Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Abstract

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin-myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin-myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.

Keywords: actin; collective force; mechanics; myosin; velocity.

Figure 1

Models for attachment- and detachment-limited myosin-based actin movement.A, a five-state kinetic scheme for the actin–myosin ATPase reaction. Myosin displaces an actin filament a distance d, with a working step (a lever arm rotation) induced by strong binding to that actin at a rate k_att. Actin–myosin detachment occurs with ADP (D) release followed by ATP (T) binding at an overall rate, k_det. B, in an independent force generator model (top) the working step of a myosin head generates force that is localized to that head independent of the system force. The system force is calculated as a sum of molecular forces. In a thermodynamic model (bottom) the working step of a myosin head generates force that equilibrates with and directly contributes to the system force. C, actin sliding velocities in an independent force generator model are described as the mechanical step, d, of a single myosin head divided by the length of time that myosin head remains bound to actin, 1/k_det. D, actin sliding velocities in a thermodynamic force model are described as the distance, L, myosin heads (through steps of size d) collectively move an actin filament before reaching a stall force divided by the bulk (N-dependent) time it takes those myosin heads to detach from actin.

Figure 2

Experimental and theoretical effects of (-)-blebbistatin on the N-dependence of V.A, mathematical expression for V(N) developed by Uyeda and Spudich based on the independent force model (32) with d = 10 nm, k_det = 300 s⁻¹, k_att = 55 s⁻¹ (black lines), 8 s⁻¹ (red lines), and 2 s⁻¹ (blue lines). B, mathematical expression for V(N) based on a collective displacement model (33) with L = 10 nm, k_det = 300 s⁻¹, d = 10 nm, k_att = 55 s⁻¹ (black line), 8 s⁻¹ (red line), and 2 s⁻¹ (blue line). C, a thermodynamic force computer simulation (see Experimental procedures) with strain-dependent, reversible kinetics and stiffness of a collective spring of 0.04 pN/nm, reverse weak-to-strong rate 0.01 s⁻¹, k_det = 300 s⁻¹, d = 10 nm, k_att = 55 s⁻¹ (black square), 8 s⁻¹ (red circle), and 2 s⁻¹ (blue triangle). D, the effects of k_att on V(N) were measured in an in vitro motility assay using (-)-blebbistatin to inhibit k_att. The plot shows V measured at different myosin surface densities (N) in the presence of 0 (black squares), 10 (red circles), and 50 μM (blue triangles) (-)-blebbistatin (decreasing k_att) with least squares fits (lines) giving values for K_M and V_max of 16.1 ± 4.9 and 2.9 ± 0.3 μm/s for control, 13.3 ± 90.6 and 1.4 ± 0.3 μm/s for 10 μM, and 6.4 ± 1.3 and 0.5 ± 0.02 μm/s for 50 μM.

Figure 3

The N-dependence of actin-activated ATPase activity, v(N), measured in a motility assay. The baseline myosin ATPase activity (light gray circles) was measured in the absence of actin at different N and fit to a line (light gray). The ATPase activity measured in the presence of 0.15 μM actin (black squares) is the total ATPase activity of myosin heads interacting with actin (actin-activated ATPase) and the majority of myosin heads that are not interacting with actin (baseline myosin ATPase). Subtracting the baseline ATPase (light gray circles) from the total ATPase (black squares) gives the actin-activated ATPase rate, v(N) (gray triangles), which is fitted to a hyperbolic function (gray line).

Figure 4

v(N) and V(N) measured at two different ionic strengths in similar in vitro motility assays.A, v(N) was measured at both 50 (black squares) and 100 (gray circles) mM KCl and fitted to hyperbolic functions (lines) giving K_M values of 46 ± 32 and 23 ± 13 for 50 and 100 mM KCl, respectively. B, V(N) measured under nearly identical conditions (only with 0.15 μM instead of 0.01 μM actin) to those in (A) at both 50 (black squares) and 100 (gray circles) mM KCl and fitted to hyperbolic functions (lines) giving K_M values of 16 ± 8 and 17 ± 9 for 50 and 100 mM KCl, respectively.

Figure 5

The effects of a mechanical load on V(N) measured in an in vitro motility assay.A, V(N) measured in an in vitro motility assay after incubating motility flow cells with 0 (black squares), 0.5 (dark gray circles), and 1 (light gray circles) μg/ml α-actinin. The data were fitted to hyperbolic functions (lines), giving values for K_M of 19 ± 5, 16 ± 7, and 38 ± 13. B, actin-activated ATPase activity, v, measured in an in vitro motility assay (N = 5 and 1.0 μM actin) with (light gray bar) and without (dark gray bar) 1 μg/ml α-actinin shows v decreases from 0.59 to 0.26 μM P_i/min upon addition of 1 μg/ml α-actinin (p = 0.018). The 1 μg/ml α-actinin control (myosin without actin) is indicated with the black bar.

Figure 6

N-Dependence of pCa₅₀in a motility assay. The calcium dependence of thin filament sliding velocities was measured in an in vitro motility assay, and the data were fit to a Hill equation to obtain the calcium concentration at half-maximal activation reported as the pCa₅₀ (inset) as previously described (41). These experiments were repeated at different N to obtain pCa₅₀(N) at both 50 (black squares) and 100 (gray circles) mM KCl. The data at or below N = 50 were fit to lines with y-intercepts of 4.8 and 4.5 and slopes of 0.02 and 0.02 for 50 and 100 mM KCl, respectively. The data above N = 50 were averaged (horizontal lines) to estimate maximum pCa₅₀ values of 5.9 and 5.7 at 50 and 100 mM KCl. The N at saturation is the intercept of the maximum pCa₅₀ and the linear fit, and the pseudo K_M is half the N at saturation.

Figure 7

Collective force model with saturation kinetics.A, computer simulations of V(N) obtained at different k_att values based on a collective force model with saturation attachment kinetics (open symbols) are overlaid with V(N) data from Figure 2D obtained at different blebbistatin concentrations (solid symbols). Parameters of the simulation are d = 10 nm, k_det = 400 s⁻¹, and k_att of 30 s⁻¹ (black symbols), 5 s⁻¹ (red symbols), and 1.5 s⁻¹ (blue symbols). B, in computer simulations of F(N) based on a collective force model with saturation attachment kinetics, force is generated collectively by myosin heads when they displace a single mechanical spring with spring constant κ = 0.04 pN/nm. F(N) increases linearly with N and saturates at the same N as V(N) when myosin heads saturate.

Figure 8

ATP dependence of V at 5 and 100 μg/ml myosin. The [ATP] dependence of V at high (100 μg/ml; gray circles) and low (5 μg/ml; black squares) myosin fitted to a hyperbola (lines), giving K_M values of 0.01 ± 0.002 at 5 μg/ml and 0.04 ± 0.007 at 100 μg/ml.