Inferring crossbridge properties from skeletal muscle energetics

Work is generated in muscle by myosin crossbridges during their interaction with the actin filament. The energy from which the work is produced is the free energy change of ATP hydrolysis and efficiency quantifies the fraction of the energy supplied that is converted into work. The purpose of this review is to compare the efficiency of frog skeletal muscle determined from measurements of work output and either heat production or chemical breakdown with the work produced per crossbridge cycle predicted on the basis of the mechanical responses of contracting muscle to rapid length perturbations. We review the literature to establish the likely maximum crossbridge efficiency for frog skeletal muscle (0.4) and, using this value, calculate the maximum work a crossbridge can perform in a single attachment to actin (33 × 10⁻²¹ J). To see whether this amount of work is consistent with our understanding of crossbridge mechanics, we examine measurements of the force responses of frog muscle to fast length perturbations and, taking account of filament compliance, determine the crossbridge force-extension relationship and the velocity dependences of the fraction of crossbridges attached and average crossbridge strain. These data are used in combination with a Huxley-Simmons-type model of the thermodynamics of the attached crossbridge to determine whether this type of model can adequately account for the observed muscle efficiency. Although it is apparent that there are still deficiencies in our understanding of how to accurately model some aspects of ensemble crossbridge behaviour, this comparison shows that crossbridge energetics are consistent with known crossbridge properties.     

On the molecular dynamics of the chemo-mechanical conversion in muscle contraction

The molecular dynamics of energy conversion by the actomyosin system in muscle contraction is studied by comparing two different types of model on the motion of crossbridge on thin filament. The motion is associated with a transition between two stable states in Huxley and Simmons' model while in Shimizu et al.'s model with a transition from an unstable to a stable state. The rate of the transition, which is proportional to the velocity of shortening of muscle in steady state, is calculated by representing the motion of crossbridge by that of a Brownian particle moving on a one-dimensional linear potential. In the case of the Huxley-Simmons model the energy conversion process is essentially a thermal one and the velocity of shortening depends sharply on the number of crossbridges on muscular filament, which is proportional to the overlapping length between thin and thick filaments. On the other hand, in the case of the Shimizu model the energy conversion process is a deterministic one which means that muscle is able to shorten smoothly and that the velocity of shortening is almost independent of the overlapping length. Experimental observations by Gordon et al. are consistent with the latter model.     

Mechanism and significance of early, rapid shortening in sensitized airway smooth muscle

It has been reported that sensitization of animals to allergens increases both early shortening velocity and myosin light-chain kinase of their airway smooth muscle without increasing force generated by these muscles. Since early shortening sets muscle length for the duration of a contraction, these responses might be expected to produce greater airway obstruction. Here, it is explained how the more rapid early shortening without increased force production is predicted by the 2-stage process of activation followed by contraction posited by the crossbridge theory of contraction when the rate, but not the extent, of activation is increased. The experimental results are reproduced by a simple model in which activation rate is increased 1.6-fold without any other changes in contractile parameters. These results reinforce suggestions that sensitized animals are a model for reactive airway disease.     

Characterization of the myosin adenosine triphosphate (M.ATP) crossbridge in rabbit and frog skeletal muscle fibers.

In the presence of ATP and absence of Ca2+, muscle crossbridges have either MgATP or MgADP.Pi bound at the active site (S. B. Marston and R. T. Tregear, Nature [Lond.], 235:22:1972). The behavior of these myosin adenosine triphosphate (M.ATP) crossbridges, both in relaxed skinned rabbit psoas and frog semitendinosus fibers, was analyzed. At very low ionic strength, T = 5 degrees C, mu = 20 mM, these crossbridges spend a large fraction of the time attached to actin. In rabbit, the attachment rate constants at low salt are 10(4) - 10(5) s-1, and the detachment rate constants are approximately 10(4) s-1. When ionic strength is increased up to physiological values by addition of 140 mM potassium propionate, the major effect is a weakening of the crossbridge binding constant approximately 30-40-fold. This effect occurs because of a large decrease, approximately 100-fold, in the crossbridge attachment rate constants. The detachment rate constants decrease only 2-3-fold. The effect of ionic strength on crossbridge binding in the fiber is very similar to the effect of ionic strength on the binding of myosin subfragment-1 to unregulated actin in solution. Thus, the effect of increasing ionic strength in fibers appears to be a direct effect on crossbridge binding rather than an effect on troponin-tropomyosin. The finding that crossbridges with ATP bound at the active site can and do attach to actin over a wide range of ionic strengths strongly suggests that troponin-tropomyosin keeps a muscle relaxed by blocking a step subsequent to crossbridge attachment. Thus, rather than troponin-tropomyosin serving to keep a muscle relaxed by inhibiting attachment, it seems quite possible that the main way in which troponin-tropomyosin regulates muscle activity is by preventing the weakly-binding relaxed crossbridges from going on through the crossbridge cycle into more strongly-binding states.     

