Mechanics of single kinesin molecules measured by optical trapping nanometry

Modeling motility of the kinesin dimer from molecular properties of individual monomers

Conventional kinesin is a homodimeric motor protein that unidirectionally transports organelles along filamentous microtubule (MT) by hydrolyzing ATP molecules. There remain two central questions in biophysical studies of kinesin: (1) the molecular physical mechanism by which the kinesin dimer, made of two sequentially identical monomers, selects a unique direction (MT plus end) for long-range transport and (2) the detailed mechanisms by which local molecular properties of individual monomers affect the motility properties of the dimer motor as a whole. On the basis of a previously proposed molecular physical model for the unidirectionality of kinesin, this study investigates the synergic motor performance of the dimer from well-defined molecular properties of individual monomers. During cargo transportation and also in single-molecule mechanical measurements, a load is often applied to the coiled-coil dimerization domain linking the two motor domains ("heads"). In this study, the share of load directly born by each head is calculated, allowing for an unambiguous estimation of load effects on the ATP turnover and random diffusion of individual heads. The results show that the load modulations of ATP turnover and head diffusion are both essential in determining the performance of the dimer under loads. It is found that the consecutive run length of the dimer critically depends upon a few pathways, leading to the detachment of individual heads from MT. Modifying rates for these detachment pathways changes the run length but not the velocity of the dimer, consistent with mutant experiments. The run length may increase with or without the ATP concentration, depending upon a single rate for pure mechanical detachment. This finding provides an explanation to a previous controversy concerning ATP dependence of the run length, and related quantitative predictions of this study can be tested by a future experiment. This study also finds that the experimental observations for assisting loads can be quantitatively explained by load-biased head diffusion. We thus conclude that the dimer motility under resisting as well as assisting loads is governed by essentially the same mechanisms.

The roles of noncatalytic ATP binding and ADP binding in the regulation of dynein motile activity in flagella

The regulation of dynein activity to produce microtubule sliding in flagella has not been well understood. To gain more insight into the roles of ATP and ADP in the regulation, we examined the effects of fluorescent ATP analogues and fluorescent ADP analogues on the ATPase activity and motile activity of dynein. 21S dynein purified from the outer arms of sea urchin sperm flagella hydrolyzed BODIPY(R) FL ATP (FL-ATP) at 78% of the rate for ATP hydrolysis. FL-ATP at 0.1-1 mM, however, induced neither microtubule translocation on a dynein-coated glass surface nor sliding disintegration of elastase-treated axonemes. Direct observation of single molecules of the fluorescent analogues showed that both the ATP and ADP analogues were stably bound to dynein over several minutes (dissociation rates = 0.0038-0.0082/s). When microtubule translocation on 21S dynein was induced by ATP, the initial increase of the mean velocity was accelerated by preincubation of the dynein with ADP. Similar increase was also induced by the preincubation with the ADP analogues. Even after preincubation with ADP, FL-ATP did not induce sliding disintegration of elastase-treated axonemes. After preincubation with a nonhydrolyzable ATP analogue, AMPPNP (adenosine 5'-(beta:gamma-imido)triphosphate), however, FL-ATP induced sliding disintegration in approximately 10% of the axonemes. These results indicate that both noncatalytic ATP binding and stable ADP binding, in addition to ATP hydrolysis, are involved in the regulation of the chemo-mechanical transduction in axonemal dynein.

Processivity of single-headed kinesin motors

The processive movement of single-headed kinesins is studied by using a ratchet model of non-Markov process, which is built on the experimental evidence that the strong binding of kinesin to microtubule in rigor state induces a large apparent change in the local microtubule conformation. In the model, the microtubule plays a crucial active role in the kinesin movement, in contrast to the previous belief that the microtubule only acts as a passive track for the kinesin motility. The unidirectional movement of single-headed kinesin is resulted from the asymmetric periodic potential between kinesin and microtubule while its processivity is determined by its binding affinity for microtubule in the weak ADP state. Using the model, various experimental results for monomeric kinesin KIF1A, such as the mean step size, the step-size distribution, the long run length and the mean velocity versus load, can be well explained quantitatively. This local conformational change of the microtubule may also play important roles in the processive movement of conventional two-headed kinesins. An experiment to verify the model is suggested.

