Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin

We have estimated the step size of the myosin cross-bridge (d, displacement of an actin filament per one ATP hydrolysis) in an in vitro motility assay system by measuring the velocity of slowly moving actin filaments over low densities of heavy meromyosin on a nitrocellulose surface. In previous studies, only filaments greater than a minimum length were observed to undergo continuous sliding movement. These filaments moved at the maximum speed (Vo), while shorter filaments dissociated from the surface. We have now modified the assay system by including 0.8% methylcellulose in the ATP solution. Under these conditions, filaments shorter than the previous minimum length move, but significantly slower than Vo, as they are propelled by a limited number of myosin heads. These data are consistent with a model that predicts that the sliding velocity (v) of slowly moving filaments is determined by the product of vo and the fraction of time when at least one myosin head is propelling the filament, that is, v = vo [1-(1-ts/tc)N], where ts is the time the head is strongly bound to actin, tc is the cycle time of ATP hydrolysis, and N is the average number of myosin heads that can interact with the filament. Using this equation, the optimum value of ts/tc to fit the measured relationship between v and N was calculated to be 0.050. Assuming d = vots, the step size was then calculated to be between 10nm and 28 nm per ATP hydrolyzed, the latter value representing the upper limit. This range is within that of geometric constraint for conformational change imposed by the size of the myosin head, and therefore is not inconsistent with the swinging cross-bridge model tightly coupled with ATP hydrolysis.     

Calcium regulation of thin filament movement in an in vitro motility assay.

The ability of calcium to regulate thin filament sliding velocity was studied in an in vitro motility assay system using cardiac troponin and tropomyosin and rhodamine-phalloidin-labeled skeletal actin and skeletal heavy meromyosin to propel the filaments. Measurements showed that both the number of thin filaments sliding and their sliding speed (Sf) were dependent on the calcium concentration in the range of pCa 5 to 9. Thin filament motility was completely inhibited only if troponin and tropomyosin were added at a concentration of 100 nM to the motility assay solution and the pCa was more than 8. The filament sliding speed was dependent on the pCa in a noncooperative fashion (Hill coefficient = 1) and reached maximum at 5 microns/s at a pCa of 5. The number of filaments moving uniformly decreased from > 90% at pCa 5-6 to near zero in less than 1 pCa unit. This behavior may be explained by a hypothesis in which the regulatory proteins control the number of cross-bridge heads interacting with the thin filaments rather than the rate at which they individually hydrolyze ATP or translocate the thin filaments.     

Inhibition of the relative movement of actin and myosin by caldesmon and calponin.

Contractile activity of myosin II in smooth muscle and non-muscle cells requires phosphorylation of myosin by myosin light chain kinase. In addition, these cells have the potential for regulation at the thin filament level by caldesmon and calponin, both of which bind calmodulin. We have investigated this regulation using in vitro motility assays. Caldesmon completely inhibited the movement of actin filaments by either phosphorylated smooth muscle myosin or rabbit skeletal muscle heavy meromyosin. The amount of caldesmon required for inhibition was decreased when tropomyosin is present. Similarly, calponin binding to actin resulted in inhibition of actin filament movement by both smooth muscle myosin and skeletal muscle heavy meromyosin. Tropomyosin had no effect on the amount of calponin needed for inhibition. High concentrations of calmodulin (10 microM) in the presence of calcium completely reversed the inhibition. The nature of the inhibition by the two proteins was markedly different. Increasing caldesmon concentrations resulted in graded inhibition of the movement of actin filaments until complete inhibition of movement was obtained. Calponin inhibited actin sliding in a more "all or none" fashion. As the calponin concentration was increased the number of actin filaments moving was markedly decreased, but the velocity of movement remained near control values.     

