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Biophysical Journal
SUPPLEMENTARY INFORMATION
Comparison of multiple- and single- molecule fluorescence polarization data
Fluorescence polarization was measured from actin filaments decorated with myosin fragments that had been exchanged with fluorescently labeled RLC and used directly without diluting with unlabeled myosin fragments. Under these conditions approximately 350 myosin heads were imaged onto each of the photodetectors, ~50% of them labeled with rhodamine. These multiple molecule experiments were performed for comparison with the single molecule fluorescence polarization experiments described later, to test the configuration of the microscope optics and numerical corrections of the fluorescence signals. The filaments selected were aligned either along the x- or y-axes as described in Methods.
Two sets of parameters were calculated to analyze the polarization data measured in heavily labeled samples: ratios of polarized fluorescence, as defined in Forkey et al. (2005), and order parameters (<P2> and <P4>), defined in Dale et al. (1999) and further described for the present case in Forkey et al. (2005).
Due to symmetries of the setup about the optical axis, each polarization ratio with a filament aligned along the x-axis has an equivalent ratio for y-aligned filaments given by swapping excitation paths and detector polarizations. Pairs of polarization ratios expected to be equal are plotted as adjacent blue (x-oriented filaments) and green (y-oriented filaments) boxes in Fig. S1. All of the symmetry-related ratios match within their uncertainties, indicating that the optical alignment is symmetrical and that the polarization ratios are consistent with the predicted evanescent wave polarization. In addition, the matches confirm that the calibration procedure produces correction factors which appropriately compensate for imperfections in the optics and detectors (see Forkey et al., 2005 for a similar analysis using labeled actin).
The single molecule data can be compared to the data from more heavily labeled filaments by adding together the intensities of many single molecules, which label actin filaments oriented in the same direction. Data accumulated in this manner are termed ‘summed singles’. The particular filaments in each microscopic field were chosen for orientation close (10) to the x-axis. Near equivalence of corresponding ratios, generated by summing the intensities from many individual molecules (Fig. S1, yellow dots), indicates that the single molecule polarized fluorescence intensities accurately reflect the probe orientation and that the single- and multi-molecule measurements represent equivalent angular distributions.
The analysis of the multi-molecule results made use of the assumption that the probes obey cylindrical symmetry about the actin filament. This assumption might not be valid if the myosin heads on the side of the filament facing the microscope slide were distorted by their interaction with the surface. We tested the assumption of cylindrical symmetry by introducing a weighting factor, C0, describing the extent of asymmetry between the projections of the probe ensemble onto planes parallel and perpendicular to the slide. As described in the accompanying paper (Forkey et al., 2005), fluorescence intensities, including instrumental effects and the numerical aperture of the collecting objective, were determined by fitting the filament model to the data while including C0 as one of the adjustable parameters. For S1(104-BR-115), C0 = 1.06 ± 0.01, indicating that the probe dipole projection onto the plane perpendicular to the slide is less than that parallel to the slide. For the other three samples, C0 was 0.90 - 0.94 (all with s.e.m. = 0.01). These results are consistent with corresponding measurements on actin filaments labeled with rhodamine at Cys374, giving C0 = 0.87 ± 0.04 (mean ± s.e.m.; Forkey et al., 2005). The values thus found for C0 were all near 1.0 indicating cylindrical symmetry.
The filaments could be made non-cylindrical, intentionally, by adding a low concentration of ATP to dissociate the myosin heads bound to actin and then removing the ATP again. The heads that remain after ATP treatment presumably interact with the surface. Total filament intensity was highly variable after ATP treatment, possibly because some of the heads, dissociated from the filament, bound directly to the surface nearby. <P2> changed (-0.300 ± 0.007 before ATP and -0.13 ± 0.03 after), consistent with this idea. Addition and removal of ATP resulted in a broad range of C0 values for individual filaments, 0.25 - 2.02, although the average C0 was still 1.03. It follows that the C0 parameter is sensitive to the symmetry of the filaments and the untreated filaments, with C0 1, had nearly cylindrical probe distributions.
