Geometrical factors influencing muscle force development. I. The effect of filament spacing upon axial forces.

The influence of geometry on the force and stiffness measured during muscle contraction at different sarcomere lengths is examined by using three specific models of muscle cross-bridge geometry which are based upon the double-hinge model of H. E. Huxley (Science [Wash. D.C.]. 1969, 164:1356-1366) extended to three dimensions. The force generated during muscle contraction depends upon the orientation of the individual cross-bridge force vectors and the distribution of the cross-bridges between various states. For the simplest models, in which filament separation has no effect upon cross-bridge distribution, it is shown that changes in force vectors accompanying changes in myofilament separation between sarcomere lengths 2.0 and 3.65 microgram in an intact frog skeletal muscle fiber have only a small effect upon axial force. The simplest models, therefore, produce a total axial force proportional to the overlap between the actin and myosin filaments and independent of filament separation. However, the analysis shows that it is possible to find assumptions that produce a cross-bridge model in which the axial force is not independent of filament spacing. It is also shown that for some modes of attachment of subfragment-1 (S1) to actin the azimuthal location of the actin site is important in determining the axial force. A mode of S1 attachment to actin similar to that deduced by Moore et al. (J. Mol. Biol., 1970, 50:279-294), however, exhibits rather constant cross-bridge behavior over a wide range of actin site location.     

Orientation of cross-bridges in skeletal muscle measured with a hydrophobic probe.

Cis-parinaric acid (PA) binds to a hydrophobic pocket formed between the heavy chain of myosin subfragment-1 (S1) and the 41-residue N-terminal of essential light chain 1 (A1). The binding is strong (Ka = 5.6 x 10(7) M-1) and rigid (polarization = 0.334). PA does not bind to myofibrils in which A1 has been extracted or replaced with alkali light chain 2 (A2). As in the case of S1 labeled with other probes, polarization of fluorescence of S1-PA added to myofibrils depended on fractional saturation of actin filament with S1, i.e., on whether the filaments were fully or partially saturated with myosin heads. Because fluorescence quantum yield of PA is enhanced manyfold upon binding, and because PA binds weakly to myofibrillar structures other then A1, the dye is a convenient probe of cross-bridge orientation in native muscle fibers. The polarization of a fiber irrigated with PA was equal to the polarization of S1-PA added to fibers at nonsaturating concentration. Cross-linking of S1 added to fibers at nonsaturating concentration showed that each S1 bound to two actin monomers of a thin filament. These results suggest that in rigor rabbit psoas muscle fiber each myosin cross-bridge binds to two actins.     

Filament compliance effects can explain tension overshoots during force development

Spatially explicit stochastic simulations of myosin S1 heads attaching to a single actin filament were used to investigate the process of force development in contracting muscle. Filament compliance effects were incorporated by adjusting the spacing between adjacent actin binding sites and adjacent myosin heads in response to cross-bridge attachment/detachment events. Appropriate model parameters were determined by multi-dimensional optimization and used to simulate force development records corresponding to different levels of Ca(2+) activation. Simulations in which the spacing between both adjacent actin binding sites and adjacent myosin S1 heads changed by approximately 0.06 nm after cross-bridge attachment/detachment events 1), exhibited tension overshoots with a Ca(2+) dependence similar to that measured experimentally and 2), mimicked the observed k(tr)-relative tension relationship without invoking a Ca(2+)-dependent increase in the rate of cross-bridge state transitions. Tension did not overshoot its steady-state value in control simulations modeling rigid thick and thin filaments with otherwise identical parameters. These results underline the importance of filament geometry and actin binding site availability in quantitative theories of muscle contraction.     

Electron cryomicroscopy of acto-myosin-S1 during steady-state ATP hydrolysis.

The structure of the complex of actin and myosin subfragment-1 (S1) during steady-state ATP hydrolysis has been examined by electron microscopy. This complex is normally dissociated by ATP in vitro but was stabilized here by low ionic strength. Optimal conditions for attachment were established by light-scattering experiments that showed that approximately 70% of S1 could be bound in the presence of ATP. Micrographs of the unstained complex in vitreous water suggest that S1 attaches to actin in a variety of configurations in ATP; this contrasts with the single attached configuration seen in the presence of ADP. The data are therefore compatible with the idea that a change in attached configuration of the myosin cross-bridge is the origin of muscle force. In control experiments where ATP was allowed to hydrolyze completely the binding of the S1 seemed cooperative.     

Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap.

Purified smooth muscle myosin in the in vitro motility assay propels actin filaments at 1/10 the velocity, yet produces 3-4 times more force than skeletal muscle myosin. At the level of a single myosin molecule, these differences in force and actin filament velocity may be reflected in the size and duration of single motion and force-generating events, or in the kinetics of the cross-bridge cycle. Specifically, an increase in either unitary force or duty cycle may explain the enhanced force-generating capacity of smooth muscle myosin. Similarly, an increase in attached time or decrease in unitary displacement may explain the reduced actin filament velocity of smooth muscle myosin. To discriminate between these possibilities, we used a laser trap to measure unitary forces and displacements from single smooth and skeletal muscle myosin molecules. We analyzed our data using mean-variance analysis, which does not rely on scoring individual events by eye, and emphasizes periods in the data with constant properties. Both myosins demonstrated multiple but similar event populations with discrete peaks at approximately +11 and -11 nm in displacement, and 1.5 and 3.5 pN in force. Mean attached times for smooth muscle myosin were longer than for skeletal-muscle myosin. These results explain much of the difference in actin filament velocity between these myosins, and suggest that an increased duty cycle is responsible for the enhanced force-generating capacity of smooth over skeletal-muscle myosin.     

Changes in the X-ray reflections from contracting muscle during rapid mechanical transients and their structural implications

During normal contractions of vertebrate striated muscle, it is believed that the cross-bridges which produce the sliding force undergo asynchronous cyclical changes in their structure. Thus, an X-ray diffraction diagram from a muscle under these conditions will give structural information averaged over the whole range of cross-bridge states. Such diagrams show characteristic and informative differences from those given by relaxed muscle, but can give little information about changes in the configuration of the cross-bridges at different stages of their working stroke. However, it is possible to effect a partial synchronization of these changes by applying very rapid changes in length, completed in less than one millisecond to an otherwise isometrically contracting muscle. If the amplitude of these length changes is comparable to the length of the cross-bridge stroke (say 100 A per half-sarcomere), then it should bring about a transient but significant redistribution of cross-bridge states, which would show up in the X-ray diagram. We have made use of synchrotron radiation as a high intensity X-ray source in order to record such patterns with the necessary time resolution (1 ms or less) and have found major changes in the intensity of the 143 A meridional reflection accompanying the rapid length changes of the muscle. These changes appear to arise from specific configurational changes in the cross-bridges during the working stroke. A model is suggested in which the 143 A meridional intensity in a contracting muscle arises mainly from attached cross-bridges and is generated by the part of the myosin head near the S1-S2 junction. During normal contraction, cross-bridges go through their structural cycle asynchronously with each other, since they start at different times, but if the S2 changes in length rather little, then the configurational changes in the myosin heads are synchronized with the actin filament movement in such a way that the S1-S2 junction remains relatively fixed in its axial position. In a quick release, it is suggested that bringing many S1 heads simultaneously to the end of their working strokes on actin disrupts the 143 A axial repeat of their distal ends near S2, and brings about the large decrease of the 143 A meridional reflection. This model therefore involves a large change in the position of part of the myosin head structure relative to actin during the working stroke of the cross-bridge.     

The ADP release step of the smooth muscle cross-bridge cycle is not directly associated with force generation.

When smooth muscle myosin subfragment 1 (S1) is bound to actin filaments in vitro, the light chain domain tilts upon release of MgADP, producing a approximately 3.5-nm axial motion of the head-rod junction (Whittaker et al., 1995. Nature. 378:748-751). If this motion contributes significantly to the power stroke, rigor tension of smooth muscle should decrease substantially in response to cross-bridge binding of MgADP. To test this prediction, we monitored mechanical properties of permeabilized strips of chicken gizzard muscle in rigor and in the presence of MgADP. For comparison, we also tested psoas and soleus muscle fibers. Any residual bound ADP was minimized by incubation in Mg2+-free rigor solution containing 15 mM EDTA. The addition of 2 mM MgADP, while keeping ionic strength and free Mg2+ concentration constant, resulted in a slight increase in rigor tension in both gizzard and soleus muscles, but a decrease in psoas muscle. In-phase stiffness monitored during small (<0.1%) 500-Hz sinusoidal length oscillations decreased in all three muscle types when MgADP was added. The changes in force and stiffness with the addition of MgADP were similar at ionic strengths from 50 to 200 mM and were reversible. The results with gizzard muscle were similar after thiophosphorylation of the regulatory light chain of myosin. These results suggest that the axial motion of smooth muscle S1 bound to actin, upon dissociation of MgADP, is not associated with force generation. The difference between the present mechanical data and previous structural studies of smooth S1 may be explained if geometrical constraints of the intact contractile filament array alter the motions of the myosin heads.     

