Research ArticleBIOCHEMISTRY

A mixed-kinetic model describes unloaded velocities of smooth, skeletal, and cardiac muscle myosin filaments in vitro

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Science Advances  13 Dec 2017:
Vol. 3, no. 12, eaao2267
DOI: 10.1126/sciadv.aao2267
  • Fig. 1 Kinetic scheme, myosin structures, motility assay geometries, and model predictions.

    (A) Kinetic scheme for myosin (M) attachment to actin (A). D, ADP; T, ATP; Pi, phosphate. Kw, equilibrium constant for weak binding of myosin to actin; kws, forward rate constant for the weak to strong transition. We assume that −kws is insignificant. See text for other rate constants. (B to E) None of the cartoons are to scale. (B) Side polar (smooth muscle) and bipolar myosin filaments (skeletal and cardiac muscle), heads (orange), and tails (black). (C) A/Mm assay with actin filament (green) being moved by myosin heads (orange) attached to coverslip (blue). Only the S2 region of the tail (black) is shown. Before the working step (left), after the working step (middle), and after the fullest possible extension of S2 (right) by other heads undergoing the working steps (not shown for clarity). In this example, d = L = 8 nm. (D) Mf/A assay (5, 6), myosin filament (orange) moves over biotinylated actin (green) attached to PEG brush-coated coverslip (not shown). Pre-working step (left), post-working step (middle), and after full extension of S2 (right) by other working heads (not shown) giving L = 32 nm in this example. This head is now a drag head and therefore must detach from actin before further movement of the filament is possible. See movies S1 and S2 and the study of Brizendine et al. (6) for a more complete description. (E) A/Mf assay, a portion of a bipolar biotinylated myosin filament (black) attached via streptavidin to a biotinylated PEG brush-coated coverslip with physiological or fast (left) and nonphysiological or slow head-actin interactions (right). The slow heads need to spin or swivel to attach to actin, represented by a loop in the S2 domain, but the mechanism is unknown. Table 2 shows that L for the slow heads is finite, but the structural basis is unknown and therefore not depicted. (F) Mixed-kinetic model predictions at varying L’s. Plots predicted by Eq. 5 for katt = 6 s−1, d = 8 nm, kAD = 100 s−1, kT = 2 μM−1 s−1, [ATP] = 1 mM. Please see Methods for an Excel spreadsheet link to generate additional curves.

  • Fig. 2 Detachment-limited model (Eq. 1) and mixed-kinetic model (Eq. 5) fits to N dependence of filament velocities (V) at saturating [ATP].

    All experiments were performed in the observation buffer at 30°C. (A) SMM filaments moving in the Mf/A assay at 0.75 to 2.0 mM ATP from Brizendine et al. (6). Purple triangles, 26% SMM co-filaments, n = 10; orange circles, 51% SMM co-filaments; green triangles, 75% SMM co-filaments; blue diamond, rapidly diluted (short) SMM filaments; each point is the average V and N from 10 individual filament trajectories, and error bars show the SD. Red squares, SMM filaments prepared by dialysis; each point (n = 82) is V of a single filament trajectory. (B) CMM filaments moving in the Mf/A assay at 0.75 to 2.0 mM ATP. Blue diamonds, CMM filaments, n = 95; green triangles, 50% CMM co-filaments, n = 62; orange circles, 30% CMM co-filaments, n = 19. (C) SKM filaments moving in the Mf/A assay at 0.75 to 2.0 mM ATP. Purple triangles, 25% SKM co-filaments, n = 38; orange circles, 50% SKM co-filaments, n = 47; green triangles, 75% SKM co-filaments, n = 41; blue diamonds, SKM filaments prepared by rapid dilution (short), n = 122; red squares, SKM filaments prepared by dialysis. Each point (n = 102) is V of a single filament trajectory. For (A) to (C): Fits to Eq. 1 with d fixed at 8 nm (dashed lines) and d = 8 nm, r = 0.05, and kAD = 36, 50, and 100 s−1, respectively, for (A), (B), and (C) (blue). See Table 1 for a summary of fit parameters. (D) V of actin moving on SKM filaments in the A/Mf assay at 1 mM ATP. Gray triangles, fast and slow V measured from a single actin filament trajectory moving across a single myosin filament (n = 25); red circles, V from a single actin filament trajectory (n = 42); cyan squares, V from a single actin filament trajectory (n = 21). All plots show a fit to Eq. 5 (black lines). See Table 2 for a summary of fit parameters.