Comparison of labeled filaments with rigor muscle fibers
Order parameters (Dale et al., 1999; Forkey et al., 2005), describing the orientation, , of the probe dipole relative to the filament axis, and the extent of nanosecond wobble, calculated from the single- and multi-molecule intensity measurements, are listed in Table S1. Experiments using the same bifunctionally labeled RLCs exchanged into muscle fibers were reported by Corrie et al. (1999) and Hopkins et al. (2002) and converted into order parameters for comparison here (Table S1). The extent of nanosecond wobble, represented by <P2d> in Table S1, was fixed when fitting the single molecule data. Allowing <P2d> to vary by setting it as an additional adjustable parameter did not change the overall distributions. Values for the fast wobble, <P2d>, were in the range of 0.85 – 0.9 indicating half-angles of rapid wobble of 20° – 25°, except for S1(104-BR-115) decorated filaments, which was consistently higher. For S1(104-BR-115), <P2d> is not significantly different from 1.0, seemingly indicating that the probe wobble is negligible. NMR studies have provided evidence for weak
TABLE S1 Order parameters from the present samples and published data are compared. The 2nd- and 4th-rank order parameters of the Legendre polynomial series are calculated from the intensity measurement of single- and multi-molecule experiments. ‘Filaments’ are heavily labeled. ‘Singles’ are order parameters calculated from the distributions of angles determined from individual molecules. ‘Summed singles’ are order parameters calculated by summing the eight polarized fluorescence intensities from all of the single molecules and then treating the sums as if they were obtained from a filament. <P2> gives information about the dipole orientation with respect to the actin axis, increasing as the dipole becomes more parallel to actin. <P4> gives higher resolution orientation information. The extent of rapid motion (< 4 ns) is indicated by <P2d>. *Values were fixed for <P2d> when fitting single molecule data, as described in Forkey et al. (2005); <P2d> = 0.864 corresponds to a wobble cone with half-angle (f) 25° and <P2d> = 0.911 corresponds to 20°.
RLC association with S1 fragments, as indicated by high mobility (Prince et al., 1981), and for modulation of RLC-heavy chain affinity by Ca2+ and phosphorylation (Ribeiro et al., 1984). Thus some of the RLC subunits in our preparations might be mobile relative to the heavy chain, especially S1(104-BR-115), which gave higher background intensities, more variable polarization data (Fig. S1) and higher value for <P2d>.
P4> was close to zero in all cases. The <P2> values represent an average of the probe orientation distributions (<P2> = (3 <cos2-1)/2, where is the probe orientation relative to actin). The values of <P2> for all of the labeled filaments are negative indicating that the orientation, , of the probes (averaged over cos2) is more perpendicular to the filament axis than the ‘magic angle’, 54.7 (Dale et al., 1999). Consistent with measurements made in muscle fibers, both S1(104-BR-115) and HMM(104-BR-115) have more negative values of <P2> than S1(100-BR-108) and HMM(100-BR-108), indicating that (104-BR-115) is more perpendicular to the filament axes. Overall, the polarized fluorescence intensities reported here are quite similar to those expected from the earlier experiments on muscle fibers.
Maximum Entropy Analysis
Since the orientations of the probes are known with respect to the myosin crystal structure, the measured orientation distributions of the two probes can be combined to determine the orientation distribution of the light chain domain (LCD). The reference frame used to define the orientation of the LCD is shown in Fig. S2.
A maximum entropy (ME) analysis is used to combine the 100-BR-108 and 104-BR-115 data and to determine the broadest protein orientation distribution compatible with the polarized fluorescence intensity data (van der Heide et al., 2000). This analysis has the advantage that no arbitrary assumptions about the shapes of the distributions are needed. ME distributions are calculated from the values of <P2> and <P4> (Table S1) for the two probes and presented as two-dimensional contour plots with the angular coordinates, L (-180° to 180°) on the abscissa and L (0° to 180°), on the ordinate (Fig. S3). In these contour plots, dark colors indicate orientations in which the LCD is not found and hotter colors indicate more likely orientations. The light chain does not necessarily occupy the whole region of lighter colors, because narrower distributions in the same general region are also compatible with the data (van der Heide et
FIGURE S2 Reference frame (Hopkins et al., 2002). The lever axis represents a line connecting Cys707 and Lys843 (residue numbers from chicken skeletal muscle myosin heavy chain). The orientation of the lever arm is given in terms of its polar angle (L, L) with respect to an actin filament. The axial angle, L, is defined as 0 along the actin axis. A hook axis is defined along the short -helix between Pro830 and Lys843. The azimuthal angle, L, is the rotation of the light chain region around the lever axis. L defined as 0 when the hook axis is coplanar with the lever and fiber axes and its Lys843 end points towards the M line or pointed end of actin; increasing L denotes counter-clockwise rotation of the LCD as viewed from Lys843.
