Weakly attached cross-bridges in relaxed frog muscle fibers.

Tension responses due to small, rapid length changes (completed within 40 microseconds) were obtained from skinned single frog muscle fiber segments (4-10 mm length) incubated in relaxing and rigor solutions at various ionic strengths. The first 2 ms of these responses can be described with a linear model in which the fiber is regarded as a rod, composed of infinitesimally small, identical segments, containing one undamped elastic element and two or three damped elastic elements and a mass in series. Rigor stiffness changed less than 10% in a limited range, 40-160 mM, of ionic strength conditions. Equatorial x-ray diffraction patterns show a similar finding for the filament spacing and intensity ratio I(11)/I(10). Relaxed fibers became stiffer under low ionic strength conditions. This stiffness increment can be correlated with a decreasing filament spacing and (an increased number of) weakly attached cross-bridges. Under low ionic strength conditions an additional recovery (1 ms time constant) became noticeable which might reflect characteristics of weakly attached cross-bridges.     

Structural characterization of weakly attached cross-bridges in the A*M*ATP state in permeabilized rabbit psoas muscle

It is well established that in a skeletal muscle under relaxing conditions, cross-bridges exist in a mixture of four weak binding states in equilibrium (A*M*ATP, A*M*ADP*P(i), M*ATP, and M*ADP*P(i)). It has been shown that these four weak binding states are in the pathway to force generation. In the past their structural, biochemical, and mechanical properties have been characterized as a group. However, it was shown that the myosin heads in the M*ATP state exhibited a disordered distribution along the thick filament, while in the M*ADP*P(i) state they were well ordered. It follows that the structures of the weakly attached states of A*M*ATP and A*M*ADP*P(i) could well be different. Individual structures of the two attached states could not be assigned because protocol for isolating the two states has not been available until recently. In the present study, muscle fibers are reacted with N-phenylmaleimide such that ATP hydrolysis is inhibited, i.e., the cross-bridge population under relaxing conditions is distributed only between the two states of M*ATP and A*M*ATP. Two-dimensional x-ray diffraction was applied to determine the structural characteristics of the attached A*M*ATP state. Because the detached state of M*ATP is disordered and does not contribute to layer line intensities, changes as a result of increasing attachment in the A*M*ATP state are attributable to that state alone. The equilibrium toward the attached state was achieved by lowering the ionic strength. The results show that upon attachment, both the myosin and the first actin associated layer lines increased intensities, while the sixth actin layer line was not significantly affected. However, the intensities remain weak despite substantial attachment. The results, together with modeling (see J. Gu, S. Xu and L. C. Yu, 2002, Biophys. J. 82:2123-2133), suggest that there is a wide range of orientation of the attached A*M*ATP cross-bridges while the myosin heads maintain some degree of helical distribution on the thick filament, suggesting a high degree of flexibility in the actomyosin complex. Furthermore, the lack of sensitivity of the sixth actin layer line suggests that the binding site on actin differs from the putative site for rigor binding. The significance of the flexibility in the A*M*ATP complex in the process of force generation is discussed.     

Mesoscopic analysis of motion and conformation of cross-bridges

The orientation of a cross-bridge is widely used as a parameter in determining the state of muscle. The conventional measurements of orientation, such as that made by wide-field fluorescence microscopy, electron paramagnetic resonance (EPR) or X-ray diffraction or scattering, report the average orientation of 10¹²–10⁹ myosin cross-bridges. Under conditions where all the cross-bridges are immobile and assume the same orientation, for example in normal skeletal muscle in rigor, it is possible to determine the average orientation from such global measurements. But in actively contracting muscle, where a parameter indicating orientation fluctuates in time, the measurements of the average value provide no information about cross-bridge kinetics. To avoid problems associated with averaging information from trillions of cross-bridges, it is necessary to decrease the number of observed cross-bridges to a mesoscopic value (i.e. the value affected by fluctuations around the average). In such mesoscopic regimes, the averaging of the signal is minimal and dynamic behavior can be examined in great detail. Examples of mesoscopic analysis on skeletal and cardiac muscle are provided.     

