Three-dimensional disorder of dipolar probes in a helical array. Application to muscle cross-bridges.

Fluorescence polarization and EPR experiments on azimuthally randomized helices bearing extrinsic (dipolar) probes yield information about the axial orientation and order of the probes. If the orientation of the probe on the structure bearing it is known and disorder is absent, the orientation of the structure may be ascertained. For cases where less probe orientation information is available and/or disorder is present, the available structural information is correspondingly reduced. Here we examine the available data on probes attached to cross-bridges in muscle fibers: four plausible cases of three-dimensional cross-bridge disorders are numerically modeled muscle in states of rigor and relaxation. In rigor, where the reported probe disorder is small (Thomas and Cooke, 1980), it was found that the cross-bridge disorder was also small. On the other hand, for the relaxed state where the probes are found to be completely disordered, the cross-bridges may have a considerable amount of order. This possibility is in concert with the results of x-ray diffraction, in which the presence of well-developed myosin-based layer lines indicates considerable order in relaxed muscle.     

Comparison of Orientation and Rotational Motion of Skeletal Muscle Cross-bridges Containing Phosphorylated and Dephosphorylated Myosin Regulatory Light Chain

Calcium binding to thin filaments is a major element controlling active force generation in striated muscles. Recent evidence suggests that processes other than Ca²⁺ binding, such as phosphorylation of myosin regulatory light chain (RLC) also controls contraction of vertebrate striated muscle (Cooke, R. (2011) Biophys. Rev. 3, 33–45). Electron paramagnetic resonance (EPR) studies using nucleotide analog spin label probes showed that dephosphorylated myosin heads are highly ordered in the relaxed fibers and have very low ATPase activity. This ordered structure of myosin cross-bridges disappears with the phosphorylation of RLC (Stewart, M. (2010) Proc. Natl. Acad. Sci. U.S.A. 107, 430–435). The slower ATPase activity in the dephosporylated moiety has been defined as a new super-relaxed state (SRX). It can be observed in both skeletal and cardiac muscle fibers (Hooijman, P., Stewart, M. A., and Cooke, R. (2011) Biophys. J. 100, 1969–1976). Given the importance of the finding that suggests a novel pathway of regulation of skeletal muscle, we aim to examine the effects of phosphorylation on cross-bridge orientation and rotational motion. We find that: (i) relaxed cross-bridges, but not active ones, are statistically better ordered in muscle where the RLC is dephosporylated compared with phosphorylated RLC; (ii) relaxed phosphorylated and dephosphorylated cross-bridges rotate equally slowly; and (iii) active phosphorylated cross-bridges rotate considerably faster than dephosphorylated ones during isometric contraction but the duty cycle remained the same, suggesting that both phosphorylated and dephosphorylated muscles develop the same isometric tension at full Ca²⁺ saturation. A simple theory was developed to account for this fact.     

Cross-bridge duty cycle in isometric contraction of skeletal myofibrils

During interaction of actin with myosin, cross-bridges impart mechanical impulses to thin filaments resulting in rotations of actin monomers. Impulses are delivered on the average every tc seconds. A cross-bridge spends a fraction of this time (ts) strongly attached to actin, during which it generates force. The "duty cycle" (DC), defined as the fraction of the total cross-bridge cycle that myosin spends attached to actin in a force generating state (ts/ tc), is small for cross-bridges acting against zero load, like freely shortening muscle, and increases as the load rises. Here we report, for the first time, an attempt to measure DC of a single cross-bridge in muscle. A single actin molecule in a half-sarcomere was labeled with fluorescent phalloidin. Its orientation was measured by monitoring intensity of the polarized TIRF images. Actin changed orientation when a cross-bridge bound to it. During isometric contraction, but not during rigor, actin orientation oscillated between two values, corresponding to the actin-bound and actin-free state of the cross-bridge. The average ts and tc were 3.4 and 6 s, respectively. These results suggest that, in isometrically working muscle, cross-bridges spend about half of the cycle time attached to actin. The fact that 1/ tc was much smaller than the ATPase rate suggests that the bulk of the energy of ATP hydrolysis is used for purposes other than performance of mechanical work.     