The influence of doubly attached crossbridges on the mechanical behavior of skeletal muscle fibers under equilibrium conditions.

A simple model of a double-headed crossbridge is introduced to explain the retardation of force decay after an imposed stretch in skeletal muscle fibers under equilibrium conditions. The critical assumption in the model is that once one of the heads of a crossbridge is attached to one of the available actin sites, the attachment of the second head will be restricted to a level of strain determined by the attachment of the first head. The crossbridge structure, namely the connection of both heads of a crossbridge to the same tail region, is assumed to impose this constraint on the spatial configurations of crossbridge heads. The unique feature of the model is the prediction that, in the presence of a ligand (PPi, ADP, AMP-PNP) and absence of Ca2+, the halftime of force decay is many times larger than the inverse rate of detachment of a crossbridge head measured in solution. This prediction is in agreement with measured values of half-times of force decay in fibers under similar conditions (Schoenberg, M., and E. Eisenberg. 1985. Biophys. J. 48:863-871f). It is predicted that a crossbridge head is more likely to re-attach to its previously strained position than remain unattached while the other head is attached, leading to the slow decay of force. Our computations also show that the apparent cooperativity in crossbridge binding observed in experiments (Brenner, B., L. C. Yu, L. E. Greene, E. Eisenberg, and M. Schoenberg. 1986. Biophys. J. 50:1101-1108) can be partially accounted by the double-headed crossbridge attachment.(ABSTRACT TRUNCATED AT 250 WORDS)     

Force suppression and the crossbridge cycle in swine carotid artery

Cyclic nucleotides can relax arterial smooth muscle without reductions in crossbridge phosphorylation, a process termed force suppression. There are two potential mechanisms for force suppression: 1) phosphorylated crossbridges binding to thin filaments could be inhibited or 2) the attachment of thin filaments to anchoring structures could be disrupted. These mechanisms were evaluated by comparing histamine-stimulated swine arterial smooth muscle with and without forskolin-induced force suppression and with and without latrunculin-A-induced actin filament disruption. At matched force, force suppression was associated with higher crossbridge phosphorylation and shortening velocity at low loads when compared with tissues without force suppression. Shortening velocity at high loads, noise temperature, hysteresivity, and stiffness did not differ with and without force suppression. These data suggest that crossbridge phosphorylation regulates the crossbridge cycle during force suppression. Actin disruption with latrunculin-A was associated with higher crossbridge phosphorylation when compared with tissues without actin disruption. Shortening velocity, noise temperature, hysteresivity, and stiffness did not differ with and without actin disruption. These data suggest that actin disruption interferes with regulation of crossbridge cycling by crossbridge phosphorylation. Stiffness was linearly dependent on stress, suggesting that the force per attached crossbridge was not altered with force suppression or actin disruption. These data suggest a difference in the mechanical characteristics observed during force suppression and actin disruption, implying that force suppression does not mechanistically involve actin disruption. These data are most consistent with a model where force suppression involves the inhibition of phosphorylated crossbridge binding to thin filaments. force suppression; heat shock protein 20; vascular smooth muscle     

Possible cooperativity in crossbridge detachment in muscle fibers having magnesium pyrophosphate at the active site.

When rabbit psoas muscle fibers bathed in solutions containing the ATP analogue magnesium pyrophosphate (MgPPi) are first stretched rapidly and then held isometric, a force is generated during the stretch which decays during the subsequent isometric period (Schoenberg, M., and E. Eisenberg. 1985. Biophys. J. 48:863-871). Previously we showed that the force decay is due to crossbridge heads detaching and reattaching in positions of lesser strain, the rate of decay of force reflecting the crossbridge detachment rate constants. Since the crossbridge detachment rate constants with MgPPi bound to the active site are so much faster than without analogue bound, at subsaturating concentrations of analogue, if the heads act independently and nucleotide association and dissociation is rapid, the rate of force decay should simply be proportional to the number of heads with bound analogue. That is, the analogue concentration dependence of the rate of force decay should have the same form as the Michaelis-Menten equation. Here we report that the concentration dependence of the rate of force decay is not described by the Michaelis equation, but is instead sigmoidal. This suggests possible cooperativity in the detachment of the crossbridge heads, the amount of cooperativity being described by an interaction coefficient of approximately 2. One idea put forward to explain the data is that both of the heads of a crossbridge may need to bind analogue before the crossbridge can relax a substantial fraction of the tension it supports.     