Caldesmon inhibits formation of strongly bound myosin cross-bridges and activates an ability of weakly bound cross-bridges to transform actin monomers to the off-conformation

The effect of caldesmon and its actin-binding C-terminal 35 kDa fragment on conformational alterations of actin in a muscle fiber at relaxation, rigor and at simulation of strong and weak binding of myosin heads to actin was studied by polarizational fluorimetry technique. The strong and weak binding forms were mimicked during binding of F-actin of ghost muscle fibers to myosin subfragment-1 modified with NEM (NEM-S1) or pPDM (pPDM-S1), respectively. As a test for alterations in actin conformation, changes in orientation and mobility of a fluorescent probe, TRITC-phalloidin, bound specifically to F-actin were used. The results obtained have shown that during transition of the muscle fiber from the relaxed state into the rigor and during binding of actin filaments to NEM-S1, changes of polarization parameters take place, which are characteristic of formation between actin and myosin of the strong binding and of transformation of actin subunits from the "turned-off" (inactive) to the "turned-on" (active) conformation. Binding of pPDM-S1 to actin and relaxation of the muscle fiber are accompanied, on the contrary, by the changes of orientation and of the fluorescent probe mobility, which are typical of formation of the weak ("non-force-producing") form of actin-myosin binding and of transformation of actin subunits from the active conformation into the inactive one. Caldesmon and its C-terminal fragment markedly inhibit formation of the strong binding at rigor and activate transition of actin monomers to the switched off conformation at relaxation of muscle fiber. In parallel experiments, these regulatory proteins have been shown to inhibit an active force developed at the transition of a muscle fiber from relaxation to rigor. Besides, caldesmon and its fragment decrease the rate of actin filament sliding over myosin in an in vitro motility assay. Caldesmon is suggested to regulate the smooth muscle contraction in an allosterical manner. The alterations in actin conformation inhibit formation of strong binding of myosin cross bridges to actin and activate the ability of weakly bound cross bridges to switch actin monomers from the "on" to the "off" conformation.     

Predominant attached state of myosin cross-bridges during contraction and relaxation at low ionic strength

The chemical states of a cross-bridge--nucleotide complex were studied using a fluorescent ATP analogue, 1-N6-etheno-2-aza-ATP(epsilon-2-aza-ATP). The fluorescence of epsilon-2-aza-ATP at specific emission wavelengths was enhanced by 12.5 times upon binding to myosin in a relaxed muscle and the fluorescence from the resultant myosin(M)-epsilon-2-aza-ADP-Pi intermediate was 2.5 times greater than that from a M-epsilon-2-aza-ADP complex. Similar enhancements of the fluorescence of epsilon-2-aza-ATP and epsilon-2-aza-ADP were observed upon binding to heavy meromyosin in solution. Binding of F-actin did not change the fluorescence of epsilon-2-aza-ATP or epsilon-2-aza-ADP bound to heavy meromyosin. When a muscle went from a relaxed state to a state of isometric contraction or contraction with shortening, the fluorescence intensity decreased only slightly or not at all, i.e. the fluorescence of nucleotides bound to most of the myosin heads during contraction is the same as that of the M-epsilon-2-aza-ADP-Pi intermediate. These results suggest that an actomyosin(AM)-epsilon-2-aza-ADP-Pi intermediate is the predominant attached state during contraction. When the ionic strength of the relaxing solution was decreased, cross-bridges formed at 6 degrees C without tension generation. At 20 degrees C, a large tension was produced although the shortening velocity was negligibly small or zero. The fluorescence intensity decreased by 15% at 20 degrees C but only a small decrease of 3% was observed at 6 degrees C, suggesting that the predominant complexes in the attached state were AM-epsilon-2-aza-ATP and/or AM-2-aza-ADP-Pi at 6 degrees C and AM-epsilon-2-aza-ADP at 20 degrees C. Thus, the identification of the actomyosin-nucleotide complexes existing before and after the force-generating step lent further support to the conclusion that the sliding force is generated by conformational changes in actomyosin when the (epsilon-2-aza-)ADP-Pi complex is bound to it.     

Evidence for structurally different attached states of myosin cross-bridges on actin during contraction of fish muscle.