Form birefringence of muscle.

We investigate the sensitivity of measurements of muscle birefringence to cross-bridge dynamics in the resting, active, and rigor states. The theory of form birefringence is reviewed, and an optical model is constructed for the form birefringence of muscle. Values for the parameters in the model are selected or deduced from the literature. As an illustration of the use of the model, plausible distributions for the orientations of cross-bridges in the resting, active, and rigor states are constructed using a model for cross-bridge dynamics suggested by Huxley and Kress (1985). The general magnitude of the predictions of our model is comparable with that of published measurements of muscle birefringence. However, the precise values of the predicted birefringence for the resting, active, and rigor states are sensitive to the assumed orientations of cross-bridges. We also investigate the dependence of muscle birefringence on sarcomere length and on disorder in the orientation of the myofilament array. We conclude that measurements of muscle birefringence can play a useful role in distinguishing between proposed models of cross-bridge dynamics.     

Observation of two orientations from rigor cross-bridges in glycerinated muscle fibers

The fluorescence polarization from rhodamine labels specifically attached to the fast-reacting thiol of the myosin cross-bridge in glycerinated muscle fibers has been measured to determine the angular distribution of the cross-bridges in different physiological states of the fibers as a function of temperature. To investigate the fibers at temperatures below 0 degree C, we have added glycerol to the bathing solution as an anti-freezing agent. We find that the fluorescence polarization from the rhodamine probe detects distinct angular distributions of the cross-bridges in isometric-active, rigor, MgADP, and low ionic strength relaxed fibers at 4 degrees C. We also find that the rigor cross-bridges in the presence of glycerol can maintain at least two distinct orientations relative to the actin filament, one dominant at temperatures T greater than 2 degrees C and another dominant at T less than -10 degrees C. MgADP cross-bridges in the presence of glycerol maintain approximately the same orientation for all temperatures investigated. The rigor cross-bridge orientation at T less than -10 degrees C is similar to both the MgADP cross-bridge orientation in the presence of glycerol and the active muscle cross-bridge orientation at 4 degrees C. These findings show that the rigor cross-bridge in the presence of glycerol has at least two distinct orientations while attached to actin: one of them dominant at high temperature, the other dominant at low temperature or when MgADP is present. The latter orientation resembles that present in isometric-active fibers.(ABSTRACT TRUNCATED AT 250 WORDS)     

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Models in which many cross-bridges attach simultaneously can explain the filament movement per ATP split during muscle contraction

Contractile filaments in skeletal muscle are moved by less than 2 nm for each ATP used. If just one cross-bridge is attached to each thin filament at any instant then this distance represents the fundamental myosin cross-bridge step size (i.e. the distance one cross-bridge moves a thin filament in one ATP-splitting cycle). However, most contraction models assume many cross-bridges are attached at any instant along each thin filament. The purpose of this study was to establish whether the net filament sliding per ATP used could be explained quantitatively in terms of a cross-bridge model in which multiple cross-bridges are attached along each thin filament. It was found that the relationship between net filament sliding per ATP split and the load against which the muscle shortens is compatible with such a model and furthermore predicts that the cross-bridge step size is between 7.5 and 12.5 nm over most of the range of loads. These values were similar for different muscle fibre types.     

Millisecond-scale biochemical response to change in strain

Muscle fiber contraction involves the cyclical interaction of myosin cross-bridges with actin filaments, linked to hydrolysis of ATP that provides the required energy. We show here the relationship between cross-bridge states, force generation, and Pi release during ramp stretches of active mammalian skeletal muscle fibers at 20°C. The results show that force and Pi release respond quickly to the application of stretch: force rises rapidly, whereas the rate of Pi release decreases abruptly and remains low for the duration of the stretch. These measurements show that biochemical change on the millisecond timescale accompanies the mechanical and structural responses in active muscle fibers. A cross-bridge model is used to simulate the effect of stretch on the distribution of actomyosin cross-bridges, force, and Pi release, with explicit inclusion of ATP, ADP, and Pi in the biochemical states and length-dependence of transitions. In the simulation, stretch causes rapid detachment and reattachment of cross-bridges without release of Pi or ATP hydrolysis.     