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.     

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.     

Ca2+-sensitive cross-bridge dissociation in the presence of magnesium pyrophosphate in skinned rabbit psoas fibers.

We find that at 6 degrees C in the presence of 4 mM MgPPi, at low or moderate ionic strength, skinned rabbit psoas fibers exhibit a stiffness and an equatorial x-ray diffraction pattern similar to that of rigor fibers. As the ionic strength is increased in the absence of Ca2+, both the stiffness and the equatorial x-ray diffraction pattern approach those of the relaxed state. This suggests that, as in solution, increasing ionic strength weakens the affinity of myosin cross-bridges for actin, which results in a decrease in the number of cross-bridges attached. The effect is Ca2+-sensitive. Assuming that stiffness is a measure of the number of cross-bridge heads attached, in the absence of Ca2+, the fraction of attached cross-bridge heads varies from approximately 75% to approximately 25% over an ionic strength range where ionic strength in solution weakens the binding constant for myosin subfragment-1 binding to unregulated actin by less than a factor of 3. Therefore, this phenomenon appears similar to the cooperative Ca2+-sensitive binding of S1 to regulated actin in solution (Greene, L. E., and E. Eisenberg, 1980, Proc. Natl. Acad. Sci. USA, 77:2616). By comparing the binding constants in solution and in the fiber under similar conditions, we find that the "effective actin concentration," that is, the concentration that gives the same fraction of S1 molecules bound to actin in solution as cross-bridge heads are bound to actin in a fiber, is in the millimolar range.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Three Filament Model of Skeletal Muscle Stability and Force Production

Ever since the 1950s, muscle force regulation has been associated with the cross-bridge interactions between the two contractile filaments, actin and myosin. This gave rise to what is referred to as the "two-filament sarcomere model". This model does not predict eccentric muscle contractions well, produces instability of myosin alignment and force production on the descending limb of the force-length relationship, and cannot account for the vastly decreased ATP requirements of actively stretched muscles. Over the past decade, we and others, identified that a third myofilament, titin, plays an important role in stabilizing the sarcomere and the myosin filament. Here, we demonstrate additionally how titin is an active participant in muscle force regulation by changing its stiffness in an activation/force dependent manner and by binding to actin, thereby adjusting its free spring length. Therefore, we propose that skeletal muscle force regulation is based on a three filament model that includes titin, rather than a two filament model consisting only of actin and myosin filaments.     

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the “Driven by Detachment (DbD)” mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.     

Identification of actin filaments in the rhabdomeral microvilli of Drosophila photoreceptors

The phototransductive microvilli of arthropod photoreceptors each contain an axial cytoskeleton. The present study shows that actin filaments are a component of this cytoskeleton in Drosophila. Firstly, actin was detected in the rhabdomeral microvilli and in the subrhabdomeral cytoplasm by immunogold labeling with antiactin. Secondly, the rhabdomeres were labeled with phalloidin, indicating the presence of filamentous actin. Finally, the actin filaments were decorated with myosin subfragment-1. The characteristic arrowhead complex formed by subfragment-1 decoration points towards the base of the microvilli, so that the fast growing end of each filament is at the distal end of the microvillus, where it is embedded in a detergent-resistant cap. Each microvillus contains more than one actin filament. Decorated filaments extend the entire length of each microvillus and project into the subrhabdomeral cytoplasm. This organization is comparable to that of the actin filaments in intestinal brush border microvilli. Similar observations were made with the photoreceptor microvilli of the crayfish, Procambarus. Our results provide an indication as to how any myosin that is associated with the rhabdomeres might function.     

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.     