Using data from fast time-resolved x-ray diffraction experiments on the synchrotrons at Daresbury and (Deutsches Elektronen Synchrotron [DESY]), it is shown that during contraction of fish muscle there are at least two distinct configurations of myosin cross-bridges on actin, that they appear to have different tension producing properties and that they probably differ in the axial tilt of the cross-bridges on actin. Evidence is presented for newly observed myosin-based layer lines in patterns from active fish muscle, together with intensity changes of the actin layer lines. On the equator, the 110 reflection changes much faster (time for 50% change t1/2 = 21 +/- 4 ms after activation) than the 100 reflection (t1/2 = 35 +/- 8 ms) and tension (t1/2 = 41 +/- 3 ms) during the rising phase of tetanic contractions. These and higher order reflections have been used to show the time course of mass attachment at actin during this rising phase. Mass arrival (t1/2 = 25 ms) precedes tension by approximately 15 ms. Analysis has been carried out to evaluate the effects of changes in sarcomere length during the tetanus. It is shown that any such effects are very small. Difference "equatorial" electron density maps between active muscle at a time when mass arrival at actin is just complete, but the tension is still rising, and at a later time well into the tension plateau, show that the structural difference between the lower and higher force states corresponds to mass movement consistent with axial swinging of heads from a nonstereospecific actin attached state (low force) to a more stereospecific (high force) state.     

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

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

X-ray diffraction studies of cross-bridges weakly bound to actin in relaxed skinned fibers of rabbit psoas muscle.

X-ray diffraction patterns were obtained from skinned rabbit psoas muscle under relaxing and rigor conditions over a wide range of ionic strengths (50-170 mM) and temperatures (1 degree C-30 degrees C). For the first time, an intensification of the first actin-based layer line is observed in the relaxed muscle. The intensification, which increases with decreasing ionic strength at various temperatures, including 30 degrees C, parallels the formation of weakly attached cross-bridges in the relaxed muscle. However, the overall intensities of the actin-based layer lines are low. Furthermore, the level of diffuse scattering, presumably a measure of disorder among the cross-bridges, is little affected by changing ionic strength at a given temperature. The results suggest that the intensification of the first actin layer line is most likely due to the cross-bridges weakly bound to actin, and that the orientations of the weakly attached cross-bridges are hardly distinguishable from the detached cross-bridges. This suggests that the orientations of the weakly attached cross-bridges are not precisely defined with respect to the actin helix, i.e., nonstereospecific. Intensities of the myosin-based layer lines are only marginally affected by changing ionic strength, but markedly by temperature. The results could be explained if in a relaxed muscle the cross-bridges are distributed between a helically ordered and a disordered population with respect to myosin filament structure. Within the disordered population, some are weakly attached to actin and others are detached. The fraction of cross-bridges in the helically ordered assembly is primarily a function of temperature, while the distribution between the weakly attached and the detached within the disordered population is mainly affected by ionic strength. Some other notable features in the diffraction patterns include a approximately 1% decrease in the pitch of the myosin helix as the temperature is raised from 4 degrees C to 20 degrees C.     

Computer simulation of movement-generating cross-bridges.

A stochastic computational method was developed to study properties of cross-bridge models for muscle contraction, by following the time history of individual cross-bridge model of Andrew Huxley (1957) and a modified two-state model with more realistic behavior during steady stretching are used as examples. The method can readily compute steady-state force during shortening and stretching and force-transients following rapid changes in length. Computations of velocity with a steady load and of velocity transients are more sensitive to the randomness inherent in the stochastic method.     

Stretch activation and nonlinear elasticity of muscle cross-bridges.

When active insect fibrillar flight muscle is stretched, its ATPase rate increases and it develops "negative viscosity," which allows it to perform oscillatory work. We use a six-state model for the cross-bridge cycle to show that such "stretch activation" may arise naturally as a nonlinear property of a cross-bridge interacting with a single attachment site on a thin filament. Attachment is treated as a thermally activated process in which elastic energy must be supplied to stretch or compress the cross-bridge spring. We find that stretch activation occurs at filament displacements where, before the power stroke, the spring is initially in compression rather than in tension. In that case, pulling the filaments relieves the initial compression and reduces the elastic energy required for attachment. The result is that the attachment rate is enhanced by stretching. The model also displays the "delayed tension" effect observed in length-step experiments. When the muscle is stretched suddenly, the power stroke responds very quickly, but there is a time lag before dissociation at the end of the cycle catches up with the increased attachment rate. This lag is responsible for the delayed tension and hence also for the negative viscosity.     

Effect of actin on the tryptic digestion of myosin subfragment 1 in the weakly attached state.