Muscle force and stiffness during activation and relaxation. Implications for the actomyosin ATPase

Isolated skinned frog skeletal muscle fibers were activated (increasing [Ca2+]) and then relaxed (decreasing [Ca2+]) with solution changes, and muscle force and stiffness were recorded during the steady state. To investigate the actomyosin cycle, the biochemical species were changed (lowering [MgATP] and elevating [H2PO4-]) to populate different states in the actomyosin ATPase cycle. In solutions with 200 microM [MgATP], compared with physiological [MgATP], the slope of the plot of relative steady state muscle force vs. stiffness was decreased. At low [MgATP], cross-bridge dissociation from actin should be reduced, increasing the population of the last cross-bridge state before dissociation. These data imply that the last cross-bridge state before dissociation could be an attached low-force-producing or non-force-producing state. In solutions with 10 mM total Pi, compared to normal levels of MgATP, the maximally activated muscle force was reduced more than muscle stiffness, and the slope of the plot of relative steady state muscle force vs. stiffness was reduced. Assuming that in elevated Pi, Pi release from the cross-bridge is reversed, the state(s) before Pi release would be populated. These data are consistent with the conclusion that the cross-bridges are strongly bound to actin before Pi release. In addition, if Ca2+ activates the ATPase by allowing for the strong attachment of the myosin to actin in an A.M.ADP.Pi state, it could do so before Pi release. The calcium sensitivity of muscle force and stiffness in solutions with 4 mM [MgATP] was bracketed by that measured in solutions with 200 microM [MgATP], where muscle force and stiffness were more sensitive to calcium, and 10 mM total Pi, where muscle force and stiffness were less sensitive to calcium. The changes in calcium sensitivity were explained using a model in which force-producing and rigor cross-bridges can affect Ca2+ binding or promote the attachment of other cross-bridges to alter calcium sensitivity.     

Modeling rigor cross-bridge patterns in muscle I. Initial studies of the rigor lattice of insect flight muscle.

We have undertaken some computer modeling studies of the cross-bridge observed by Reedy in insect flight muscle so that we investigate the geometric parameters that influence the attachment patterns of cross-bridges to actin filaments. We find that the appearance of double chevrons along an actin filament indicates that the cross-bridges are able to reach 10--14 nm axially, and about 90 degrees around the actin filament. Between three and five actin monomers are therefore available along each turn of one strand of actin helix for labeling by cross-bridges from an adjacent myosin filament. Reedy's flared X of four bridges, which appears rotated 60 degrees at successive levels on the thick filament, depends on the orientation of the actin filaments in the whole lattice as well as on the range of movement in each cross-bridge. Fairly accurate chevrons and flared X groupings can be modeled with a six-stranded myosin surface lattice. The 116-nm long repeat appears in our models as "beating" of the 14.5-nm myosin repeat and the 38.5-nm actin period. Fourier transforms of the labeled actin filaments indicate that the cross-bridges attach to each actin filament on average of 14.5 nm apart. The transform is sensitive to changes in the ease with which the cross-bridge can be distorted in different directions.     