A model to account for the elastic element in muscle crossbridges in terms of a bending myosin rod

We advance a structural model to account for the rapid elastic element seen in mechanical transient experiments on vertebrate skeletal muscle (A.F. Huxley & Simmons 1971 Nature, Lond. 233, 533-538). In contrast to other crossbridge models, ours does not envisage a myosin rod made up of two rigid portions connected by a hinge, but rather a gradually bending rod portion connecting the heads to the thick filament shaft. We propose that, in relaxed muscle, the subfragment 2 (S2) portion of the myosin rod is bound to the thick filament shaft by ionic interactions analogous to those between the light meromyosin (LMM) portions of the rod that constitute the body of the shaft. These interactions probably involve the alternating zones of positive and negative charge seen in myosin rod amino acid sequences. As the crossbridge cycle that generates tension begins, we propose that part of S2 detaches from the thick filament shaft and bends to enable the myosin head to attach to actin. When tension develops in the crossbridge, the S2 is straightened and more of it becomes detached from the shaft so that the junction between S2 and the myosin heads moves 3-4 nm axially. As tension declines at the end of the crossbridge stroke, we propose that S2 rebinds to the thick filament shaft and that this provides the restoring force to return the junction of the heads and S2 to its original axial position. Thus this movement would have the characteristics of an elastic element; detailed calculations indicate that it would have properties similar to those observed experimentally. Furthermore, this model can account for the radial attractive force seen in rigor and in contracting muscle, the decrease in stiffness when interfilament spacing is increased in skinned muscle, and the increased rate of proteolysis observed at the S2-LMM junction in contracting muscle.     

A program for developing a comprehensive mathematical description of the crossbridge cycle of muscle.

We describe a computer modeling system for determining the changes of force, fraction of attached crossbridges, and crossbridge flux rate through a specifiable transition in response to length changes imposed on a crossbridge model of muscle. The crossbridge cycle is divided into multiple attached and detached states. The rates of transition from one state to another are defined by rate coefficients that can either be constant or vary with the position of the crossbridge relative to the thin-filament attachment site. This scheme leads to a system of differential equations defining the rates of change for the fractions of bridges in each state. Solutions for this system of equations are obtained at specified times during and after a length change using a method for systems with widely varying time constants (C. W. Gear, 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ). Crossbridges are divided into discrete populations that differ both in their axial displacement with respect to thin filament attachment sites and with respect to the twist of the actin helix. Separate solutions are made for the individual populations and are then averaged to obtain the ensemble response. Force is determined as the sum of the product of the force associated with each state multiplied by the fraction of bridges in that state. A measure of metabolic rate is determined as the net flux through one of the crossbridge transitions. When the force-extension characteristics of the individual crossbridges are linear and the filaments are noncompliant the fraction of attached bridges is equivalent to sarcomere stiffness. To illustrate the operation of the program, we also describe here some results obtained with a simplified scheme.     

Adenosine 5''-triphosphate consumption by smooth muscle as predicted by the coupled four-state crossbridge model.

We have proposed a four-state crossbridge model to explain contraction and the latch state in arterial smooth muscle. Ca(2+)-dependent crossbridge phosphorylation was the only postulated regulatory mechanism and the latchbridge (a dephosphorylated, attached crossbridge) was the only novel element in the model. In this study, we used the model to predict rates of ATP consumption by crossbridge phosphorylation (JPhos) and cycling (JCycle) during isometric and isotonic contractions in arterial smooth muscle; then we compared model predictions with experimental data. The model predicted that JPhos and JCycle were similar in magnitude in isometric contractions, and both increased almost linearly with myosin phosphorylation. The predicted relationship between isometric stress and ATP consumption was quasihyperbolic, but approximately linear when myosin phosphorylation was below 35%, in agreement with most of the available data. Muscle shortening increased the predicted values of JCycle up to 3.7-fold depending on shortening velocity and the level of myosin phosphorylation. The predicted maximum work output per ATP was 7.4-7.8 kJ/mol ATP and was relatively insensitive to changes in myosin phosphorylation. The predicted increase in JCycle with shortening was in agreement with available data, but the model prediction that work output per ATP was insensitive to changes in myosin phosphorylation was unexpected and remains to be tested in future experiments.     

