Stiffness of carbodiimide-crosslinked glycerinated muscle fibres in rigor and relaxing solutions at high salt concentrations

Characteristics of chemically cross-linked myosin gels

Myosin gels, 10 mm x 10 mm x 1 mm in size, were obtained by chemical cross-linking of scallop myosin using 1-ethyl-3-(3-dimethylaminoprolyl) carbodiimide hydrochloride (EDC), glutaraldehyde (GA), or transglutaminase (TG). All myosin gels showed high Mg-ATPase activity, although it sensitively depended on the species of cross-linker used. Among cross-linkers used, myosin gel cross-linked by TG showed the highest sensitivity, almost as high as that of native myosin. The motility assay of native actin filament on the myosin gel showed that all these myosin gels can give motion to actin filament. Among them the one cross-linked by TG had the highest average velocity and the lowest threshold concentration of ATP for movement of the actin filament and the values are nearly the same as that of native myosin. In order to give the actin filament motion with preferential direction, we attempted to make myosin gel with oriented structure by applying a shear stress. Myosin gel with oriented filament array 1 cm long and 50 microm in diameter was obtained. We found that actin filaments prefer to move along the axis of the oriented myosin gel with an increased velocity.

Transmission of polarized light in skeletal muscle

Experiments were conducted to study polarized light transmission in fresh bovine skeletal muscle of varying thicknesses. Two-dimensional polarization-sensitive transmission images were acquired and analyzed using a numerical parametric fitting algorithm. The total transmittance intensity and degree-of-polarization were calculated for both central ballistic and surrounding scattering regions. Full Mueller matrix images were derived from the raw polarization images and the polar decomposition algorithm was applied to extract polarization parameters. The results suggest that polarized light propagation through skeletal muscle is affected by strong birefringence, diattenuation, multiple scattering induced depolarization and the sarcomere diffraction effect.

Comparative biomechanics of thick filaments and thin filaments with functional consequences for muscle contraction

The scaffold of striated muscle is predominantly comprised of myosin and actin polymers known as thick filaments and thin filaments, respectively. The roles these filaments play in muscle contraction are well known, but the extent to which variations in filament mechanical properties influence muscle function is not fully understood. Here we review information on the material properties of thick filaments, thin filaments, and their primary constituents; we also discuss ways in which mechanical properties of filaments impact muscle performance.

Cross-bridge movement and stiffness during the rise of tension in skeletal muscle--a theoretical analysis

Predictions for the time courses of cross-bridge attachment. N(t), stiffness, S(t), and force, T(t), during the tetanus rise were analysed for a special class of cross-bridge models where cross-bridges initially attach in a non-stereospecific weak-binding state, AW. This state is in rapid equilibrium (equilibrium constant K) with detached states and the force generating transition (rate constant F+) is delayed. One model (model IA) which assumed step-function rise of activation at onset of tetanus, gave a poor fit to the experimental data (judged by root mean square error, RMSe approximately 0.038) but the experimentally observed lead of N(t) over T(t) was reproduced qualitatively. An activation mechanism where K increased towards its maximum value according to an exponential function (Model IB) improved the fit considerably (RMSe approximately 0.013). However, the activation time constant (r = 30 ms) derived in the fit was too high to reflect Ca2+ binding to troponin. In a further developed model (model II) both Ca2+ -binding to troponin and cross-bridge attachment were assumed to be required for full activation. This more complex model gave a good fit to the experimental data (RMSe approximately 0.013) with a realistic time constant for Ca2+ binding to troponin (9 ms). In both model IB and model II the best fit was obtained with F+ approximately 40 s(-1). An extended version of model IB, with distributed cross-bridge attachment and a series elastic element, gave a fit of similar quality (RMSe approximately 0.009) as obtained with model IB and model II and with a similar value of F+. The results support the view that weakly bound cross-bridges (state AW) may account for the lead of cross-bridge movement over force during tension rise. It is also shown that, if the stiffness of the myofilaments is non-linear (stiffness increasing with tension) the experimentally observed lead of S(t) over T(t) may, to a significant degree, be attributed to cross-bridges in the state AW.