al., 2000). The maps always show at least two regions of high probability due to symmetries in the optical method, uncertainty of the actin polarity in vitro, and symmetry of the actin polarity in a muscle sarcomere. The central region of the map from muscle fibers (-90° < L < 90°) corresponds to the half sarcomere with M line above and Z line at the bottom.
The angular distributions measured from single molecules (Fig. S3b) and those previously
reported in muscle fibers (Fig. S3a; Hopkins et al. 2002; Corrie et al., 1999) are very similar. The contours from the single molecule plots are broader, probably due to the smaller sample of molecules and the photon noise in the single molecule data. The region of high probability is tilted on all of the contour plots indicating a correlation between L and L. Molecules at higher L angles are located at higher L (counter-clockwise rotation about the lever axis viewed from the thick filament).
In the contour plots from muscle fibers (Fig. S3a), whether the dispersion of angles and resulting correlation between tilt (L) and twist (L) is due to static disorder in the population of molecules or to microsecond motions cannot be directly determined. However, single molecule experiments enable distinction of mobile and static fractions in the same experiment because the polarized fluorescence intensities carry information about microsecond timescale motions (Forkey et al., 2000; Forkey et al., 2005).
When the components of probe wobble in the 4 ns < t < 10 ms time range (<P2p> and <P4p>), are ‘factored out’ of the order parameters, <P2s> = <P2>/<P2p> and <P4s> = <P4>/<P4p>, (Bell et al., 2002, Forkey et al., 2005), and ME distributions are calculated for the static distributions (Fig. S3c), two narrower peaks emerge in place of the one broad distribution. For HMM (upper panel), these peaks are at L = 80°, L = 20° and L = 125°, L = 70°. The dominant peak (80°, 20°) is at the same orientation as that measured for endogenous heads in muscle fibers. The smaller peak in Fig. S3c corresponds to the higher (L, Lorientations occupied by a tail of the main peak from the fiber data. Because there is a minor peak present in the static ME distribution plot and a marked valley between the peaks, the tails of the distributions in panels A and B can be interpreted as caused by a combination of static disorder and mobility of the myosin heads.
Similar distributions (with two significant peaks) are seen in the contour plots representing S1 (Fig. S3c lower; L = 80°, L = 25° and L = 125°, L = 65°). The second peak is unexpected given that at most 15% of S1 heads are at a second orientation based on Gaussian models of the individual L distributions (Table 1 of the main text). In all cases, the two peaks may either indicate two preferred angular positions of the heads, or they may be artifactual ‘fringes’ due to the limited number of probes used (van der Heide et al., 2000). Simulations of the distributions starting with single orientation peaks in the positions of the brighter areas in Fig. S3c did result in such fringes when the order parameters were calculated and then ME distributions recovered from those order parameters (see also van der Heide et al., 2000). We believe that the appearance of the extra peaks in Fig. S3c for S1, relative to panels A and B, is most likely a spurious phenomenon due to insufficient number of probes to accurately delimit the RLC orientation. This artifact does not influence the width of each peak in the contour plot, so the more narrow shape of the peaks in panels c (widths in the L direction are approximately half of those of panel b) indicates that dynamic motions contribute substantially to the breadth of the orientation distributions in panel b.
Peaks derived by fitting Gaussian distribution to the data (presented in the main text of the paper) are overlaid in Fig. 3c. The data support the notion overall that both heads of an HMM molecule are attached to actin in rigor, but the actin filament constrains the molecules so that pairs of peaks emerge for HMM, corresponding to binding at two different angles.
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