Changes in orientation of actin during contraction of muscle

It is well documented that muscle contraction results from cyclic rotations of actin-bound myosin cross-bridges. The role of actin is hypothesized to be limited to accelerating phosphate release from myosin and to serving as a rigid substrate for cross-bridge rotations. To test this hypothesis, we have measured actin rotations during contraction of a skeletal muscle. Actin filaments of rabbit psoas fiber were labeled with rhodamine-phalloidin. Muscle contraction was induced by a pulse of ATP photogenerated from caged precursor. ATP induced a single turnover of cross-bridges. The rotations were measured by anisotropy of fluorescence originating from a small volume defined by a narrow aperture of a confocal microscope. The anisotropy of phalloidin-actin changed rapidly at first and was followed by a slow relaxation to a steady-state value. The kinetics of orientation changes of actin and myosin were the same. Extracting myosin abolished anisotropy changes. To test whether the rotation of actin was imposed by cross-bridges or whether it reflected hydrolytic activity of actin itself, we labeled actin with fluorescent ADP. The time-course of anisotropy change of fluorescent nucleotide was similar to that of phalloidin-actin. These results suggest that orientation changes of actin are caused by dissociation and rebinding of myosin cross-bridges, and that during contraction, nucleotide does not dissociate from actin.     

Application of surface plasmon coupled emission to study of muscle

Muscle contraction results from interactions between actin and myosin cross-bridges. Dynamics of this interaction may be quite different in contracting muscle than in vitro because of the molecular crowding. In addition, each cross-bridge of contracting muscle is in a different stage of its mechanochemical cycle, and so temporal measurements are time averages. To avoid complications related to crowding and averaging, it is necessary to follow time behavior of a single cross-bridge in muscle. To be able to do so, it is necessary to collect data from an extremely small volume (an attoliter, 10(-18) liter). We report here on a novel microscopic application of surface plasmon-coupled emission (SPCE), which provides such a volume in a live sample. Muscle is fluorescently labeled and placed on a coverslip coated with a thin layer of noble metal. The laser beam is incident at a surface plasmon resonance (SPR) angle, at which it penetrates the metal layer and illuminates muscle by evanescent wave. The volume from which fluorescence emanates is a product of two near-field factors: the depth of evanescent wave excitation and a distance-dependent coupling of excited fluorophores to the surface plasmons. The fluorescence is quenched at the metal interface (up to approximately 10 nm), which further limits the thickness of the fluorescent volume to approximately 50 nm. The fluorescence is detected through a confocal aperture, which limits the lateral dimensions of the detection volume to approximately 200 nm. The resulting volume is approximately 2 x 10(-18) liter. The method is particularly sensitive to rotational motions because of the strong dependence of the plasmon coupling on the orientation of excited transition dipole. We show that by using a high-numerical-aperture objective (1.65) and high-refractive-index coverslips coated with gold, it is possible to follow rotational motion of 12 actin molecules in muscle with millisecond time resolution.     

Is the Cross-Bridge Stiffness Proportional to Tension during Muscle Fiber Activation?

The cross-bridge stiffness can be used to estimate the number of S1 that are bound to actin during contraction, which is a critical parameter for elucidating the fundamental mechanism of the myosin motor. At present, the development of active tension and the increase in muscle stiffness due to S1 binding to actin are thought to be linearly related to the number of cross-bridges formed upon activation. The nonlinearity of total stiffness with respect to active force is thought to arise from the contribution of actin and myosin filament stiffness to total sarcomere elasticity. In this work, we reexamined the relation of total stiffness to tension during activation and during exposure to N-benzyl-p-toluene sulphonamide, an inhibitor of cross-bridge formation. In addition to filament and cross-bridge elasticity, our findings are best accounted for by the inclusion of an extra elasticity in parallel with the cross-bridges, which is formed upon activation but is insensitive to the subsequent level of cross-bridge formation. By analyzing the rupture tension of the muscle (an independent measure of cross-bridge formation) at different levels of activation, we found that this additional elasticity could be explained as the stiffness of a population of no-force-generating cross-bridges. These findings call into question the assumption that active force development can be taken as directly proportional to the cross-bridge number.     

