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

Significance Myosin-5 carries cargoes inside cells by walking along helical F-actin filaments. Myosin-5 avoids walking helically by taking long steps equal to F-actin’s helical repeat. Previous measurements of step length show a broader spread of values than expected from the spatial resolution of the technique. We used iSCAT and electron microscopies, which have subnanometer precision, and find that the broad peak is really a family of narrow peaks that correspond to steps spanning different numbers of subunits along F-actin. We show that disorder within F-actin is the reason myosin-5 varies its step length because the F-actin subunit best oriented for walking in a straight line changes from step to step. Thus F-actin disorder has important impacts on cellular functions.

Test 1: Consecutive crossover correlation.The first test examines the relationship between successive crossover spacings by creating a scatter plot from pairs of adjacent crossover spacings (Figure S5A).For a perfect helix, measured without error, all spacings will be identical (Figure S5A i).Introducing position error in the measurement, which generates a crossover spacing error (see Supplementary Methods) along a perfect helix, the data points cluster into an ellipse with major axis having slope -1, because an overlong crossover estimate tends to be followed by a short one (and vice versa) (Figure S5A ii).The result is that the standard deviation of the data projected onto an axis of slope -1 (SD-1) is much greater than that projected onto the orthogonal axis of slope +1 (SD+1).The ratio of the two SDs (SD-1/ SD+1) is 1.73 (Figure S5A ii, inset), and is essentially independent of the magnitude of error from picking (Figure S6B).In contrast, the randomness inherent in CAD scatters the points in all directions from the mean center (Figure S5A iii).The non-linear relationship between crossover spacing and subunit rotation angle results in a SD slightly higher on the axis of slope +1 than on the orthogonal axis of slope -1, yielding a SD ratio of 0.97 (Figure S5A iii, inset).This value is, again, invariant with CAD magnitude (Figure S6D).As expected, a combination of CAD and position error produces an intermediate SD ratio between the two limiting values (Figure S5A iv).This modelling thus shows that an SD ratio below 1.73 is an indicator of CAD, but does not directly yield a value for CAD because the magnitudes of CAD and position error interact to determine the net SD ratio (Figure S6B and D).
In the cryoEM images, the polarity of each filament could be assigned by eye and the locations of the series of crossovers were clear (Figure S5C).For n = 371 crossovers picked in n = 54 actin filaments, the mean spacing (x) was 37.95 nm with an SD of 2.19 nm.The mean spacing implies a mean rotation per subunit (ϕ) of -166.96°,close to the value (-166.85°)reported for these images (6).The scatter plot of successive crossover spacings yielded a SD ratio of 1.36, well below the value for position error (1.73), and this thus indicates a strong contribution from CAD (Figure S5D).Test 2: Cumulative variance.The second test for CAD derives from its cumulative nature.For a family of filaments, the set of measurements of the distance along a filament between crossovers separated by a given number of crossovers will have a mean and SD.For a perfect helix picked with zero error, the SD will always be zero (Figure S5B i).Modelling confirms that when position error is added, the SD of crossover distance does not depend on how many crossovers intervene, because the magnitude of SD derives only from the position errors at the start and end crossover locations in the image (Figure S5B ii).For a helix with CAD there is additional variability because the crossover spacings really are shorter and longer.The further one progresses along the filament, the broader the range of possible crossover positions will be and thus the SD of crossover position rises with crossover number (Figure S5B iii).More detailed analysis of large numbers of long model filaments and using a range of CAD magnitudes confirms the rise in SD and also shows that the variance of crossover distance rises linearly with crossover number (Figure S7A and B).The SD of crossover distance rises linearly with CAD over the range 0 -10°(Figure S7F).Position error increases the SD through an addition to the variance value.It thus adds a constant offset to the variance values and has no effect on the slope (Figure S7C).Helical geometrical arguments relate crossover spacing to subunit rotation and this in turn allows a least squares estimation of both CAD and position error (see Supplementary Methods).
