The Location and Rate of the Phosphate Release Step in the Muscle Cross-Bridge Cycle.

It is controversial whether the phosphate (Pi) release step in the cross-bridge cycle occurs before or after the first tension-generating step and whether it is fast or slow. We have therefore modified our previous model of the frog cross-bridge cycle by including a Pi release step either before (model A) or after (model B) the first tension-generating step and refined the two models by downhill simplex runs against experimental data for the force-velocity relation and the tension transients after length steps. Pi release step was initially made slow (70 s-1), but after refinement, it became fast (∼500 s-1 for model A and ∼6000 s-1 for model B). The two models gave similar fits to the experimental tension transients after length steps, but model A gave a better fit to the lengthening limb of the force-velocity relation than model B. 50 mM Pi inhibited the isometric tension of model A by ∼50% but that of model B by only ∼25%. The half-inhibition was at 6.0 mM Pi for model A and at 1.6 mM Pi for model B. The values for model A were consistent with experimental data. We also simulated the effect Pi jump as in caged Pi experiments. For model A, a Pi jump induced a tension fall at a rate similar to the experimental phase II. There was then a small rise in tension to the steady state mimicking the experimental phase III. The initial tension fall was caused by detachment of M⋅ADP⋅Pi myosin heads from actin and reversal of the first tension-generating step. For model B, the fall in tension was more rapid and due to reversal of the first tension-generating step, and phase III was not observed. We conclude that, as in model A, the Pi release step is before the first tension-generating step and is moderately fast.

The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study.

In experiments on active muscle, we examined the tension decline and its temperature sensitivity at the onset of ramp shortening and at a range of velocities. A segment (∼1.5 mm long) of a skinned muscle fibre isolated from rabbit psoas muscle was held isometrically (sarcomere length ∼2.5 µm) at 8-9°C, maximally Ca2+-activated and a ramp shortening applied. The tension decline with a ramp shortening showed an early decrease of slope (the P1 transition) followed by a slower decrease in slope (the P2 transition) to the steady (isotonic) force. The tension level at the initial P1 transition and the time to that transition decreased as the velocity was increased; the length change to this transition increased with shortening velocity to a steady value of ∼8 nm half-sarcomere-1 A small, rapid, temperature jump (T-jump) (3-4°C, <0.2 ms) applied coincident with the onset of ramp shortening showed force enhancement by T-jump and changed the tension decline markedly. Analyses showed that the rate of T-jump-induced force rise increased linearly with increase of shortening velocity. These results provide crucial evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is endothermic.

Reinterpretation of the Tension Response of Muscle to Stretches and Releases.

We have reexamined the experimental time courses of tension in frog muscle after rapid length steps. The early tension recoveries are biexponential. After 3 nm/hs stretches and releases, the rates of the immediate rapid tension changes are similar but the subsequent tension fall after a stretch is much slower than the rise after a release. After 1.5 nm/hs length steps, the entire tension responses are more nearly mirror images. To identify the underlying processes, we used a model of the muscle cross-bridge cycle with two tension-generating (tensing) steps. Analysis of the time course of the tension, the rates of the steps in the cycle, and their contributions to tension provided insights into previously puzzling features of the experimental response. After a stretch, the initial rapid tension fall in the model is caused principally by the reversal of the first tensing step, but after a few milliseconds the tensing step resumes its forward direction. We conclude that the remaining response should not be included in phase 2, the period of early tension recovery. With this exclusion, T2, the tension at the end of this period, rises with an increase of stretch. The rate of early tension recovery also increases with stretch size, showing that the reversal of the first tensing step is strain sensitive. After small length steps, the fast and slow components of the early tension recovery are both caused mainly by the first tensing step. The fast component is triggered by the initial sliding of the filaments, and the slow component is due to further sliding that occurs as the tension recovers. With small length steps (<0.5 nm/hs), the time course of the response to a stretch is the reverse of that to a release.

The endothermic ATP hydrolysis and crossbridge attachment steps drive the increase of force with temperature in isometric and shortening muscle.

The isometric tetanic tension of skeletal muscle increases with temperature because attached crossbridge states bearing a relatively low force convert to those bearing a higher force. It was previously proposed that the tension-generating step(s) in the crossbridge cycle was highly endothermic and was therefore itself directly targeted by changes in temperature. However, this did not explain why a rapid rise in temperature (a temperature jump) caused a much slower rate of rise of tension than a rapid length step. This led to suggestions that the step targeted by a temperature rise is not the tension-generating step but is an extra step in the attached pathway of the crossbridge cycle, perhaps located on a parallel pathway. This enigma has been a major obstacle to a full understanding of the operation of the crossbridge cycle. We have now used a previously developed mechano-kinetic model of the crossbridge cycle in frog muscle to simulate the temperature dependence of isometric tension and shortening velocity. We allowed all five steps in the cycle to be temperature-sensitive. Models with different starting combinations of enthalpy changes and activation enthalpies for the five steps were refined by downhill simplex runs and scored by their ability to fit experimental data on the temperature dependence of isometric tension and the relationship between force and shortening velocity in frog muscle. We conclude that the first tension-generating step may be weakly endothermic and that the rise of tension with temperature is largely driven by the preceding two strongly endothermic steps of ATP hydrolysis and attachment of M.ADP.Pi to actin. The refined model gave a reasonable fit to the available experimental data and after a temperature jump the overall rate of tension rise was much slower than after a length step as observed experimentally. The findings aid our understanding of the crossbridge cycle by showing that it may not be necessary to include an additional temperature-sensitive step.

