Mechanics of single kinesin molecules measured by optical trapping nanometry.

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.     

Mechanical and chemical properties of cysteine-modified kinesin molecules.

To probe the structural changes within kinesin molecules, we made the mutants of motor domains of two-headed kinesin (4-411 aa) in which either all the five cysteines or all except Cys45 were mutated. A residual cysteine (Cys45) of the kinesin mutant was labeled with an environment-sensitive fluorescent probe, acrylodan. ATPase activity, mechanical properties, and fluorescence intensity of the mutants were measured. Upon acrylodan-labeled kinesin binding to microtubules in the presence of 1 mM AMPPNP, the peak intensity was enhanced by 3.4-fold, indicating the structural change of the kinesin head by the binding. Substitution of cysteines decreased both the maximum microtubule-activated ATPase and the sliding velocity to the same extent. However, the maximum force and the step size were not affected; the force produced by a single molecule was 6-6.5 pN, and a step size due to the hydrolysis of one ATP molecule by kinesin molecules was about 10 nm for all kinesins. This step size was close to a unitary step size of 8 nm. Thus, the mechanical events of kinesin are tightly coupled with the chemical events.     

Kinesin force generation measured using a centrifuge microscope sperm-gliding motility assay.

To measure force generation and characterize the relationship between force and velocity in kinesin-driven motility we have developed a centrifuge microscope sperm-gliding motility assay. The average (extrapolated) value of maximum isometric force at low kinesin density was 0.90 +/- 0.14 pN. Furthermore, in the experiments at low kinesin density, sperm pulled off before stall at forces between 0.40 and 0.75 pN. To further characterize our kinesin-demembranated sperm assay we estimated maximum isometric force using a laser trap-based assay. At low kinesin density, 4.34 +/- 1.5 pN was the maximum force. Using values of axoneme stiffness available from other studies, we concluded that, in our centrifuge microscope-based assay, a sperm axoneme functions as a lever arm, magnifying the centrifugal force and leading to pull-off before stall. In addition, drag of the distal portion of the axoneme is increased by the centrifugal force (because the axoneme is rotated into closer proximity to the glass surface) and represents an additional force that the kinesin motor must overcome.     

The force exerted by a single kinesin molecule against a viscous load.

Kinesin is a motor protein that uses the energy derived from the hydrolysis of ATP to power the transport of organelles along microtubules. To probe the mechanism of this chemical-to-mechanical energy transduction reaction, the movement of microtubules across glass surfaces coated with kinesin was perturbed by raising the viscosity of the buffer solution. When the viscosity of the solution used in the low density motility assay was increased approximately 100-fold through addition of polysaccharides and polypeptides, the longer microtubules, which experienced a larger drag force from the fluid, moved more slowly than the shorter ones. The speed of movement of a microtubule depended linearly on the drag force loading the motor. At the lowest kinesin density, where dilution experiments indicated that the movement was caused by a single kinesin molecule, extrapolation of the linear relationship yielded a maximum time-averaged drag force of 4.2 +/- 0.5 pN per motor (mean +/- experimental SE). The magnitude of the force argues against one type of "ratchet" model in which the motor is hypothesized to rectify the diffusion of the microtubule; at high viscosity, diffusion is too slow to account for the observed speeds. On the other hand, our data are consistent with models in which force is a consequence of strain developed in an elastic element within the motor; these models include a different "ratchet" model (of the type proposed by A. F. Huxley in 1957) as well as "power-stroke" models.     

Fast backward steps and detachment of single kinesin molecules measured under a wide range of loads

To understand force generation under a wide range of loads, the stepping of single kinesin molecules was measured at loads from −20 to 42 pN by optical tweezers with high temporal resolution. The optical trap has been improved to halve positional noise and increase bandwidth by using 200-nm beads. The step size of the forward and backward steps was 8.2 nm even over a wide range of loads. Histograms of the dwell times of backward steps and detachment fit well to two independent exponential equations with fast (~0.4 ms) and slow (>3 ms) time constants, indicating the existence of a fast step in addition to the conventional slow step. The dwell times of the fast steps were almost independent of the load and ATP concentration, while those of the slow backward steps and detachment depended on those. We constructed the kinetic model to explain the fast and slow steps under a wide range of loads.     