Applying this test to the cryoEM data, the SD of crossover distance does indeed increase with the number of crossovers traversed, confirming that CAD is present in the F-actin (Figure S5E).The data points are noisy because of the random fluctuations expected within the relatively small dataset (n = 54 filaments analyzed).The least squares fit yielded an estimate of 2.24°per subunit for CAD (Figure S7F), with a crossover error SD of 1.30 nm, implying a position error of 0.92 nm (Figure S6D).Applying these estimates to the first test (above) predicts a SD ratio of 1.31, close to the value of 1.36 observed.
Therefore, we conclude that CAD is an overlooked feature of F-actin.The CAD of 2.24°per subunit in this cryoEM dataset is lower than is usually found.However, further analysis of an earlier cryoEM dataset(7) also found a low value (2.5°) which was ascribed to suppression of CAD by compression and shear forces in the thin ice layer needed for high resolution cryoEM (8,9).

Orientation of myosin-5a in the iSCAT assay.
To fully understand the geometric implications of the experimental results, one must consider the geometry of the myosin-5a molecule relative to the experimental imaging axis.It is possible to rule out the scenario where the myosin-5a molecule binds and remains parallel to the glass surface, along the side of actin filament, for the entirety of its processive run.Due to BSA surface blocking, possible myosin binding sites on the side of the actin filaments are far more inaccessible as compared to those on the top.Binding of myosin-5a on top of the filaments will therefore minimize surface interactions with the gold label.Additionally, through experimental comparison of myosin-5a which has been labelled either at the motor or at the end of the coiled-coil domain, a significant contrast difference is seen between the motor-bound and coiled-coil-bound gold particles with the actin filament in focus.This difference in contrast is consistent with

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an approximately 40 -60 nm difference in height above the actin (10).Should myosin commonly bind and process on the side of the actin, parallel to the glass surface, no such contrast difference would have been observed.
Also, the off-axis unbound state reported in Andrecka et al. (10) -Figure 8 -has a mostly circular probability distribution.
If a myosin-5a molecule started off parallel to the coverslip and rotated around the actin azimuth during its processive run, this distribution would become elliptical over the course of the run with the long axis at right angles to the actin filament axis.No such change in the distribution shape was observed.Also, as the myosin rotated around the actin the mean distance between the center of the 20 nm bead and the coverslip would vary from 10 -25 nm above the glass surface.We would expect this to be accompanied by a change in signal contrast, however contrast of the bead shows little change between successive bound states (10).
For these reasons, together with those discussed in Andrecka et al. (10) (specifically, in the section "Revealing the unbound head motion in three dimensions"), we determine that the myosin-5a in these experiments mostly binds and processively moves on top of the actin filament, perpendicular to the glass surface, with a limited range of angles bounded by the actin filament attachment to PEG-PLL/glass surface.

Supplementary Methods
Protein purification.Rabbit skeletal muscle G-actin was prepared as described (11) and stored in liquid nitrogen until use.For cryoEM and nsEM, F-actin was prepared by a two-step procedure in which the divalent cation in the G-actin is first exchanged from Ca 2+ to Mg 2+ by addition of 0. 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 -1090) with an N-terminal AviTag biotinylation sequence (12,13) 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 (14).Details of the amino acid sequence of this construct can be found in Figure S9.
For cryoEM, the melanocyte-specific isoform of full-length mouse myosin-5a heavy chain (15) was expressed together with calmodulin in Sf9 cells, purified using an N-terminal FLAG tag, dialyzed against 100 mM KCl, 0.1 mM EGTA, 1 mM DTT, 0.1 mM PMSF, 10 mM MOPS, pH 7.0 and stored drop-frozen in liquid nitrogen, similar to as described before (14).It was incubated with 4 moles of purified calmodulin per mole myosin overnight on ice, prior to cryoEM data collection.
Single molecule motility assay using iSCAT microscopy.Biotinylation of the myosin-5a HMM construct (approximately 100 µl of ∼ 4 -5 µM) with BirA ligase (Avidity, Aurora, Colorado), was performed on ice for ∼12 hours as described in detail by the manufacturer protocol (16).After this reaction, dialysis against 1 L of buffer containing 50 mM KCl, 0.1 mM EGTA, 1 mM DTT, 10 mM MOPS, pH 7.3, was performed for ∼30 minutes (2x; total ∼1 hr), to remove excess biotin.Biotinylated myosin-5a HMM was then used immediately for the iSCAT assay, or aliquoted and frozen in liquid nitrogen and stored in either liquid nitrogen storage or the -80 °C freezer for future use.
