moves the lever to a smaller angle to actin (13, 47) it might be expected that when the motors are separated by more actin subunits, the rate of ADP release from the trail head would be accelerated, resulting in a shorter dwell time, than would be observed with shorter separations. Conversely, short steps suggest a larger lever angle, slower ADP release, and longer dwell time. Because iSCAT resolves varying stride lengths, we have been able to test this idea. There is the complication that a stride may comprise a short step plus a long step in either order, but the shortest strides will comprise only short steps, or longest strides only long steps. The two dwell times that refer to a given stride are those of the B state that precedes it and the A state that follows it (Fig. 1E and Fig. 6A). Therefore, we have analyzed these dwell times for each stride length.

We found that there was no significant difference between the dwell times for the A states compared to those of the B states, regardless of stride length, in agreement with our earlier study (26), and thus confirming that the gold bead did not affect stepping kinetics. Violin plots of combined A-state and B-state data were similar across all stride lengths, with the most common stride lengths showing the greatest range of values, as expected (Fig. 6B). Consequently, there was meager evidence of dependence of rate constant on stride length (Fig. 6 C and D, and SI Appendix, Fig. S8), with rate constants for the two fitting models of $k_s\approx 4.5{\text{s}}^{-1}$ and $k_f\approx 12{\text{s}}^{-1}$ (Fig. 6C and SI Appendix, S7A) or $k\approx 7s^{-1}$ (Fig. 6D and SI Appendix, S8B) and no significant difference between the models as a fit to the data. We conclude that the walking rate, and thus ATPase kinetics, of myosin-5a is not greatly dependent on step length.

In contrast to common statements that myosin-5a walks by taking 36 nm steps along actin, we find that only about half the steps span the canonical 13 subunits (35.75 nm). Almost a quarter span 15 subunits with progressively smaller proportions spanning 11, 17 and 9 subunits. Because of this diversity of step lengths, neither the average step nor average stride length corresponds to an actual movement, as these average values fall between the separation of actin-binding sites. These results from the iSCAT assay pertain also to previous assays that used F-actin attached to a coverslip or suspended between a pair of beads in the optical trap. This is because in each case only a limited azimuth of F-actin is available for the myosin to walk along. The presence of a family of unresolved steps or strides in the previous data explains why the breadth of the observed distribution was broader than would have been expected from the resolution of the methods used.

We show that CAD exists within F-actin specimens prepared for cryoEM by modern methods. Remarkably, CAD is of sufficient magnitude to account for the relative frequencies of the step and stride lengths found in the iSCAT data for myosin walking along a single azimuth of the actin filament. This nicely resolves the paradox of how myosin-5a could take steps of varying length while still walking straight on the helical F-actin. Recent high-resolution cryoEM structures of F-actin (17, 18, 48–50) disregard this feature of F-actin structure, instead emphasizing a precise (average) value for subunit rotation (close to $-$166.5° per subunit). However to obtain high resolution, these studies use thin ice, which has been shown to suppress CAD by shear and compressional forces (44, 45). Thus, high-resolution cryoEM can lead to misleading conclusions by suppressing inherent structural flexibility. High-resolution studies also restrict the reconstructed volume to 3 to 8 actin subunits (17, 51) which further reduces the impact of disorder. When a longer segment of filament is used, resolution falls (17), as is expected from CAD.

Our study has revealed the biological significance of CAD in influencing the behavior of myosin motors. Although CAD has been well-characterized for F-actin purified from skeletal muscle (27, 28), there are no data on CAD in cytoskeletal actin isoforms (52), and also no data for the influence of cytoskeletal tropomyosin or for CAD in actin filaments bundled by cross-linking proteins such as fascin or fimbrin. Although for some of these complexes, there are data on filament flexibility, there is no established causal linkage between the magnitude of CAD and flexibility. Our study therefore indicates a need for further research to characterize CAD in the cellular environment and to understand the roles of CAD in determining cellular behavior. Understanding the temperature dependence of CAD magnitude and dynamics would also be beneficial for understanding the importance of CAD in F-actin under physiological conditions for warm- and cold-blooded animals.

