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.     

Effect of adenosine triphosphate analogues on skeletal muscle fibers in rigor.

It is commonly believed, for both vertebrate striated and insect flight muscle, that when the ATP analogue adenyl-5'-yl imidodiphosphate (AMPPNP) is added to the muscle fiber in rigor, it causes the fiber to lengthen by 0.15%. This has been interpretated (Marston S.B., C.D. Roger, and R.T. Tregear. 1976. J. Mol. Biol. 104:263-267) as suggesting (a) that in rigor the crossbridge is fixed to, i.e., almost never detaches from the actin filament; (b), that the crossbridge remains fixed to the actin filament after AMPPNP addition; and (c) that the ability of AMPPNP to cause apparent lengthening of a muscle fiber is due to its ability to cause a conformational change in the myosin crossbridge that has an axial component of approximately 1.6 nm/half-sarcomere. The present study, done only on chemically-skinned rabbit psoas fibers, confirms that AMPPNP can cause muscle fibers to lengthen by 0.15% but only for a narrow set of experimental conditions. When experimental conditions are varied over a wider range, it becomes apparent that the extent of lengthening of a rigor muscle fiber upon AMPPNP addition depends almost entirely on the strain present in the rigor fiber before AMPPNP addition. Addition of AMPPNP to an unstrained rigor fiber (one supporting zero tension), induces zero length change while addition of AMPPNP to very highly strained rigor fibers induces length changes greater than 0.15%. The data thus do not support the hypotheses that the crossbridges remain fixed to the actin filament after AMPPNP addition and that the size of the apparent length change induced by AMPPNP is related to the size of the axial component of a conformational change.(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     

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 biphasic force-velocity relationship in whole rat skeletal muscle in situ.

Edman has reported that the force-velocity relationship (FVR) departs from Hill's classic hyperbola near 0.80 of measured isometric force (J Physiol 404: 301-321, 1988). The purpose of this study was to investigate the biphasic nature of the FVR in the rested state and after some recovery from fatigue in the rat medial gastrocnemius muscle in situ. Force-velocity characteristics were determined before and during recovery from fatigue induced by intermittent stimulation at 170 Hz for 100 ms each second for 6 min. Force-velocity data were obtained for isotonic contractions with 100 ms of 200-Hz stimulation, including several measurements with loads above 0.80 of measured isometric force. The force-velocity data obtained in this study were fit well by a double-hyperbolic equation. A departure from Hill's classic hyperbola was found at 0.88+/-0.01 of measured isometric force, which is higher than the approximately 0.80 reported by Edman et al. for isolated frog fibers. After 45 min of recovery, maximum shortening velocity was 86+/-2% of prefatigue, but neither curvature nor predicted isometric force was significantly different from prefatigue. The location of the departure from Hill's classic hyperbola was not different after this recovery from the fatiguing contractions. Including an isometric point in the data set will not yield the same values for maximal velocity and the degree of curvature as would be obtained using the double hyperbola approach. Data up to 0.88 of measured isometric force can be used to fit data to the Hill equation.     

Force-velocity relationship in single muscle fibres

In recent papers, it has been shown experimentally that the force-velocity relationship in single muscle fibres presents deviations from hyperbolicity at high values of the load (Edman, Mulieri & Scubon-Mulieri, 1976; Edman & Hwang,1977). It has been shown independently and on theoretical bases, that the parameter “b” in Hill's characteristic equation also presents deviations from its normal value at low values of the speed of shortening, i.e. at high values of the load (Morel, Pinset-Härström & Gingold, 1976). In the present paper, it is shown that both the experimental and the theoretical results are in excellent agreement and a theoretical force-velocity relationship is proposed.     

Alterations of crossbridge angle induced by beta, gamma-imido-adenosine-triphosphate. Electron microscope and optical diffraction studies on myofibrillar fragments of abdominal muscles of the crayfish Orconectes limosus.