Newly biotinylated or stored myosin-5a HMM sample (750 nM) was diluted 10x in motility buffer (MB; 40 mM KCl, 5 mM MgCl2, 0.1 mM EGTA, 5 mM DTT, 20 mM MOPS, pH 7.3) supplemented with 0.1 mg/ml BSA and 5 µM calmodulin.This was kept as a stock myosin solution (75 nM), on ice for the day of the experiment.
After F-actin was pipetted into the flow cell, attachment of F-actin to the surface of the coverslip was monitored via the iSCAT microscope, as it can monitor label free proteins (20).The chamber was then washed extensively with MB (500 µl) and the surface was blocked additionally with 1 mg/ml BSA in MB (100 µl).Prior to making the final assay mix, 0.1 M ATP (pH 7.0) was diluted in MB to 1 mM ATP.This was then further diluted to 10 µM ATP in the final assay mix.
The final assay composition in which stepping of myosin-5a HMM with a gold nanoparticle attached was observed, was as follows: 77 pM 20 nm gold nanoparticle attached with 25 pM myosin-5a HMM (i.e., 10x dilution of previously mentioned stock), 10 µM ATP, 5 µM calmodulin, 40 mM KCl, 5 mM MgCl2, 0.1 mM EGTA, 5 mM DTT, 20 mM MOPS (pH 7.3).Data collection was performed at room temperature (19 -22 °C) and flow cells were not used for more than 30 minutes.

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Description of iSCAT microscopy and data collection.Interferometric scattering microscopy was performed as described previously (21,22).In iSCAT microscopy, 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 x 30 µm 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× magnification (31.8 nm/pixel).The true magnification was determined using a calibrated resolution grid (Thorlabs) (Figure S1D).
Because of the potential for creating mirror inversions of the iSCAT image, both in the iSCAT microscope and in the analysis software, we confirmed that a clockwise, circular translation of the sample (as viewed from above the sample, i.e. the coverslip on the far side of the actin filaments) resulted in a clockwise rotation of the iSCAT image and that this was unchanged by the software.By combining this information with the fact that myosin-5a always processes towards the barbed end of actin, we define left and right relative to an actin filament as if viewing the filament and motor from above, with the actin filament aligned along the y-axis and myosin walking up the y-axis.
nsEM sample preparation and data collection.For nsEM, 20 µM F-actin was stabilized with 24 µM phalloidin.F-actin and the myosin-5a HMM construct used for iSCAT assays, but without the gold bead, were each diluted in 50 mM NaCl, 1 mM MgCl2, 0.1 mM EGTA, 10 µM ATP, 10 mM MOPS, pH 7.0.Equal volumes of F-actin and myosin were then mixed to give final concentrations of 500 nM and 25 nM respectively.Samples were incubated for 30s, applied to UV-treated carbon film on copper EM grids and stained using 1% uranyl acetate.Micrographs were recorded on a JEOL 1200EX microscope using an AMT XR-60 CCD camera at 0.31 nm/pixel, calibrated using catalase crystals.
CryoEM sample preparation and data collection.Full-length mouse myosin-5a in 100 mM KCl, 0.1 mM EGTA, 1 mM DTT, 10 mM MOPS, pH 7.0 was incubated with 4 moles calmodulin per mole myosin overnight in ice.ATP was added from 7.8 mM stock solution to give 0.2 mM ATP, then mixed with a small volume of 83 µM F-actin and 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.Final conditions: 0.83 µM myosin-5a, 3.6 µM calmodulin, 2.1 µM F-actin, 0.20 mM ATP, 95 mM KCl, 48 µM MgCl2, 0.12 mM EGTA, 10 mM MOPS, pH 7.0 at 22°C.Specimens were imaged in an FEI F20 FEG cryoEM at ∼4 µm underfocus and recorded as 2x2k CCD images at 0.589 nm/pixel, calibrated with catalase crystal.