Previous studies have directly shown that myosin-5a molecules can walk left-handed around a suspended actin filament that has been stabilized by phalloidin (30–32). Phalloidin increases average actin subunit rotation to $-$167° (46). This moves the 13th subunit to an average azimuth 11° left of straight ahead and correspondingly the 15th subunit moves to be only 15° to the right. Thus, walking straight on such filaments requires a high proportion of 15 subunit steps. For myosin taking mainly 13 subunit steps, as we observe by both cryoEM and nsEM, the molecule would twirl left-handed around the filament more strongly than for phalloidin-free F-actin. This may account for the shorter pitch of twirling ($\sim$2 to 3 $\mathrm{\mu }$m) (30–32), which is comparable to our prediction of 1.3 $\mathrm{\mu }$m for phalloidin F-actin and shorter than our prediction of 5.1 $\mathrm{\mu }$m for phalloidin-free F-actin. This can be compared to an average run length of $\sim$1.3 $\mathrm{\mu }$m (53–55), from previous studies. The earlier conclusion that left-handed twirling along phalloidin-stabilized F-actin implied that myosin took 11 and 13 subunit steps (30) is incorrect, because it assumed $-$166.154° rotation per subunit for F-actin (i.e., 13/6 helical symmetry) rather than $-$167°.

In studying myosin-5a walking on F-actin by cryoEM, we found it difficult to get the walking molecules into the holes of the EM support film. Nevertheless, our small dataset clearly shows that the converter of the leading motor domain is held in a stressed, near-primed position through tethering to the trail head. Thus, the flash-frozen, unstained walking molecule appears similar to our previous studies using nsEM at very low ATP concentrations (6, 33), and also to the nsEM data presented here that were obtained at ten times higher ATP concentration than previously.

The “Telemark skier” analogy used to describe the appearance of doubly attached myosin-5a (6) has since been interpreted by some to mean that both motor domains are in an unprimed conformation, with the lead lever bent back to create the knee of the skier (19). The EM data presented here confirms that this is not the case. The leading lever is not bent. Instead, the knee of the leading leg of the skier is actually the lever–motor junction, with the lower leg being formed from the motor domain together with the actin subunit it is attached to and appearing angled backward because the motor is attached to the leading side of the prominent subdomain 1 of actin. In contrast, in the trailing head, actin subdomain 1, the motor domain and the lever are all roughly colinear, creating the different shape resembling the trailing leg of the skier. As the powerstroke of myosin-5a is similar in distance to the canonical step length of 35.75 nm (56), a primed myosin head could easily bind to create the next leading head, with the subsequent rapid release of phosphate (42) generating stress within the doubly attached molecule as the head is unable to adopt the preferred unprimed (postpowerstroke) structure of actomyosin.ADP.

Our nsEM, performed at the same ATP concentration as the iSCAT assay shows that for 11-subunit motor separation, this tethering is insufficient to prevent converter movement to the unprimed position, with concomitant distortion of the leading lever but little change in the trailing lever (Fig. 3C). This may explain why we find that the stepping rate is not slower for short steps, but it is unknown whether this also reduces gating of lead motor ADP release.

Our analysis indicates that myosin-5a has to take variable length steps in the iSCAT assay because the sample geometry restricts azimuthal variation, forcing the motor domain to attach to the subunit of the disordered actin filament that is closest to straight ahead. Thus, the mechanical properties of the myosin cannot be directly assessed, only that there is sufficient compliance within the molecule to allow it to vary its step length over the range observed. However, a similar range of step lengths to that found by iSCAT, albeit that 13-subunit steps are more strongly favored, is found by both cryoEM and nsEM, in which the myosin is free to explore around the actin filament to locate binding sites. This similarity indicates that myosin-5a has a preferred lever–lever angle that places the motors $\sim$36 nm apart, as we previously proposed from iSCAT data (26). The greater frequency of 13-subunit steps in the EM data, unaffected by the change in actin azimuths produced by phalloidin stabilization of F-actin, indicates that when the myosin is free to explore around the actin filament to overcome the effects of CAD, there is a still a preference for binding with a 13-subunit motor separation, reinforcing the idea of a preferred geometry for the singly attached molecule.