Backward movements of cross-bridges by application of stretch and by binding of MgADP to skeletal muscle fibers in the rigor state as studied by x-ray diffraction

The effects of the applied stretch and MgADP binding on the structure of the actomyosin cross-bridges in rabbit and/or frog skeletal muscle fibers in the rigor state have been investigated with improved resolution by x-ray diffraction using synchrotron radiation. The results showed a remarkable structural similarity between cross-bridge states induced by stretch and MgADP binding. The intensities of the 14.4- and 7.2-nm meridional reflections increased by approximately 23 and 47%, respectively, when 1 mM MgADP was added to the rigor rabbit muscle fibers in the presence of ATP-depletion backup system and an inhibitor for muscle adenylate kinase or by approximately 33 and 17%, respectively, when rigor frog muscle was stretched by approximately 4.5% of the initial muscle length. In addition, both MgADP binding and stretch induced a small but genuine intensity decrease in the region close to the meridian of the 5.9-nm layer line while retaining the intensity profile of its outer portion. No appreciable influence was observed in the intensities of the higher order meridional reflections of the 14.4-nm repeat and the other actin-based reflections as well as the equatorial reflections, indicating a lack of detachment of cross-bridges in both cases. The changes in the axial spacings of the actin-based and the 14.4-nm-based reflections were observed and associated with the tension change. These results indicate that stretch and ADP binding mediate similar structural changes, being in the correct direction to those expected for that the conformational changes are induced in the outer portion distant from the catalytic domain of attached cross-bridges. Modeling of conformational changes of the attached myosin head suggested a small but significant movement (about 10-20 degrees) in the light chain-binding domain of the head toward the M-line of the sarcomere. Both chemical (ADP binding) and mechanical (stretch) intervensions can reverse the contractile cycle by causing a backward movement of this domain of attached myosin heads in the rigor state.

Behavior of N-phenylmaleimide- and p-phenylenedimaleimide-reacted muscle crossbridge heads

The finding of Barnett et al. (Biophys. J. 61 (1992) 358) that NPM-reacted crossbridge heads do not bind strongly to actin in rigor solution is not easily interpreted in terms of the solution studies of Xie and Schoenberg (Biochemistry 37 (1998) 8048) who found strong binding of NPM-reacted myosin subfragment-1 to actin in solutions devoid of MgATP. For this reason, the current work uses stiffness measurement to re-investigate the binding of rabbit skeletal muscle crossbridges to actin in rigor solution. It is found that NPM-reacted crossbridge heads bind strongly to actin in rigor solution providing one is extremely careful to reduce MgATP contamination to levels well below those that would have a detectable effect on unmodified fibers. The reason for this is that NPM-reacted crossbridge heads, which hydrolyze MgATP extremely slowly, are especially susceptible to contaminant MgATP. The new fiber results show a strong correlation with the solution results. A further manifestation of this correlation is that pPDM-reacted crossbridge heads are different from NPM-reacted ones in that, like in solution, they remain weakly binding to actin even at extremely low MgATP levels. The findings suggest that the covalent crosslinking of SH1 and SH2 by pPDM is likely playing a significant role in locking pPDM-reacted crossbridge heads in a weakly binding conformation.

Force production by chemically crosslinked myosin-actin crossbridges in rabbit skinned fibers in response to MgATP depletion

In order to study the contractile property of myosin crossbridges attached to thin filaments, myosin heads were crosslinked to the filaments at their interface in single skinned rabbit psoas fibers with a zero-length chemical crosslinker, 1-(3-dimethylamino-propyl)-3-ethylcarbodiimide (EDC). The results obtained show that a partially crosslinked single fiber produces a large rigor-like force when MgATP is depleted from the myofibrillar space. Such crosslinked fibers contain two types of crosslinked myosin heads: one with one of the two heads of the myosin molecule crosslinked to actin with the other head uncrosslinked; the other has both heads crosslinked to actin. The results of this work suggest that a crosslinked myosin head of the former type produces a much larger force than the latter type.