Caldesmon freezes the structure of actin filaments during the actomyosin ATPase cycle

Hybrid contractile apparatus was reconstituted in skeletal muscle ghost fibers by incorporation of skeletal muscle myosin subfragment 1 (S1), smooth muscle tropomyosin and caldesmon. The spatial orientation of FITC-phalloidin-labeled actin and IAEDANS-labeled S1 during sequential steps of the acto-S1 ATPase cycle was studied by measurement of polarized fluorescence in the absence or presence of nucleotides conditioning the binding affinity of both proteins. In the fibers devoid of caldesmon addition of nucleotides evoked unidirectional synchronous changes in the orientation of the fluorescent probes attached to F-actin or S1. The results support the suggestion on the multistep rotation of the cross-bridge (myosin head and actin monomers) during the ATPase cycle. The maximal cross-bridge rotation by 7 degrees relative to the fiber axis and the increase in its rigidity by 30% were observed at transition between A**.M**.ADP.Pi (weak binding) and A--.M--.ADP (strong binding) states. When caldesmon was present in the fibers (OFF-state of the thin filament) the unidirectional changes in the orientation of actin monomers and S1 were uncoupled. The tilting of the myosin head and of the actin monomer decreased by 29% and 90%, respectively. It is suggested that in the "closed" position caldesmon "freezes" the actin filament structure and induces the transition of the intermediate state of actomyosin towards the weak-binding states, thereby inhibiting the ATPase activity of the actomyosin.     

Kinetic analysis of Drosophila muscle myosin isoforms suggests a novel mode of mechanochemical coupling

The molecular mechanism of myosin function was addressed by measuring transient kinetic parameters of naturally occurring and chimeric Drosophila muscle myosin isoforms. We assessed the native embryonic isoform, the native indirect flight muscle isoform, and two chimeric isoforms containing converter domains exchanged between the indirect flight muscle and embryonic isoforms. Myosin was purified from the indirect flight muscles of transgenic flies, and S1 was produced by alpha-chymotryptic digestion. Previous studies in vertebrate and scallop myosins have shown a correlation between actin filament velocity in motility assays and cross-bridge detachment rate, specifically the rate of ADP release. In contrast, our study showed no correlation between the detachment rate and actin filament velocity in Drosophila myosin isoforms and further that the converter domain does not significantly influence the biochemical kinetics governing the detachment of myosin from actin. We suggest that evolutionary pressure on a single muscle myosin gene may maintain a fast detachment rate in all isoforms. As a result, the attachment rate and completion of the power stroke or the equilibrium between actin.myosin.ADP states may define actin filament velocity for these myosin isoforms.     

Non-specific termination of simian virus 40 DNA replication.

Axial X-ray diffraction patterns have been studied from relaxed, contracted and rigor vertebrate striated muscles at different sarcomere lengths to determine which features of the patterns depend on the interaction of actin and myosin. The intensity of the myosin layer lines in a live, relaxed muscle is sometimes less in a stretched muscle than in the muscle at rest-length; the intensity depends not only on the sarcomere length but on the time that has elapsed since dissection of the muscle. The movement of cross-bridges giving rise to these intensity changes are not caused solely by the withdrawal of actin from the A-band.When a muscle contracts or passes into rigor many changes occur that are independent of the sarcomere length: the myosin layer lines decrease in intensity to about 30% of their initial value when the muscle contracts, and disappear completely when the muscle passes into rigor. Both in contracting and rigor muscles at all sarcomere lengths the spacings of the meridional reflections at 143 Å and 72 Å are 1% greater than from a live relaxed muscle at rest-length. It is deduced that the initial movement of cross-bridges from their positions in resting muscle does not depend on the interaction of each cross-bridge with actin, but on a conformational change in the backbone of the myosin filament: occurring as a result of activation. The possibility is discussed that the conformational change occurs because the myosin filament, like the actin filament, has an activation control mechanism. Finally, all the X-ray diffraction patterns are interpreted on a model in which the myosin filament can exist in one of two possible states: a relaxed state which gives a diffraction pattern with strong myosin layer lines and an axial spacing of 143.4 Å, and an activated state which gives no layer lines but a meridional spacing of 144.8 Å.     

Cross-bridge binding to actin and force generation in skinned fibers of the rabbit psoas muscle in the presence of antibody fragments against the N-terminus of actin.