The molecular basis of muscle contraction is thought to consist of cyclic movements of parts of the myosin molecules (crossbridges). Unitl now different states of the proposed crossbridge cycle could be stablilized and demonstrated by electron microscopy only in the case of highly specialized insect flight muscles. In this paper evidence is presented that it is also possible to induce crossbridge positions corresponding to the rigor [16] and the pseudorelaxed state [3] in non-insect muscles. Homogenization of myofibrils of the abdominal flexors of the crayfish Orconectes limosus in rigor or AMP.PNP-containing solutions brings about two different crossbridge patterns: The formation of crossbridges attached to the actin filaments in a mainly acute (rigor) or in a mainly perpendicular angle (pseudo-relaxed). Optical diffraction patterns taken from electron micrographs of sarcomere fragments are likewise compatible with those taken from sarcomeres of insect flight muscles fixed in comparable conditions [2,3].     

Electron tomography of fast frozen, stretched rigor fibers reveals elastic distortions in the myosin crossbridges

As a first step toward freeze-trapping and 3-D modeling of the very rapid load-induced structural responses of active myosin heads, we explored the conformational range of longer lasting force-dependent changes in rigor crossbridges of insect flight muscle (IFM). Rigor IFM fibers were slam-frozen after ramp stretch (1000 ms) of 1-2% and freeze-substituted. Tomograms were calculated from tilt series of 30 nm longitudinal sections of Araldite-embedded fibers. Modified procedures of alignment and correspondence analysis grouped self-similar crossbridge forms into 16 class averages with 4.5 nm resolution, revealing actin protomers and myosin S2 segments of some crossbridges for the first time in muscle thin sections. Acto-S1 atomic models manually fitted to crossbridge density required a range of lever arm adjustments to match variably distorted rigor crossbridges. Some lever arms were unchanged compared with low tension rigor, while others were bent and displaced M-ward by up to 4.5 nm. The average displacement was 1.6 +/- 1.0 nm. "Map back" images that replaced each unaveraged 39 nm crossbridge motif by its class average showed an ordered mix of distorted and unaltered crossbridges distributed along the 116 nm repeat that reflects differences in rigor myosin head loading even before stretch.     

Tomographic Three-dimensional Reconstruction of Insect Flight Muscle Partially Relaxed by AMPPNP and Ethylene Glycol