Mechanical and structural properties underlying contraction of skeletal muscle fibers after partial 1-ethyl-3-[3-dimethylamino)propyl]carbodiimide cross-linking

We show prolonged contraction of permeabilized muscle fibers of the frog during which structural order, as judged from low-angle x-ray diffraction, was preserved by means of partial cross-linking of the fibers using the zero-length cross-linker 1-ethyl-3-[3-dimethylamino)propyl]carbodiimide. Ten to twenty percent of the myosin cross-bridges were cross-linked, allowing the remaining 80-90% to cycle and generate force. These fibers displayed a well-preserved sarcomeric order and mechanical characteristics similar to those of intact muscle fibers. The intensity of the brightest meridional reflection at 14.5 nm, resulting from the projection of cross-bridges evenly spaced along the myofilament length, decreased by 60% as a relaxed fiber was deprived of ATP and entered the rigor state. Upon activation of a rigorized fiber by the addition of ATP, the intensity of this reflection returned to 97% of the relaxed value, suggesting that the overall orientation of cross-bridges in the active muscle was more perpendicular to the filament axis than in rigor. Following a small-amplitude length step applied to the active fibers, the reflection intensity decreased for both releases and stretches. In rigor, however, a small stretch increased the amplitude of the reflection by 35%. These findings show the close link between cross-bridge orientation and tension changes.

Multiple- and single-molecule analysis of the actomyosin motor by nanometer-piconewton manipulation with a microneedle: unitary steps and forces

We have developed a new technique for measurements of piconewton forces and nanometer displacements in the millisecond time range caused by actin-myosin interaction in vitro by manipulating single actin filaments with a glass microneedle. Here, we describe in full the details of this method. Using this method, the elementary events in energy transduction by the actomyosin motor, driven by ATP hydrolysis, were directly recorded from multiple and single molecules. We found that not only the velocity but also the force greatly depended on the orientations of myosin relative to the actin filament axis. Therefore, to avoid the effects of random orientation of myosin and association of myosin with an artificial substrate in the surface motility assay, we measured forces and displacements by myosin molecules correctly oriented in single synthetic myosin rod cofilaments. At a high myosin-to-rod ratio, large force fluctuations were observed when the actin filament interacted in the correct orientation with a cofilament. The noise analysis of the force fluctuations caused by a small number of heads showed that the myosin head generated a force of 5.9 +/- 0.8 pN at peak and 2.1 +/- 0.4 pN on average over the whole ATPase cycle. The rate constants for transitions into (k+) and out of (k-) the force generation state and the duty ratio were 12 +/- 2 s-1, and 22 +/- 4 s-1, and 0.36 +/- 0.07, respectively. The stiffness was 0.14 pN nm-1 head-1 for slow length change (100 Hz), which would be approximately 0.28 pN nm-1 head-1 for rapid length change or in rigor. At a very low myosin-to-rod ratio, distinct actomyosin attachment, force generation (the power stroke), and detachment events were directly detected. At high load, one power stroke generated a force spike with a peak value of 5-6 pN and a duration of 50 ms (k(-)-1), which were compatible with those of individual myosin heads deduced from the force fluctuations. As the load was reduced, the force of the power stroke decreased and the needle displacement increased. At near zero load, the mean size of single displacement spikes, i.e., the unitary steps caused by correctly oriented myosin, which were corrected for the stiffness of the needle-to-myosin linkage and the randomizing effect by the thermal vibration of the needle, was approximately 20 nm.

Unbinding force of a single motor molecule of muscle measured using optical tweezers

The unbinding and rebinding of motor proteins and their substrate filaments are the main components of sliding movement. We have measured the unbinding force between an actin filament and a single motor molecule of muscle, myosin, in the absence of ATP, by pulling the filament with optical tweezers. The unbinding force could be measured repeatedly on the same molecule, and was independent of the number of measurements and the direction of the imposed loads within a range of +/- 90 degrees. The average unbinding force was 9.2 +/- 4.4 pN, only a few times larger than the sliding force but an order of magnitude smaller than other intermolecular forces. From its kinetics we suggest that unbinding occurs sequentially at the molecular interface, which is an inherent property of motor molecules.