Fast vesicle transport in PC12 neurites: velocities and forces

Although the mechanical behavior of single-motor protein molecules such as kinesin has been carefully studied in buffer, the mechanical behavior of motor-driven vesicles in cells is much less understood. We have tracked single vesicles in neurites of PC12 cells with a spatial precision of ±30 nm and a time resolution of 120 ms. Because the neurites are thin, long, straight, and attached to the surface of planar cover glasses, the velocity of individual vesicles could be measured for times as long as 15 s and distances as long as 15 m. The velocity of anterograde vesicles was in most cases constant for periods of 1–2 s, then changed in a step-like fashion to a new constant velocity. The viscoelastic modulus felt by the vesicles within live PC12 cells was determined from the Brownian motion, using Masons generalization of the Stokes–Einstein equation. From Stokes law, the drag force at the smallest sustained velocity was 4.2±0.6 pN for vesicles of radius 0.30–0.40 m, about half the maximum force which conventional kinesin can develop during bead assays in buffer. We interpret the observed velocity steps as changes of ±1 or occasionally ±2 in the number of active motor proteins dragging that vesicle along a microtubule. Assuming that the motor is conventional kinesin, which hydrolyzes one ATP per 8 nm step along the microtubule, the motor protein efficiency in PC12 neurites is approximately 35%.     

Kinesin and cytoplasmic dynein binding to brain microsomes.

Movement of cellular organelles in a directional manner along polar microtubules is driven by the motor proteins, kinesin and cytoplasmic dynein. The binding of these proteins to a microsomal fraction from embryonic chicken brain is investigated here. Both motors exhibit saturation binding to the vesicles, and proteolysis of vesicle membrane proteins abolishes binding. The maximal binding for kinesin is 12 +/- 1.7 and 43 +/- 2 pmol per mg of vesicle protein with or without 1 mM ATP, respectively. The maximal binding for cytoplasmic dynein is 55 +/- 3.8 and 73 +/- 3.7 pmol per mg of vesicle protein with or without ATP, respectively. These values correspond to 1-6 sites per vesicle of 100-nm diameter. The nonhydrolyzable ATP analog, adenyl-5'-yl imidodiphosphate (AMP-PNP), inhibited kinesin binding to vesicles but increased kinesin binding to microtubules. An antibody to the kinesin light chain also inhibited vesicle binding to kinesin. In the absence but not presence of ATP, competition between the two motors for binding was observed. We suggest that there are two distinguishable binding sites for kinesin and cytoplasmic dynein on these organelles in the presence of ATP and a shared site in the absence of ATP.     

A rotary molecular motor that can work at near 100% efficiency

A single molecule of F1-ATPase is by itself a rotary motor in which a central gamma-subunit rotates against a surrounding cylinder made of alpha3beta3-subunits. Driven by the three betas that sequentially hydrolyse ATP, the motor rotates in discrete 120 degree steps, as demonstrated in video images of the movement of an actin filament bound, as a marker, to the central gamma-subunit. Over a broad range of load (hydrodynamic friction against the rotating actin filament) and speed, the F1 motor produces a constant torque of ca. 40 pN nm. The work done in a 120 degree step, or the work per ATP molecule, is thus ca. 80 pN nm. In cells, the free energy of ATP hydrolysis is ca. 90 pN nm per ATP molecule, suggesting that the F1 motor can work at near 100% efficiency. We confirmed in vitro that F1 indeed does ca. 80 pN nm of work under the condition where the free energy per ATP is 90 pN nm. The high efficiency may be related to the fully reversible nature of the F1 motor: the ATP synthase, of which F1 is a part, is considered to synthesize ATP from ADP and phosphate by reverse rotation of the F1 motor. Possible mechanisms of F1 rotation are discussed.     

Coupled chemical and mechanical reaction steps in a processive Neurospora kinesin.