Rigor insect flight muscle (IFM) can be relaxed without ATP by increasing ethylene glycol concentration in the presence of adenosine 5′-[β′γ- imido]triphosphate (AMPPNP). Fibers poised at a critical glycol concentration retain rigor stiffness but support no sustained tension (“glycol-stiff state”). This suggests that many crossbridges are weakly attached to actin, possibly at the beginning of the power stroke. Unaveraged three-dimensional tomograms of “glycol-stiff” sarcomeres show crossbridges large enough to contain only a single myosin head, originating from dense collars every 14.5 nm. Crossbridges with an average 90° axial angle contact actin midway between troponin subunits, which identifies the actin azimuth in each 38.7-nm period, in the same region as the actin target zone of the 45° angled rigor lead bridges. These 90° “target zone” bridges originate from the thick filament and approach actin at azimuthal angles similar to rigor lead bridges. Another class of glycol-PNP crossbridge binds outside the rigor actin target zone. These “nontarget zone” bridges display irregular forms and vary widely in axial and azimuthal attachment angles. Fitting the acto-myosin subfragment 1 atomic structure into the tomogram reveals that 90° target zone bridges share with rigor a similar contact interface with actin, while nontarget crossbridges have variable contact interfaces. This suggests that target zone bridges interact specifically with actin, while nontarget zone bridges may not. Target zone bridges constitute only ∼25% of the myosin heads, implying that both specific and nonspecific attachments contribute to the high stiffness. The 90° target zone bridges may represent a preforce attachment that produces force by rotation of the motor domain over actin, possibly independent of the regulatory domain movements. Force production by myosin heads during muscle contraction has long been modeled as a transition of attached crossbridges from a 90° to a 45° axial angle. Efforts to image crossbridge forms and angles intermediate between 90° heads in ATP-relaxed insect flight muscle (IFM)¹ and the 45° angled bridges in rigor have used nucleotide analogs such as adenosine 5′-[β′γ-imido] triphosphate (AMPPNP) in stable equilibrium states to drive the crossbridges backwards from the 45° angle in rigor to an attached 90° preforce form, otherwise similar to myosin heads in ATP-relaxed fibers (Reedy et al., 1988; Tregear et al., 1990). However, AMPPNP alone will not fully relax IFM, and crossbridges binding AMPPNP retain many rigor-like features (Schmitz et al., 1996; Winkler et al., 1996). On the other hand, AMPPNP in combination with ethylene glycol will relax IFM. When poised at a critical glycol concentration, muscle stiffness is as high as rigor, suggesting crossbridge attachment, but fibers will not bear sustained tension (Clarke et al., 1984; Tregear et al., 1984). Two-dimensional (2-D) analysis of electron micrographs showed that this stiff glycol-PNP state resembled ATP-relaxed fibers in having dense collars every 14.5 nm along the thick filament and thin crossbridges originating from these collars at various axial angles around 90°. However, unlike relaxed muscle, stiff glycol-PNP fibers showed both 90° angled bridges that were regularly spaced every 38.7 nm and more intensity on the 19.3-nm layer line in optical and x-ray diffraction patterns (Reedy et al., 1988; Tregear et al., 1990). Crossbridges in this partially relaxed, glycol-PNP state are important because they may represent the form of the initial attachment of myosin with bound nucleotide preceding force generation (Marston and Tregear, 1984; Tregear et al., 1984; Reedy et al., 1988). This putative preforce 90° crossbridge could not be characterized in 3-D because its variable form and lattice arrangement precluded imaging by averaging methods of 3-D reconstruction. Recently, nonaveraging tomographic methods have been developed and successfully applied to rigor and aqueous-PNP, facilitating characterization of variable crossbridge forms that occur in situ (Taylor and Winkler, 1995, 1996; Schmitz et al., 1996; Winkler and Taylor, 1996). IFM is superb for structural study because the symmetry and spatial arrangement of filaments results in paired crossbridges on opposite sides of the actin filament. This in turn has given rise to a unique shorthand terminology. The individual crossbridge forms are not unique to IFM, only their symmetrical placement about the thin filament. The filament arrangement also facilitates the microtomy of a type of thin section with coplanar filaments that provide views of the entire crossbridge. The best of these, the myac layer, is a 25-nm-thick longitudinal section containing alternating myosin and actin filaments. In rigor, the maximum number of myosin heads attach to actin, forming doublet pairs every 38.7 nm, the “double chevrons” (Reedy, 1968). “Lead bridges,” which form the pair proximal to the M-band, consist of both heads of a myosin molecule and show an overall axial angle of 45° (Taylor et al., 1984). “Rear bridges,” which form the pair proximal to the Z-disk, consist of a single myosin head angled closer to 90°. Crossbridges originate from the thick filament along helical tracks so the azimuths of their origins follow a regular pattern. Relative to the thin filament in the myac layer, the lead bridges originate from the left-front and back-right of the adjacent thick filaments, while