Decreased thin filament density and length in human atrophic soleus muscle fibers after spaceflight.

Soleus muscle fibers were examined electron microscopically from pre- and postflight biopsies of four astronauts orbited for 17 days during the Life and Microgravity Sciences Spacelab Mission (June 1996). Myofilament density and spacing were normalized to a 2. 4-microm sarcomere length. Thick filament density ( approximately 1, 062 filaments/microm(2)) and spacing ( approximately 32.5 nm) were unchanged by spaceflight. Preflight thin filament density (2, 976/microm(2)) decreased significantly (P < 0.01) to 2,215/microm(2) in the overlap A band region as a result of a 17% filament loss and a 9% increase in short filaments. Normal fibers had 13% short thin filaments. The 26% decrease in thin filaments is consistent with preliminary findings of a 14% increase in the myosin-to-actin ratio. Lower thin filament density was calculated to increase thick-to-thin filament spacing in vivo from 17 to 23 nm. Decreased density is postulated to promote earlier cross-bridge detachment and faster contraction velocity. Atrophic fibers may be more susceptible to sarcomere reloading damage, because force per thin filament is estimated to increase by 23%.     

Measurement of sarcomere shortening in skinned fibers from frog muscle by white light diffraction.

A new optical-electronic method has been developed to detect striation spacing of single muscle fibers. The technique avoids Bragg-angle and interference-fringe effects associated with laser light diffraction by using polychromatic (white) light. The light is diffracted once by an acousto-optical device and then diffracted again by the muscle fiber. The double diffraction reverses the chromatic dispersion normally obtained with polychromatic light. In frog skinned muscle fibers, active and passive sarcomere shortening were smooth when observed by white light diffraction, whereas steps and pauses occurred in the striation spacing signals obtained with laser illumination. During active contractions skinned fibers shortened at high rates (3-5 microns/s per half sarcomere, 0-5 degrees C) at loads below 5% of isometric tension. Compression of the myofibrillar lateral filament spacing using osmotic agents reduced the shortening velocity at low loads. A hypothesis is presented that high shortening velocities are observed with skinned muscle fibers because the cross-bridges cannot support compressive loads when the filament lattice is swollen.     

Response of equatorial x-ray reflections and stiffness to altered sarcomere length and myofilament lattice spacing in relaxed skinned cardiac muscle

Low angle x-ray diffraction measurements of myofilament lattice spacing (D(1,0)) and equatorial reflection intensity ratio (I(1,1)/I(1,0)) were made in relaxed skinned cardiac trabeculae from rats. We tested the hypothesis that the degree of weak cross-bridge (Xbr) binding, which has been shown to be obligatory for force generation in skeletal muscle, is modulated by changes in lattice spacing in skinned cardiac muscle. Altered weak Xbr binding was detected both by changes in I(1,1)/I(1,0) and by measurements of chord stiffness (chord K). Both measurements showed that, similar to skeletal muscle, the probability of weak Xbr binding at 170-mM ionic strength was significantly enhanced by lowering temperature to 5 degrees C. The effects of lattice spacing on weak Xbr binding were therefore determined under these conditions. Changes in D(1,0), I(1,1)/I(1,0), and chord K by osmotic compression with dextran T500 were determined at sarcomere lengths (SL) of 2.0 and 2.35 micro m. At each SL increasing [dextran] caused D(1,0) to decrease and both I(1,1)/I(1,0) and chord K to increase, indicating increased weak Xbr binding. The results suggest that in intact cardiac muscle increasing SL and decreasing lattice spacing could lead to increased force by increasing the probability of initial weak Xbr binding.     

An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle

The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl⁻ binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small.     

Cooperative Cross-Bridge Activation of Thin Filaments Contributes to the Frank-Starling Mechanism in Cardiac Muscle

Myosin cross-bridges play an important role in the regulation of thin-filament activation in cardiac muscle. To test the hypothesis that sarcomere length (SL) modulation of thin-filament activation by strong-binding cross-bridges underlies the Frank-Starling mechanism, we inhibited force and strong cross-bridge binding to intermediate levels with sodium vanadate (Vi). Force and stiffness varied proportionately with [Ca²⁺] and [Vi]. Increasing [Vi] (decreased force) reduced the pCa₅₀ of force-[Ca²⁺] relations at 2.3 and 2.0 μm SL, with little effect on slope (n_H). When maximum force was inhibited to ∼40%, the effects of SL on force were diminished at lower [Ca²⁺], whereas at higher [Ca²⁺] (pCa < 5.6) the relative influence of SL on force increased. In contrast, force inhibition to ∼20% significantly reduced the sensitivity of force-[Ca²⁺] relations to changes in both SL and myofilament lattice spacing. Strong cross-bridge binding cooperatively induced changes in cardiac troponin C structure, as measured by dichroism of 5′ iodoacetamido-tetramethylrhodamine-labeled cardiac troponin C. This apparent cooperativity was reduced at shorter SL. These data emphasize that SL and/or myofilament lattice spacing modulation of the cross-bridge component of cardiac thin-filament activation contributes to the Frank-Starling mechanism.     