A viscoplastic model for the active component in cardiac muscle

The HMK model (Hunter et al. in Prog Biophys Mol Biol 69:289–331, 1998) proposes mechanobiological equations for the influence of intracellular calcium concentration \(\hbox {Ca}_\mathrm{i}\) on the evolution of bound calcium concentration \(\hbox {Ca}_\mathrm{b}\) and the tropomyosin kinetics parameter z, which model processes in the active component of the tension in cardiac muscle. The inelastic response due to actin-myosin crossbridge kinetics is modeled in the HMK model with a function Q that depends on the history of the rate of total stretch of the muscle fiber. Here, an alternative model is proposed which models the active component of the muscle fiber as a viscoplastic material. In particular, an evolution equation is proposed for the elastic stretch \(\lambda _\mathrm{a} \) in the active component. Specific forms of the constitutive equations are proposed and used to match experimental data. The proposed viscoplastic formulation allows for separate modeling of three processes: the high rate deactivation of crossbridges causing rapid reduction in active tension; the high but lower rate reactivation of crossbridges causing recovery of active tension; and the low rate relaxation effects characterizing the Hill model of muscles.     

Equilibrium muscle crossbridge behavior: The interaction of myosin crossbridges with actin

The interaction of myosin crossbridges with actin under equilibrium conditions is reviewed. Similarities and differences between the weakly- and strongly-binding interactions of myosin crossbridges with actin filaments are discussed. A precise, narrow definition of weakly- binding crossbridges is given. It is postulated that the fundamental interaction of crossbridges with actin is that the crossbridge heads are mobile after attachment in the first case but not in the second. It is argued that because the weakly-binding crossbridge heads are mobile after attachment, the heads appear to function independently of each other. The lack of head mobility in attached strongly-binding crossbridges makes the strongly-binding crossbridge heads appear to act cooperatively. This model of the strongly-binding crossbridge gives an explanation for two important and otherwise unexplained observations. It explains why the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and why, in the presence of analogues or in rigor, the rate constant of force decay after a small stretch is often significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution. The model of the weakly-binding crossbridge accurately describes the behavior of the myosin·ATP crossbridge.     

The sliding filament model of muscle contraction. II. The energetic and dynamical predictions of a quantum mechanical transducer model

A theoretical model of a molecular energy transducing unit designed for the production of mechanical work is constructed and its consequences examined and compared with the experimentally determined myothermal and dynamic properties of vertebrate striated muscle. The model rests on a number of independent assumptions which include: the almost instantaneous generation of mechanical force by the occurrence of a radiationless transition between vibronic states of the transducer (crossbridge) at a point of potential energy surface crossing; transmission of this force to the load via the active sites on the thin filament by means of non-bonding repulsive forces, no energy being required for detachment; “detachment” consists of a second radiationless transition at a lower energy point than the first force generating transition, the energy difference appearing largely as work. The method of force generation completely avoids problems such as the “force-rate dilemma” which occur repeatedly in any discussion where state populations are near-Boltzmann and also leads without further arbitrary assumptions to such concepts as “attached but non force-producing states” and strongly position dependent “attachment” and “detachment” rate constants since these can only be appreciable near potential energy surface crossings. The kinetics and energetics of a transducer of this type operating cyclically and converting ATP → ADP + P_i are considered and shown to lead to length-tension and energetic behaviour very similar to that exhibited by vertebrate striated muscle, both for contraction and stretching. The existence of a limiting tension for stretching is predicted by the model as is the decrease of the rate of enthalpy release rate below the isometric value. At the limiting tension the rate of enthalpy release by the transducers is virtually zero, as observed. However, the stretching only inhibits the ATP hydrolysis, the cyclic synthesis from ADP and work being impossible with this model. The response to rapid length step changes automatically contains the asymmetry observed experimentally (with respect to lengthening and shortening) and arbitrary assumptions over and above those giving adequate explanation of the steady-state properties are not required. The asymmetry arises mainly as a consequence of the non-bonded pushing action of the crossbridges. This same assumption predicts the occurrence of an asymmetric thermoelastic ratio for active muscle with respect to stretching and contraction. The quantitative aspects of the model are satisfactory as it simultaneously reconciles the numerical magnitudes of macroscopic quantities such as isometric tension, maximum contraction velocity, limiting tension sustainable on stretching, isometric heat rate and resting heat rate with molecular parameters such as the filament and crossbridge periodicities, molecular vibrational relaxation rates, recurrence times for the radiationless transitions occurring, etc. This is achieved without any parameter optimization and only a very much smaller number of unknown parameters than the number of observed results accounted for. Many of the entities occurring in the model cycle (vibronic states of crossbridges, ATP, etc.) appear to be in one-to-one correspondence with many of the kinetic entities postulated to account for the biochemical kinetic results obtained for the actomyosin ATPase system in vitro. Finally, the rigor state has to be viewed in a different way from the conventional one; on the basis that the present model states which are part of the contraction cycle but sparsely populated during the latter (and hence are of chemical kinetic but not dynamical importance) are heavily populated during the rigor state. The mechanical properties of the rigor state would then be determined by these molecular states which would be very short-lived during the contraction cycle. If this is correct the rigor state could yield much more information about inaccessible parts of the contraction cycle than is presently supposed. The model leads one to expect a rather different response to quick length step changes in the rigor state from that of the active state, in contrast to current interpretations in terms of a large number of attached crossbridges, unable to detach due to the absence of ATP.     