A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics.

We examined whether cross-bridge cycle models with one or two tension-generating steps can account for the force-velocity relation of and tension response to length steps of frog skeletal muscle. Transition-state theory defined the strain dependence of the rate constants. The filament stiffness was non-Hookean. Models were refined against experimental data by simulated annealing and downhill simplex runs. Models with one tension-generating step were rejected, as they had a low efficiency and fitted the experimental data relatively poorly. The best model with two tension-generating steps (stroke distances 5.6 and 4.6 nm) and a cross-bridge stiffness of 1.7 pN/nm gave a good account of the experimental data. The two tensing steps allow an efficiency of up to 38% during shortening. In an isometric contraction, 54.7% of the attached heads were in a pre-tension-generating state, 44.5% of the attached heads had undergone the first tension-generating step, and only 0.8% had undergone both tension-generating steps; they bore 34%, 64%, and 2%, respectively, of the isometric tension. During slow shortening, the second tensing step made a greater contribution. During lengthening, up to 93% of the attached heads were in a pre-tension-generating state yet bore elevated tension by being dragged to high strains before detaching.

Crossbridge and filament compliance in muscle: implications for tension generation and lever arm swing.

The stiffness of myosin heads attached to actin is a crucial parameter in determining the kinetics and mechanics of the crossbridge cycle. It has been claimed that the stiffness of myosin heads in the anterior tibialis muscle of the common frog (Rana temporaria) is as high as 3.3 pN/nm, substantially higher than its value in rabbit muscle (~1.7 pN/nm). However, the crossbridge stiffness measurement has a large error since the contribution of crossbridges to half-sarcomere compliance is obtained by subtracting from the half-sarcomere compliance the contributions of the thick and thin filaments, each with a substantial error. Calculation of its value for isometric contraction also depends on the fraction of heads that are attached, for which there is no consensus. Surprisingly, the stiffness of the myosin head from the edible frog, Rana esculenta, determined in the same manner, is only 60% of that in Rana temporaria. In our view it is unlikely that the value of such a crucial parameter could differ so substantially between two frog species. Since the means of the myosin head stiffness in these two species are not significantly different, we suggest that the best estimate of the stiffness of the myosin heads for frog muscle is the average of these data, a value similar to that for rabbit muscle. This would allow both frog and rabbit muscles to operate the same low-cooperativity mechanism for the crossbridge cycle with only one or two tension-generating steps. We review evidence that much of the compliance of the myosin head is located in the pliant region where the lever arm emerges from the converter and propose that tension generation ("tensing") caused by the rotation and movement of the converter is a separate event from the passive swinging of the lever arm in its working stroke in which the strain energy stored in the pliant region is used to do work.

Stabilization of helical order in the thick filaments by blebbistatin: further evidence of coexisting multiple conformations of myosin.

The degree of helical order of the thick filament of mammalian skeletal muscle is highly dependent on temperature and the nature of the ligand. Previously, we showed that there was a close correlation between the conformation of the myosin heads on the surface of the thick filaments and the extent of their helical order. Helical order required the heads to be in the closed conformation. In addition, we showed that, with the same ligand bound at the active site, three conformations of myosin coexisted in equilibrium. Hitherto, however, there was no detectable helical order as measured by x-ray diffraction under the temperatures studied for myosin with MgADP and the nucleotide-free myosin, raising the possibility that the concept of multiple conformations has limited validity. In this study, blebbistatin was used to stabilize the closed conformation of myosin. The degree of helical order is substantially improved with MgATP at low temperature or with MgADP or in the absence of nucleotide. The thermodynamic parameters of the disorder<-->order transition and the characteristics of the ordered array were not significantly altered by binding blebbistatin. The simplest explanation is that the binding of blebbistatin increases the proportion of myosin in the closed conformation from being negligible to substantial. These results provide further evidence for the coexistence of multiple conformations of myosin under a wide range of conditions and for the closed conformation being directly coupled to helical order.

Structural studies of arthrin: monoubiquitinated actin.