  • Fig. 3 A/Mm data for SKM.

    All experiments were performed in the observation buffer at 30°C. (A) Relationship between [myosin] applied to the coverslip (μg ml−1) and N. Red points are averages of two to six independent experiments; error bars show the SD; the red line is a linear fit, slope = 0.34 N ml μg−1. Black squares, data from Harris and Warshaw (17). (B) N dependence of V at 1 mM (red), 100 μM (green), and 20 μM ATP (blue). N values correspond to applied SKM concentrations between 5 and 400 μg ml−1. (C) Contour plot of L versus kAD showing dependence of R2 values from the fit to 1000 μM ATP data from (B) (see fig. S2 for plots of 20 and 100 μM ATP data). Color scale shows the range of R2 values. (D) ATP dependence of V at N = 34 (100 μg ml−1). For (B) and (D), each point is an average of 40 individual actin filament trajectories, and error bars show the SD. Respective lines show the best fits to Eq. 5.

  • Fig. 4 ATP dependence of filament V at fixed N from the Mf/A assay.

    (A) SKM filaments formed by rapid dilution. (B) CMM filaments formed by rapid dilution. For both plots, each point is an average of 40 individual trajectories. Error bars show the SD. Red lines show the fits to Eq. 5 (see Table 2 for results). R2 = 0.95 and 0.96, respectively. All experiments were performed in the observation buffer at 30°C.

  • Table 1 Results of fitting Eq. 1 to filament V versus N data with d fixed at 8 nm.

    Data from Fig. 2 (A to C) were fit to Eq. 1 to obtain kAD and r, which were used to calculate katt and v using Eqs. 2 and 6. For kAD and r, the ± is the SE of the least-squares fit. Errors for katt and v were propagated.

    ParametersMeasured or literature valueReferenceValues resulting from fit (Fig. 2, A to C, dashed lines)
    SMMFig. 2A
    r0.05(33)0.0042 ± 0.0004
    kAD (s−1)36 ± 5(40)197 ± 8
    katt (s−1)1.89*0.83 ± 0.09
    vmax (s−1 head−1)0.49 ± 0.01(5)0.83 ± 0.08
    kT0.5 ± 0.01(5)
    CMMFig. 2B
    r0.05(33)0.019 ± 0.002
    kAD (s−1)50(32, 3639)139 ± 4
    katt (s−1)2.6*2.69 ± 0.25
    vmax (s−1 head−1)1.5 ± 0.1Fig. S1A2.6 ± 0.2
    kT1.1 ± 0.1Fig. S1C
    SKMFig. 2C
    r0.05(33)0.0200 ± 0.0009
    kAD (s−1)100 ± 8(20)575 ± 8
    katt (s−1)5.3*11.3 ± 0.6
    vmax (s−1 head−1)Range, 8–20Fig. S1B, (2931)11.0 ± 0.5
    kT1.9 ± 0.1Fig. S1C

    *Calculated from Eq. 2 using indicated literature values of r (33) and kAD.

    †Calculated from Eq. 6.

    • Table 2 Summary of fitting parameters to data from Figs. 2 to 4 using Eq. 5.

      For each fitted value, the ± is the SE of the least-squares fit. For average values, the ± is the SD. For all fits to SKM filament data, fixed values are as follows: kT = 1.9 μM−1 s−1 (from fig. S1C), d = 8 nm, and kAD = 190 s−1 (from Fig. 3C and fig. S2). For all fits to CMM data, fixed values are as follows: kT = 1.1 μM−1 s−1 (from fig. S1C), d = 8 nm, and kAD = 50 s−1 (32, 3639).