Quantification and Statistical Analysis.
iSCAT stride length analysis.iSCAT images were collected at 200 Hz and averaged down by a factor of 2 to identify the AB transitions (Figure 1C).The imaging frame rate was limited to 100 Hz (although iSCAT detection does allow much faster rates) to reduce the effects of label-linker flexibility, which increase localization noise at higher speeds and reduce our ability to identify the AB transition.An estimate of the localization precision achieved under these experimental conditions was determined by the positional fluctuations (σ ∼ 0.91 nm, SD) (10) of a surface-attached label recorded under the same conditions as the trajectory in Figure 1C.For actin-bound myosin-gold conjugates the localization noise increases (σ = 1.6 ± 0.3 nm) (10), but remains on average ∼ 2 nm which allows detection of the AB transitions on the order of 5 nm.
The pixel values of the gold particle were fitted with a 2-dimensional Gaussian to determine its x, y position (Figure 1C and D and Figure S1B and C) at nanometer precision.Myosin-5a strides were measured as the distance between the centers of two successive B states.The start and end of each B state was identified using a step detection algorithm (23).The mean x, y coordinates (xi, y i ) of each B state and the Euclidian distance between these mean x, y coordinates calculated: The data can be visualized as either an xy-plot (Figure 1C) or a distance-time trace (Figure 1E).To plot a distance time trace, the x and y values of the first data point in the run, at time = 0, (x0, y0) were subtracted from each of the values in the run (x, y) followed by addition in quadrature: However, distance-time traces do not adequately represent behavior during a dwell period because there is systematic underestimation of the contribution of bead movements orthogonal to the line joining the first data point to the mean center of the dwell position.
Myosin-5a strides, illustrated as blue arrows on the schematic, (Figure 1B) and highlighted as blue transitions on the example data trace (Figure 1C and E) were clear from these trajectories, as were the AB transitions, illustrated as red arrows on the schematic (Figure 1B) and highlighted as red portions on the example data trace, where they show as a decrease in distance (Figure 1C and E), as previously published (10).The spread of particle localizations was calculated as the standard deviation of the gold particle during its stationary state (B-state, in this case) (Figure 1C), the uncertainty of particle positions is reported as the standard error of the mean (Figure 1D).The error on stride distances (σ Stride ) (Figure 1D) was calculated by error propagation of the standard errors of the means: Stride distribution analysis.Myosin-5a stride lengths were plotted as a histogram (Figure 2A) binned using a bin-width optimization algorithm (24).The binned data were then fit with a sum of seven Gaussian functions, each with the same fixed width and different means and areas, using a least-squares method.The fixed width was determined as the value (1.195 nm) that minimized the error on the total fitted area of the sum of seven Gaussian functions.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.The KDE plot was created using an adaptive bandwidth algorithm (25).
To test whether consecutive strides were independent events, all pairs of consecutive strides (629 pairs from 96 runs that totaled 725 strides) were entered into a 9x9 grid (stride lengths 20 to 36 actin subunits).The relative frequency of each stride length was used to calculate the expected number of each pair for a chi-square test of the null hypothesis that strides are independent.There was no pattern to the distribution across the grid of differences between observed and expected values.
Using the 22 cells for which the expected numbers were greater than 5, p>0.05, so the null hypothesis was accepted.
Myosin-5a cryoEM analysis.Among 1,137 myosin-5a molecules identified in 57 micrographs, we found frequent (55%) extended molecules bound to F-actin by both motor domains (Figure S3), and small proportions bound by one motor domain (9%) or bridging between two actin filaments (4%).Very few (2%) compact molecules were associated with actin, as expected from our earlier work (26).Remaining molecules were not attached to actin and were either extended (11%) or compact (18%).
Image processing comprised the following steps carried out within the SPIDER software package (27).Images were contrast inverted (protein light) and CTF corrected by phase flipping.Decorated and undecorated F-actin filaments were segmented, aligned, and classified on features within actin to generate classes of polar filaments as judged by substructural detail.Those possessing bound myosin molecules were then selected (493 molecules) into a separate data set.To measure the distance between leading and trailing head motors along the actin filament we classified the images based on features around the motor domain, thus putting leading and trailing motor domains into different classes.We then marked the position of the motor domain (by eye) in averaged images of those classes where the motor domain was clearly visible.The distance between paired motors could then be computed from the raw images.Identifying the position of the motor domain was helped because the position of the actin subunits to which they are bound was very clear in these image averages.For generating averaged images, having identified F-actin polarity (above) it was then necessary to mirror invert those images of myosin-bound molecules so that when displayed with F-actin running horizontally, all the myosin molecules were above the filament.This was done by image classification based on myosin features.Then all actin-bound myosin molecules were brought into a common alignment in which the molecules were walking to the right.
