Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction

The Skeletal Actomyosin Bond Changes Between the ADP and Rigor States.

Rat skeletal actomyosin bond rupture force was first measured over ≈3 orders of magnitude range of loading rates. A laser trap was used to hold an actin-coated bead against the side of a skeletal heavy meromyosin (HMM)-coated target (Fig. 2A), and the target moved away from the laser trap over a range of velocities. Higher velocities (v) at a given trap stiffness (α) resulted in higher loading rates (r_f = vα). Bond lifetime and rupture force were measured in both the ADP and rigor states over a range of loading rates. As expected, they were loading rate dependent, with rupture forces increasing at higher loading rates. The absolute values of our rigor bond data compare favorably with the results of Nakajima et al. (18), who measured a rupture force of ≈15 pN at a loading rate of 334 pN/s, and with Nishizaka et al. (19), who measured a rupture force of 8–10 pN at 12 pN/s under rigor conditions. Interestingly, at high loading rates, actomyosin–ADP bonds appear “stronger” than rigor bonds. This result indicates a conformational change in the actomyosin bond upon ADP release.

The data were analyzed within the general framework of a Bell-type bond model k_off(f) = k_off^o exp(x_βf/k_BT), where x_β is the characteristic bond length, k_B is Boltzmann’s constant, T is the absolute temperature, and k_off^o is the unloaded dissociation rate constant (22). The Bell model clearly predicts faster bond dissociation rates under external loads, a situation commonly referred to as a “slip” bond (23). This response is illustrated in Fig. 2B. Evans and Ritchie (24) found a convenient relationship in measuring bond mechanics in terms of bond rupture force measured as a function of loading rate rather than at fixed loads. A single Bell-type energy barrier results in a linear increase in the force at which the bond most often ruptures, f*, when plotted against the logarithm of loading rate, r_f. That is (24–28),

Evans and Ritchie (24) also proposed that within a single bond there might be multiple energy barriers that can be thought of as multiple physical or kinetic barriers to bond rupture. When a bond breaks, these barriers break sequentially in time, with outer barriers presumably rupturing before inner barriers (outer and inner indicating larger and smaller relative bond lengths, respectively). Each of these barriers would give rise to its own linear regime.

Interpreted within this model, the bond rupture force data revealed two distinct energy barriers represented by the two linear regimes of each plot (Fig. 3). Similar phenomena have been observed by several research groups in other molecular systems (25–28). The two energy barriers separated at loading rates between 20 and 200 pN/s depending on the nucleotide state. The outer energy barrier remained unchanged between the ADP and rigor states (Table 1) and was similar to control beads (nonspecific binding) except for a >5-fold higher frequency of bond formation. In contrast, the inner barrier underwent large changes in both characteristic bond length (x_β, 5-fold increase) and unloaded dissociation rate (k_off^o, 4-fold decrease) upon ADP loss. In other words, although the dissociation rate of the rigor actomyosin bond is lower when unloaded, it is considerably more sensitive to load than the actomyosin–ADP bond.

Data from kinesin have shown that bonds involving two heads are stronger than those involving one (29). Assuming this finding applies to actomyosin, the higher rupture force of the inner barrier in the ADP state relative to rigor may be explained by both heads binding to actin in the ADP state and one head dissociating from actin in rigor. To address this possibility, single-headed HMM bond lifetimes in the two states were measured at key loading rates. The data for both the rigor and ADP states superimpose with the two-headed data (Fig. 3), refuting this hypothesis. Values for the outer barrier in rigor are similar to those reported by Nishizaka et al. (17) for single-headed binding in the only comparable study of these phenomena.

Actomyosin Is a Catch Bond That Is Stronger in the ADP State than in Rigor.

Step loads (1.8–26.4 pN) were applied to acto-HMM bonds by rapidly displacing the laser trap relative to the target, and the bond lifetimes were measured at both the rigor and ADP states. As demonstrated in Fig. 4A, actomyosin bond lifetimes increase with increasing load up to a maximum at ≈6 pN, a behavior known as a catch bond (Fig. 2B) (23). Above 6 pN, bond lifetimes decrease with increasing loads. Similar “catch–slip” behavior, with first increasing and then decreasing bond lifetimes, has been observed by others in selectin–PSGL-1 bonds (30, 31). Bond lifetimes in the ADP state were 24% longer than that in the rigor state at the optimal load.

