Search

Dimeric motor proteins, kinesin-1, cytoplasmic dynein-1, and myosin-V, move stepwise along microtubules and actin filaments with a regular step size. The motors take backward as well as forward steps. The step ratio r and dwell time τ, which are the ratio of the number of backward steps to the number of forward steps and the time between consecutive steps, respectively, were observed to change with the load. To understand the movement of motor proteins, we constructed a unified and simple mathematical model to explain the load dependencies of r and of τ measured for the above three types of motors quantitatively. Our model consists of three states, and the forward and backward steps are represented by the cycles of transitions visiting different pairs of states among the three, implying that a backward step is not the reversal of a forward step. Each of r and τ is given by a simple expression containing two exponential functions. The experimental data for r and τ for dynein available in the literature are not sufficient for a quantitative analysis, which is in contrast to those for kinesin and myosin-V. We reanalyze the data to obtain r and τ of native dynein to make up the insufficient data to fit them to the model. Our model successfully describes the behavior of r and τ for all of the motors in a wide range of loads from large assisting loads to superstall loads., (Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The stepwise movements generated by myosin, dynein, and kinesin were observed in living cells in an attempt to understand the molecular mechanisms of movement within cells. First, the sequential process of the transport of vesicles, including human epidermal factor 2 receptor, after endocytosis was observed for long periods in three dimensions using quantum dots (QDs) and a three-dimensional confocal microscope. QD vesicles, after being endocytosed into the cells, moved along the membrane by transferring actin filaments and were then rapidly transported toward the nucleus along microtubules. Second, the position of vesicles was detected with a precision up to 1.9 nm and 330 micros using a new two-dimensional tracking method. The movement of the QDs transported by myosin VI lying just beneath the cell membrane consisted of 29- and 15-nm steps with a transition phase between these two steps. QD vesicles were then transported toward the nucleus or away from the nucleus toward the cell membrane with successive 8-nm steps. The stepwise movements of these motor proteins in cells were observed using new imaging methods that allowed the molecular mechanisms underlying traffic to and from the membrane to be determined.

Conventional kinesin has a double-headed structure consisting of two motor domains and moves processively along a microtubule using the two heads cooperatively. The movement of single and multiple truncated heads of Drosophila kinesin was measured using a laser trap and nanometer detecting apparatus. Single molecules of single-headed kinesin bound to the microtubules with a 3.5 nm biased displacement toward the plus end of the microtubule. The position of these single-headed kinesin molecules bound to a microtubule did not change until they had dissociated, indicating that single kinesin heads utilize nonprocessive movement processes. Two molecules of single-headed kinesin moved continuously along a microtubule with a lower velocity and force than that of single molecules of double-headed kinesin. The biased binding of the heads determines the directionality of movement, whereas two molecules of single-headed kinesin move continuously without dissociation from a microtubule.

We have analyzed the mechanics of individual kinesin molecules by optical trapping nanometry. A kinesin molecule was adsorbed onto a latex bead, which was captured by an optical trap and brought into contact with an axoneme that was bound to a glass surface. The displacement of kinesin during force generation was determined by measuring the position of the beads with nanometer accuracy. As the displacement of kinesin was attenuated because of the compliance of the kinesin-to-bead and kinesin-to-microtubule linkages, the compliance was monitored during force generation and was used to correct the displacement of kinesin. Thus the velocity and the unitary steps could be obtained accurately over a wide force range. The force-velocity curves were linear from 0 to a maximum force at 10 microM and 1 mM ATP, and the maximum force was approximately 7 pN, which is larger by approximately 30% than values previously reported. Kinesin exhibited forward and occasionally backward stepwise displacements with a size of approximately 8 nm. The histograms of step dwell time show a monotonic decrease with time. Model calculations indicate that each kinesin head steps by 16-nm, whereas kinesin molecule steps by 8-nm.

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.

