Single-molecule measurement of the stiffness of the rigor myosin head.

The force-extension curve of single myosin subfragment-1 molecules, interacting in the rigor state with an actin filament, has been investigated at low [ATP] by applying a slow triangle-wave movement to the optical traps holding a bead-actin-bead dumbbell. In combination with a measurement of the overall stiffness of the dumbbell, this allowed characterization of the three extensible elements, the actin-bead links and the myosin. Simultaneously, another method, based on an analysis of bead position covariance, gave satisfactory agreement. The mean covariance-based estimate for the myosin stiffness was 1.79 pN/nm (SD = 0.7 pN/nm; SE = 0.06 pN/nm (n = 166 myosin molecules)), consistent with a recent report (1.7 pN/nm) from rabbit muscle fibers. In the triangle-wave protocol, the motion of the trapped beads during interactions was linear within experimental error over the physiological range of force applied to myosin (+/-10 pN), consistent with a Hookean model; any nonlinear terms could not be characterized. Bound states subjected to forces that resisted the working stroke (i.e., positive forces) detached at a significantly lower force than when subjected to negative forces, which is indicative of a strain-dependent dissociation rate.

Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence.

We have analyzed the fluctuations of the red blood cell membrane in both the temporal ((omega(s(-1))) and spatial (q(m(-1))) frequency domains. The cells were examined over a range of osmolarities leading to cell volumes from 50% to 170% of that in the isotonic state. The fluctuations of the isotonic cell showed an approximately q(-3)-dependence, indicative of a motion dominated by bending, with an inferred bending modulus of approximately 9 x 10(-19) J. When the cells were osmotically swollen to just below the point of lysis (166% of physiological volume), a q(-1)-dependence of the fluctuations supervened, implying that the motion was now dominated by membrane tension; estimated as approximately 1.3 x 10(-4) nm(-1). When, on the other hand, the cells were osmotically dehydrated, the fluctuation amplitude progressively decreased. This was caused by a rise in internal viscosity, as shown by measurements on resealed ghosts containing a reduced hemoglobin concentration, which displayed no such effect. We examined, in addition, cells depleted of ATP, before the onset of echinocytosis, and could observe no change in fluctuation amplitude. We conclude that the membrane fluctuations of the red cell are governed by bending modulus, membrane tension, and cytosolic viscosity, with little or no dependence on the presence or absence of ATP.

Strain-dependent kinetics of the myosin working stroke, and how they could be probed with optical-trap experiments.

The strain-dependent kinetics of the myosin working stroke under load is derived from a flat-energy-landscape model for its untethered lever-arm, and compared with other scenarios in the literature. The "flat landscape" scenario is compatible with muscle-fiber experiments, but is more critically relevant to single-myosin experiments with an optically trapped actin filament. In such experiments, the strain dependence of stroke kinetics may be explored by comparing event-averaged and time-averaged displacements of the filament. With a specific kinetic model of the cross-bridge cycle, we have previously shown that the event-averaged displacement underestimates the working stroke. Here we predict that the two kinds of averaging give diverging estimates of the working stroke as the resolving time of the event detector is decreased to 1 ms or less, the discrepancy being critically dependent on the strain dependence of the stroke rate. Such analysis of trap displacement data offers the possibility of testing the strain-dependent stroke rate predicted by the flat-landscape model.

Reconciling the working strokes of a single head of skeletal muscle myosin estimated from laser-trap experiments and crystal structures.

Myosin generates force by a rotation of its lever arm. Crystal structures of myosin II indicate an unloaded working stroke of 10-12 nm, a range confirmed by recent x-ray interference experiments. However, when an actin filament, held between two weakly, optically trapped beads is made to interact with a single head of skeletal myosin, the bead displacements have often been reported as having a mean value of 5-6 nm, a value that is commonly interpreted as the working stroke. In general, the observed displacement is not expected to be equal to the working stroke because the kinetics of the stroke is necessarily strain-dependent: this effect biases the frequency of binding events to different actin sites so that displacements smaller than the working stroke are preferentially selected. Our analysis is tailored to current trap experiments, in which the time resolution is insufficient to detect pre-rigor states. If the preceding transitions are in equilibrium, the mean displacement is zero, contrary to observations in the presence of ATP. However, under ATP-cycling conditions, we find that the mean displacement is deflated to 0.3-0.7 of the true working stroke, depending on the equilibrium constant of the stroke and the rate at which the first myosin product state can detach from actin. The primary working stroke of processive myosin motors as measured by optical trapping is similarly uncertain.

Kinetics of force recovery following length changes in active skinned single fibres from rabbit psoas muscle: analysis and modelling of the late recovery phase.