Characterization of in vitro motility assays using smooth muscle and cytoplasmic myosins

We have used two in vitro motility assays to study the relative movement of actin and myosin from turkey gizzards (smooth muscle) and human platelets. In the Nitella-based in vitro motility assay, myosin-coated polymer beads move over a fixed substratum of actin bundles derived from dissection of the alga, Nitella, whereas in the sliding actin filament assay fluorescently labeled actin filaments slide over myosin molecules adhered to a glass surface. Both assay systems yielded similar relative velocities using smooth muscle myosin and actin under our standard conditions. We have studied the effects of ATP, ionic strength, magnesium, and tropomyosin on the velocity and found that with the exception of the dependence on MgCl2, the two assays gave very similar results. Calcium over a concentration of pCa 8 to 4 had no effect on the velocity of actin filaments. Phosphorylated smooth muscle myosin propelled filaments of smooth muscle and skeletal muscle actin at the same rate. Phosphorylated smooth muscle and cytoplasmic myosin monomers also moved actin filaments, demonstrating that filament formation is not required for movement.     

An exact analysis of the sliding motion in contractile system: A simplified model of muscle system

A system involving two kinds of sliding filaments is analysed with special attention to the actomyosin system. Rigorous results are obtained about the statistical effect originating from many active sites distributed on both filaments. It is necessary for the occurrence of smooth motion in sliding filament that the spatial periods of active sites on both filaments are relatively incommensurable, and that the number of active sites on each filament is large enough. Sufficient conditions for smooth contraction are derived under the assumption that both filaments are rigid; this is called rigid rod approximation in the present paper. The elastic mode of the filaments, during the sliding process, is analysed by perturbation theory based on the rigid rod approximation. A stochastic theory is briefly discussed in reference to the cooperative generation of contractile force, which is concerned in Hill's relation of muscle contraction.     

Troponin is a potential regulator for actomyosin interactions

Troponin extracted from rabbit skeletal muscle directly binds to an actin filament in a molar ratio of 1:1 even in the absence of tropomyosin. An actin filament decorated with troponin did not exhibit significant difference from pure actin filaments in the maximum rate of actomyosin ATP hydrolysis and the sliding velocity of the filament examined by means of an in vitro motility assay. However, the relative number of troponin-bound actin filaments moving in the absence of calcium ions decreased to half that in their presence. The amount of HMM bound to the filaments was less than 4% of actin monomers in the presence of TNs. In addition, actin filaments could not move when Tn molecules were bound in the molar ratio of about 1:1 although they sufficiently bind to myosin heads. These results indicate that troponin can transform an actin monomer within a filament into an Off-state without sterically blocking of the myosin-binding sites with tropomyosin molecules.     

Steady-state force–velocity relation of ATP-dependent sliding between slime mold myosin, arranged on paramyosin filaments, and algal cell actin cables

To investigate characteristics of ATP-dependent sliding of a non-muscle cell myosin, obtained from a cellular slime mold Dictyostelium discoideum, on actin filament, we prepared hybrid thick filaments, in which Dictyostelium myosin was regularly arranged around paramyosin filaments obtained from a molluscan smooth muscle. A single to a few hybrid filaments were attached to a polystyrene bead (diameter, 4.5 μm; specific gravity, 1.5), and the filaments were made to slide on actin filament arrays (actin cables) in the internodal cell of an alga Chara corallina, mounted on the rotor of a centrifuge microscope. The filament-attached bead was observed to move with a constant velocity under a constant external load for many seconds. The steady-state force–velocity relation of Dictyostelium myosin sliding on actin cables was hyperbolic in shape except for large loads ≤0.7–0.8 P₀, being qualitatively similar to that of skeletal muscle fibres, despite a considerable variation in the number of myosin molecules interacting with actin cables. Comparison of the P–V curves between Dictyostelium myosin and muscle myosins sliding on actin cables suggests that the time of attachment to actin in a single attachment–detachment cycle is much longer in Dictyostelium myosin than in muscle myosins.     

Direct observation of molecular motility by light microscopy

We used video-fluorescence microscopy to directly observe the sliding movement of single fluorescently labeled actin filaments along myosin fixed on a glass surface. Single actin filaments labeled with phalloidin-tetramethyl-rhodamine, which stabilizes the filament structure of actin, could be seen very clearly and continuously for at least 60 min in 02-free solution, and the sensitivity was high enough to see very short actin filaments less than 40 nm long that contained less than eight dye molecules. The actin filaments were observed to move along double-headed and, similarly, single-headed myosin filaments on which the density of the heads varied widely in the presence of ATP, showing that the cooperative interaction between the two heads of the myosin molecule is not essential to produce the sliding movement. The velocity of actin filament independent of filament length (greater than 1 micron) was almost unchanged until the density of myosin heads along the thick filament was decreased from six heads/14.3 nm to 1 head/34 nm. This result suggests that five to ten heads are sufficient to support the maximum sliding velocity of actin filaments (5 micron/s) under unloaded conditions. In order for five to ten myosin heads to achieve the observed maximum velocity, the sliding distance of actin filaments during one ATP cycle must be more than 60 nm.     