Myosin-5a nsEM analysis.Data analysis was conducted primarily in SPIDER software (27).Molecules with both motors bound to actin were picked as two coordinate pairs, corresponding to both motor domain positions (n=1073 molecules).Using the coordinates, images were rotated to bring the actin horizontal with both motor domains positioned above the actin.Visual inspection of the stack of images was used to split the data into two, one subset with molecules walking right, one subset with molecules walking left.Leading heads from each dataset were subjected to reference-free alignment with restricted rotation and shift to create an aligned stack in which motor domains were superimposed.The same was done for trailing heads in each dataset.Each of the four aligned stacks was classified and divided into 20 classes per stack (= total of 80 classes) using K-means classification using a mask focused on the motor domain.A position was marked in the clearest class averages created from each dataset, corresponding to the contact point between the motor domain and actin (55/80 classes = 69% selected for defining contact points).These coordinates, along with the rotations and shifts from previous steps, were used to compute the location of the contact point in the original images and the motor-motor distance was calculated (n=566 molecules).
Datasets were subdivided into classes based on motor-motor distances and averaging of these subclasses was used to validate the assignment of directionality and motor-motor distance measurement.Motor-motor distances were plotted as a histogram with adaptive bandwidth KDE (Figure 3F) using the same method as the iSCAT analysis (Figure 2A).
Analysis of cryoEM data for the presence of CAD.CryoEM images of frozen hydrated chicken skeletal ADP-F-actin, at a resolution of 0.103 nm/pixel, were downloaded from EMPIAR dataset 11128 (1).Subunit detail was enhanced by Fourier bandpass Gaussian filtering between 50 and 20 pixels using Fiji-ImageJ 1.53.This allowed filament polarity to be assigned from the polar appearance between the crossovers (Figure S5C).Starting at the pointed (−) end of an uncluttered segment of an actin filament, consecutive crossover positions in a filament were marked by eye, using the Multipoint utility of Fiji-ImageJ, to create a dataset from n = 54 filaments.The sets of x, y coordinates generated for filament segments were further analyzed using Microsoft Excel to determine each crossover spacing and standard deviations of spacings.Distances from the starting Fineberg et al.
crossover position to each subsequent crossover position were also computed.However, clutter sometimes limited the length of filament segment that could be used, with the result that crossover distances to the subsequent crossovers 1 -4 could be measured on all 54 segments, but distances to crossovers 5, 6, 7, and 8 could be measured on only 51, 39, 28, and 18 segments respectively.
Creating model actin filaments.Model filaments were built by sequential addition of subunits starting at the pointed (−) end, according to the following rules.The 3D coordinates of the centers of the n th actin subunit in a filament aligned along the x axis are given by the following set of parametric equations: where r f is the filament radius, ϕ is the mean rotation per subunit, di is the variable rotation per subunit, and ∆x is the rise per subunit.ϕ was set to -166.39°, r f to 6.5 nm, d0 to 0°, and ∆x to 2.75 nm.For visualization, the azimuth of the initial subunit (µ 0 ) is set to 60°, changing this initial value equates to a rotation of the whole filament around the x axis.For each sequential subunit the value of di was an independent, random selection from a Gaussian distribution of values having a mean of 0°and a standard deviation of d.Visualization of these filaments (Figure 1B, Figure 4A, Figure 4B, and Figure 5A) were created in Adobe Illustrator using the calculated coordinates as guides for actin subunit centers.Myosin motor binding site coordinates were estimated, for purposes of visualization, in a similar manner centered at r f = 6.6 nm and setting the initial azimuth value to 110°.