We show using single molecule optical trapping and transient kinetics that the unusually fast Neurospora kinesin is mechanically processive, and we investigate the coupling between ATP turnover and the mechanical actions of the motor. Beads carrying single two-headed Neurospora kinesin molecules move in discrete 8 nm steps, and stall at approximately 5 pN of retroactive force. Using microtubule-activated release of the fluorescent analogue 2'-(3')-O-(N-methylanthraniloyl) adenosine 5'-diphosphate (mantADP) to report microtubule binding, we found that initially only one of the two motor heads binds, and that the binding of the other requires a nucleotide 'chase'. mantADP was released from the second head at 4 s(-1) by an ADP chase, 5 s(-1) by 5'-adenylylimidodiphosphate (AMPPNP), 27 s(-1) by ATPgammaS and 60 s(-1) by ATP. We infer a coordination mechanism for molecular walking, in which ATP hydrolysis on the trailing head accelerates leading head binding at least 15-fold, and leading head binding then accelerates trailing head unbinding at least 6-fold.     

The force exerted by the membrane potential during protein import into the mitochondrial matrix

The force exerted on a targeting sequence by the electrical potential across the inner mitochondrial membrane is calculated on the basis of continuum electrostatics. The force is found to vary from 3.0 pN to 2.2 pN (per unit elementary charge) as the radius of the inner membrane pore (assumed aqueous) is varied from 6.5 to 12 A, its measured range. In the present model, the decrease in force with increasing pore width arises from the shielding effect of water. Since the pore is not very much wider than the distance between water molecules, the full shielding effect of water may not be present; the extreme case of a purely membranous pore without water gives a force of 3.2 pN per unit charge, which should represent an upper limit. When applied to mitochondrial import experiments on the protein barnase, these results imply that forces between 11 +/- 2 pN and 13.5 +/- 2.5 pN catalyze the unfolding of barnase in those experiments. A comparison of these results with unfolding forces measured using atomic force microscopy is made.     

Differences in zero-force and force-driven kinetics of ligand dissociation from beta-galactoside-specific proteins (plant and animal lectins, immunoglobulin G) monitored by plasmon resonance and dynamic single molecule force microscopy

Protein-carbohydrate interactions are involved in diverse regulatory processes. To help understand the mechanics and kinetics of dissociation of receptor-ligand complexes, we have analyzed the separation of lactose and the N-glycan chains of asialofetuin (ASF) from three lectins and an immunoglobulin G fraction by surface plasmon resonance at zero force and by atomic force microscopy with variations of the external force. While the (AB)2 agglutinins from Ricinus communis (RCA) and Viscum album (VAA) show structural homology, the homodimeric galectin-1 from bovine heart (BHL) has no similarity to the two plant lectins except for sharing this monosaccharide specificity. The beta-galactoside-binding immunoglobulin G (IgG) fraction from human serum provides a further model system with distinct binding-site architecture. The k(off) constants for the two plant agglutinins were independent of the nature of the ligand at 1.1-1.3 x 10(-3) s(-1), whereas the geometry of ligand and binding site presentation affected this parameter for BHL (0.5 x 10(-3) s(-1) for lactose and 1 x 10(-3) s(-1) for ASF) and IgG (1.3 x 10(-3) s(-1) for lactose and 0.55 x 10(-3) s(-1) for ASF). When assessing comparatively the rupture forces at a loading rate of 3 nN/s with lactose as ligand, 34 +/- 6 pN (BHL), 36 +/- 4 pN (IgG), 47 +/- 7 pN (VAA), and 58 +/- 9 pN (RCA) were measured. For the same loading rate the rupture forces for the receptor-ASF interactions were found to be 37 +/- 3 pN (BHL), 43 +/- 5 pN (VAA), 45 +/- 6 pN (IgG), and 65 +/- 9 pN (RCA). The variation of the pulling velocity revealed in all cases a linear dependence between the rupture force and the natural logarithm of the loading rate. Performing probability density and Monte Carlo calculations, the potential barrier widths, which determine the inverse dynamic dependence with the rate of force elevation, increased from 4 A (RCA) and 7 A (VAA and IgG) to 10 A (BHL) for the receptor-lactose interactions. Presenting ASF as ligand potential widths of 4 A for RCA and IgG and 6 A for VAA and BHL were obtained. Since the dissociation kinetics at zero force apparently cannot predict the behavior in force-driven experiments, these results reveal new insights into biological functions. The dissociation kinetics under force helps to explain the difference in the toxic potency of VAA and RCA and points to a function of the galectin in cis-crosslinking and in transient trans-bridging.     