Relationship between the flexibility and the motility of actin filaments: effects of pH

Both the sliding velocity of fluorescently labeled actin filament and its persistence length as an index of the bending flexibility of the filament were examined in the motility assay as varying the pH values of the solution for preparing actin filaments. When the pH value was varied from 5.0 to 9.0 in the solution in which actin filaments were formed from the constituent monomers, the motile performance of Mg²⁺ bound actin filaments (Mg-F-actin) was apparently suppressed compared to the case of Ca²⁺ bound ones (Ca-F-actin). The persistence length for Ca-F-actin gradually increased with the increase of the pH value while the similar length for Mg-F-actin remained rather independent of the value. The largest sliding velocity of the filament, on the other hand, obtained at the persistence length of roughly 6 μm for both cases of Mg-F-actin and Ca-F-actin.     

Direction and speed of actin filaments moving along thick filaments isolated from molluscan smooth muscle

The active movement of fluorescence-labeled actin filaments along thick filaments isolated from molluscan smooth muscle was observed. Along a single thick filament, actin filaments moved toward the center of the thick filament at the speed of 1.19 +/- 0.38 microns s-1 (mean +/- SD, n = 42) and detached themselves from it upon reaching the central zone. Movement of actin also occurred in the opposite direction, i.e., away from the center, albeit at a much lower velocity (0.09 +/- 0.07 microns s-1, n = 17). Thus, the thick filament shows functional bipolarity in terms of velocity but does not determine the direction of the movement.     

Mechanochemical coupling in actomyosin energy transduction studied by in vitro movement assay

In order to study the mechanochemical coupling in actomyosin energy transduction, the sliding distance of an actin filament induced by one ATP hydrolysis cycle was obtained by using an in vitro movement assay that permitted quantitative and simultaneous measurements of (1) the movements of single fluorescently labeled actin filaments on myosin bound to coverslip surfaces and (2) the ATPase rates. The sliding distance was determined as (the working stroke time in one ATPase cycle, tws) x (the filament velocity, v). tws was obtained from the ATPase turnover rate of myosin during the sliding (kt), the ATP hydrolysis time (delta t) and the ON-rate at which myosin heads enter into the working stroke state when they encounter actin (kON); tws approximately 1/kt-delta t-1/kON. kt was estimated from the ATPase rates of the myosin-coated surface during the sliding of actin filaments. delta t has been determined as less than 1/100 per second, kON was estimated by analyzing the movements of very short (40 nm) filaments. The resulting sliding distance during one ATP hydrolysis cycle near zero load was greater than 100 nm, which is about ten times longer than that expected for a single attachment-detachment cycle between an actin and a myosin head. This leads to the conclusion that the coupling between the ATPase and attachment-detachment cycles is not determined rigidly in a one-to-one fashion.     

Calcium-triggered movement of regulated actin in vitro. A fluorescence microscopy study