rear bridges originate from the left-back and right-front. At their actin ends, the crossbridge attachments follow the changing rotation of the actin protomers along the actin helix. The combination of the azimuth of the origin and the azimuth of the crossbridge contact to actin define the azimuthal angle of the crossbridge.Target zone is the name given to the region of the thin filament where crossbridges bind (Reedy, 1968); by implication this is the region of the thin filament where actin monomers are most favorably placed for actomyosin interaction. In our previous 3-D reconstructions of rigor and aqueous-PNP (Schmitz et al., 1996; Winkler et al., 1996), it was recognized that troponin maintained a constant position with respect to the most regularly positioned crossbridges, the lead bridges, and could thus be used as a landmark to determine the actin dyad orientation in the lead bridge target zone. The most sterically favorable actin position for crossbridge binding in the IFM lattice is midway between troponin densities, where lead bridges bind. The strained structure of the rigor rear bridges suggests that they bind at the very edge of the target zone (Schmitz et al., 1996; Winkler et al., 1996). The target zone defined by lead bridges alone is narrower than target zones previously considered for rigor muscle (Reedy, 1968) because it does not include rear bridge targets. When aqueous AMPPNP was added to rigor IFM, the tension dropped by two thirds, but the stiffness remained as high as rigor. This initially suggested a reversal of the power stroke, but 3-D reconstructions revealed that the lead bridges remained attached, midway between troponin densities, at axial and azimuthal angles close to rigor. The drop in tension without a large change in axial angle seemed to contradict the lever arm hypothesis for motion producing force. However, a cause for the loss of tension was found in tomograms, which showed that rear bridges detached and were replaced by nonrigor bridges bound to actins outside of the rigor target zone, to sites not selected by crossbridges even under the high-affinity conditions of rigor. These nontarget bridges in aqueous-PNP had variable axial and azimuthal angles and appeared to bind actin with variable contact interfaces. This suggested that they were nonspecifically bound to actin. Moreover, their variable structure did not suggest how a simple axial angle change could convert them to a familiar form, such as an angled rigor bridge. However, an intriguing doublet crossbridge group with a consistent structure was recognized in aqueous-PNP. Immediately M-ward of the “lead” rigor-like bridge was a “nonrigor” bridge bound at a 90° or antirigor angle. In this doublet, called a mask motif, both lead and M-ward nonrigor bridge pairs had similar azimuths and contact interfaces with actin and bound within the lead bridge target zone. A simple angle change could convert the M-ward, nonrigor bridge in a mask motif to a single headed lead bridge. Thus, in the mask motif, the lead bridge could be at the end of the power stroke, with the M-ward, nonrigor bridge near the beginning. The pairing of rigor and antirigor angled crossbridges bound to the same target zone suggests that crossbridges might act as a relay during muscle contraction (Schmitz et al., 1996). The affinity of myosin for actin in aqueous-PNP is high compared with weak binding intermediates thought to represent the beginning of the power stroke (Green and Eisenberg, 1980; Biosca et al., 1990). Therefore, the M-ward crossbridge in the mask motif may not represent the best candidate for a preforce crossbridge. Thus, it is important to characterize crossbridge structure in a state with lower actomyosin affinity, such as the stiff glycol-PNP state, where earlier 2-D analysis indicated that weakly attached 90° bridges are prevalent (Reedy et al., 1988). In this work, we have used two spatially invariant features, troponin position and lead crossbridge origins, to identify distinct classes of crossbridges. The invariant position of troponin recognized in 3-D reconstructions allows us to identify the lead bridge target zone and the actin dyad orientation relative to the bound crossbridges. In addition, the “front-back” rule for the azimuth of the origins of the lead target zone bridges distinguishes crossbridges that bind actin with the correct azimuth for specific binding from those that bind nonspecifically. By fitting the myosin subfragment 1 (S1) atomic structure to the in situ bridges, we can compare the positions of the motor and regulatory domains. Previous results and models have introduced the idea that during a power stroke, the crossbridge rotates over the actin binding site while acting as a long, relatively rigid lever arm (Huxley and Simmons, 1971), while others propose that the motor domain position remains constant and light chain domain movements provide a shorter lever arm (Rayment et al., 1993b ; Whittaker et al., 1995). Our previous results (Reedy et al., 1987, 1988; Schmitz et al., 1996; Winkler et al., 1996) and the present work show (a) that regulatory domain position can vary significantly while motor domain position remains constant and (b) that the motor domain can bind actin with varying orientations. This work supports the possibility that both rotation of the motor domain on actin and movements of the regulatory domain could contribute to the power stroke.     