Force generation and work production by covalently cross-linked actin-myosin cross-bridges in rabbit muscle fibers

To separate a fraction of the myosin cross-bridges that are attached to the thin filaments and that participate in the mechanical responses, muscle fibers were cross-linked with 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide and then immersed in high-salt relaxing solution (HSRS) of 0.6 M ionic strength for detaching the unlinked myosin heads. The mechanical properties and force-generating ability of the cross-linked cross-bridges were tested with step length changes (L-steps) and temperature jumps (T-jumps) from 6-10 degrees C to 30-40 degrees C. After partial cross-linking, when instantaneous stiffness in HSRS was 25-40% of that in rigor, the mechanical behavior of the fibers was similar to that during active contraction. The kinetics of the T-jump-induced tension transients as well as the rate of the fast phase of tension recovery after length steps were close to those in unlinked fibers during activation. Under feedback force control, the T-jump initiated fiber shortening by up to 4 nm/half-sarcomere. Work produced by a cross-linked myosin head after the T-jump was up to 30 x 10(-21) J. When the extent of cross-linking was increased and fiber stiffness in HSRS approached that in rigor, the fibers lost their viscoelastic properties and ability to generate force with a rise in temperature.

Tension relaxation induced by pulse photolysis of caged ATP in partially crosslinked fibers from rabbit psoas muscle

Muscle contractile force is thought to be generated by ATP-induced conformational changes in myosin crossbridges. In the present study, we investigated the response to ATP binding of force-bearing, attached cross-bridges. For this investigation, skinned fibers, in which myosin heads were in part covalently crosslinked to thin filaments with a zero-length crosslinker, were prepared. Caged ATP [the P3-1-(2-nitro)phenylethyl ester of ATP] was then pulse-photolyzed in these crosslinked fibers, which retained ATP-induced "rigor" tension, and then the subsequent tension changes were followed at 14-16 degrees C and ionic strengths of 0.1-2 M. A rapid tension decrease was observed after the photolysis in the partially crosslinked fibers. The rate of the decrease was not any different from that in the uncrosslinked fibers compared at ionic strength of 0.2 M. This and other results thus indicate a kinetic similarity in the crosslinked and uncrosslinked crossbridges in response to ATP binding. These findings also suggest that ATP-induced structural changes take place in the attached crossbridges at a rate similar to that of the ATP-induced dissociation of crossbridges from thin filaments.

Tension transients in skeletal muscle fibres of the frog at varied tonicity of the extracellular medium

Length steps (complete in 0.2 ms; amplitude < 2% of the fibre length) were applied during the tetanus plateau of intact frog muscle fibres (1.7-3.2 degrees C). The effects of varied tonicity on the early changes in tension in response to the length steps were studied. The solutions were made hypotonic by reduction of the NaCl concentration from 115.5 mM to 92.4 mM and hypertonic by addition of 98 mmol sucrose per litre of the normal Ringer fluid. In all solutions tested, the length step first caused tension to change simultaneously with the step reaching an extreme value T1. After completion of the length change, tension recovered quickly to an intermediate level T2 and, after a period with slowing or reversal of the recovery, it returned slowly to the steady-state value. The maximum isometric tension was significantly reduced by increases in tonicity. In contrast, there were only small effects of varied tonicity on the peak tension-change in response to a length step (the stiffness) and on the amplitude of the fast force recovery (T2-T1) after releases. The slope of the T2-curve (a plotting of T2 versus amplitude of the length step) was reduced for releases and increased for stretches when tonicity was raised. Furthermore, the T2-curve intersected the length axis for smaller releases at high tonicity levels. The reduced isometric tension to stiffness ratio at raised tonicity could be interpreted as a reduced average force per crossbridge. Simulations using the crossbridge model of Huxley and Simmons (1971) showed that the lack of change of the recovery amplitude (T2-T1) after releases and the changes in the T2-slope are in accordance with this interpretation. The shift of the T2 length intercept is consistent with the idea that the distance traversed by the crossbridges during the power-stroke is reduced by raised tonicity.