We previously reported setting up an in vitro system for the observation of actin filament sliding along myosin filaments. The system involved a minute amount of fluorescently labelled F-actin, and its movement was monitored by fluorescence microscopy. Here, we report observations of the Ca2+-dependent movement of F-actin complex with tropomyosin plus troponin (regulated actin) added to the movement system in place of pure F-actin. In a wide range of pCa (-log10[Ca2+]) between 3 and 5.5 at 30 degrees C, regulated actin filaments moved rapidly, and the average velocity depended little on the Ca2+ concentration (about 7.5 microns/s). However, when the Ca2+ concentration was decreased to pCa = 5.8 or lower, the filaments suddenly stopped moving. In striking contrast to these observations, unregulated actin moved rapidly within the whole pCa range examined, the average velocity (about 7.5 microns/s) being essentially Ca2+-independent. These observations indicate that (1) tropomyosin-troponin actually gave Ca2+-sensitivity to F-actin, and (2) the movement system was regulated by Ca2+ in an on-off fashion within a narrow range of Ca2+ concentration. In a pCa range between 5.8 and 6.0, regulated actin filaments did not exhibit thermal motion; instead, they had fixed positions in the specimen, possibly because they remained associated with myosin filaments in the background, without sliding past each other. Although regulated actin moved fast in the presence of 1 mM-CaCl2 (pCa = 3) at 30 degrees C, it became entirely non-motile as the temperature was decreased to 25 degrees C or lower. Such a sharp movement/temperature relation was never found for unregulated actin. We assayed regulated actin-activated myosin ATPase in the same conditions as used for microscopy, and found that the ATPase activity depended both on pCa and on the temperature considerably less than the movement of regulated actin. The results suggest that the sliding velocity in the in vitro system would not be proportional to the rate of actin-activated ATPase.     

Plasticity in canine airway smooth muscle

The large volume changes of some hollow viscera require a greater length range for the smooth muscle of their walls than can be accommodated by a fixed array of sliding filaments. A possible explanation is that smooth muscles adapt to length changes by forming variable numbers of contractile units in series. To test for such plasticity we examined the muscle length dependence of shortening velocity and compliance, both of which will vary directly with the number of thick filaments in series. Dog tracheal smooth muscle was studied because its cells are arrayed in long, straight, parallel bundles that span the length of the preparation. In experiments where muscle length was changed, both compliance and velocity showed a strong dependence on muscle length, varying by 1.7-fold and 2.2-fold, respectively, over a threefold range of length. The variation in isometric force was substantially less, ranging from a 1.2- to 1.3-fold in two series of experiments where length was varied by twofold to an insignificant 4% variation in a third series where a threefold length range was studied. Tetanic force was below its steady level after both stretches and releases, and increased to a steady level with 5-6 tetani at 5 min intervals. These results suggest strongly that the number of contractile units in series varies directly with the adapted muscle length. Temporary force depression after a length change would occur if the change transiently moved the filaments from their optimum overlap. The relative length independence of the adapted force is explained by the reforming of the filament lattice to produce optimum force development, with commensurate changes of velocity and compliance.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

Study of reciprocal effects of cardiac myosin and tropomyosin isoforms on actin-myosin interaction with in vitro motility assay

Interaction of myosin with actin in striated muscle is controlled by Ca²⁺ via thin filament associated proteins: troponin and tropomyosin. In cardiac muscle there is a whole pattern of myosin and tropomyosin isoforms. The aim of the current work is to study regulatory effect of tropomyosin on sliding velocity of actin filaments in the in vitro motility assay over cardiac isomyosins. It was found that tropomyosins of different content of α- and β-chains being added to actin filament effects the sliding velocity of filaments in different ways. On the other hand the velocity of filaments with the same tropomyosins depends on both heavy and light chains isoforms of cardiac myosin.     

Fluctuations in sliding motion generated by independent and random actions of protein motors

We consider theoretical fluctuations in the in vitro sliding movement of individual cytoskeletal filaments generated by an ensemble of protein motors whose actions are assumed to be statistically independent and random. We show that the mean square deviation of the sliding distances of a filament for a given period of time around their average is proportional to the inverse of the filament length. This result provides a basis for an experimental test of the general assumption on the independent and random actions of protein motors.     

Preparation of bead-tailed actin filaments: estimation of the torque produced by the sliding force in an in vitro motility assay.

By coating covalently the surface of a polystyrene bead (diameter = 1 micron) with gelsolin, we have succeeded in attaching the bead selectively at the barbed end of an actin filament and forming a 1:1 bead-actin filament complex. On a layer of heavy meromyosin on a nitrocellulose-coated coverglass, this bead-actin filament complex slid smoothly, trailing the bead at its end. Therefore we called this preparation "bead-tailed" actin filaments. The sliding velocity was indistinguishable from that of nonbeaded filaments. With use of this system, we tried to detect the axial rotation (rotation around the filament axis) in a sliding actin filament. Although a single bead at the tail end did not serve as the marker for the axial rotation, we occasionally found another bead bound to the tail bead. In this case, the orientation of the bead-aggregate could be followed continuously with a video monitor while the filament was sliding over heavy meromyosin. We observed that actin filaments slid over distances of many tens of micrometers without showing a complete turn of the bead-aggregates. On the basis of the calculation of rotational friction drag on the bead-aggregate, we estimate that the rotational component of the sliding force and the torque produced on a sliding actin filament (length < or = 10 microns) did not accumulate > 1 pN and 5 pN.nm, respectively. In the present system of randomly oriented heavy meromyosin lying on a nitrocellulose film without an external load.     