The symmetrical Gaussian spread of the frequencies of shorter and longer steps further suggests a thermally driven fluctuation in motor separation that allows both longer and shorter steps. This could arise from bending within the levers and at the lever–motor junctions and from fluctuations in the lever–lever angle. An estimate of the ease of such fluctuations can be derived from the observed spread of step lengths. The SD of the distribution of step lengths leads to an estimate for the stiffness of the molecule along the actin filament axis, through the Equipartition Principle, as stiffness, $\kappa =k_{B}T/{\sigma }^2$. For our nsEM data, $\sigma$ = 3.289 nm (Table 1) yielding $\kappa =0.374\text{pN/nm}$. If we suppose that the lever–lever angle is fixed, then since the two heads are mechanically in series, the stiffness of each head would be 0.748 pN/nm. A similar SD (3.0 nm) was reported by Oke (57) also using nsEM, indicating a similar stiffness.

Because we have been able to examine the dependence of stepping kinetics on stride length, we can use this estimate of myosin-5a stiffness to compare our data with earlier optical trap measurements of the impact of external force on kinetics of ADP release and ATP binding by single myosin-5a heads (13, 58, 59). Our EM data indicate that a 13-subunit motor separation has least strain. A 15-subunit separation implies a forward displacement of the lever–lever junction of 2.75 nm, and thus an assisting force on the trailing head of $2.75\times 0.374=1.03\text{pN}$. For a 17-subunit separation, the force would be 2.06 pN, which would be expected to produce a marked acceleration of ADP release based on measurements made using optical trapping under different resisting loads (58–60). This should, thus, result in a reduction in B-state dwell time. It remains to be understood why this acceleration was not detected, but we note that in the iSCAT assay the orientation of the head with respect to the actin filament axis is closely specified (and relevant to myosin walking in the cell), whereas in the optical trap, the orientation of the head is not known.

Our demonstration of variable step and stride lengths for myosin-5a (Fig. 7) provides a framework for understanding how the molecule manages to transport cargoes through the complex and crowded cytoskeletal matrix. The molecule is sufficiently flexible that it can vary its motor separation to accommodate variations in track structure, and even to switch between tracks (26, 61, 62), yet it is stiff enough to move cargo forward. F-actin has intrinsic angular disorder that likely gives it the structural plasticity to fulfill its many cellular roles as single filaments, networks, and bundles through interactions with other proteins, but at the expense of requiring myosins to cope with its disorder. It is tempting to visualize cargo transport in the cell as analogous to railway tracks along which engines are pulling carriages, and thus to imagine actin filaments as fixed tracks with myosin-5 molecules marching robotically along them. Our data show that the nanoscopic reality is less certain and more subtle. Unlike in macroscopic transport systems, both motor and track are “soft,” containing elements of random disorder that create adaptability.

Rabbit skeletal muscle G-actin was prepared using the standard method as described (63) and stored in liquid nitrogen until use. For the iSCAT measurements and nsEM, a mouse myosin-5a HMM-like construct (i.e., having the two heads together with the proximal coiled coil, like heavy meromyosin derived from muscle myosin-2; myosin-5a amino acid sequence 1 to 1,090) with an N-terminal AviTag biotinylation sequence (64, 65) and C- terminal eGFP and FLAG sequence was expressed in the presence of calmodulin, using the Sf9/baculovirus expression system and purified as described previously (66). The amino acid sequence of this construct can be found in SI Appendix, Fig. S9. For cryoEM, the melanocyte-specific isoform of full-length mouse myosin-5a heavy chain (67) was expressed together with calmodulin in Sf9 cells, purified using an N-terminal FLAG tag, and stored drop-frozen in liquid nitrogen, similar to as described before (66).