Single-molecule behavior of monomeric and heteromeric kinesins

Conventional kinesin is capable of long-range, processive movement along microtubules, a property that has been assumed to be important for its role in membrane transport. Here we have investigated whether the Caenorhabditis elegans monomeric kinesin unc104 and the sea urchin heteromeric kinesin KRP85/95, two other members of the kinesin superfamily that function in membrane transport, are also processive. Both motors were fused to green fluorescent protein, and the fusion proteins were tested for processive ability using a single-molecule fluorescence imaging microscope. Neither unc104-GFP nor KRP85/95-GFP exhibited processive movement (detection limit approximately 40 nm), although both motors were functional in multiple motor microtubule gliding assays (v = 1760 +/- 540 and 202 +/- 37 nm/s, respectively). Moreover, the ATP turnover rates (5.5 and 3.1 ATPs per motor domain per second, respectively) are too low to give rise to the observed microtubule gliding velocities, if only a single motor were driving transport with an 8 nm step per ATPase cycle. Instead, the results suggest that these motors have low duty cycles and that high processivity may not be required for efficient vesicle transport. Conventional kinesin's unusual processivity may be required for efficient transport of protein complexes that cannot carry multiple motors.     

Direct long-term observation of kinesin processivity at low load

The hand-over-hand stepping mechanism of kinesin at low loads is inadequately understood because the number of molecular steps taken per encounter with the microtubule is difficult to measure: optical traps do not register steps at zero load, while evanescent wave microscopy of single molecules of GFP-kinesin suffers from premature photobleaching. Obtaining low-load data is important because it can efficiently distinguish between alternative proposed mechanisms for molecular walking. We report a novel experiment that records the missing data. We fused kinesin to gelsolin, creating a construct that severs and caps rhodamine-phalloidin actin filaments, setting exactly one kinesin molecule on one end of each fluorescent actin filament. Single kinesin molecules labeled in this way can be tracked easily and definitively using a standard epifluorescence microscope. We use the new system to show that, contrary to a recent report, kinesin run length at low load is independent of ATP concentration in the muM to mM range of ATP concentration. Adding competitor ADP in the presence of saturating ATP decreases both velocity and run length. Based on these data, we propose a simplified model for the mechanism of processive stepping.     

Membrane tether formation from outer hair cells with optical tweezers

Optical tweezers were used to characterize the mechanical properties of the outer hair cell (OHC) plasma membrane by pulling tethers with 4.5-microm polystyrene beads. Tether formation force and tether force were measured in static and dynamic conditions. A greater force was required for tether formations from OHC lateral wall (499 +/- 152 pN) than from OHC basal end (142 +/- 49 pN). The difference in the force required to pull tethers is consistent with an extensive cytoskeletal framework associated with the lateral wall known as the cortical lattice. The apparent plasma membrane stiffness, estimated under the static conditions by measuring tether force at different tether length, was 3.71 pN/microm for OHC lateral wall and 4.57 pN/microm for OHC basal end. The effective membrane viscosity was measured by pulling tethers at different rates while continuously recording the tether force, and estimated in the range of 2.39 to 5.25 pN x s/microm. The viscous force most likely results from the viscous interactions between plasma membrane lipids and the OHC cortical lattice and/or integral membrane proteins. The information these studies provide on the mechanical properties of the OHC lateral wall is important for understanding the mechanism of OHC electromotility.     

Condensin extrudes DNA loops in steps up to hundreds of base pairs that are generated by ATP binding events

The condensin SMC protein complex organizes chromosomal structure by extruding loops of DNA. Its ATP-dependent motor mechanism remains unclear but likely involves steps associated with large conformational changes within the ∼50 nm protein complex. Here, using high-resolution magnetic tweezers, we resolve single steps in the loop extrusion process by individual yeast condensins. The measured median step sizes range between 20–40 nm at forces of 1.0–0.2 pN, respectively, comparable with the holocomplex size. These large steps show that, strikingly, condensin typically reels in DNA in very sizeable amounts with ∼200 bp on average per single extrusion step at low force, and occasionally even much larger, exceeding 500 bp per step. Using Molecular Dynamics simulations, we demonstrate that this is due to the structural flexibility of the DNA polymer at these low forces. Using ATP-binding-impaired and ATP-hydrolysis-deficient mutants, we find that ATP binding is the primary step-generating stage underlying DNA loop extrusion. We discuss our findings in terms of a scrunching model where a stepwise DNA loop extrusion is generated by an ATP-binding-induced engagement of the hinge and the globular domain of the SMC complex.     