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.     

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.     

Reciprocal coupling between troponin C and myosin crossbridge attachment

The attachment of cycling myosin crossbridges to actin and the resultant muscle contraction are regulated in skeletal muscle by the binding of Ca2+ to the amino-terminal, regulatory sites of the troponin C (TnC) subunit of the thin filament protein troponin. Conversely, the attachment of crossbridges to actin has been shown to alter the affinity of TnC for Ca2+. In this study, fluorescently labeled TnC incorporated into reconstituted thin filaments was used to investigate the relationship between crossbridge attachment to actin and structural changes in the amino-terminal region of TnC. Fluorescence intensity changes were measured under the following conditions: saturating [Ca2+] in the absence of crossbridges, rigor crossbridge attachment in the presence and absence of Ca2+, and cycling crossbridge attachment. The percent of heavy meromyosin crossbridges associated with the thin filaments under these conditions was also determined. The results show that, in addition to the binding of Ca2+ to TnC, the attachment of both rigor and cycling crossbridges to actin alters the structure of TnC near the regulatory, Ca2+-specific sites of the molecule. A differential coupling between weakly versus strongly bound crossbridge states and TnC structure was detected, suggesting a possible differential regulation of these states by conformational changes in TnC. These findings illustrate a reciprocal coupling, via thin filament protein interactions, between structural changes in TnC and the attachment of myosin crossbridges to actin, such that each can influence the other, and indicate that TnC is not simply an on-off switch but may exist in a number of different conformations.     

A model of force production that explains the lag between crossbridge attachment and force after electrical stimulation of striated muscle fibers.

Whereas the mechanical behavior of fully activated fibers can be explained by assuming that attached force-producing crossbridges exist in at least two configurations, one exerting more force than the other (Huxley A. F., and R. M. Simmons. 1971. Nature [Lond.]. 233:533-538), and the behavior of relaxed fibers can be explained by assuming a single population of weakly binding rapid-equilibrium crossbridges (Schoenberg, M. 1988. Biophys. J. 54:135-148), it has not been possible to explain the transition between rest and activation in these terms. The difficulty in explaining why, after electrical stimulation of resting intact frog skeletal muscle fibers at 1-5 degrees C, force development lags stiffness development by more than 15 ms has led a number of investigators to postulate additional crossbridge states. However, postulation of an additional crossbridge state will not explain the following three observations: (a) Although the lag between force and stiffness is very different after stimulation, during the redevelopment of force after an extended period of high velocity shortening, and during relaxation of a tetanus, nonetheless, the plots of force versus stiffness in each of these cases are approximately the same. (b) When the lag between stiffness and force during the rising phase of a twitch is changed nearly fourfold by changing temperature, again the plot of force versus stiffness remains essentially unchanged. (c) When a muscle fiber is subjected to a small quick length change, the rate constant for the isometric force recovery is faster when the length change is applied during the rising phase of a tenanus than when it is applied on the plateau. We have been able to explain all the above findings using a model for force production that is similar to the 1971 model of Huxley and Simmons, but which makes the additional assumption that the force-producing transition envisioned by them is a cooperative one, with the back rate constant of the force-producing transition decreasing as more crossbridges attach.     

Dependency of the force-velocity relationships on Mg ATP in different types of muscle fibers from Xenopus laevis.

MgATP binding to the actomyosin complex is followed by the dissociation of actin and myosin. The rate of this dissociation process was determined from the relationship between the maximum velocity of shortening and the MgATP concentration. It is shown here that the overall dissociation rate is rather similar in different types of muscle fibers. The relation between MgATP concentration and the maximum shortening velocity was investigated in fast and slow fibers and bundles of myofibrils of the iliofibularis muscle of Xenopus laevis at 4 degrees C from which the sarcolemma was either removed mechanically or made permeable by means of a detergent. A small segment of each fiber was used for a histochemical determination of fiber type. At 5 mM MgATP, the fast fibers had a maximum shortening velocity (Vmax) of 1.74 +/- 0.12 Lo/s (mean +/- SEM) (Lo: segment length at a sarcomere length of 2.2 microns). For the slow fibers Vmax was 0.41 +/- 0.15 Lo/s. In both cases, the relationship between Vmax and the ATP concentration followed the hyperbolic Michaelis-Menten relation. A Km of 0.56 +/- 0.06 mM (mean +/- SD) was found for the fast fibers and of 0.16 +/- 0.03 mM for the slow fibers. Assuming that Vmax is mainly determined by the crossbridge detachment rate, the apparent second order dissociation rate for the actomyosin complex in vivo would be 3.8.10(5) M-1s-1 for the fast fibers and 2.9.10(5) M-1 s-1 for the slow fibers. Maximum power output as a function of the MgATP concentration was derived from the force-velocity relationships.(ABSTRACT TRUNCATED AT 250 WORDS)     