The force-velocity relationship for microtubule sliding in demembranated sperm flagella of the sea urchin

We studied the relationship between the force and velocity of microtubule sliding in demembranated sperm flagella of the sea urchin, Hemicentrotus pulcherrimus, under auxotonic conditions following a quick release of the tension between sliding microtubules. The shape of the force-velocity curve was independent of the concentration of Mg-ATP over the range of 3.7 to 350 microM and appeared either linear or was the reverse of the hyperbolic curve seen for muscle. The power, calculated as the product of velocity and force, passed through a peak at c. 0.7 Fmax (the maximal isometric force). Thus, the maximal power is attained at a larger relative load than in muscle. The sliding velocity at 0.1 Fmax showed a hyperbolic dependence on Mg-ATP concentration, with a Km of 210 microM and a Vmax of 19 micron.sec-1. The maximal force did not significantly change over the Mg-ATP concentration range of 3.7 to 350 microM. These results are discussed in terms of a crossbridge model similar to the one originally proposed by Huxley. It is suggested that the dynein crossbridge cycle is characterized by a relatively rapid rate of attachment and a relatively slow rate of detachment.     

Dynamic stiffness and crossbridge action in muscle

Small sinusoidal vibrations at 300 HZ were applied to frog sartorius muscle to measure the dynamic stiffness (Young's modulus) throughout the course of tetanus. For a peak-to-peak amplitude of 0.4% the dynamic Young's modulus increased from 1.5 X 10(5) Nm-2 in the resting state to 2 X 10(7) Nm-2 in tetanus. After correction for the external connective tissue, the dynamic Young's modulus of the muscle was almost directly proportional to the tension throughout the development of tetanus. The ratio of dynamic Young's modulus to tensile stress thus remained constant (with a value at 300 Hz of approximately 100), consistently with Huxley and Simmon's identification of the crossbridges as the source of both tension and stiffness. For a single crossbridge the ratio of stiffness to tension was 8.2 X 10(7) m-1 at 300 Hz; it is deduced from literature data that the limiting value at high frequencies is about 1.6 X 10(8) m-1. This ratio is interpreted on Harrington's (1971) model to show that crossbridge action can be explained by a helix-coil transition of about 80 out of the 260 residues in each S-2 myosin strand. It is also shown that a helix-coil model can account for the observed rapid relaxation of muscle without invoking any complex behaviour of the crossbridge head.     

Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers

Muscle contraction is driven by the cyclical interaction of myosin with actin, coupled with ATP hydrolysis. Myosin attaches to actin, forming a crossbridge that produces force and movement as it tilts or rocks into subsequent bound states before finally detaching. It has been hypothesized that the kinetics of one or more of these mechanical transitions are dependent on load, allowing muscle to shorten quickly under low load, but to sustain tension economically, with slowly cycling crossbridges under high load conditions. The idea that muscle biochemistry depends on mechanical output is termed the 'Fenn effect'. However, the molecular details of how load affects the kinetics of a single crossbridge are unknown. Here, we describe a new technique based on optical tweezers to rapidly apply force to a single smooth muscle myosin crossbridge. The crossbridge produced movement in two phases that contribute 4 nm + 2 nm of displacement. Duration of the first phase depended in an exponential manner on the amplitude of applied load. Duration of the second phase was much less affected by load, but was significantly shorter at high ATP concentration. The effect of load on the lifetime of the bound crossbridge is to prolong binding when load is high, but to accelerate release when load is low or negative.     