Redevelopment of isometric force following shortening of skeletal muscle is thought to result from a redistribution of cross-bridge states. We varied the initial force and cross-bridge distribution by applying various length-change protocols to active skinned single fibres from rabbit psoas muscle, and observed the effect on the slowest phase of recovery ('late recovery') that follows transient changes. In response to step releases that reduced force to near zero ( approximately 8 nm (half sarcomere)(-1)) or prolonged shortening at high velocity, late recovery was well described by two exponentials of approximately equal amplitude and rate constants of approximately 2 s(-1) and approximately 9 s(-1) at 5 degrees C. When a large restretch was applied at the end of rapid shortening, recovery was accelerated by (1) the introduction of a slow falling component that truncated the rise in force, and (2) a relative increase in the contribution of the fast exponential component. The rate of the slow fall was similar to that observed after a small isometric step stretch, with a rate of 0.4-0.8 s(-1), and its effects could be reversed by reducing force to near zero immediately after the stretch. Force at the start of late recovery was varied in a series of shortening steps or ramps in order to probe the effect of cross-bridge strain on force redevelopment. The rate constants of the two components fell by 40-50% as initial force was raised to 75-80% of steady isometric force. As initial force increased, the relative contribution of the fast component decreased, and this was associated with a length constant of about 2 nm. The results are consistent with a two-state strain-dependent cross-bridge model. In the model there is a continuous distribution of recovery rate constants, but two-exponential fits show that the fast component results from cross-bridges initially at moderate positive strain and the slow component from cross-bridges at high positive strain.

Kinetics of muscle contraction and actomyosin NTP hydrolysis from rabbit using a series of metal-nucleotide substrates.

Mechanical properties of skinned single fibres from rabbit psoas muscle have been correlated with biochemical steps in the cross-bridge cycle using a series of metal-nucleotide (Me.NTP) substrates (Mn(2+) or Ni(2+) substituted for Mg(2+); CTP or ITP for ATP) and inorganic phosphate. Measurements were made of the rate of force redevelopment following (1) slack tests in which force recovery followed a period of unloaded shortening, or (2) ramp shortening at low load terminated by a rapid restretch. The form and rate of force recovery were described as the sum of two exponential functions. Actomyosin-Subfragment 1 (acto-S1) Me.NTPase activity and Me.NDP release were monitored under the same conditions as the fibre experiments. Mn.ATP and Mg.CTP both supported contraction well and maintained good striation order. Relative to Mg.ATP, they increased the rates and Me.NTPase activity of cross-linked acto-S1 and the fast component of a double-exponential fit to force recovery by approximately 50% and 10-35%, respectively, while shortening velocity was moderately reduced (by 20-30%). Phosphate also increased the rate of the fast component of force recovery. In contrast to Mn(2+) and CTP, Ni.ATP and Mg.ITP did not support contraction well and caused striations to become disordered. The rates of force recovery and Me.NTPase activity were less than for Mg.ATP (by 40-80% and 50-85%, respectively), while shortening velocity was greatly reduced (by approximately 80%). Dissociation of ADP from acto-S1 was little affected by Ni(2+), suggesting that Ni.ADP dissociation does not account for the large reduction in shortening velocity. The different effects of Ni(2+) and Mn(2+) were also observed during brief activations elicited by photolytic release of ATP. These results confirm that at least one rate-limiting step is shared by acto-S1 ATPase activity and force development. Our results are consistent with a dual rate-limitation model in which the rate of force recovery is limited by both NTP cleavage and phosphate release, with their relative contributions and apparent rate constants influenced by an intervening rapid force-generating transition.

The ATP hydrolysis and phosphate release steps control the time course of force development in rabbit skeletal muscle.

The time course of isometric force development following photolytic release of ATP in the presence of Ca(2+) was characterized in single skinned fibres from rabbit psoas muscle. Pre-photolysis force was minimized using apyrase to remove contaminating ATP and ADP. After the initial force rise induced by ATP release, a rapid shortening ramp terminated by a step stretch to the original length was imposed, and the time course of the subsequent force redevelopment was again characterized. Force development after ATP release was accurately described by a lag phase followed by one or two exponential components. At 20 degrees C, the lag was 5.6 +/- 0.4 ms (s.e.m., n = 11), and the force rise was well fitted by a single exponential with rate constant 71 +/- 4 s(-1). Force redevelopment after shortening-restretch began from about half the plateau force level, and its single-exponential rate constant was 68 +/- 3 s(-1), very similar to that following ATP release. When fibres were activated by the addition of Ca(2+) in ATP-containing solution, force developed more slowly, and the rate constant for force redevelopment following shortening-restretch reached a maximum value of 38 +/- 4 s(-1) (n = 6) after about 6 s of activation. This lower value may be associated with progressive sarcomere disorder at elevated temperature. Force development following ATP release was much slower at 5 degrees C than at 20 degrees C. The rate constant of a single-exponential fit to the force rise was 4.3 +/- 0.4 s(-1) (n = 22), and this was again similar to that after shortening-restretch in the same activation at this temperature, 3.8 +/- 0.2 s(-1). We conclude that force development after ATP release and shortening-restretch are controlled by the same steps in the actin-myosin ATPase cycle. The present results and much previous work on mechanical-chemical coupling in muscle can be explained by a kinetic scheme in which force is generated by a rapid conformational change bracketed by two biochemical steps with similar rate constants -- ATP hydrolysis and the release of inorganic phosphate -- both of which combine to control the rate of force development.