In iSCAT microscopy (68, 69), a 445 nm diode laser beam is scanned across the sample using a pair of orthogonal acousto-optic deflectors (Gooch & Housego) mapped into the back focal plane of the objective (PlanApo N 60x, 1.42 NA, Olympus) with a 4f telescope, giving an approximately 30 $\times$ 30 $\mathrm{\mu }$m illumination. The illumination and detection paths are separated using a quarter-wave plate beneath the objective and polarizing beam splitter after the 4f telescope. The detected signal is imaged onto a CMOS camera (MV-D1024-160-CL-8, Photonfocus) at approximately 333$\times$ magnification (31.8 nm/pixel). The true magnification was determined using a calibrated resolution grid (Thorlabs) (SI Appendix, Fig. S1D).

Myosin-5a HMM construct was biotinylated and bound to streptavidin-conjugated 20 nm gold nanoparticles. The flow cell was prepared using 50 $\times$ 25 and 25 $\times$ 25 mm #1.5 coverslips separated with 100 $\mathrm{\mu }$m double sided tape as described (70, 71). The flow cell was loaded with F-actin and monitored via the iSCAT microscope, as it can monitor label-free proteins (72). After blocking with BSA, a myosin-5 ATP mixture was introduced. The final assay composition in which stepping was observed, was as follows: 77 pM 20 nm gold nanoparticle attached with 25 pM myosin-5a HMM, 10 $\mathrm{\mu }$M ATP, 5 $\mathrm{\mu }$M calmodulin, 40 mM KCl, 5 mM MgCl${}_2$, 0.1 mM EGTA, 5 mM DTT, 20 mM MOPS (pH 7.3). Data collection was performed at room temperature (19 to 22 °C) and flow cells were not used for more than 30 min.

iSCAT images were collected at 200 Hz and averaged to 100 Hz. After 2D Gaussian fitting, the x,y positions of the gold particles were used to calculate myosin stride sizes. Binned stride lengths were fit with a sum of seven Gaussian functions using a least-squares method. The probabilities of step lengths were calculated by a least squares best-fit solution to the set of simultaneous equations containing the probabilities of the underlying step lengths. Dwell time models were fit with maximum likelihood functions, minimizing a single global negative log-likelihood function for all strides.

For nsEM, F-actin was stabilized with equimolar phalloidin and mixed with the same myosin-5a construct used in the iSCAT assays but without gold beads, in the presence of 10 $\mathrm{\mu }$M ATP. The final mixture comprised 500 nM F-actin, 25 nM myosin in 50 mM NaCl, 1 mM MgCl${}_2$, 0.1 mM EGTA, 10 $\mathrm{\mu }$M ATP, 10 mM MOPS, pH 7.0. After 30 s incubation, samples were negative stained with uranyl acetate on carbon filmed EM grids and imaged by CCD camera at 0.31 nm/pixel. For cryoEM, full-length mouse myosin-5a was incubated with four moles calmodulin per mole myosin overnight in ice. ATP was added, then F-actin, to give a final mixture comprising 0.83 $\mathrm{\mu }$M myosin-5a, 3.6 $\mathrm{\mu }$M calmodulin, 2.1 $\mathrm{\mu }$M F-actin, 0.20 mM ATP, 95 mM KCl, 48 $\mathrm{\mu }$M MgCl${}_2$, 0.12 mM EGTA, 10 mM MOPS, pH 7.0 at 22 °C. The mixture was applied within 10 s to a lacey carbon grid (glow discharged in amylamine), quickly blotted with Ca-free paper and flash frozen in ethane slush. Images were recorded at $\sim 4\mathrm{\mu }\text{m}$ underfocus by CCD camera at 0.589 nm/pixel.

A.F., Y.T., J.A., J.R.S., P.K., and P.J.K. designed research; A.F., Y.T., K.T, J.A., N.B., and S.A.B. performed research; A.F., Y.T., N.B., G.Y., D.C., J.A.H., J.R.S., P.K., and P.J.K. contributed new reagents/analytic tools; Y.T., J.A., J.R.S., P.K., and P.J.K. conceptualization and supervision; Y.T., J.A., and P.J.K. writing original draft; A.F., Y.T., K.T., J.A., N.B., G.Y., S.A.B., A.P.C., and P.J.K. analyzed data; and A.F., Y.T., J.A., N.B., A.P.C., J.R.S., P.K., and P.J.K. wrote the paper.

The authors declare no competing interest.