To assess the significance of the NH2-terminus of actin for cross-bridge action in muscle, skinned fibers of rabbit psoas muscle were equilibrated with Fab fragments of antibodies directed against the first seven N-terminal residues of actin. With the antibody fragment, active force is more inhibited than relaxed fiber stiffness, or stiffness in rigor or in the presence of magnesium pyrophosphate. Inhibition of stiffness in rigor or with magnesium pyrophosphate does not necessarily indicate involvement of the NH2-terminus of actin in strong cross bridge binding to actin but may simply result from the large size of the Fab. At high Fab concentrations, active force is essentially abolished, whereas stiffness is still detectible under all conditions. Thus, complete inhibition of active force apparently is not due to interference with cross-bridge binding to actin but may result from the Fab-mimicking inhibition of the thin filament by Troponin-1 binding to the NH2-terminus of actin at low Ca2+. However, although Troponin-1 is released from the NH2-terminus at high Ca2+, the Fab is not, thus disallowing force generation upon increase in Ca2+. These data are consistent with involvement of the NH2-terminus of actin in both weak cross-bridge binding to actin and Ca2+ regulation of the thin filament.     

X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction.

To clarify the extensibility of thin actin and thick myosin filaments in muscle, we examined the spacings of actin and myosin filament-based reflections in x-ray diffraction patterns at high resolution during isometric contraction of frog skeletal muscles and steady lengthening of the active muscles using synchrotron radiation as an intense x-ray source and a storage phosphor plate as a high sensitivity, high resolution area detector. Spacing of the actin meridional reflection at approximately 1/2.7 nm-1, which corresponds to the axial rise per actin subunit in the thin filament, increased about 0.25% during isometric contraction of muscles at full overlap length of thick and thin filaments. The changes in muscles stretched to approximately half overlap of the filaments, when they were scaled linearly up to the full isometric tension, gave an increase of approximately 0.3%. Conversely, the spacing decreased by approximately 0.1% upon activation of muscles at nonoverlap length. Slow stretching of a contracting muscle increased tension and increased this spacing over the isometric contraction value. Scaled up to a 100% tension increase, this corresponds to a approximately 0.26% additional change, consistent with that of the initial isometric contraction. Taken together, the extensibility of the actin filament amounts to 3-4 nm of elongation when a muscle switches from relaxation to maximum isometric contraction. Axial spacings of the layer-line reflections at approximately 1/5.1 nm-1 and approximately 1/5.9 nm-1 corresponding to the pitches of the right- and left-handed genetic helices of the actin filament, showed similar changes to that of the meridional reflection during isometric contraction of muscles at full overlap. The spacing changes of these reflections, which also depend on the mechanical load on the muscle, indicate that elongation is accompanied by slight changes of the actin helical structure possibly because of the axial force exerted by the actomyosin cross-bridges. Additional small spacing changes of the myosin meridional reflections during length changes applied to contracting muscles represented an increase of approximately 0.26% (scaled up to a 100% tension increase) in the myosin periodicity, suggesting that such spacing changes correspond to a tension-related extension of the myosin filaments. Elongation of the myosin filament backbone amounts to approximately 2.1 nm per half sarcomere. The results indicate that a large part (approximately 70%) of the sarcomere compliance of an active muscle is caused by the extensibility of the actin and myosin filaments; 42% of the compliance resides in the actin filaments, and 27% of it is in the myosin filaments.     

Axial and radial forces of cross-bridges depend on lattice spacing

Nearly all mechanochemical models of the cross-bridge treat myosin as a simple linear spring arranged parallel to the contractile filaments. These single-spring models cannot account for the radial force that muscle generates (orthogonal to the long axis of the myofilaments) or the effects of changes in filament lattice spacing. We describe a more complex myosin cross-bridge model that uses multiple springs to replicate myosin's force-generating power stroke and account for the effects of lattice spacing and radial force. The four springs which comprise this model (the 4sXB) correspond to the mechanically relevant portions of myosin's structure. As occurs in vivo, the 4sXB's state-transition kinetics and force-production dynamics vary with lattice spacing. Additionally, we describe a simpler two-spring cross-bridge (2sXB) model which produces results similar to those of the 4sXB model. Unlike the 4sXB model, the 2sXB model requires no iterative techniques, making it more computationally efficient. The rate at which both multi-spring cross-bridges bind and generate force decreases as lattice spacing grows. The axial force generated by each cross-bridge as it undergoes a power stroke increases as lattice spacing grows. The radial force that a cross-bridge produces as it undergoes a power stroke varies from expansive to compressive as lattice spacing increases. Importantly, these results mirror those for intact, contracting muscle force production.