The structure of myosin subfragment 1 (S1) in the weakly attached complex with actin was studied at three specific sites, at the 50-kDa/20-kDa and 27-kDa/50-kDa junctions, and at the N-terminal region, using tryptic digestion as a structure-exploring tool. The structure of S1 at the vicinity of the 50-kDa/20-kDa junction is pH dependent in the weakly attached state because the tryptic cleavage at this site was fully protected by actin at pH 6.2, but the protection was only partial at pH 8.0. Since the actin protection is complete in rigor at both pH values, the results indicate that the structure of S1 at the 50-kDa/20-kDa junction differs in the two states at pH 8.0, but not at pH 6.2. Actin restores the ADP-suppressed tryptic cleavage after Lys213 at the 27-kDa/50-kDa junction in the strongly attached state, but not in the weakly attached state, which indicates structural difference between the two states at this site. ATP and ADP open a new site for tryptic cleavage in the N-terminal region of the S1 heavy chain between Arg23 and Ile24. Actin was found to suppress this cleavage in both weakly and strongly attached states, which shows that, in the vicinity of this site, the structure of S1 is similar in both states. The results indicate that the binding of S1 to actin induces localized changes in the S1 structure, and the extent of these changes is different in the various actin-S1 complexes.     

The fish tail motion forms an attached leading edge vortex

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail''s delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.     

Radial equilibrium lengths of actomyosin cross-bridges in muscle.

Radial equilibrium lengths of the weakly attached, force-generating, and rigor cross-bridges are determined by recording their resistance to osmotic compression. Radial equilibrium length is the surface-to-surface distance between myosin and actin filaments at which attached cross-bridges are, on average, radially undistorted. We previously proposed that differences in the radial equilibrium length represent differences in the structure of the actomyosin cross-bridge. Until now the radial equilibrium length had only been determined for various strongly attached cross-bridge states and was found to be distinct for each state examined. In the present work, we demonstrate that weakly attached cross-bridges, in spite of their low affinity for actin, also exert elastic forces opposing osmotic compression, and they are characterized by a distinct radial equilibrium length (12.0 nm vs. 10.5 nm for force-generating and 13.0 nm for rigor cross-bridge). This suggests significant differences in the molecular structure of the attached cross-bridges under these conditions, e.g., differences in the shape of the myosin head or in the docking of the myosin to actin. Thus, the present finding supports our earlier conclusion that there is a structural change in the attached cross-bridge associated with the transition from a weakly bound configuration to the force-generating configuration. The implications for imposing spatial constraints on modeling actomyosin interaction in the filament lattice are discussed.     

Fluorescence resonance energy transfer within the complex formed by actin and myosin subfragment 1. Comparison between weakly and strongly attached states

Fluorescence resonance energy transfer measurements have been made between Cys-374 on actin and Cys-177 on the alkali light chain of myosin subfragment 1 (S1) using several pairs of donor-acceptor chromophores. The labeled light chain was exchanged into subfragment 1 and the resulting fluorescently labeled subfragment 1 isolated by ion-exchange chromatography on SP-Trisacryl. The efficiency of energy transfer was measured by steady-state fluorescence in a strong binding complex of acto-S1 and found to represent a spatial separation between the two probes of 5.6-6.3 nm. The same measurements were then made with weak binding acto-S1 complexes generated in two ways. First, actin was complexed with p-phenylenedimaleimide-S1, a stable analogue of S1-adenosine 5'-triphosphate (ATP), obtained by cross-linking the SH1 and SH2 heavy-chain thiols of subfragment 1 [Greene, L. E., Chalovich, J. M., & Eisenberg, E. (1986) Biochemistry 25, 704-709]. Large increases in transfer efficiency indicated that the two probes had moved closer together by some 3 nm. Second, weak binding complexes were formed between subfragment 1 and actin in the presence of the regulatory proteins troponin and tropomyosin, the absence of calcium, and the presence of ATP [Chalovich, J. M., & Eisenberg, E. (1982) J. Biol. Chem. 257, 2432-2437]. The measured efficiency of energy transfer again indicated that the distance between the two labeled sites had moved closer by about 3 nm. These data support the idea that there is a considerable difference in the structure of the acto-S1 complex between the weakly and strongly bound states.     

Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges

The mechanics of membrane-membrane adhesion are developed for the approximation that the molecular cross-bridging forces are continuously distributed as a normal stress (force per unit area). The significance of the analysis is that the finite range of the cross-bridging forces and the microscopic contact angle are not assumed negligible. Since the cross-bridging and adhesion forces are finite range interactions, there are two membrane regions: a free zone where the membranes are not subject to attractive forces; and an adherent zone where the membranes are held together by attractive stresses. The membrane is treated as an elastic continuum. The approach is to analyze the mechanics for each zone separately and then to require continuity of the solutions at the interface between the zones. Final solution yields the membrane contour and stresses proximal to and within the contact zone as well as the microscopic contact angle at the edge of the contact zone. It is demonstrated that the classical Young equation is consistent with this model. The results show that the microscopic contact angle becomes appreciable when the strength of adhesion is large or the length of the cross-bridge is large; however, the microscopic contact angle approaches zero as the membrane elastic stiffness increases. The solution predicts the width of the contact zone over which molecular bonds are stretched. It is this boundary region where increased biochemical activity is expected. In the classical model presented here, the level of tension necessary to oppose spreading of the contact is equal to the minimal level of tension required to separate the adherent membranes. This behavior is in contrast with that derived for the case of discrete molecular cross-bridges where the possibility of different levels of tension associated with adhesion and separation is introduced. The discrete cross-bridge case is the subject of a companion paper.     

Cation-induced attachment of ciliary dynein cross-bridges

Isolated, demembranated Unio gill cilia that have been activated and fixed for thin-section electron microscopy in the presence of 2 mM MgSO4 have 87% of their outer dynein arms attached to an adjacent B subfiber. The distribution of attached arms is uniform with respect to doublet position in the cilium. When both 0.1 mM ATP and Mg++ are added to the activation and fixation solutions, the frequency of bridged arms is reduced to 48%. At the same time, the distribution of the attached arms appears to have been systematically modified with respect to doublet position and the active bend plane. Those doublet pairs positioned in the bend plane where interdoublet sliding is minimal retain a greater number of bridged arms than those doublet pairs positioned outside the bend plane where sliding is maximal. These observations imply a functional coupling of the Mg++-induced bridging of the dynein arms and the subsequent binding and hydrolysis of ATP that results in a force-generating cross-bridge cycle.     

Detailed mechanics of membrane-membrane adhesion and separation. II. Discrete kinetically trapped molecular cross-bridges

In general, membrane-membrane adhesion involves specific molecular binding and cross-bridging reactions. The ideal, classical view is that near equilibrium the forces required to separate adhesive contacts are essentially equal to those induced in the membrane when the contact is formed. In contrast to the classical view, experimental observations often show that negligible levels of tension are induced by the adhesive contact even though the tension required to separate the contact is large enough to rupture the membrane. The deviation in tension levels associated with contact formation and separation appears to be due to the sparse distribution of strong molecular cross-bridges. Here, the mechanics of membrane-membrane adhesion and separation is developed for the case of discrete, kinetically trapped cross-bridges. The solution is obtained by numerical computation of the membrane contour that minimizes the total free energy (membrane elastic energy of deformation plus cross-bridge energies) in the contact zone. This solution is matched with the analytical solution for membrane stresses and geometry derived for the adjacent, unbridged zone. The results yield specific values of the macroscopic tension applied to the membrane in the plane region away from the contact zone and the microscopic angle at the edge of the contact zone. Two disparate values of the macroscopic tension are found: (a) the minimum tension required to separate the adherent membranes; and (b) the maximum tension induced in the membranes when the contact is formed (i.e., the level of tension at which the contact will just begin to spread).(ABSTRACT TRUNCATED AT 250 WORDS)     

Structural origin of weakly ordered nitroxide motion in spin‐labeled proteins

A disulfide-linked nitroxide side chain (R1) used in site-directed spin labeling of proteins often exhibits an EPR spectrum characteristic of a weakly ordered z-axis anisotropic motion at topographically diverse surface sites, including those on helices, loops and edge strands of β-sheets. To elucidate the origin of this motion, the first crystal structures of R1 that display simple z-axis anisotropic motion at solvent-exposed helical sites (131 and 151) and a loop site (82) in T4 lysozyme have been determined. Structures of 131R1 and 151R1 determined at cryogenic or ambient temperature reveal an intraresidue C_α—H···S_δ interaction that immobilizes the disulfide group, consistent with a model in which the internal motions of R1 are dominated by rotations about the two terminal bonds (Columbus, Kálai, Jeko, Hideg, and Hubbell, Biochemistry 2001;40:3828–3846). Remarkably, the 131R1 side chain populates two rotamers equally, but the EPR spectrum reflects a single dominant dynamic population, showing that the two rotamers have similar internal motion determined by the common disulfide-backbone interaction. The anisotropic motion for loop residue 82R1 is also accounted for by a common disulfide-backbone interaction, showing that the interaction does not require a specific secondary structure. If the above observations prove to be general, then significant variations in order and rate for R1 at noninteracting solvent-exposed helical and loop sites can be assigned to backbone motion because the internal motion is essentially constant.