Cross-bridge attachment and stiffness during isotonic shortening of intact single muscle fibers.

Equatorial x-ray diffraction pattern intensities (I10 and I11), fiber stiffness and sarcomere length were measured in single, intact muscle fibers under isometric conditions and during constant velocity (ramp) shortening. At the velocity of unloaded shortening (Vmax) the I10 change accompanying activation was reduced to 50.8% of its isometric value, I11 reduced to 60.7%. If the roughly linear relation between numbers of attached bridges and equatorial signals in the isometric state also applies during shortening, this would predict 51-61% attachment. Stiffness (measured using 4 kHz sinusoidal length oscillations), another putative measure of bridge attachment, was 30% of its isometric value at Vmax. When small step length changes were applied to the preparation (such as used for construction of T1 curves), no equatorial intensity changes could be detected with our present time resolution (5 ms). Therefore, unlike the isometric situation, stiffness and equatorial signals obtained during ramp shortening are not in agreement. This may be a result of a changed crossbridge spatial orientation during shortening, a different average stiffness per attached crossbridge, or a higher proportion of single headed crossbridges during shortening.     

Electron microscopy and image analysis of myosin filaments from scallop striated muscle

Thick filaments have been isolated from the striated adductor muscle of the scallop and examined by electron microscopy after negative staining. Many filaments appear intact, and reveal a centrally located bare-zone and a well-defined helical surface array of myosin crossbridges characterized by a 145 A axial period and prominent helical tracks of pitch 480 A. Heavy-metal shadowing shows that these helices are right-handed. A small perturbation of alternate crossbridge levels produces an axial period of 290 A, which is most prominent in a region on either side of the bare-zone. Image analysis reveals that the crossbridge array has 7-fold rotational symmetry, one of the possibilities suggested by earlier X-ray diffraction studies of native filaments in scallop muscle. A low-resolution three-dimensional reconstruction shows elongated surface projections ("crossbridges") that probably represent unresolved pairs of myosin heads. They run almost parallel to the filament surface, but are slewed slightly from the axis so that they lie along the right-handed helical tracks of pitch 480 A. The connection to the filament backbone probably occurs at the end of the crossbridges nearer the bare-zone; thus, their sense of tilt appears to be opposite to that of rigor attachment to actin. The 290 A period arises from a different distribution of crossbridge density at alternate levels; in addition, there are weak connections between the top of one crossbridge and the bottom of the next, 145 A away. The prominence of the 290 A period near the bare-zone suggests that anti-parallel molecular interactions are mainly responsible for this perturbation.     

Titin-induced force enhancement and force depression: A ‘sticky-spring’ mechanism in muscle contractions?

The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening.In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges.Incorporation of a simple ‘sticky-spring’ mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.     

Actomyosin-ADP States, Interhead Cooperativity, and the Force-Velocity Relation of Skeletal Muscle

Despite intense efforts to elucidate the molecular mechanisms that determine the maximum shortening velocity and the shape of the force-velocity relationship in striated muscle, our understanding of these mechanisms remains incomplete. Here, this issue is addressed by means of a four-state cross-bridge model with significant explanatory power for both shortening and lengthening contractions. Exploration of the parameter space of the model suggests that an actomyosin-ADP state (AM^∗ADP) that is separated from the actual ADP release step by a strain-dependent isomerization is important for determining both the maximum shortening velocity and the shape of the force-velocity relationship. The model requires a velocity-dependent, cross-bridge attachment rate to account for certain experimental findings. Of interest, the velocity dependence for shortening contraction is similar to that for population of the AM^∗ADP state (with a velocity-independent attachment rate). This accords with the idea that attached myosin heads in the AM^∗ADP state position the partner heads for rapid attachment to the next site along actin, corresponding to the apparent increase in attachment rate in the model.     