Rapid double 8-nm steps by a kinesin mutant

The mechanism by which conventional kinesin walks along microtubules is poorly understood, but may involve alternate binding to the microtubule and hydrolysis of ATP by the two heads. Here we report a single amino-acid change that affects stepping by the motor. Under low force or low ATP concentration, the motor moves by successive 8-nm steps in single-motor laser-trap assays, indicating that the mutation does not alter the basic mechanism of kinesin walking. Remarkably, under high force, the mutant motor takes successive 16-nm displacements that can be resolved into rapid double 8-nm steps with a short dwell between steps, followed by a longer dwell. The alternating short and long dwells under high force demonstrate that the motor stepping mechanism is inherently asymmetric, revealing an asymmetric phase in the kinesin walking cycle. Our findings support an asymmetric two-headed walking model for kinesin, with cooperative interactions between the two heads. The sensitivity of the 16-nm displacements to nucleotide and load raises the possibility that ADP release is a force-producing event of the kinesin cycle.     

Measuring kinesin's first step

A variety of models have recently emerged to explain how the molecular motor kinesin is able to maintain processive movement for over 100 steps. Although these models differ in significant features, they all predict that kinesin's catalytic domains intermittently separate from each other as the motor takes 8-nm steps along the microtubule. Furthermore, at some point in this process, one molecule of ATP is hydrolyzed per step. However, exactly when hydrolysis and product release occur in relation to this forward step have not been established. Furthermore, the rate at which this separation occurs as well as the speed of motor stepping onto and release from the microtubule have not been measured. In the absence of this information, it is difficult to critically evaluate competing models of kinesin function. We have addressed this issue by developing spectroscopic probes whose fluorescence is sensitive to motor-motor separation or microtubule binding. The kinetics of these fluorescence changes allow us to directly measure how fast kinesin steps onto and releases from the microtubule and provide insight into how processive movement is maintained by this motor.     

Force-induced bidirectional stepping of cytoplasmic dynein

Cytoplasmic dynein is a minus-end-directed microtubule motor whose mechanism of movement remains poorly understood. Here, we use optical tweezers to examine the force-dependent stepping behavior of yeast cytoplasmic dynein. We find that dynein primarily advances in 8 nm increments but takes other sized steps (4-24 nm) as well. An opposing force induces more frequent backward stepping by dynein, and the motor walks backward toward the microtubule plus end at loads above its stall force of 7 pN. Remarkably, in the absence of ATP, dynein steps processively along microtubules under an external load, with less force required for minus-end- than for plus-end-directed movement. This nucleotide-independent walking reveals that force alone can drive repetitive microtubule detachment-attachment cycles of dynein's motor domains. These results suggest a model for how dynein's two motor domains coordinate their activities during normal processive motility and provide new clues for understanding dynein-based motility in living cells.     

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.     

Temperature dependence of force, velocity, and processivity of single kinesin molecules

Using the bead assay in optical microscopy equipped with optical tweezers, we have examined the effect of temperature on the gliding velocity, force, and processivity of single kinesin molecules interacting with a microtubule between 15 and 35 degrees C. The gliding velocity increased with the Arrhenius activation energy of 50 kJ/mol, consistent with the temperature dependence of the microtubule-dependent ATPase activity. Also, the average run length, i.e., a measure of processivity of kinesin, increased on increasing temperature. On the other hand, the generated force was independent of temperature, 7.34 +/- 0.33 pN (average +/- S.D., n = 70). The gliding velocities decreased almost linearly with an increase in force irrespective of temperature, implying that the efficiency of mechano-chemical energy conversion is maintained constant in this temperature range. Thus, we suggest that the force generation is attributable to the temperature-insensitive nucleotide-binding state(s) and/or conformational change(s) of kinesin-microtubule complex, whereas the gliding velocity is determined by the ATPase rate.