Dynamical role of "protein friction" in the sliding movement of protein motors in vitro

When protein motors interact with a sliding cytoplasmic-filament through a weak-binding interaction (thus, without ATP splitting), this interaction cycle results in friction opposing the sliding movement. The friction is owing to the flexible nature of the heads of these motors as globular proteins. Under a certain condition, the friction becomes proportional to the sliding velocity. This viscous-like friction by protein motor is called protein friction. Since the protein friction is more than 10 times larger than the hydrodynamic viscous drag, we propose that the sliding velocity in the in vitro motility system is limited when the active sliding force generated by protein motors is balanced by the protein friction. The model of the protein friction hypothesis is consistent with many experimental data of the in vitro motility systems such as those of mixture experiments with different myosins and the ATP-concentration dependence of the sliding velocity. By relating the coefficient of the protein friction to the diffusion coefficient, we show that the model is consistent with the data on the one-dimensional Brownian movement of a microtubule on a dynein-coated glass surface in the presence of vanadate and ATP. The model also shows that the Brownian movement is driven directly by the thermally-generated structural fluctuations of the dynein heads rather than the atomic collision of solvent molecules. Thus, the model implies that the thermal structural fluctuations of the protein motor heads underlie the ATP-induced sliding movement by protein motors and hence protein motors are a Brownian actuator.

Effects of ionic strength on force transients induced by flash photolysis of caged ATP in covalently crosslinked rabbit psoas muscle fibers

Single fibers from glycerinated rabbit psoas muscle were treated with 1-ethyl-3[3-(dimethylamino) propyl] carbodiimide (EDC), after rigor was induced, to crosslink myosin heads to actin. The optimally pre-stretched (approximately 1.8%), partially crosslinked fibers produce a large force when MgATP is depleted, and this force is abolished when MgATP is reintroduced, even in high ionic strength solution of 0.5 M (Tawada et al. 1989). We investigated the rate of force decay in the crosslinked, force-producing fibers using pulse photolysis of caged ATP (Goldman et al. 1984). The decay of force was fast, the rate of which depending both on the ionic strength and on the amount of ATP released (0.2-2.2 mM) with the second-order rate constant of 0.5-1 x 10(5) M-1s-1 at the ionic strength of 0.5 M. At high ionic strength (1-2M) force decayed at lower rate. At low ionic strength (0.1-0.2 M), however, force decayed more rapidly, but force redeveloped subsequently, which is probably caused by uncrosslinked myosin heads.

Crossbridge rotation in EDC-crosslinked striated muscle fibers

The rotatability of the strong- and weak-binding myosin heads was tested by stretching glycerinated rabbit psoas fibers after crosslinking the heads to actin by using a carbodiimide EDC. The equatorial 1,1 reflection intensity (I1,1) decreased by approximately 10% upon 1% stretch in the presence of various ligands (ATP, ATP-gamma-S, pyrophosphate and AMPPNP). As the action of ligands to dissociate actomyosin increased, the relaxation of tension response to stretch and the I1,1 decrease were accelerated. This result is best explained if the ligand converts the crosslinked head to a weak-binding state, in which the head is rotatable because of its acquired elasticity. Conversely, the weak-to-strong transition was induced in the crosslinked system by removing a ligand (ATP-gamma-S) from myosin. Force was produced upon weak-to-strong transition and was accounted for by the increased stiffness of each crosslinked myosin head. However, the comparison of stress-strain curves for the weak- and strong-binding myosin showed that the equilibrium angle of myosin attachment was unchanged, making it unlikely that the weak-to-strong transition is the sole mechanism for active contraction. The calcium-activated force of the same crosslinked fibers showed several features in marked contrast to the force produced by the weak-to-strong transition. This leads to a possibility that the active force is supported by a third class of intermediate which is distinct not only from the weak-binding but also from the strong-binding intermediates in a classical sense.

Protein friction exerted by motor enzymes through a weak-binding interaction

Recently Vale et al. (1989, Cell 59, 915-925.) reported an observation of the one-dimensional Brownian movement of microtubules bound to flagellar dynein through a weak-binding interaction. In this study, we propose a theoretical model of this phenomenon. Our model consists of a rigid microtubule associated with a number of elastic dynein heads through a weak-binding interaction at equilibrium. The model implies that (1) the Brownian motion of the microtubule is not directly driven by the atomic collision of the solvent particles, but is driven by the thermally-generated structural fluctuations of the dynein heads which interact with the microtubule; (2) dynein heads through a weak-binding interaction exert a frictional drag force on the sliding motion of the microtubule and the drag force is proportional to the sliding velocity the same as in hydrodynamic viscous friction. This protein friction, with such viscous-like characteristics, may well play a role as a velocity-limiting factor in the normal ATP-induced sliding movement of motile proteins.