Equilibrium muscle cross-bridge behavior. Theoretical considerations. II. Model describing the behavior of strongly-binding cross-bridges when both heads of myosin bind to the actin filament.

A model has been developed for characterizing the interaction between strongly-binding myosin cross-bridges and actin in muscle fibers under equilibrium conditions where both heads of the myosin cross-bridge bind to actin. The model, that of Anderson and Schoenberg (1987. Biophys. J. 52:1077-1082) is quite similar to that of Schoenberg (1985. Biophys. J. 48:467-475), except that explicit account is taken of the fact that each crossbridge has two heads which can bind to actin. The key assumption that allows this model to explain a large body of data unexplained by the Schoenberg (1985) model is that the two crossbridge heads are not totally independent of one another after attachment. After the first head attaches, the second head is then free to attach only to an actin site distal to the first head. This means that when the more distally attached head subsequently detaches and reattaches (as the heads continually do), it will not reattach in a position of lesser strain and reduce the force it supports, but instead will remain attached in its strained position until the proximally attached head also detaches. This model gives an explanation for two important and otherwise unexplained observations made previously: it explains why at ionic strengths in the range of 50-120 mM, (a) the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and (b) why in the presence of analogues or in rigor the rate constant of force decay after a small stretch is significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution.     

Two attached non-rigor crossbridge forms in insect flight muscle

We have performed thin-section electron microscopy on muscle fibers fixed in different mechanically monitored states, in order to identify structural changes in myosin crossbridges associated with force production and maintenance. Tension and stiffness of fibers from glycerinated Lethocerus flight muscle were monitored during a sequence of conditions using AMPPNP and then AMPPNP plus increasing concentrations of ethylene glycol, which brought fibers through a graded sequence from rigor relaxation. Two intermediate crossbridge forms distinct from the rigor or relaxed forms were observed. The first was produced by AMPPNP at 20 degrees C, which reduced isometric tension 60 to 70% below rigor level without reducing rigor stiffness. Electron microscopy of these fibers showed that, in spite of the drop in tension, no obvious change from the 45 degrees crossbridge angle characteristic of rigor occurred. However, the thick filament ends of the crossbridges were altered from their rigor positions, so that they now marked a 14.5 nm repeat, and formed four separate origins at each crossbridge level. The bridges were also less slewed and bent than rigor bridges, as seen in transverse sections. The second crossbridge form was seen in glycol-AMPPNP at 4 degrees C, just below the glycol concentration that produced mechanical relaxation. These fibers retained 90% of rigor stiffness at 40 Hz oscillation, but would not bear sustained tension. Stiffness was also high in the presence of calcium at room temperature under similar conditions. Electron microscopy showed crossbridges projecting from the thick filaments at an angle that centered around 90 degrees, rather than the 45 degree angle familiar from rigor. This coupling of relaxed appearance with persistent stiffness suggests that the 90 degree form may represent a weakly attached crossbridge state like that proposed to precede force development in current models of the crossbridge power stroke.     

Structural changes in muscle crossbridges accompanying force generation

We have investigated the structure of the crossbridges in muscles rapidly frozen while relaxed, in rigor, and at various times after activation from rigor by flash photolysis of caged ATP. We used Fourier analysis of images of cross sections to obtain an average view of the muscle structure, and correspondence analysis to extract information about individual crossbridge shapes. The crossbridge structure changes dramatically between relaxed, rigor, and with time after ATP release. In relaxed muscle, most crossbridges are detached. In rigor, all are attached and have a characteristic asymmetric shape that shows strong left-handed curvature when viewed from the M-line towards the Z-line. Immediately after ATP release, before significant force has developed (20 ms) the homogeneous rigor population is replaced by a much more diverse collection of crossbridge shapes. Over the next few hundred milliseconds, the proportion of attached crossbridges changes little, but the distribution of the crossbridges among different structural classes continues to evolve. Some forms of attached crossbridge (presumably weakly attached) increase at early times when tension is low. The proportion of several other attached non-rigor crossbridge shapes increases in parallel with the development of active tension. The results lend strong support to models of muscle contraction that have attributed force generation to structural changes in attached crossbridges.