Here, we report on the structure and in situ location of arthrin (monoubiquitinated actin). Labelling of insect muscle thin filaments with a ubiquitin antibody reveals that every seventh subunit along the filament long-pitch helices is ubiquitinated. A three-dimensional reconstruction of frozen-hydrated arthrin filaments was produced. This was based on a novel algorithm that divides filament images into short segments that are used for single-particle image processing. Difference maps with an actin filament reconstruction locate ubiquitin at the side of actin sub-domain 1 opposite where myosin binds. Consistent with the reconstructions, peptide mapping places the ubiquitin linkage on lysine 118 in actin. Molecular modelling was used to generate arthrin monomers from ubiquitin and actin crystal structures. Filament models constructed from these monomers were compared with the arthrin reconstruction. The reconstruction suggests ubiquitin attached to Lys118 adopts one or a few conformers, stabilized by a small interface with actin. The function of actin ubiquitination is not known, but may involve regulation of muscle contractile activity.

Probing muscle myosin motor action: x-ray (m3 and m6) interference measurements report motor domain not lever arm movement.

The key question in understanding how force and movement are produced in muscle concerns the nature of the cyclic interaction of myosin molecules with actin filaments. The lever arm of the globular head of each myosin molecule is thought in some way to swing axially on the actin-attached motor domain, thus propelling the actin filament past the myosin filament. Recent X-ray diffraction studies of vertebrate muscle, especially those involving the analysis of interference effects between myosin head arrays in the two halves of the thick filaments, have been claimed to prove that the lever arm moves at the same time as the sliding of actin and myosin filaments in response to muscle length or force steps. It was suggested that the sliding of myosin and actin filaments, the level of force produced and the lever arm angle are all directly coupled and that other models of lever arm movement will not fit the X-ray data. Here, we show that, in addition to interference across the A-band, which must be occurring, the observed meridional M3 and M6 X-ray intensity changes can all be explained very well by the changing diffraction effects during filament sliding caused by heads stereospecifically attached to actin moving axially relative to a population of detached or non-stereospecifically attached heads that remain fixed in position relative to the myosin filament backbone. Crucially, and contrary to previous interpretations, the X-ray interference results provide little direct information about the position of the myosin head lever arm; they are, in fact, reporting relative motor domain movements. The implications of the new interpretation are briefly assessed.

Generalized Crick equations for modeling noncanonical coiled coils.

Crick envisaged the alpha-helical coiled coil to result from systematic bending of an alpha-helix such that every seventh residue was structurally equivalent, and he derived equations for the coordinates of the backbone atoms. Crick's predictions were vindicated experimentally and coiled-coil sequences were shown to have hydrophobic residues alternately spaced 3 and 4 residues apart. Nonetheless, in some coiled coils such canonical heptad repeats are interrupted by inserts of 3 or 4 residues generating decad and hendecad motifs. The supercoiling of the coiled coils varies with the sequence pattern, being left- or right-handed in purely heptad-based or hendecad-based motifs, respectively. To model coiled coils with a mixture of motifs, we describe how Crick's equations can be modified for cases where the pitch is not constant. Using the analogy of the bending of a beam, we took the tilt angle to change linearly with distance along the major helix and the pitch of a motif to be affected by neighboring motifs depending on the rigidity of the alpha-helical strands. We tested our approach by fitting the two-, three-, and four-stranded noncanonical coiled coils of GrpE, hemagglutinin, and tetrabrachion. The backbone atoms of the model and crystal structures agreed with root mean square deviations of <1.1 A.

Evaluation of the symmetric model for myosin-linked regulation: effect of site-directed mutations in the regulatory light chain on scallop myosin.

Regulatory myosins are controlled through mechanisms intrinsic to their structures and can alternate between activated and inhibited states. However, the structural difference between these two states is unclear. Scallop (Pecten maximus) striated adductor myosin is activated directly by calcium. It has been proposed that the two heads of scallop myosin are symmetrically arranged and interact through their regulatory light chains [Offer and Knight (1996) J. Mol. Biol. 256, 407-416], the interface being strengthened in the inhibited state. By contrast, vertebrate smooth-muscle myosin is activated by phosphorylation. Its structure in the inhibited state has been determined from two-dimensional crystalline arrays [Wendt, Taylor, Trybus and Taylor (2001) Proc. Natl. Acad. Sci. U.S.A. 98, 4361-4366] and is asymmetric, requiring no interaction between regulatory light chains. Using site-directed mutagenesis of the scallop regulatory light chain, we have tested the symmetric model for scallop adductor muscle myosin. Specifically, we have made myosin hybrid molecules from scallop (P. maximus) myosin, in which the normal regulatory light chains have been replaced by expressed light chains containing mutations in three residues proposed to participate in the interaction between regulatory light chains. The mutations were R126A (Arg126-->Ala), K130A and E131A; made singly, in pairs or all three together, these mutations were designed to eliminate hydrogen bonding or salt linkages between heads, which are key features of this model. Functional assays to address the competence of these hybrid myosins to bind calcium specifically, to exhibit a calcium-regulated myofibrillar Mg-ATPase and to display calcium-dependent actin sliding were performed. We conclude that the symmetrical model does not describe the inhibited state of scallop regulatory myosin and that an asymmetric structure is a plausible alternative.