A physical model of ATP-induced actin-myosin movement in vitro

The nature of the mechanism limiting the velocity of ATP-induced unidirectional movements of actin-myosin filaments in vitro is considered. In the sliding process two types of "cyclic" interactions between myosin heads and actin are involved, i.e., productive and nonproductive. In the productive interaction, myosin heads split ATP and generate a force which produces sliding between actin and myosin. In the nonproductive interaction "cycle," on the other hand, myosin heads rapidly attach to and detach from actin "reversibly," i.e., without splitting ATP or generating an active force. Such a nonproductive interaction "cycle" causes irreversible dissipation of sliding energy into heat, because the myosin cross-bridges during this interaction are passive elastic structures. This consideration has led us to postulate that such cross-bridges, in effect, exert viscous-like frictional drag on moving elements. Energetic considerations suggest that this frictional drag is much greater than the hydrodynamic viscous drag. We present a model in which the sliding velocity is limited by the balance between the force generated by myosin cross-bridges in the productive interaction and the frictional drag exerted by other myosin cross-bridges in the nonproductive interaction. The model is consistent with experimental findings of in vitro sliding, including the dependence of velocity on ATP concentration, as well as the sliding velocity of co-polymers of skeletal muscle myosin and phosphorylated and unphosphorylated smooth muscle myosins.

Covalent crosslinking of myosin subfragment-1 and heavy meromyosin to actin at various molar ratios: different correlations between ATPase activity and crosslinking extent

This paper describes a systematic study of crosslinking of skeletal muscle myosin subfragment-1 (S1) and heavy meromyosin (HMM) to F-actin in the rigor state with 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimide (EDC). We followed the time courses of S1 or HMM head crosslinking at various actin:S1 or actin:HMM head molar ratios and the resulting superactivation of ATPase activity. The ATPase activity of the covalent complexes was measured at 0.5 M KCl, where the covalent complexes retain superactivated ATPase activity but the activity of uncrosslinked myosin heads is not activated by actin. S1 crosslinking was slowest at the actin:S1 molar ratio of 1:1, but faster at larger molar ratios, where more than 80% of added S1 could be crosslinked to actin. In spite of the dependence of crosslinking rate on actin:S1 ratio, there were two linear correlations between ATPase activity and the extent of S1 crosslinking to actin: one for S1 crosslinked to actin at actin:S1 molar ratios more than 2.7:1 and the other for S1 crosslinked at a molar ratio of 1:1. Extrapolation of the former correlation line to 100% crosslinked S1 gave an ATPase activity of 39 s-1 for actin-S1 covalent complex at 25 degrees C, whereas that of the other correlation line gave 21 s-1. The latter smaller activity suggests that the interface between actin and S1 in their rigor complexes at a molar ratio of 1:1 is different from that at molar ratios of more than 2.7:1. The acto-HMM crosslinking rate depended on the ratio of actin to HMM head, like that of S1 crosslinking to actin. The ATPase activity of crosslinked actin-HMM was, unlike that of actin-S1 covalent complexes, bell-shaped as a function of the crosslinked heads, but chymotryptic conversion of HMM to S1 in the covalent complexes made the bell-shaped characteristics disappear and increased the activity close to that of actin-S1 covalent complexes. These results indicate that some physical constraint imposed on myosin heads suppresses the actin-activated ATPase activity of HMM crosslinked to actin.