Analysis of crossover distances of model filaments. A side view of each model filament was studied by only considering the
x and y coordinates.The filaments were modelled as two coaxial, long-pitched sinusoids by taking alternate subunits along the helical axis.The coordinates of the intersections of these two sinusoids were calculated using the Shapely package for Python (28).If picking error is included in the model, randomly generated noise from a Gaussian distribution with mean 0 nm and standard deviation of the picking error was added to the intersection coordinates.Crossover distances were calculated by taking the Euclidean distance between adjacent crossovers.
Adjacent crossover spacings were plotted as scatter graphs (Figure S5A).To fit a regression line through this scatter, we used orthogonal distance regression (ODR) a specific case of Deming regression in which the error variances in x and y are equal (29,30).This yielded a slope of -1.00 ± 0.016.Therefore, to obtain a measure of the ellipticity of the scatter plot we computed the standard deviation of the data projected onto an axis of slope -1 (SD-1) and the orthogonal axis of slope +1 (SD+1).To do this, the (x, y) coordinates of the data points were first rotated clockwise by an angle θ = 45°about their mean using the following transformation matrix: cos θ sin θ − sin θ cos θ and then SD-1 and SD+1were calculated as the SD of the y and x coordinates respectively.The ratio of the two SD values was calculated as SD-1/SD+1.Variation in this ratio for given conditions was determined through 1000 iterations and plotted as a Gaussian with mean and standard deviation of the ratios in this iterative dataset (Figure S5A, inset).Additionally, variation in the ratio as a function of both CAD and picking error was determined from 50 CAD values from 0 -10°and 25 error values, evenly spaced, from 0 -5 nm (Figure S6).The value of any one of these three values (ratio, CAD, error) can be determined from the other two by interpolation of this dataset using a Clough-Tocher 2D interpolator function (29).
The SD of distance along the model filaments as a function of crossover number was determined by taking the standard deviations of the Euclidean distance between each crossover and the first crossover of a sample of filaments (Figure S5B and Figure S7A).The variance is calculated as the square of these values (Figure S7B and C).A least squares linear fit to the variance is obtained (29).
Determining CAD and picking error in EM data.The average SD in crossover spacing due to the presence of CAD was calculated.
From inspection of a helical net projection of the actin helix (Figure S4), it is apparent from similar triangles that for a given mean crossover spacing, x, as measured in the EM data, x / -180 = Δx / (-180ϕ), where Δx is the spacing of actin subunits along the actin filament axis.Thus, the mean rotation per subunit, ϕ, can be calculated: For a given RMSD variable rotation per subunit, d, the RMSD CAD at the n th subunit, σn, is given by: 6 of 18 Fineberg et al.
Dividing σn by the mean crossover spacing, expressed in number of subunits, the range of values for the rotation per subunit, ϕ± can be obtained: This can be converted into a range of values for crossover spacing by substitution of ∆ϕ ± into the equation for ϕ above.
Each of the resulting values, x+ and x−, is subtracted from x and the unsigned residuals are averaged to give the contribution that CAD makes to the crossover spacing SD value.The square of this value will give the contribution to the variance, Var CAD .
The contribution of error from picking to the observed variance of crossover spacings in the EM data, Var EM , can thus be calculated as: Var Pick = Var EM − Var CAD [13] With the square root of this value giving the SD of error from picking for a crossover spacing.Since two crossover picks are made to determine a crossover spacing, the variance of each pick will be half that associated with the spacing measurement, and hence the SD for picking a crossover is (error from picking)/ √ 2.
Through least squares fitting (29), an optimal CAD value can be obtained from the measured mean crossover spacing in a data set that produces a line of best fit of form (n Var CAD + Var Pick ) (Figure S7E -F).

Actin disorder analysis.
For an actin filament with exactly 13 subunits in 6 turns of the left-handed short-pitch helix, the rotation around that helix per subunit, ϕ, (-166.154°inthis case) is such that 13ϕ = 6(-360).The difference in azimuth around the actin filament axis between the zero th and the 13 th subunit, µ13 = 13ϕ − 6(−360).If ϕ has a larger value, µ13 will be negative.For the 11 th subunit, µ11 = 11ϕ − 5(−360).Generalizing for 0 • < µn < 360 • , µn = nϕ modulo 360 [14] It is convenient to set the zeroth subunit to 0°, and −180 • < µn < 180 • .Adjusting the equation, µn = (nϕ + 180) modulo 360 − 180 [15] A characteristic of cumulative angular disorder is that the magnitude of disorder of a subunit is independent of the subunits around it.Therefore, the variance (σn 2 ) in subunit azimuth relative to a given starting subunit increases linearly with the number of subunits traversed, and thus: Where d is the RMSD disorder value in degrees.