We measured isotonic sliding distance of single skinned fibers from rabbit psoas muscle when known and limited amounts of ATP were made available to the contractile apparatus. The fibers were immersed in paraffin oil at 20 degrees C, and laser pulse photolysis of caged ATP within the fiber initiated the contraction. The amount of ATP released was measured by photolyzing 3H-ATP within fibers, separating the reaction products by high-pressure liquid chromatography, and then counting the effluent peaks by liquid scintillation. The fiber stiffness was monitored to estimate the proportion of thick and thin filament sites interacting during filament sliding. The interaction distance, Di, defined as the sliding distance while a myosin head interacts with actin in the thin filament per ATP molecule hydrolyzed, was estimated from the shortening distance, the number of ATP molecules hydrolyzed by the myosin heads, and the stiffness. Di increased from 11 to 60 nm as the isotonic tension was reduced from 80% to 6% of the isometric tension. Velocity and Di increased with the concentration of ATP available. As isotonic load was increased, the interaction distance decreased linearly with decrease of the shortening velocity and extrapolated to 8 nm at zero velocity. Extrapolation of the relationship between Di and velocity to saturating ATP concentration suggests that Di reaches 100-190 nm at high shortening velocity. The interaction distance corresponds to the sliding distance while cross-bridges are producing positive (working) force plus the distance while they are dragging (producing negative forces). The results indicate that the working and drag distances increase as the velocity increases. Because Di is larger than the size of either the myosin head or the actin monomer, the results suggest that for each ATPase cycle, a myosin head interacts mechanically with several actin monomers either while working or while producing drag.

The mechanical compliance (reciprocal of stiffness) of thin filaments was estimated from the relative compliance of single, skinned muscle fibers in rigor at sarcomere lengths between 1.8 and 2.4 micron. The compliance of the fibers was calculated as the ratio of sarcomere length change to tension change during imposition of repetitive cycles of small stretches and releases. Fiber compliance decreased as the sarcomere length was decreased below 2.4 micron. The compliance of the thin filaments could be estimated from this decrement because in this range of lengths overlap between the thick and thin filaments is complete and all of the myosin heads bind to the thin filament in rigor. Thus, the compliance of the overlap region of the sarcomere is constant as length is changed and the decrease in fiber compliance is due to decrease of the nonoverlap length of the thin filaments (the I band). The compliance value obtained for the thin filaments implies that at 2.4-microns sarcomere length, the thin filaments contribute approximately 55% of the total sarcomere compliance. Considering that the sarcomeres are approximately 1.25-fold more compliant in active isometric contractions than in rigor, the thin filaments contribute approximately 44% to sarcomere compliance during isometric contraction.

Connectin (titin) is a large filamentous protein (single peptide) with a molecular mass of approximately 3 MDa, contour length approximately 900 nm, and diameter approximately 4 nm, and resides in striated muscle. Connectin links the thick filaments to the Z-lines in a sarcomere and produces a passive elastic force when muscle fiber is stretched. The aim of this study is to elucidate some aspects of physical properties of isolated beta-connectin (titin 2), a proteolytic fragment of connectin, by means of dynamic light-scattering (DLS) spectroscopy. The analysis of DLS spectra for beta-connectin gave the translational diffusion coefficient of 3.60 x 10(-8) cm2/s at 10 degrees C (or the hydrodynamic radius of 44.1 nm), molecular mass little smaller than 3.0 MDa (for a literature value of sedimentation coefficient), the root-mean-square end-to-end distance of 163 nm (or the radius of gyration of 66.6 nm), and the Kuhn segment number of 30 and segment length of 30 nm (or the persistence length of 15 nm). These results permitted to estimate the flexural rigidity of 6.0 x 10(-20) dyn x cm2 for filament bending, and the elastic constant of 7 dyn/cm for extension of one persistence length. Based on a simple model, implications of the present results in muscle physiology are discussed.