Cargo Transport: Two Motors Are Sometimes Better Than One

Molecular motor proteins are crucial for the proper distribution of organelles and vesicles in cells. Much of our current understanding of how motors function stems from studies of single motors moving cargos in vitro. More recently, however, there has been mounting evidence that the cooperation of multiple motors in moving cargos and the regulation of motor-filament affinity could be key mechanisms that cells utilize to regulate cargo transport. Here, we review these recent advances and present a picture of how the different mechanisms of regulating the number of motors moving a cargo could facilitate cellular functions.

Exploring mechanochemical processes in the cell with optical tweezers

Force and torque, stress and strain or work are examples of mechanical and elastic actions which are intimately linked to chemical reactions in the cell. Optical tweezers are a light-based method which allows the real-time manipulation of single molecules and cells to measure their interactions. We describe the technique, briefly reviewing the operating principles and the potential capabilities to the study of biological processes. Additional emphasis is given to the importance of fluctuations in biology and how single-molecule techniques allow access to them. We illustrate the applications by addressing experimental configurations and recent progresses in molecular and cell biology.

Application of Fluorescence Correlation Spectroscopy to the Measurement of Local Temperature in Solutions under Optical Trapping Condition

Fluorescence correlation spectroscopy (FCS) was applied to the quantitative evaluation of the local heating in small domains <1 microm in solutions under the laser trapping condition in the presence of a near-infrared (NIR) laser beam at 1064 nm. On the basis of the translational diffusion coefficient of fluorescent molecules obtained by FCS, the relationship between temperature rise and the incident NIR laser power, DeltaT/DeltaP, were determined to be 62 +/- 6, 49 +/- 7, and 23 +/- 1 deg K/W in ethylene glycol, ethanol, and water, respectively, while no remarkable temperature increase was observed for deuterated water. The value of DeltaT/DeltaP linearly increased as a function of alpha/lambda (alpha is the extinction coefficient of solvent at the wavelength and lambda is the thermal conductivity of the medium). The validity and the applicability of the present method for the measurement of the local temperature increase were discussed by comparing the present results with previous ones by other various methods.

Identification of a strong binding site for kinesin on the microtubule using mutant analysis of tubulin

The kinesin-binding site on the microtubule has not been identified because of the technical difficulties involved in the mutant analyses of tubulin. Exploiting the budding yeast expression system, we succeeded in replacing the negatively charged residues in the alpha-helix 12 of beta-tubulin with alanine and analyzed their effect on kinesin-microtubule interaction in vitro. The microtubule gliding assay showed that the affinity of the microtubules for kinesin was significantly reduced in E410A, D417A, and E421A, but not in E412A mutant. The unbinding force measurement revealed that in the former three mutants, the kinesin-microtubule interaction in the adenosine 5'-[beta,gamma-imido]triphosphate state (AMP-PNP state) became less stable when a load was imposed towards the microtubule minus end. In parallel with this decreased stability, the stall force of kinesin was reduced. Our results implicate residues E410, D417, and E421 as crucial for the kinesin-microtubule interaction in the strong binding state, thereby governing the size of kinesin stall force.

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.

Laser manipulation in liquid crystals: an approach to microfluidics and micromachines

Laser trapping of particles in three dimensions can occur as a result of the refraction of strongly focused light through micrometre-sized particles. The use of this effect to produce laser tweezers is extremely common in fields such as biology, but it is only relatively recently that the technique has been applied to liquid crystals (LCs). The possibilities are exciting: droplets of LCs can be trapped, moved and rotated in an isotropic fluid medium, or both particles and defects can be trapped and manipulated within a liquid crystalline medium. This paper considers both the possibilities. The mechanism of transfer of optical angular momentum from circularly polarized light to small droplets of nematic LCs is described. Further, it is shown that droplets of chiral LCs can be made to rotate when illuminated with linearly polarized light and possible mechanisms are discussed. The trapping and manipulation of micrometre-sized particles in an aligned LC medium is used to provide a measure of local shear viscosity coefficients and a unique test of theory at low Ericksen number in LCs.