Modelling an actin filament as a cylinder, a Gaussian azimuthal probability distribution of the n th motor binding location will be 'wrapped' around the circular cross section of the cylinder.This imposes a periodic boundary condition upon the distribution.Consequently, estimated azimuthal probability distributions (Figure 5C and F) for each step length (n) were calculated as wrapped normal distributions, with mean µn, using(31): The distributions were rescaled by a common factor such that their values at an angle of µ = 0 • summed to 1 (Figure 5D and G).Optimal ϕ and d values were obtained through least-squares fitting of the values of probability of each subunit being at zero azimuth to the iSCAT values of relative frequencies of step and stride lengths.

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iSCAT dwell-time analysis.The dwell-time analysis takes account of the fact that the duration of each step along actin is determined by the rate constants of ADP release from the trail head and the subsequent ATP binding to it that triggers trail head detachment from actin.Fitting of the dwell time measurements therefore uses the formula for a two-step reaction (32), in which k1 conventionally refers to the second order ATP binding step and k2 to the first order ADP release step, though these events occur in the reverse order in an attached head.At the concentration of ATP used in the iSCAT assay (10 µM), the observed first order rate constants of both processes are expected to be about 10 s -1 as discussed previously (10).We therefore analyzed the dwell times using two models (Figure S8), one setting them to be equal, the other (arbitrarily) setting ks to be less than k f .In the latter case we are not specifying which of the two enzymatic steps has the smaller rate constant.
Dwell times for the A and B states were pooled into a single dataset distinguished by the stride length preceding or succeeding the A and B state respectively.Rate constants for each stride length were determined through maximum likelihood fitting by minimizing a single global negative log-likelihood function for all strides.The distribution used is a convolution of two exponentials (33) of the form: if the two rates are not equal this evaluates to: and if the two rate constants are equal, ks = k f = k:   The net can be thought of as being created by sliding a hollow cylinder around a horizontal actin filament, marking the positions of the subunits on it, then cutting the cylinder lengthways and opening it out flat.The single, short-pitch, left-handed helix that passes through all the subunits is marked with short dashes; the two long-pitch, right-handed helices are marked by long dashes.Each crossover is where the long pitch helices cross the 0°and -180°lines.The net shown corresponds to the classical F-actin 13/6 helical geometry (13 subunits in exactly 6 turns of the short-pitch helix), but the concept is general.The rotation per subunit (ϕ) of -166.154°, the rise per subunit (∆x) of 2.75 nm, and the crossover spacing (x) of 35.75 nm are all shown.CAD that produces a net decrease of subunit rotation over the 13 subunits (CAD -) is shown by the red dashed line, which can be seen to move the crossover position to the left, shortening crossover spacing.CAD + (green dashed line) is the complementary phenomenon.Note the two similar triangles: the larger (orange) has apexes at 0°, -180°, actin subunit 13; and the smaller (blue) has apexes at -166.154°, -180°, actin subunit 1.
0° CAD, 0 nm Error to 70 crossovers per filament.The hue scales with cumulative angular disorder (CAD).Linear fits to the variances all have R 2 ≥ 0.992. (C) Variation of gradient with picking error (10000 filaments).There is minimal change to the gradient with picking errors of 0 nm (circles), 2 nm (crosses), and 4 nm (squares).Note that the offset caused by picking error is given by 2(picking error) 2 (so is 8 nm 2 and 32 nm 2 , respectively), and can be measured as the intercept on the variance axis.(D) Standard deviation plot and (E) variance plot for the cryo-EM data from F-actin (1).Variance plot has line resulting from least squares fitting to estimate both CAD and measurement error.(F) Calculated standard deviation of the first crossover as a function of CAD.A linear fit (R 2 = 0.9997) is shown.Interpolation of the cryoEM data at a gradient value of √ 3.10 as determined in (E) returns a CAD of 2.24 ± 0.05°for the cryo-EM data.