Thick-filament strain and interfilament spacing in passive muscle: effect of titin-based passive tension

We studied the effect of titin-based passive tension on sarcomere structure by simultaneously measuring passive tension and low-angle x-ray diffraction patterns on passive fiber bundles from rabbit skinned psoas muscle. We used a stretch-hold-release protocol with measurement of x-ray diffraction patterns at various passive tension levels during the hold phase before and after passive stress relaxation. Measurements were performed in relaxing solution without and with dextran T-500 to compress the lattice toward physiological levels. The myofilament lattice spacing was measured in the A-band (d_1,0) and Z-disk (d_Z) regions of the sarcomere. The axial spacing of the thick-filament backbone was determined from the sixth myosin meridional reflection (M6) and the equilibrium positions of myosin heads from the fourth myosin layer line peak position and the I_1,1/I_1,0 intensity ratio. Total passive tension was measured during the x-ray experiments, and a differential extraction technique was used to determine the relations between collagen- and titin-based passive tension and sarcomere length. Within the employed range of sarcomere lengths (∼2.2–3.4 μm), titin accounted for >80% of passive tension. X-ray results indicate that titin compresses both the A-band and Z-disk lattice spacing with viscoelastic behavior when fibers are swollen after skinning, and elastic behavior when the lattice is reduced with dextran. Titin also increases the axial thick-filament spacing, M6, in an elastic manner in both the presence and absence of dextran. No changes were detected in either I_1,1/I_1,0 or the position of peaks on the fourth myosin layer line during passive stress relaxation. Passive tension and M6 measurements were converted to thick-filament compliance, yielding a value of ∼85 m/N, which is several-fold larger than the thick-filament compliance determined by others during the tetanic tension plateau of activated intact muscle. This difference can be explained by the fact that thick filaments are more compliant at low tension (passive muscle) than at high tension (tetanic tension). The implications of our findings are discussed.     

Cardiac myofilaments: mechanics and regulation

The mechanical properties of the cardiac myofilament are an important determinant of pump function of the heart. This report is focused on the regulation of myofilament function in cardiac muscle. Calcium ions form the trigger that induces activation of the thin filament which, in turn, allows for cross-bridge formation, ATP hydrolysis, and force development. The structure and protein-protein interactions of the cardiac sarcomere that are responsible for these processes will be reviewed. The molecular mechanism that underlies myofilament activation is incompletely understood. Recent experimental approaches have been employed to unravel the mechanism and regulation of myofilament mechanics and energetics by activator calcium and sarcomere length, as well as contractile protein phosphorylation mediated by protein kinase A. Central to these studies is the question whether such factors impact on muscle function simply by altering thin filament activation state, or whether modulation of cross-bridge cycling also plays a part in the responses of muscle to these stimuli.     

Roles for cardiac MyBP-C in maintaining myofilament lattice rigidity and prolonging myosin cross-bridge lifetime

We investigated the influence of cardiac myosin binding protein-C (cMyBP-C) and its constitutively unphosphorylated status on the radial and longitudinal stiffnesses of the myofilament lattice in chemically skinned myocardial strips of the following mouse models: nontransgenic (NTG), effective null for cMyBP-C (t/t), wild-type cMyBP-C expressed into t/t (WT_t/t), and constitutively unphosphorylated cMyBP-C (AllP-_t/t). We found that the absence of cMyBP-C in the t/t and the unphosphorylated cMyBP-C in the AllP-_t/t resulted in a compressible cardiac myofilament lattice induced by rigor not observed in the NTG and WT_t/t. These results suggest that the presence and phosphorylation of the N-terminus of cMyBP-C provides structural support and radial rigidity to the myofilament lattice. Examination of myofilament longitudinal stiffness under rigor conditions demonstrated a significant reduction in cross-bridge-dependent stiffness in the t/t compared with NTG controls, but not in the AllP-_t/t compared with WT_t/t controls. The absence of cMyBP-C in the t/t and the unphosphorylated cMyBP-C in the AllP-_t/t both resulted in a shorter myosin cross-bridge lifetime when myosin isoform was controlled. These data collectively suggest that cMyBP-C provides radial rigidity to the myofilament lattice through the N-terminus, and that disruption of the phosphorylation of cMyBP-C is sufficient to abolish this structural role of the N-terminus and shorten cross-bridge lifetime. Although the presence of cMyBP-C also provides longitudinal rigidity, phosphorylation of the N-terminus is not necessary to maintain longitudinal rigidity of the lattice, in contrast to radial rigidity.     