History-dependent properties of skeletal muscle myofibrils contracting along the ascending limb of the force–length relationship

There is a history dependence of skeletal muscle contraction: stretching activated muscles induces a long-lasting force enhancement, while shortening activated muscles induces a long-lasting force depression. These history-dependent properties cannot be explained by the current model of muscle contraction, and its mechanism is unknown. The purposes of this study were (i) to evaluate if force enhancement and force depression are present at short lengths (the ascending limb of the force–length (FL) relationship), (ii) to evaluate if the history-dependent properties are associated with sarcomere length (SL) non-uniformity and (iii) to determine the effects of cross-bridge (de)activation on force depression. Rabbit psoas myofibrils were isolated and attached between two microneedles for force measurements. Images of the myofibrils were projected onto a linear photodiode array for measurements of SL. Myofibrils were activated by either Ca²⁺ or MgADP; the latter induces cross-bridge attachment to actin independently of Ca²⁺. Activated myofibrils were subjected to three stretches or shortenings (approx. 4% SL at approx. 0.07 µm s⁻¹ sarcomere⁻¹) along the ascending limb of the FL relationship separated by periods (approx. 5 s) of isometric contraction. Force after stretch was higher than force after shortening at similar SLs. The differences in force could not be explained by SL non-uniformity. The FL relationship produced by Ca²⁺- and MgADP-activated myofibrils were similar in stretch experiments, but after shortening MgADP activation produced forces that were higher than Ca²⁺ activation. Since MgADP induces the formation of strongly bound cross-bridges, this result suggests that force depression following shortening is associated with cross-bridge deactivation.     

Modeling residual force enhancement with generic cross-bridge models

The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by Huxley (A.F. Huxley, Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem. 7 (1957) 255) could, if suitably modified, fit experimental data showing residual force enhancement. Here we prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement.     

Probing cross-bridge angular transitions using multiple extrinsic reporter groups.

15N- and 2H-substituted maleimido-TEMPO spin label ([15N,2H]MTSL) and the fluorescent label 1,5-IAEDANS were used to specifically modify sulfhydryl 1 of myosin to study the orientation of myosin cross-bridges in skeletal muscle fibers. The electron paramagnetic resonance (EPR) spectrum from muscle fibers decorated with labeled myosin subfragment 1 ([15N,2H]MTSL-S1) or the fluorescence polarization spectrum from fibers directly labeled with 1,5-IAEDANS was measured from fibers in various physiological conditions. The EPR spectra from fibers with the fiber axis oriented at 90 degrees to the Zeeman field show a clear spectral shift from the rigor spectrum when the myosin cross-bridge binds MgADP. This shift is attributable to a change in the torsion angle of the spin probe from cross-bridge rotation and is observable due mainly to the improved angular resolution of the substituted probe. The EPR data from [15N,2H]MTSL-S1 decorating fibers are combined with the fluorescence polarization data from the 1,5-IAEDANS-labeled fibers to map the global angular transition of the labeled cross-bridges due to nucleotide binding by an analytical method described in the accompanying paper [Burghardt, T. P., & Ajtai, K. (1992) Biochemistry (preceding paper in this issue)]. We find that the spin and fluorescent probes are quantitatively consistent in the finding that the actin-bound cross-bridge rotates through a large angle upon binding MgADP. We also find that, if the shape of the cross-bridge is described as an ellipsoid with two equivalent minor axes, then cross-bridge rotation takes place mainly about an axis parallel to the major axis of the ellipsoid. This type of rotation may imitate the rotation motion of cross-bridges during force generation.     

Spin-label study of actin-myosin-nucleotide interactions in contracting glycerinated muscle fibers