There are several published models describing the catch–slip behavior observed here (32–35). We fit the data as a single bound state and two parallel pathways to bond dissociation (35). Interpreted within this model, bond lifetime is determined by competition between two parallel dissociation pathways. One pathway (slip) is “slow” and increases only slowly in response to imposed loads. The other (catch) is very fast but becomes rapidly slower in response to imposed loads. This model is represented by the equation 1/t̄_on = k_c^oe^f·xc/kbT + k_s^oe^f·xs/kbT, which is the sum of two Bell models. Subscripts c and s indicate the catch and slip pathways, respectively, and t̄_on is the mean bond lifetime. Lifetime is maximal at the critical force, f_crit, which is similar for ADP and rigor (6.4 and 7.1 pN, respectively). The slip pathway does not differ between the ADP and rigor states (Table 2). The catch pathway, in contrast, has a 50% higher unloaded dissociation rate and an effective 3-fold increased sensitivity to load (e_ADP^x_c/e_rigor^x_c) in the ADP state relative to rigor.

The same measurement was performed in the presence of 1 mM Na₄P₂O₇ (pyrophosphate; PP_i), which is thought to be analogous to the prehydrolysis, myosin–ATP state (36). As expected, the measured lifetimes were much shorter than for rigor and ADP states at any given load and were load independent. Although the measured lifetimes in the PP_i state were indistinguishable from actin-free controls, the binding frequency with PP_i was much higher than control, suggesting the interactions in the presence of PP_i were weak but specific between myosin and actin.

To determine the bond lifetimes in the same physical system but at near-zero load, an actin-coated bead was captured and placed adjacent to the HMM-coated surface in the presence and absence of ADP. Bonds were allowed to form and break with low, semirandom loads ultimately determined by the separation distance between trap center and the bound position of the microsphere. Bond lifetime was measured by a small baseline shift and reduction in Brownian motion. The trap stiffness and detector sensitivity were both altered in close proximity to the target. Thus, fits to power spectral density were used to calibrate the laser trap in that position. The average measured load was 0.07 ± 0.01 pN, and lifetimes for rigor and ADP states under this load were 3.8 ± 0.7 and 2.7 ± 0.7 s, respectively. Experiments with control beads yielded no such interactions. These data are consistent with solution studies where it has been shown that the bond lifetime in the rigor state is longer than that in the ADP state (37).

Lifetime of the Actomyosin Bond Is Loading History-Dependent.

As mentioned earlier, there are several models describing catch–slip behavior. Most of these models predict the unbinding rate to depend only on the instantaneous load (34, 35) and not on loading history. One thus should be able to predict our loading rate vs. rupture force data based on our instantaneous load data. We thus assumed the inverse mean bond lifetime 1/t_on as equivalent to k_off(f). Based on these measures of k_off(f), we performed stochastic simulations to predict the characteristic rupture forces at various loading rates. The predicted rupture forces consistently underestimate the measured rupture force by ≈5-fold (Fig. 3, dashed line) in rigor. This result demonstrates that the actomyosin bond is sensitive to loading history as well as absolute load, similar to the response of selectin–PSGL-1 bonds (21, 32).

A recent “allosteric catch bond” model suggests that a bound molecule may switch at a load-dependent rate between two conformations with different dissociation rates (33). This model would allow for history dependence. However, this model also predicts that at any given load one would observe a double-exponential decay over time of the bound fraction of molecules. The bound fraction of actomyosin at a variety of loads were distributed as a single exponential (Fig. 4B), which appears to eliminate the allosteric model as describing actomyosin interactions. Thus, an analytical description of history dependence in actomyosin bonds is lacking and requires further study.

Proteins.

Myosin and HMM were prepared from rat skeletal muscle as described (50). Single-headed HMM (sh_HMM) was prepared by papain digestion essentially as described with minor modifications (51). All proteins were stored in liquid nitrogen in 50% glycerol, if not used immediately.

F-actin was polymerized from rabbit G-actin (Cytoskeleton, Denver), stabilized by phalloidin, and then covalently coupled to 1.2 μm (diameter) carboxylated polystyrene beads (Bangs Laboratories, Fishers, IN) by using 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide hydrochloride (EDAC; Sigma). After quenching the remaining active sites on the beads in 100 mM ethanolamine (Sigma), the actin-beads were blocked with 1 mg/ml BSA to reduce nonspecific interactions. HMM was likewise used instead of native myosin to reduce nonspecific interactions between actin and the myosin tail (50).