THE MYOFILAMENT LATTICE: STUDIES ON ISOLATED FIBERS : II. The Effects of Osmotic Strength, Ionic Concentration, and pH upon the Unit-Cell Volume

The effects of osmotic concentration, ionic strength, and pH on the myofilament lattice spacing of intact and skinned single fibers from the walking leg of crayfish (Orconectes) were determined by electron microscopy and low-angle X-ray diffraction. Sarcomere lengths were determined by light diffraction. It is demonstrated that the interfilament spacing in the intact fiber is a function of the volume of the fiber. It is also shown that the interfilament spacing of the skinned (but not of the intact) fiber is affected in a predictable manner by ionic strength and pH insofar as these parameters affect the electrostatic repulsive forces between the filaments. From these combined observations it is demonstrated that the unit-cell volume of the in vivo myofilament lattice behaves in a manner similar to that described for liquid-crystalline solutions.     

Sarcomere lattice geometry influences cooperative myosin binding in muscle

In muscle, force emerges from myosin binding with actin (forming a cross-bridge). This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca²⁺ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca²⁺ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model), while the other comprises only one thick and one thin filament (two-filament model). Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments.     

Radial displacement of myosin cross-bridges in mouse myocardium due to ablation of myosin binding protein-C

Myosin binding protein-C (cMyBP-C) is a thick filament accessory protein, which in cardiac muscle functions to regulate the kinetics of cross-bridge interaction with actin; however, the underlying mechanism is not yet understood. To explore the structural basis for cMyBP-C function, we used synchrotron low-angle X-ray diffraction to measure interfilament lattice spacing and the equatorial intensity ratio, I(11)/I(10), in skinned myocardial preparations isolated from wild-type (WT) and cMyBP-C null (cMyBP-C(-/-)). In relaxed myocardium, ablation of cMyBP-C appeared to result in radial displacement of cross-bridges away from the thick filaments, as there was a significant increase ( approximately 30%) in the I(11)/I(10) ratio for cMyBP-C(-/-) (0.37+/-0.03) myocardium as compared to WT (0.28+/-0.01). While lattice spacing tended to be greater in cMyBP-C(-/-) myocardium (44.18+/-0.68 nm) when compared to WT (42.95+/-0.43 nm), the difference was not statistically significant. Furthermore, liquid-like disorder in the myofilament lattice was significantly greater ( approximately 40% greater) in cMyBP-C(-/-) myocardium as compared to WT. These results are consistent with our working hypothesis that cMyBP-C normally acts to tether myosin cross-bridges nearer to the thick filament backbone, thereby reducing the likelihood of cross-bridge binding to actin and limiting cooperative activation of the thin filament.     

Lateral forces in the filament lattice of vertebrate striated muscle in the rigor state.

The repulsive pressure between filaments in the lattice of skinned rabbit and frog striated muscle in rigor has been measured as a function of interfilament spacing, using the osmotic pressure generated by solutions of large, uncharged polymeric molecules (dextran and polyvinylpyrrolidone). The pressure/spacing measurements have been compared with theoretically derived curves for electrostatic pressure. In both muscles, the major part of the experimental curves (100-2,000 torr) lies in the same region as the electrostatic pressure curves, providing that a thick filament charge diameter of approximately 30 nm in rabbit and approximately 26 nm in frog is assumed. In chemically skinned or glycerol-extracted rabbit muscle the fit is good; in chemically skinned frog sartorius and semitendinosus muscle the fit is poor, particularly at lower pressures where a greater spacing is observed than expected on theoretical grounds. The charge diameter is much larger than the generally accepted value for thick filament backbone diameter. This may be because electron microscope results have underestimated the amount of filament shrinkage during sample preparation, or because most of the filament charge is located at some distance from the backbone surface, e.g., on HMM-S2. Decreasing the ionic strength of the external solution, changing the pH, and varying the sarcomere length all give pressure/spacing changes similar to those expected from electrostatic pressure calculations. We conclude that over most of the external pressure range studied, repulsive pressure in the lattice is predominantly electrostatic.     