14 D
Fig. S1.Essential principles of iSCAT microscopy.(A) Schematic of iSCAT showing incident, reflected and scattered light (Ei, Er, and Es respectively).A coverslip (blue) supporting actin and myosin-5 labelled with a gold bead is imaged in an inverted microscope using an oil-immersion objective (grey).(B) (Left) Raw iSCAT image of unlabeled actin network with gold-labelled myosin-5a.(Right) Image with static background subtracted, which reveals only the gold nanoparticle that has moved since the static background image was recorded.Scale bar (black) = 1 µm.(C) Image of the gold nanoparticle highlighted in (B) and the 2D Gaussian fit subtracted to show the fit residual.Data are shown as both an XY plus contrast axis plot and an image.(D) Calibration of iSCAT camera pixels.Calculated conversion factor from pixels to nanometers, as determined by use of a resolution grid (Inset; scale bar (white) = 2 µm).Microscope adjustments were carried out between calibrations 2 and 3. Violin plot envelopes are kernel density estimates of the distributions with bandwidth determined by Scott's rule of thumb.Grey dashed lines indicate two global means before and after microscope adjustment, together with standard error of mean.

Fig. S2 .
Fig. S2.Characteristics of myosin-5a processive runs.(A) Distribution of stride lengths for all tracked myosin-5a molecules.Molecules have been grouped by the number of strides in the run.Box plots of lengths of strides in processive run with each box corresponding to a single myosin molecule (N = 96 molecules, 725 strides).Boxes show quartiles of the dataset with error bars extending 1.5 times the inter-quartile range.Median and mean stride lengths marked in horizontal black and grey lines respectively.(B) Stride length is independent of processive run length.Data from each group in (A) have been combined.Grey dots mark every individual stride.Boxes show quartiles of each dataset with error bars extending 1.5 times the interquartile range.Median and mean stride lengths marked in horizontal black and grey lines respectively.

5 .Fig. S7 .
Fig. S5.Analysis of actin filament CAD from cryoEM images.(A) Scatter plots of successive actin crossover spacings in simulated actin filaments (100 subunits, 1,000 filaments) with and without CAD and Gaussian error in picking crossovers.Error bars (red) denote 1.96 × the standard deviations along lines of slope -1 and +1.Insets:Gaussian distributions of the spread in the ratio of the standard deviations along the lines of slope -1 and +1, generated from 100 repeats.(B) The standard deviation of sequential crossover distances in 1,000 filaments, under the same conditions as in (A).(C) CryoEM image of F-actin (1), bandpass filtered to enhance subunit detail.Arrows mark position of crossovers.Triangles mark the position of triangles formed by three bold actin subunits on the barbed (+) side of each crossover that allows assignment of filament polarity.Scale bar: 20 nm.(D) Scatter plot of crossover spacing (i) against the neighboring crossover spacing towards the barbed end (i+1).(E) Measurement of the spread (SD) of values among a set of actin filaments, of the distance along the actin of a series of 8 consecutive crossovers away from a starting crossover.

Fig. S8 .
Fig. S8.Fitting of trailing head dwell times to a two-step reaction sequence.Panels show dwell time distributions (bars) and results of a global maximum likelihood fitting (dashed lines) to a convolution of two exponentials.(A) Rate constants assumed to be different.ks is set to be lower than k f and can therefore correspond to either the rate constant for ADP release or of the subsequent ATP binding step.(B) Rate constants assumed to be the same.(C) Dwell time rate constants with error estimates are tabulated from a global maximum likelihood fitting of the dwell time data to a convolution of two exponentials when the two rate constants are allowed to differ and when they are constrained to be the same.
Fig. S9.Myosin-5a HMM-like construct amino acid sequence.Mouse myosin-5a heavy chain amino acid sequence 1 -1090 with an N-terminal AviTag biotinylation sequence and C-terminal eGFP and FLAG sequences.Total: 1352 amino acids, displayed at 60 residues per line.