Some motile properties of fast characean myosin

We improved a motility assay system by using an affinity-purified antibody against the C-terminal globular domain of characean myosin. This improvement allowed us to study the sensitivity to ionic strength or the processivity of characean myosin. The sliding velocity of actin filaments on a characean myosin-coated surface was unaffected by ionic strength. This property is unlike that of skeletal or smooth muscle myosin and suggests that the binding manner of characean myosin to actin is different from that in other muscle myosins. The sliding velocity decreased when the MgADP concentration was raised. The extent of inhibition by MgADP on the motile activity of characean myosin was almost the same as in skeletal muscle or cardiac myosin. The number of sliding filaments on the characean myosin-coated surface decreased drastically with a decrease in the motor density. The motor density required to produce a successful movement of actin filament was about 200 molecules/microm(2). These results suggest that the characean myosin is not a processive motor protein.     

Assembly of smooth muscle myosin minifilaments: effects of phosphorylation and nucleotide binding

Small bipolar filaments, or "minifilaments," are formed when smooth muscle myosin is dialyzed against low ionic strength pyrophosphate or citrate/Tris buffers. Unlike synthetic filaments formed at approximately physiological ionic conditions, minifilaments are homogeneous as indicated by their hypersharp boundary during sedimentation velocity. Electron microscopy and hydrodynamic techniques were used to show that 20-22S smooth muscle myosin minifilaments are 380 nm long and composed of 12-14 molecules. By varying solvents, a continuum of different size polymers in the range of 15-30S could be obtained. Skeletal muscle myosin, in contrast, preferentially forms a stable 32S minifilament (Reisler, E., P. Cheung, and N. Borochov. 1986. Biophys. J. 49:335-342), suggesting underlying differences in the assembly properties of the two myosins. Addition of salt to the smooth muscle myosin minifilaments caused unidirectional growth into a longer "side-polar" type of filament, whereas bipolar filaments were consistently formed by skeletal muscle myosin. As with synthetic filaments, addition of 1 mM MgATP caused dephosphorylated minifilaments to dissociate to a mixture of folded monomers and dimers. Phosphorylation of the regulatory light chain prevented disassembly by nucleotide, even though it had no detectable effect on the structure of the minifilament. These results suggest that differences in filament stability as a result of phosphorylation are due largely to conformational changes occurring in the myosin head, and are not due to differences in filament packing.     

Regulation of the actin-myosin interaction by titin.

Titin is known to interact with actin thin filaments within the I-band region of striated muscle sarcomeres. In this study, we have used a titin fragment of 800 kDa (T800) purified from striated skeletal muscle to measure the effect of this interaction on the functional properties of the actin-myosin complex. MALDI-TOF MS revealed that T800 contains the entire titin PEVK (Pro, Glu, Val, Lys-rich) domain. In the presence of tropomyosin-troponin, T800 increased the sliding velocity (both average and maximum values) of actin filaments on heavy-meromyosin (HMM)-coated surfaces and dramatically decreased the number of stationary filaments. These results were correlated with a 30% reduction in actin-activated HMM ATPase activity and with an inhibition of HMM binding to actin N-terminal residues as shown by chemical cross-linking. At the same time, T800 did not affect the efficiency of the Ca(2+)-controlled on/off switch, nor did it alter the overall binding energetics of HMM to actin, as revealed by cosedimentation experiments. These data are consistent with a competitive effect of PEVK domain-containing T800 on the electrostatic contacts at the actin-HMM interface. They also suggest that titin may participate in the regulation of the active tension generated by the actin-myosin complex.