Using optical tweezers to relate the chemical and mechanical cross-bridge cycles.

In most current models of muscle contraction there are two translational steps, the working stroke, whereby an attached myosin cross-bridge moves relative to the actin filament, and the repriming step, in which the cross-bridge returns to its original orientation. The development of single molecule methods has allowed a more detailed investigation of the relationship of these mechanical steps to the underlying biochemistry. In the normal adenosine triphosphate cycle, myosin.adenosine diphosphate.phosphate (M.ADP.Pi) binds to actin and moves it by ca. 5 nm on average before the formation of the end product, the rigor actomyosin state. All the other product-like intermediate states tested were found to give no net movement indicating that M.ADP.Pi alone binds in a pre-force state. Myosin states with bound, unhydrolysed nucleoside triphosphates also give no net movement, indicating that these must also bind in a post-force conformation and that the repriming, post- to pre-transition during the forward cycle must take place while the myosin is dissociated from actin. These observations fit in well with the structural model in which the working stroke is aligned to the opening of the switch 2 element of the ATPase site.

Repriming the actomyosin crossbridge cycle.

The central features of the mechanical cycle that drives the contraction of muscle are two translational steps: the working stroke, whereby an attached myosin crossbridge moves relative to the actin filament, and the repriming step, in which the crossbridge returns to its original orientation. Although the mechanism of the first of these is understood in some detail, that of the second has received less attention. Here, we show that repriming occurs after detachment of the crossbridge from the actin, rather than intervening between two actomyosin states with ATP bound [Eisenberg, E. & Greene, L. E. (1980) Annu. Rev. Physiol. 42, 293-309]. To discriminate between these two models we investigated the single-molecule mechanics of the myosin-actin interaction in the presence of ATP analogues such as GTP, for which the hydrolytic step itself limits the actomyosin GTPase rate to a much lower rate than for ATP. The lifetimes of bound states was proportional to 1/[GTP], indicating that during the bound period myosin was in the actomyosin rigor configuration. Moreover, despite the very low actomyosin GTPase, the rate of actin binding and formation of the rigor state was higher than with ATP; it follows that most interactions with actin result in the release of GTP and not of the products, GDP and phosphate. There was no significant movement of the actin during this interaction, so repriming must occur while myosin is dissociated, as in the original Lymn-Taylor scheme [Lymn, R. W. & Taylor, E. W. (1971) Biochemistry 10, 4617-4624].

The working stroke upon myosin-nucleotide complexes binding to actin.

For many years, it has been known that myosin binds to actin tightly, but it had not been possible to devise a muscle fiber experiment to determine whether this binding energy is directly coupled to the working stroke of the actomyosin crossbridge cycle. Addressing the question at the single-molecule level with optical tweezers allows the problem to be resolved. We have compared the working stroke on the binding of four myosin complexes (myosin, myosin-ADP, myosin-pyrophosphate, and myosin-adenyl-5'yl imidodiphosphate) with that observed while hydrolyzing ATP. None of the four was observed to give a working stroke significantly different from zero. A working stroke (5.4 nm) was observed only with ATP, which indicates that the other states bind to actin in a rigor-like conformation and that myosin products (M.ADP.Pi), the state that binds to actin during ATPase activity, binds in a different, prestroke conformation. We conclude that myosin, while dissociated from actin, must be able to take up at least two mechanical conformations and show that our results are consistent with these conformations corresponding to the two states characterized at high resolution, which are commonly referred to in terms of having open and closed nucleotide binding pockets.

Mechanokinetics of rapid tension recovery in muscle: the Myosin working stroke is followed by a slower release of phosphate.

Crystallographic and biochemical evidence suggests that the myosin working stroke that generates force in muscle is accompanied by the release of inorganic phosphate (Pi), but the order and relative speed of these transitions is not firmly established. To address this problem, the theory of A. F. Huxley and R. M. Simmons for the length-step response is averaged over elastic strains imposed by filament structure and extended to include a Pi-release transition. Models of this kind are applied to existing tension-recovery data from length steps at different phosphate concentrations, and from phosphate jumps upon release of caged phosphate. This body of data is simulated by the model in which the force-generating event is followed by Pi release. A version in which the Pi-release transition is slow provides a better fit than a version with rapid Pi release and a slow transition preceding force generation. If Pi is released before force generation, the predicted rate of slow recovery increases with the size of the step, which is not observed. Some implications for theories of muscle contraction are discussed.