Mechanochemical couplings of kinesin motors

Kinesins are molecular motors capable of moving processively along microtubule in a stepwise manner by hydrolyzing ATP. Numerous experimental results on various aspects of their dynamical behaviours are available in literature. Although a number of models of tightly coordinated mechanism have been proposed to explain some experimental results, up to now no good explanation has been given to all these experimental results by using a single model. We have recently proposed such a model of partially coordinated hand-over-hand moving mechanism. In this paper, we use this model to study in detail various aspects of the dynamical properties of single kinesin molecules. We show that kinesin dimers walk hand-over-hand along microtubules in a partially coordinated rather than a tightly coordinated manner. The degree of coordination depends on the ratio of the two heads' ATPase rates that are in turn determined by both internal elastic force and external load. We have tested this model using various available experimental results on different samples and obtained a good agreement between the theory and the experiments.

Overlapping hand-over-hand mechanism of single molecular motility of cytoplasmic dynein

Structural differences between dynein and kinesin suggest a unique molecular mechanism of dynein motility. Measuring the mechanical properties of a single molecule of dynein is crucial for revealing the mechanisms underlying its movement. We measured the step size and force produced by single molecules of active cytoplasmic dynein by using an optical trap and fluorescence imaging with a high temporal resolution. The velocity of dynein movement, 800 nm/s, is consistent with that reported in cells. The maximum force of 7-8 pN was independent of the ATP concentration and similar to that of kinesin. Dynein exhibited forward and occasional backwards steps of approximately 8 nm, independent of load. It is suggested that the large dynein heads take 16-nm steps by using an overlapping hand-over-hand mechanism.

Cargo-binding makes a wild-type single-headed myosin-VI move processively

Class VI myosin is an intracellular vesicle and organelle transporter that moves along actin filaments in a direction opposite to most other known myosin classes. The myosin-VI was expected to form a dimer to move processively along actin filaments with a hand-over-hand mechanism like other myosin organelle transporters. Recently, however, wild-type myosin-VI was demonstrated to be monomer and single-headed, casting a doubt on its processivity. By using single molecule techniques, we show that green-fluorescent-protein-tagged single-headed, wild-type myosin-VI does not move processively. However, when coupled to 200-nm polystyrene beads (comparable to intracellular vesicles in size) at a ratio of one head per bead, single-headed myosin-VI moves processively with large (40-nm) steps. The characteristics of this monomer-driven movement were different to that of artificial dimer-driven movement: Compared to the artificial dimer, the monomer-bead complex had a reduced stall force (1 pN compared to 2 pN), an average run length 2.5-fold shorter (91 nm compared to 220 nm) and load-dependent step size. Furthermore, we found that a monomer-bead complex moved more processively in a high viscous solution (40-fold higher than water) similar to cellular environment. Because the diffusion constant of the bead is 60-fold lower than myosin-VI heads alone in water, we propose a model in which the bead acts as a diffusional anchor for the myosin-VI, enhancing its rebinding following detachment and supporting processive movement of the bead-monomer complexes. Although a single-headed myosin-VI was able to move processively with a large cargo, the travel distance was rather short. Multiple molecules may be involved in the cargo transport for a long travel distance in cells.

Processivity of kinesin motility is enhanced on increasing temperature

Kinesin is a motor protein that processively moves step by step along a microtubule. To investigate the effects of temperature on run length, i.e., processivity of kinesin motility, we performed a single-molecular bead assay at temperature range of 20–40°C. An increase in the walking velocity of kinesin corresponded to the Arrhenius activation enthalpy of 48 kJ/mol, being consistent with the previous reports. Here, we found that the run length increased, that is, the kinesin processivity enhanced with increasing temperature. Then, we estimated the probability of detachment of kinesin from a microtubule per one 8-nm stepping event, and found that it diminishes from 0.014 to 0.006/step with increasing temperature from 20 to 40°C. And we noticed that prolonged incubation at 30, 35 and 40°C significantly slowed down the walking velocity, but further increased the run length and duration. Those results are interpreted according to the effect of temperature on the rate constants of some key kinetic steps in the ATPase cycle.