Localization of the parallel elastic components (PECs) in skinned muscle fibers was investigated by analyzing the change of the resting tension, which accompanies the dissociation of the A- and I-bands. The A-band was dissociated from both ends by increasing the concentration of KCl under relaxing conditions (0.09-0.54 M KCl, 4.0 mM MgATP, 1.0 mM Mg2+, 4.0 mM EGTA, pH 6.0-9.0, 20 degrees C). At sarcomere lengths greater than or equal to 3.5 microns, the length of the A-band was estimated by comparing the intensity of the first-order optical diffraction line with the results of model calculations. These results were supported by differential-interference microscopy and sodium dodecyl sulfate gel electrophoresis. It was shown that the resting tension decreased nearly in proportion to the residual length of the A-band. At sarcomere lengths less than or equal to 4.0 microns, the resting tension after the dissociation of the A-band was lowered to less than 10% of the initial value. On the other hand, at sarcomere lengths greater than or equal to 5.0 microns the resting tension after the dissociation of the A-band still showed approximately 35% of the initial value and did not change even after the I-band was dissociated by a solution containing KI. From these results, we propose that most of the PECs contributing to resting tension bind almost uniformly to the A-band and there are also PECs connecting Z-lines.

The 1,0 lattice spacing d1,0 in chemically and mechanically skinned single fibers of frog muscle was measured at various sarcomere lengths, L, in the range from L = 2.1 to 6.0 microns by an x-ray diffraction method. In chemically skinned fibers, d1,0 decreased with a similar slope to that of mechanically skinned fibers up to L congruent to 3 microns, but beyond this point d1,0 steeply decreased with further stretching. This steep decrease in d1,0 could be ascribed mainly to an increase in the compressing force associated with the longitudinal extension of a remnant of the sarcolemma. In mechanically skinned fibers, the gradual decrease in d1,0 continued beyond filament overlap (L greater than or equal to 3.5 microns) and was highly proportional to a resting tension. This decrease in d1,0 at L greater than or equal to 3.5 microns could be ascribed to an increase in the force exerted by lateral elastic components, which is proportional to the longitudinal resting tension. A conceptual model is proposed of a network structure of elastic components in a sarcomere.

We show in this paper that the change of the internal structure of a sarcomere in a rabbit glycerinated psoas muscle fiber can be examined by analyzing the intensity change of the first- and the second-order optical diffraction lines. A unit-cell (sarcomere)-structure model has been applied to the estimation of the length of thick filaments in a muscle fiber while they undergo dissociation. The optical factors, except for the unit-cell-structure factor, hardly changed during the dissociation of the filaments. Our results show that thick filaments dissociate from both ends on increasing the KCl concentration in the presence of 10 mM pyrophosphate and 5 mM MgCl2. Micromolar concentrations of Ca2+ suppressed to some extent the dissociation of thick filaments. The disassembly of thick filaments occurred at higher KCl concentrations in the absence of pyrophosphate. There was a correlation between the stability of the thick filament structure and cross-bridge formation, which was induced either by the addition of micromolar concentrations of Ca2+ in the presence of Mg-pyrophosphate or by removal of Mg-pyrophosphate.

Changes in the 1.0 lattice spacing during trypsin (0.25 micrograms/ml) treatment in mechanically skinned single fibers of frog muscle was examined by an x-ray diffraction method at various sarcomere lengths. The resting tension of a relaxed fiber was decreased by trypsin treatment but the stiffness of a rigor fiber was not, suggesting that elastic components were selectively digested. With progression of the digestion, the lattice spacing increased remarkably at longer sarcomere lengths and finally became independent of the sarcomere length. The increase in the lattice spacing was proportional to the decrease in the resting tension. These results support our previous suggestion (Higuchi, H., and Y. Umazume, 1986, Biophys. J., 50:385-389) that the lattice spacing decreases at long lengths due to compressive force exerted by a lateral elastic component that connects thick filaments to an axial elastic component. Consequently, it is unlikely that the decrease in the lattice spacing is determined by a decrease in the repulsive force between thick and thin filaments with stretching a fiber.