Laser Trap.

The laser trap used in these studies has been described in detail elsewhere (52). Back focal plane interferometry (53) was used to measure the position of the trapped bead relative to the trap center, thus providing measurements of displacement and force. The interferometer and the trap stiffness were calibrated by step response method (52, 54, 55) and by fits to the power spectral density (52, 53, 55).

Nitrocellulose-coated coverslips with pedestals were prepared as described (8) by spraying a glass bead suspension onto 22 × 22-mm coverslips and subsequently coating with nitrocellulose. These then were assembled into a 30-μl flow cell. A total of 1–2 μg/ml rat skeletal HMM in actin buffer (25 mM KCl/25 mM imidazole/1 mM EGTA/4 mM MgCl₂, pH 7.4) was incubated in a flow cell for 1 min at room temperature. The flow cell then was blocked with 1 mg/ml BSA for 1 min to block unbound sites on the nitrocellulose. A suspension of actin-coated beads in actin buffer then was introduced to the flow cell. An oxygen scavenger system (0.125 mg/ml glucose oxidase, 0.0225 mg/ml catalase, and 2.87 mg/ml glucose) and 10 mM DTT were included in the beads suspension. ADP at 2 mM also was included for specific experiments.

The flow cell was put onto a piezoelectric microscope stage. The bead concentration was chosen so that only a limited number of beads were present per visual field to reduce noise caused by neighboring beads and to avoid capturing multiple beads in the trap. A bead was captured in the laser trap and brought into contact with a HMM-coated glass bead on the surface (Fig. 2).

Force Spectroscopy.

To apply constant loading rates to actomyosin bonds, the surface was moved away by a piezoelectric stage at a constant velocity. The bead was displaced from the trap center only if a bond had formed between the two beads. The loading rate was varied by changing the trap stiffness (0.016–0.067 pN/nm) or the rate at which the stage moved (0.18–18 nm/ms) or both. The HMM density on the surface was estimated to be ≈20 heads per μm² to ensure that we only measured single-molecule events. The assumption of single bonds is further supported by the low frequency of bond formation. Less than 1 in 20 contacts resulted in a bond.

To apply instantaneous steps in load, the trap was stepped away from the HMM-coated surface. The bond lifetime was measured by the time the bead remained bound to the HMM-coated surface (Fig. 4C). Although the transition between trap positions required only 10 μs, the rate at which load was applied was further limited by motion of the actin-coated bead in a viscous medium against the elastic load of actomyosin. Thus, the actual time it took to complete a step load was modeled assuming the actomyosin bond to be a spring of stiffness E and the trapped bead a dashpot in parallel with a spring of stiffness α. If the trap is displaced by a distance D, the governing equation is E·ε + η·ε̇ = α(D − ε), where η is the viscous damping of the trapped bead, modeled as Stokes drag on a sphere, and ε is the strain of the bonded actomyosin pair. Solving for time-dependent strain of the tether in response to a step of the laser trap we find

where D, η, and α are known. Based on an estimated elasticity of 0.7 pN/nm for skeletal actomyosin (56, 57), our steps in load were 70% complete within 30 μs. Even over a broader range of crossbridge stiffnesses from 0.13 pN/nm (44) to 2 pN/nm (58), the time to reach 70% load ranged from 15 to 40 μs and therefore was interpreted as instantaneous.

Reasonable compliances outside the actomyosin bond will not significantly alter our conclusions. Consider a moderate load of 10 pN imposed by displacing a trap of stiffness 0.037 pN × 270 nm (typical conditions). Assuming a comparable mechanical compliance outside the actomyosin complex of 0.7 pN/nm, our actual imposed load would be diminished by only 3%.

Although it may be of concern that some bond besides the actomyosin bond ruptured during loading (e.g., myosin from surface or actin from bead), evidence is to the contrary. The loads applied here are not sufficient to break the covalent bond linking the actin filament to the microsphere. Further, repeated “touching” of the microsphere to the myosin-coated surface continued to yield specific bonds at a constant probability. This result would not be expected if the myosin were being removed from the surface.