Vectorial loading of processive motor proteins: implementing a landscape picture

Individual processive molecular motors, of which conventional kinesin is the most studied quantitatively, move along polar molecular tracks and, by exerting a force F = (F(x),F(y),F(z)) on a tether, drag cellular cargoes, in vivo, or spherical beads, in vitro, taking up to hundreds of nanometre-scale steps. From observations of velocities and the dispersion of displacements with time, under measured forces and controlled fuel supply (typically ATP), one may hope to obtain insight into the molecular motions undergone in the individual steps. In the simplest situation, the load force F may be regarded as a scalar resisting force, F(x)<0, acting parallel to the track: however, experiments, originally by Gittes et al (1996 Biophys. J. 70 418), have imposed perpendicular (or vertical) loads, F(z)>0, while more recently Block and co-workers (2002 Biophys. J. 83 491, 2003 Proc. Natl Acad. Sci. USA 100 2351) and Carter and Cross (2005 Nature 435 308) have studied assisting (or reverse) loads, F(x)>0, and also sideways (or transverse) loads [Formula: see text]. We extend previous mechanochemical kinetic models by explicitly implementing a free-energy landscape picture in order to allow for the full vectorial nature of the force F transmitted by the tether. The load-dependence of the various forward and reverse transition rates is embodied in load distribution vectors, [Formula: see text] and [Formula: see text], which relate to substeps of the motor, and in next order, in compliance matrices [Formula: see text] and [Formula: see text]. The approach is applied specifically to discuss the experiments of Howard and co-workers (1996 Biophys. J. 70 418) in which the buckling of partially clamped microtubules was measured under the action of bound kinesin molecules which induced determined perpendicular loads. But in the normal single-bead assay it also proves imperative to allow for F(z)>0: the appropriate analysis for kinesin, suggesting that the motor 'crouches' on binding ATP prior to stepping, is sketched. It yields an expression for the velocity, V (F(x),F(z);[ATP]), needed to address the buckling experiments.

Cooperative cargo transport by several molecular motors

The transport of cargo particles that are pulled by several molecular motors in a cooperative manner is studied theoretically in this article. The transport properties depend primarily on the maximal number N of motor molecules that may pull simultaneously on the cargo particle. Because each motor must unbind from the filament after a finite number of steps but can also rebind to it again, the actual number of pulling motors is not constant but varies with time between zero and N. An increase in the maximal number N leads to a strong increase of the average walking distance (or run length) of the cargo particle. If the cargo is pulled by up to N kinesin motors, for example, the walking distance is estimated to be 5(N-1)/N micrometers, which implies that seven or eight kinesin molecules are sufficient to attain an average walking distance in the centimeter range. If the cargo particle is pulled against an external load force, this force is shared between the motors, which provides a nontrivial motor-motor coupling and a generic mechanism for nonlinear force-velocity relationships. With increasing load force, the probability distribution of the instantaneous velocity is shifted toward smaller values, becomes broader, and develops several peaks. Our theory is consistent with available experimental data and makes quantitative predictions that are accessible to systematic in vitro experiments.

Kinesin crouches to sprint but resists pushing

Recent optical trap experiments have applied resisting, assisting, and sideways loads to conventional kinesin moving on microtubules at fixed [ATP]. To gain insight into intermediate motions when the motor protein takes its 8.2-nm steps, the velocity and randomness data have been analyzed by using discrete-state stochastic models with a three-dimensional "energy landscape." The bead size and tether angle play a crucial role. The analysis implies that on binding ATP the motor "crouches," the point of attachment of the tether at the necklinker junction moving downward toward the microtubule by 0.5-0.7 nm, while inching forward by only 0.1-0.2 nm, before completing the step from a transition state by a unitary "sprint" of approximately 7.8 nm. These inferences accord with high-resolution observations that exclude a previously predicted substep of 1.8-2.1 nm. Assisting and leftward loads are opposed in that the perpendicular component of the tension in the tether is enhanced by approximately 2 pN, which reduces the velocity, but sideways lurching is not supported.

Entropy rectifies the Brownian steps of kinesin

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. The physical mechanism underlying the unidirectional bias of the kinesin steps is not fully understood. Here we explored the mechanical kinetics and thermodynamics of forward and backward kinesin steps by analyzing their temperature and load dependence. Results show that the frequency asymmetry between forward and backward steps is produced by entropy. Furthermore, the magnitude of the entropic asymmetry is 6 k(B)T, more than three times greater than expected from a current model, in which a mechanical conformational change within the kinesin molecular structure directly biases the kinesin steps forward. We propose that the stepping direction of kinesin is preferably caused by an entropy asymmetry resulting from the compatibility between the kinesin and microtubule interaction based on their polar structures.