X-ray diffraction and electron microscopy from Lethocerus flight muscle partially relaxed by adenylylimidodiphosphate and ethylene glycol

The low-angle X-ray diffraction pattern from Lethocerus flight muscle fibres was recorded in rigor or under two conditions that modify crossbridge structure and behaviour, aqueous adenylylimidodiphosphate (AMPPNP) and AMPPNP + calcium in an ethylene glycol-water mixture. The effects on the 38.7 nm layer-line peaks (hk.6) of the diffraction patterns were studied in detail. In aqueous AMPPNP at room temperature, a condition in which rigor tension drops to half without loss of stiffness, the peaks remained nearly as intense as in rigor except for the 10.6, which dropped to half. In 20% (v/v) ethylene glycol-AMPPNP + 100 microM-Ca2+ at 23 degrees C (gly + pnp + Ca), a condition which removed muscle tension but left stiffness close to the rigor value, the 10.6 and 11.6 peaks greatly decreased but the 31.6 remained relatively high. The 14.5 nm meridional peak (00.16) became stronger on addition of AMPPNP and again on adding glycol + calcium. Considered in terms of constructively interfering filaments and crossbridges, the X-ray data indicated a transfer of diffracting crossbridge mass towards the thick filament as relaxation proceeds. We compared the X-ray diffraction patterns and crossbridge structure seen with electron microscopy (EM) under the same chemical conditions. EM and X-ray observations were mutually quite consistent overall. However, X-ray data indicated that more crossbridge mass was stereospecifically related to actin before fixation in the partially relaxed state (gly + pnp + Ca) than was suggested by the disordered crossbridge profiles seen by EM. We conclude that myosin heads at the start of the power stroke may both be closely related to their thick filament origins and form actin-determined attachments to the thin filament.

Covalent cross-linking of single fibers from rabbit psoas increases oscillatory power

Single fibers from chemically skinned rabbit psoas muscle were treated with 1-ethyl-3-[3-dimethyl-amino)proyl]-carbodiimide (EDC) at 20 degrees C after rigor was induced. A 22-min treatment resulted in 18% covalent cross-linking between myosin heads and the thin filament as determined by stiffness measurements. This treatment also results in covalent cross-linking among rod portions of myosin molecules in the backbone of the thick filament. The fibers thus prepared are stable and do not dissolve in solutions at ionic strengths as high as 1,000 mM. The preparation was subjected to sinusoidal analysis, and the resulting complex modulus data were analyzed in terms of three exponential processes, (A), (B), and (C). Oscillatory work (process B) was much greater in the cross-linked fibers than in untreated ones in activating solutions of physiological ionic strength (200 mM); this difference was attributed to the decline of process (A) with EDC treatment. Consequently, the Nyquist plot of the EDC-treated preparation exhibited an insect-type response. We conclude that, under these conditions, both cross-linked and non-cross-linked myosin heads contribute to the production of oscillatory power. The cross-linked preparations also exhibited oscillatory work in high ionic strength (500-1,000 mM) solutions, indicating that cross-linked myosin heads are capable of utilizing ATP to produce work. We conclude that process (A) does not relate to an elementary step in a cross-bridge cycle, but it may relate to dynamics outside the cross-bridge such as filament sliding or sarcomere rearrangement.

Effect of joule temperature jump on tension and stiffness of skinned rabbit muscle fibers

The effects of a temperature jump (T-jump) from 5-7 degrees C to 26-33 degrees C were studied on tension and stiffness of glycerol-extracted fibers from rabbit psoas muscle in rigor and during maximal Ca2+ activation. The T-jump was initiated by passing an alternating current pulse (30 kHz, up to 2.5 kV, duration 0.2 ms) through a fiber suspended in air. In rigor the T-jump induces a drop of both tension and stiffness. During maximal activation, the immediate stiffness dropped by (4.4 +/- 1.6) x 10(-3)/1 degree C (mean + SD) in response to the T-jump, and this was followed by a monoexponential stiffness rise by a factor of 1.59 +/- 0.14 with a rate constant ks = 174 +/- 42 s-1 (mean +/- SD, n = 8). The data show that the fiber stiffness, determined by the cross-bridge elasticity, in both rigor and maximal activation is not rubber-like. In the activated fibers the T-jump induced a biexponential tension rise by a factor of 3.45 +/- 0.76 (mean +/- SD, n = 8) with the rate constants 500-1,000 s-1 for the first exponent and 167 +/- 39 s-1 (mean +/- SD, n = 8) for the second exponent. The data are in accordance with the assumption that the first phase of the tension transient after the T-jump is due to a force-generating step in the attached cross-bridges, whereas the second one is related to detachment and reattachment of cross-bridges.