Impact of osmotic compression on sarcomere structure and myofilament calcium sensitivity of isolated rat myocardium

Changes in interfilament lattice spacing have been proposed as the mechanism underlying myofilament length-dependent activation. Much of the evidence to support this theory has come from experiments in which high-molecular-weight compounds, such as dextran, were used to osmotically shrink the myofilament lattice. However, whether interfilament spacing directly affects myofilament calcium sensitivity (EC(50)) has not been established. In this study, skinned isolated rat myocardium was osmotically compressed over a wide range (Dextran T500; 0-6%), and EC(50) was correlated to both interfilament spacing and I(1,1)/I(1,0) intensity ratio. The latter two parameters were determined by X-ray diffraction in a separate group of skinned muscles. Osmotic compression induced a marked reduction in myofilament lattice spacing, concomitant with increases in both EC(50) and I(1,1)/I(1,0) intensity ratio. However, interfilament spacing was not well correlated with EC(50) (r(2) = 0.78). A much better and deterministic relationship was observed between EC(50) and the I(1,1)/I(1,0) intensity ratio (r(2) = 0.99), albeit with a marked discontinuity at low levels of dextran compression; that is, a small amount of external osmotic compression (0.38 kPa, corresponding to 1% Dextran T500) produced a stepwise increase in the I(1,1)/I(1,0) ratio concomitant with a stepwise decrease in EC(50). These parameters then remained stable over a wide range of further applied osmotic compression (up to 6% dextran). These findings provide support for a "switch-like" activation mechanism within the cardiac sarcomere that is highly sensitive to changes in external osmotic pressure.     

Geometrical factors influencing muscle force development. II. Radial forces.

If the subfragment-2 (S2) portion of the myosin cross-bridge to actin does not lie parallel to the myofilament axes then when a muscle fiber contracts, there will be a radial component to the cross-bridge force. When the subfragment-1 (S1) portion of the cross-bridge attaches to actin with its long axis projecting through the filament axis, the magnitude of the radial force depends upon the azimuthal location of the actin site, but when the attachment of the S1 to actin is slewed, as in the reconstruction of Moore et al. (J. Mol. Biol., 1970, 50:279-294), then for a single cross-bridge the radial component of the cross-bridge force is not quite so sensitive to actin site location and is approximately 0.1 the axial component. In both cases, the ratio of the radial to axial force decreases with decreasing filament separation. If the radial-axial force ratio for each cross-bridge is approximately 0.1, then at full overlap in a frog skeletal muscle fiber the radial component of the cross-bridge force accompanying full activation will exert a compressive pressure of approximately 5 X 10(-3) atm. This would have little effect upon an intact muscle fiber where the volume constraints are likely osmotic, but it might produce a 1-2% change in filament spacing in a "skinned" muscle fiber from which the sarcolemma had been removed. These computations assume that the S2 link between the S1 head and the myosin filament does not support a bending moment of shear. If it does, then the radial component of the cross-bridge will be either greater or less, depending on the specific cross-bridge geometry.     

The length–tension curve in muscle depends on lattice spacing

Classic interpretations of the striated muscle length–tension curve focus on how force varies with overlap of thin (actin) and thick (myosin) filaments. New models of sarcomere geometry and experiments with skinned synchronous insect flight muscle suggest that changes in the radial distance between the actin and myosin filaments, the filament lattice spacing, are responsible for between 20% and 50% of the change in force seen between sarcomere lengths of 1.4 and 3.4 µm. Thus, lattice spacing is a significant force regulator, increasing the slope of muscle''s force–length dependence.     

Nonlinear force-length relationship in the ADP-induced contraction of skeletal myofibrils

The regulatory mechanism of sarcomeric activity has not been fully clarified yet because of its complex and cooperative nature, which involves both Ca²⁺ and cross-bridge binding to the thin filament. To reveal the mechanism of regulation mediated by the cross-bridges, separately from the effect of Ca²⁺, we investigated the force-sarcomere length (SL) relationship in rabbit skeletal myofibrils (a single myofibril or a thin bundle) at SL > 2.2 μm in the absence of Ca²⁺ at various levels of activation by exogenous MgADP (4-20 mM) in the presence of 1 mM MgATP. The individual SLs were measured by phase-contrast microscopy to confirm the homogeneity of the striation pattern of sarcomeres during activation. We found that at partial activation with 4-8 mM MgADP, the developed force nonlinearly depended on the length of overlap between the thick and the thin filaments; that is, contrary to the maximal activation, the maximal active force was generated at shorter overlap. Besides, the active force became larger, whereas this nonlinearity tended to weaken, with either an increase in [MgADP] or the lateral osmotic compression of the myofilament lattice induced by the addition of a macromolecular compound, dextran T-500. The model analysis, which takes into account the [MgADP]-and the lattice-spacing-dependent probability of cross-bridge formation, was successfully applied to account for the force-SL relationship observed at partial activation. These results strongly suggest that the cross-bridge works as a cooperative activator, the function of which is highly sensitive to as little as ≤1 nm changes in the lattice spacing.     