      Assay typeExperimentFigure no./
      reference
      ParametersL (average)
      kAD (s−1)L (nm)
      A/MmSKM 1 mM ATP V vs. N*Fig. 3B193 ± 945 ± 48 ± 3
      SKM 100 μM ATP V vs. N*Fig. 3B238 ± 1239 ± 3
      SKM 20 μM ATP V vs. NFig. 3B140 ± 967 ± 1
      SKM V vs. ATP*Fig. 3D169 ± 3111 ± 2
      Filament assayskatt (s−1)L (nm)L (average)
      Mf/ASMM V vs. NFig. 2A and (6)0.6 ± 0.159 ± 359 ± 3
      SKM V vs. NFig. 2C7.0 ± 0.222 ± 122 ± 9||
      SKM V vs. ATP§Fig. 4A14.0 ± 9.614 ± 1
      CMM V vs. NFig. 2B2.0 ± 0.124 ± 122 ± 2
      CMM V vs. ATPFig. 4B2.8 ± 3.020 ± 1
      A/MfSKM fastFig. 2D7.1 ± 0.631 ± 1
      SKM slowFig. 2D3.1 ± 0.44 ± 0

      *katt was fixed at 20 s−1 (30).

      katt was fixed at 10 s−1 (30).

      From Brizendine et al. (6), refit to Eq. 5 with fixed parameters kAD = 36 s−1, kT = 0.5 μM−1 s−1, and d = 8 nm.

      §N was fixed at 88 based on average filament length and Eq. 7.

      ||Average includes L from the fast heads in the A/Mf assay.

      N was fixed at 113 as above.

      Supplementary Materials

      • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaao2267/DC1

        Supplementary Methods

        movie S1. Cartoon depicting detachment-limited kinetics in the A/Mm assay.

        movie S2. Cartoon depicting mixed kinetics (attachment to detachment) in the Mf/A assay.

        movie S3. Example movie of SKM filaments moving in the Mf/A assay.

        movie S4. Example movie of CMM filaments moving in the Mf/A assay.

        movie S5. Example movie of actin filaments moving over SKM filaments in the A/Mf assay.

        fig. S1. Steady-state actin-activated ATPase rates and ATP-induced dissociation of actomyosin.

        fig. S2. Contour plots showing R2 dependence of fit of Eq. 5 to data from Fig. 3B.

        fig. S3. Contour plots showing R2 dependence of fit of Eq. 5 to data from Fig. 2 (A to C).

        fig. S4. Distance from origin plot of actin filament moving over a myosin filament in the A/Mf assay.

        fig. S5. Effect of rhodamine labeling and EDC cross-linking on CMM steady-state actin-activated ATPase activity.

        fig. S6. Flowchart describing algorithm to solve recursive Eq. 5.

        Supplementary Text

        Reference (59)

      • Supplementary Materials

        This PDF file includes:

        • Supplementary Methods
        • Legends for movies S1 to S5
        • fig. S1. Steady-state actin-activated ATPase rates and ATP-induced dissociation of actomyosin.
        • fig. S2. Contour plots showing R2 dependence of fit of Eq. 5 to data from Fig. 3B.
        • fig. S3. Contour plots showing R2 dependence of fit of Eq. 5 to data from Fig. 2 (A to C).
        • fig. S4. Distance from origin plot of actin filament moving over a myosin filament in the A/Mf assay.
        • fig. S5. Effect of rhodamine labeling and EDC cross-linking on CMM
          steady-state actin-activated ATPase activity.
        • fig. S6. Flowchart describing algorithm to solve recursive Eq. 5.
        • Supplementary Text
        • Reference (59)

        Download PDF

        Other Supplementary Material for this manuscript includes the following:

        • movie S1 (.mp4 format). Cartoon depicting detachment-limited kinetics in the A/Mm assay.
        • movie S2 (.mp4 format). Cartoon depicting mixed kinetics (attachment to detachment) in the Mf/A assay.
        • movie S3 (.avi format). Example movie of SKM filaments moving in the Mf/A assay.
        • movie S4 (.avi format). Example movie of CMM filaments moving in the Mf/A assay.
        • movie S5 (.avi format). Example movie of actin filaments moving over SKM filaments in the A/Mf assay.

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