Changes in force and stiffness during stretch of skeletal muscle fibers, effects of hypertonicity

Slow stretch ramps (velocity: 0.17 fiber lengths s-1) were imposed during fused tetanic contractions of intact muscle fibers of the frog (1.4-3.0 degrees C; sarcomere length: 2.12-2.21 microns). Instantaneous force-extension relations were derived both under isometric conditions and during slow stretch by applying fast (0.2 ms) length steps to the fiber. An increase in tonicity (98 mM sucrose added to control Ringer solution) led to significant reduction of the maximum isometric tension but at the same time to marked increase in the force enhancement during slow stretch. The maximum force level reached during the stretch was affected very little. Experiments on relaxed fibers showed that recruitment of passive parallel elastic components were of no relevance for these effects. Hypertonicity slightly increased the instantaneous stiffness of the active fiber both in the presence and in the absence of stretch. The total extension of the undamped fiber elasticity was considerably reduced by increased tonicity under isometric conditions but was only slightly affected during slow stretch. The change in length of the undamped cross-bride elasticity upon stretch was thus greater in the hypertonic than in the normotonic solution suggesting a greater increase in force per cross-bridge in the hypertonic medium. The contractile effects are consistent with the assumptions that hypertonicity reduces the capability of the individual cross-bridge to produce active force and, furthermore, that hypertonicity has only minor effects on the number of attached cross-bridges and the maximum load-bearing capacity of the individual bridge.

The effects of tonicity on tension and stiffness of tetanized skeletal muscle fibres of the frog

Tension and stiffness of tetanically activated skeletal muscle fibres of the frog were studied at varied tonicity of the extracellular medium (1.7-3.2 degrees C; sarcomere length, 2.13-2.22 microns). The stiffness was measured from the change in peak tension in response to fast (0.2 ms) stretches and releases of small amplitude (0.11-0.15% of the fibre length). The bathing solution was made hypotonic by reduction of NaCl and hypertonic by addition of sucrose. The osmotic strength of the solutions tested varied from 81 to 168% of the isotonic value. Maximum tetanic tension decreased markedly with increased tonicity. The active stiffness, on the other hand, increased as the tonicity was raised, and the tension/stiffness ratio (the total extension of the undamped fibre elasticity) was thus greatly reduced under these conditions. Evidence is presented to show that the change in the tension/stiffness ratio is due neither to the development of rigor cross-bridges nor to the recruitment of passive parallel-elastic elements in response to increased tonicity. Neither are viscous-like components important for explaining the effect. A change in the tension/stiffness ratio, similar to that seen in response to increased tonicity, did not occur as fibre width was reduced by increasing the sarcomere length. This suggests that the changes in the fibre volume affect this ratio mainly by mechanisms that are unrelated to changes in lateral spacing between the myofilaments.

Two attached non-rigor crossbridge forms in insect flight muscle

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

Normal modes of vibration in bovine pancreatic trypsin inhibitor and its mechanical property

The normal mode analysis of conformational fluctuation is carried out for a small globular protein, bovine pancreatic trypsin inhibitor. Results are analyzed mainly to reveal the mechanical construction of the protein molecule. We take dihedral angles, including peptide omega angles, as independent variables for the normal mode analysis. There are 306 such angles in this molecule. Motions in modes with frequencies lower than 120 cm-1 are shown to involve atoms in the whole protein molecule, and spatial change of displacement vectors is continuous, i.e., those of atoms near in space are similar. To quantitate the observation of the continuity, a correlation function of direction vectors of atomic displacements is calculated. From this function we define a quantity that is interpreted as the wave length of an equivalent elastic plane wave. From this quantity we deduce effective Young's modulus for each mode. For the mode with the lowest frequency 4.4 cm-1, it turned out to be 0.8 x 10(9) dyn cm-2, the value two orders of magnitude softer than, for instance, alpha-helices. Prompted by this observation, the four lowest frequency modes and also the harmonic motions in the thermal equilibrium are analyzed further mainly to detect relatively rigid structural elements in the molecule. From this analysis emerges a mechanical picture of the protein molecule that is made up of relatively rigid elements held together by very soft parts.