Rigor crossbridge structure in tilted single filament layers and flared-X formations from insect flight muscle

The averaged structure of rigor crossbridges in insect flight muscle has been studied in filtered images. Their three-dimensional structure has been deduced by relating tilt views of single filament layers in 25 nm longitudinal sections (myac layers and actin layers) to the flared-X appearance in 15 nm cross-sections showing single crossbridge levels. Tilting myac or actin layers around the filament axis makes crossbridges show one of two patterns. Beadlike densities appear either singly over thin filaments ("center-beading") or doubled and flanking thin filaments ("straddle-beading"). These express two different projections from the crossbridge-actin complexes as seen end-on in flared-X formations. Tannic acid/glutaraldehyde fixation gave improved actin preservation, showing, in 15 nm cross-sections, the long-pitch helical strands as "two-dot" profiles of consistent azimuth in the gaps between double chevrons. The azimuth in the flared-X arms was then inferred from lattice relationships, since it was not seen directly. The tangential attachment of comma-shaped crossbridges to the inferred actin dyad fits the binding geometry in recent actin-subfragment 1 complex reconstructions. However, averaged crossbridge structure differs between lead and rear members of double chevrons, unlike the uniform heads on decorated actin. In filtered images of myac layers, the lead bridges are dense and steeply angled; the rear chevron is seen as a dense bead over the thin filament with faint, less angled bars extending laterally. Actin layer images also suggest that rear and lead bridges differ in angle. Left and right flared-X arms are end-on views of lead and rear chevron bridges, respectively, and differ in shape. Improved fixation with tannic acid/glutaraldehyde allows us to distinguish three crossbridge domains in flared-X arms: (1) a dense bulb-like head merged into the thin filament; (2) a dense but thinner neck tangential to actin; and (3) a faint thin stem joining the necks to myosin filaments. Shape differences in lead and rear members between the head-neck-actin complexes are indicated by the names "L sigmoid" and "R dogleg". Within crossbridges, internal angles between the head-neck axis and the head-actin-head axis differ between sigmoid and dogleg by about 30 degrees, implying a flexible junction between bridge-head and bridge-neck. Lead and rear bridges are axially at least 13 nm apart on actin; the expected 60 degrees difference in azimuth is expressed by head-neck portions, but the head-actin-head axis rotates by only 30 degrees.(ABSTRACT TRUNCATED AT 400 WORDS)     

Structural changes accompanying phosphorylation of tarantula muscle myosin filaments

Electron microscopy has been used to study the structural changes that occur in the myosin filaments of tarantula striated muscle when they are phosphorylated. Myosin filaments in muscle homogenates maintained in relaxing conditions (ATP, EGTA) are found to have nonphosphorylated regulatory light chains as shown by urea/glycerol gel electrophoresis and [32P]phosphate autoradiography. Negative staining reveals an ordered, helical arrangement of crossbridges in these filaments, in which the heads from axially neighboring myosin molecules appear to interact with each other. When the free Ca2+ concentration in a homogenate is raised to 10(-4) M, or when a Ca2+-insensitive myosin light chain kinase is added at low Ca2+ (10(-8) M), the regulatory light chains of myosin become rapidly phosphorylated. Phosphorylation is accompanied by potentiation of the actin activation of the myosin Mg-ATPase activity and by loss of order of the helical crossbridge arrangement characteristic of the relaxed filament. We suggest that in the relaxed state, when the regulatory light chains are not phosphorylated, the myosin heads are held down on the filament backbone by head-head interactions or by interactions of the heads with the filament backbone. Phosphorylation of the light chains may alter these interactions so that the crossbridges become more loosely associated with the filament backbone giving rise to the observed changes and facilitating crossbridge interaction with actin.