The Neck Domain of Myosin II Primarily Regulates the Actomyosin Kinetics, not the Stepsize

In order to study the role of the neck domain of myosin in muscle contraction, we measured the steps of individual myosin II molecules engineered to have no neck domain (light chain-binding domain) by optical trapping nanometry. The actin filament and myosin cofilaments interacted on a glass surface to minimize the angle between them, and to minimize the interaction between myosin and the glass surface. The results showed that the average myosin stepsize did not change much when the neck domain was removed, but the sliding velocity decreased approximately fivefold. Furthermore, the duration of steps for neckless myosin was several times longer at saturated ATP concentration, indicating that the slower velocity was due to a slower dissociation rate of myosin heads from actin. From these data, we conclude that the neck domain of myosin-II primarily regulates the actomyosin kinetics, not the mechanics.

Mechanics of the kinesin step

Kinesin is a molecular walking machine that organizes cells by hauling packets of components directionally along microtubules. The physical mechanism that impels directional stepping is uncertain. We show here that, under very high backward loads, the intrinsic directional bias in kinesin stepping can be reversed such that the motor walks sustainedly backwards in a previously undescribed mode of ATP-dependent backward processivity. We find that both forward and backward 8-nm steps occur on the microsecond timescale and that both occur without mechanical substeps on this timescale. The data suggest an underlying mechanism in which, once ATP has bound to the microtubule-attached head, the other head undergoes a diffusional search for its next site, the outcome of which can be biased by an applied load.

Long-range cooperative binding of kinesin to a microtubule in the presence of ATP

Interaction of kinesin-coated latex beads with a single microtubule (MT) was directly observed by fluorescence microscopy. In the presence of ATP, binding of a kinesin bead to the MT facilitated the subsequent binding of other kinesin beads to an adjacent region on the MT that extended for micrometers in length. This cooperative binding was not observed in the presence of ADP or 5′-adenylylimidodiphosphate (AMP-PNP), where binding along the MT was random. Cooperative binding also was induced by an engineered, heterodimeric kinesin, WT/E236A, that could hydrolyze ATP, yet remained fixed on the MT in the presence of ATP. Relative to the stationary WT/E236A kinesin on a MT, wild-type kinesin bound preferentially in close proximity, but was biased to the plus-end direction. These results suggest that kinesin binding and ATP hydrolysis may cause a long-range state transition in the MT, increasing its affinity for kinesin toward its plus end. Thus, our study highlights the active involvement of MTs in kinesin motility.

Understanding mechanochemical coupling in kinesins using first-passage-time processes

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps, and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is explicitly taken into account. Using the method of first-passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly, are the same, although the probabilities of these events are different. It is concluded that the current theoretical view-that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis--is consistent with all available experimental observations for kinesins.

Biased binding of single molecules and continuous movement of multiple molecules of truncated single-headed kinesin

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.

Mechanochemical coupling of two substeps in a single myosin V motor

Myosin V is a double-headed processive molecular motor that moves along an actin filament by taking 36-nm steps. Using optical trapping nanometry with high spatiotemporal resolution, we discovered that there are two possible pathways for the 36-nm steps, one with 12- and 24-nm substeps, in this order, and the other without substeps. Based on the analyses of effects of ATP, ADP and 2,3-butanedione 2-monoxime (a reagent shown here to slow ADP release from actomyosin V) on the dwell time and the occurrence frequency of the main and the intermediate states, we propose that the 12-nm substep occurs after ATP binding to the bound trailing head and the 24-nm substep results from a mechanical step following the isomerization of an actomyosin-ADP state on the bound leading head. When the isomerization precedes the 12-nm substep, the 36-nm step occurs without substeps.

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

Mechanical Processes in Biochemistry

Mechanical processes are involved in nearly every facet of the cell cycle. Mechanical forces are generated in the cell during processes as diverse as chromosomal segregation, replication, transcription, translation, translocation of proteins across membranes, cell locomotion, and catalyzed protein and nucleic acid folding and unfolding, among others. Because force is a product of all these reactions, biochemists are beginning to directly apply external forces to these processes to alter the extent or even the fate of these reactions hoping to reveal their underlying molecular mechanisms. This review provides the conceptual framework to understand the role of mechanical force in biochemistry.

Single molecule processes on the stepwise movement of ATP-driven molecular motors

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.