This paper presents the results of simultaneous measurements of the electron paramagnetic resonance signal of spin-label bound to myosin cross-bridges and the mechanical response of glycerol-treated rabbit psoas fibers under isometric contraction. No observable change has been detected in vitro in the local motion of spin-label bound to myosin-ATP with conventional electron paramagnetic resonance techniques when F-actin is added, even under conditions where more than 30% of the myosin is expected to be in an attached state. In contrast, a clear change in the spin-label mobility is observed when cross-bridges are attached to thin filaments. Similar spectra are also observed when cross-bridges are in the rigor state or in an attached state in the presence of 5′-adenylyl imidodiphosphate in place of ATP. A good proportionality is found between the change in the electron paramagnetic resonance signal and the tension when substrate concentration is varied under conditions where no appreciable amount of rigor complex is present. Thus, by assuming 0 and 100% attachment in the relaxed and rigor states, respectively, the extent of cross-bridge attachment can be estimated; it is about 80% at a relatively low ATP concentration where the maximum tension is observed, while it is about 35% in the millimolar range of ATP concentration. A consistent explanation can be given for the spectra obtained both in solution and in the fiber, provided that two distinct states, the preactive and active states, exist in cross-bridges attached to thin filaments. The contribution of intermediate complexes to the force generation is discussed. The effect of Ca²⁺ control on cross-bridge attachment is also studied at various concentrations of substrate.     

Cross-bridge orientation in skeletal muscle measured by linear dichroism of an extrinsic chromophore

Linear dichroism of chromophoric labels attached to myosin heads has been used to establish cross-bridge orientation in myofibrils and muscle fibers. Generalized expressions were obtained for the dichroic ratio of a circularly symmetrical assembly of chromophores viewed through high apertures. The theoretical expressions were used to estimate the angle Θ of the absorption dipole of the dye relative to the myofibrillar axis. Myosin subfragment-1 has been labeled with tetramethyl rhodamine and diffused into the I-band of myofibrils; endogenous muscle myosin has been labeled directly. Dichroism has been measured from these preparations in the absence (rigor) and presence of MgATP and its analogs. In rigor, angle Θ was 80 °. Relaxed and contracted preparations displayed no dichroism, suggesting a high degree of cross-bridge disorder. MgAMP-PNP² and MgPP_i imposed on the cross-bridges a distribution intermediate between rigor and relaxation. In the presence of MgADP the preparations showed strong dichroism of the opposite direction to that present in rigor. No detachment of the cross-bridges occurred under these conditions and the effect was not due to the rotational displacement of the attached dye by the nucleotide. It is concluded that the formation of a ternary complex myosin-MgADP-actin makes it possible to detect a large local deformation imposed on the cross-bridge by nucleotide binding, which results in a change of the spatial attitude of the mobile region of the protein by about 40 °.     

The mechanism of muscle contraction

Knowledge of the mechanism of contraction has been obtained from studies of the interaction of actin and myosin in solution, from an elucidation of the structure of muscle fibers, and from measurements of the mechanics and energetics of fiber contraction. Many of the states and the transition rates between them have been established for the hydrolysis of ATP by actin and myosin subfragments in solution. A major goal is to now understand how the kinetics of this interaction are altered when it occurs in the organized array of the myofibril. Early work on the structure of muscle suggested that changes in the orientation of myosin cross-bridges were responsible for the generation of force. More recently, fluorescent and paramagnetic probes attached to the cross-bridges have suggested that at least some domains of the cross-bridges do not change orientation during force generation. A number of properties of active cross-bridges have been defined by measurements of steady state contractions of fibers and by the transients which follow step changes in fiber length or tension. Taken together these studies have provided firm evidence that force is generated by a cyclic interaction in which a myosin cross-bridge attaches to actin, exerts force through a "powerstroke" of 12 nm, and is then released by the binding of ATP. The mechanism of this interaction at the molecular level remains unknown.     

Cross-bridge behavior in rigor muscle

Properties of the rigor state in muscle can be explained by a simple cross-bridge model, of the type which has been suggested for active muscle, in which detachment of cross-bridges by ATP is excluded. Two attached cross-bridge states, with distinct force vs. distortion relationships, are required, in addition to a detached state, but the attached cross-bridge states in rigor muscle appear to differ significantly from the attached cross-bridge states in active muscle. The stability of the rigor force maintained in muscle under isometric conditions does not require exceptional stability of the attached cross-bridges, if the positions in which attachment of cross-bridges is allowed are limited so that the attachment of cross-bridges in positions which have minimum free energy is excluded. This explanation of the stability of the rigor state may also be applicable to the maintenance of stable rigor waves on flagella.