Velocities of unloaded muscle filaments are not limited by drag forces imposed by myosin cross-bridges

Abstract

It is not known which kinetic step in the acto-myosin ATPase cycle limits contraction speed in unloaded muscles (V0). Huxley’s 1957 model [Huxley AF (1957) Prog Biophys Biophys Chem 7:255–318] predicts that V0 is limited by the rate that myosin detaches from actin. However, this does not explain why, as observed by Bárány [Bárány M (1967) J Gen Physiol 50(6, Suppl):197–218], V0 is linearly correlated with the maximal actin-activated ATPase rate (vmax), which is limited by the rate that myosin attaches strongly to actin. We have observed smooth muscle myosin filaments of different length and head number (N) moving over surface-attached F-actin in vitro. Fitting filament velocities (V) vs. N to a detachment-limited model using the myosin step size d = 8 nm gave an ADP release rate 8.5-fold faster and ton (myosin’s attached time) and r (duty ratio) ∼10-fold lower than previously reported. In contrast, these data were accurately fit to an attachment-limited model, V = N·v·d, over the range of N found in all muscle types. At nonphysiologically high N, V = L/ton rather than d/ton, where L is related to the length of myosin’s subfragment 2. The attachment-limited model also fit well to the [ATP] dependence of V for myosin-rod cofilaments at three fixed N. Previously published V0 vs. vmax values for 24 different muscles were accurately fit to the attachment-limited model using widely accepted values for r and N, giving d = 11.1 nm. Therefore, in contrast with Huxley’s model, we conclude that V0 is limited by the actin–myosin attachment rate.

A Mixed-Kinetic Model Describes Unloaded Velocities of Smooth, Skeletal, and Cardiac Muscle Myosin Filaments in Vitro

“…However, in motility assays, the myosin heads go through the entire ATPase cycle before ADP is released. Therefore, a better estimate for k −AD comes from single-molecule measurements of the ATP dependence of t on , which (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.…”

“…Data from the M f /A assay for SMM ( Fig. 2A) are replotted from Brizendine et al (6), and data for CMM (Fig. 2B) and SKM (Fig.…”

“…1B) move over actin filaments that are attached to a polyethylene glycol (PEG)-coated coverslip surface ( Fig. 1D) (5,6). We previously called this the inverted motility assay, but for clarity, we now use the notation M f /A, which directly indicates the state of the myosin (monomers versus filaments) in addition to the geometry of the assay.…”

“…However, several studies using the A/M m assay are inconsistent with this model: (i) Measured V exceeds predicted V (5,(18)(19)(20), and (ii) recombinant HMM and S1 with decreased k −AD do not always show a corresponding decrease in V (4, 21). The detachment-limited model also poorly fits the V dependence on N of smooth muscle myosin (SMM) measured with the M f /A assay (6). Therefore, we proposed a novel mixed-kinetic model (6), which describes V as being influenced by both attachment and detachment kinetics (see movies S1 and S2).…”

“…The detachment-limited model also poorly fits the V dependence on N of smooth muscle myosin (SMM) measured with the M f /A assay (6). Therefore, we proposed a novel mixed-kinetic model (6), which describes V as being influenced by both attachment and detachment kinetics (see movies S1 and S2). It predicts that within the myosin filament, and to a lesser extent as monomers attached to the surface, the S2 region (tail proximal to the heads) can be pulled backward by other working heads.…”