Osmotic compression and stiffness changes in relaxed skinned cardiac myocytes in PVP-40 and dextran T-500.

Sarcomere lengths, cell widths, indices of stiffness, and striation pattern uniformity were determined from radially compressed isolated adult cardiac myocytes from the rat. Single cells were bathed in a series of relaxing solutions containing 0-15% concentrations of nonpenetrating long chain polymers PVP-40 and dextran T-500. There were no significant changes observed in average sarcomere lengths or in striation pattern uniformity at any concentration. But cell widths decreased and stiffness increased in both polymers in a concentration-osmotic pressure-dependent relationship. Changes in cell width and stiffness were repeatable in either polymer, but only after an initial compression with a 10 or 15% concentration solution. The observed reduction in cell width after initial compression correlates well with known myofilament lattice spacing compression in rat cardiac muscle and is qualitatively similar to compressions seen in skeletal muscle preparations. But the cardiac myofilament lattice may not be as compressible as the skeletal lattice. Like skeletal muscle, stiffness exhibits a two-phase relationship where most of the increase occurs at solution osmotic pressures greater than 20 Torr. Finally, the inherently greater passive stiffness-length relationship of cardiac muscle is maintained at higher osmotic pressures such that the passive elastic modulus is strongly length dependent.     

Behaviour of the crossbridges in stretched or compressed muscle fibres

The maximum chord of the myosin heads is comparable to the closest surface-to-surface spacing between the myofilaments in a muscle at the slack length. Therefore, when the sarcomere length increases or when the fibre is compressed, the surface-to-surface myofilament spacing becomes lower than the head long axis. We conclude that, in stretched or compressed fibres, some crossbridges cannot attach, owing to steric hindrance. When the amount of compression is limited, this hindrance may be overcome by a tilting of the heads in the plane perpendicular to the filament axes; in this case, there is no consequence as concerns the crossbridge properties. In highly compressed fibres, the crossbridges become progressively hindered and all the crossbridges are hindered for an axis-to-axis spacing representing about 60% of the spacing observed under zero external osmotic pressure. In this case, both the isometric tension and the ATPase activity of the fibre are zero. In fibres stretched up to 3.77 microns (sarcomere length corresponding to the disappearance of the overlap between the thick and the thin filaments), the ratio of hindered crossbridges over the functional crossbridges may be estimated at about 55%. In stretched fibres, a noticeable proportion of crossbridges are sterically hindered and the crossbridges performance (e.g. constants of attachment and detachment) depends on filament spacing, i.e. on sarcomere length. Therefore, we think it is probably impossible to consider the crossbridges as independent force converters, since this idea requires that the crossbridge properties are independent of sarcomere length. In this connection, all the experiments performed on osmotically compressed fibres are of major importance for the understanding of the true mechanisms of muscle contraction.     

Changes in the lateral filament spacing of skinned muscle fibres when cross-bridges attach

When a skinned fibre prepared from frog skeletal muscle goes from the relaxed to the rigor state at a sarcomere length of about 2.2 μm, the 1, 0 transverse spacing of the filament lattice, measured by X-ray diffraction, decreases by about 11%. In measurements at various sarcomere lengths, the decrease in the spacing was approximately proportional to the degree of overlap between the thick and thin filaments. This suggests that the shrinkage of the lattice is caused by a lateral force produced by cross-bridges. In order to estimate the magnitude of the lateral force, the decrease of spacing between relaxed and rigor states was compared with the shrinkage caused osmotically by adding a high molecular weight polymer, polyvinylpyrrolidone, to the bathing solution. The results indicate that the lateral force produced per unit length of thick filament in the overlap zone is of the same order of magnitude as the axially directed force produced during maximum isometric contraction (10^?10 to 10^?9 N/μm).Experiments in the presence of a high concentration of polyvinylpyrrolidone (100 g/l) show that when the lattice spacing is decreased osmotically beyond a certain value, the lateral force produced when the fibre goes into rigor changes its direction, causing the lattice to swell. This result can be explained by assuming that there is an optimum interfilament spacing at which the cross-bridges produce no lateral force. At other spacings, the lateral force tends to displace the filament lattice toward that optimum value.     

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.