Stochastic properties of actomyosin motor

The epoch-making techniques for manipulating a single myosin molecule have recently been developed, and the unitary mechanical reactions of a single actomyosin, muscle motor molecule, are directly measured. The data show that the unitary mechanical step during sliding along an actin filament of approximately 5.5 nm, but groups of two to five rapid steps in succession produce displacements of approximately 11-30 nm. The instances of multiple stepping are produced by single myosin heads during one biochemical cycle of ATP hydrolysis. Thus, the coupling between ATP hydrolysis cycle and mechanical step is variable, i.e. loose-coupling. Such a unique operation of actomyosin molecules is different from that of man-made machines, and most likely explains the flexible and effective mechanisms of molecular machines in the biosystems.

Stochastic processes in nano-biomachines revealed by single molecule detection

Proteins and their assemblies are in the size of nanometers and are exposed to thermal disturbances. Many molecular processes in these nano-biomachines are stochastic, reflecting the fact that the input energy level is comparable to that of thermal energy. These stochastic properties have been revealed by recently developed single molecule detection techniques. The movement of molecular motors, myosin, and kinesin, has been suggested to be thermally driven. Random thermal movement is biased using the energy of the ATP hydrolysis. Thus, the molecular motors may harness thermal energy. This unique mechanism may be important in understanding the operation of the biosystems.

Regional rheological differences in locomoting neutrophils

Intracellular rheology is a useful probe of the mechanisms underlying spontaneous or chemotactic locomotion and transcellular migration of leukocytes. We characterized regional rheological differences between the leading, body, and trailing regions of isolated, adherent, and spontaneously locomoting human neutrophils. We optically trapped intracellular granules and measured their displacement for 500 ms after a 100-nm step change in the trap position. Results were analyzed in terms of simple viscoelasticity and with the use of structural damping (stress relaxation follows a power law in time). Structural damping fit the data better than did viscoelasticity. Regional viscoelastic stiffness and viscosity or structural damping storage and loss moduli were all significantly lower in leading regions than in pooled body and/or trailing regions (the latter were not significantly different). Structural damping showed similar levels of elastic and dissipative stresses in body and/or trailing regions; leading regions were significantly more fluidlike (increased power law exponent). Cytoskeletal disruption with cytochalasin D or nocodazole made body and/or trailing regions approximately 50% less elastic and less viscous. Cytochalasin D completely suppressed pseudopodial formation and locomotion; nocodazole had no effect on leading regions. Neither drug changed the dissipation-storage energy ratio. These results differ from those of studies of neutrophils and other cell types probed at the cell membrane via beta(2)-integrin receptors, which suggests a distinct role for the cell cortex or focal adhesion complexes. We conclude that 1) structural damping well describes intracellular rheology, and 2) while not conclusive, the significantly more fluidlike behavior of the leading edge supports the idea that intracellular pressure may be the origin of motive force in neutrophil locomotion.

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 mum. 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 Mason's 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 mum, 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 moves by an asymmetric hand-over-hand mechanism

Kinesin is a double-headed motor protein that moves along microtubules in 8-nanometer steps. Two broad classes of model have been invoked to explain kinesin movement: hand-over-hand and inchworm. In hand-over-hand models, the heads exchange leading and trailing roles with every step, whereas no such exchange is postulated for inchworm models, where one head always leads. By measuring the stepwise motion of individual enzymes, we find that some kinesin molecules exhibit a marked alternation in the dwell times between sequential steps, causing these motors to "limp" along the microtubule. Limping implies that kinesin molecules strictly alternate between two different conformations as they step, indicative of an asymmetric, hand-over-hand mechanism.

Alternate fast and slow stepping of a heterodimeric kinesin molecule

A conventional kinesin molecule travels continuously along a microtubule in discrete 8-nm steps. This processive movement is generally explained by models in which the two identical heads of a kinesin move in a 'hand-over-hand' manner. Here, we show that a single heterodimeric kinesin molecule (in which one of the two heads is mutated in a nucleotide-binding site) exhibits fast and slow (with the dwell time at least 10 times longer than that of the fast step) 8-nm steps alternately, presumably corresponding to the displacement by the wild-type and mutant heads, respectively. Our results provide the first direct evidence for models in which the roles of the two heads alternate every 8-nm step.

Theoretical model for motility and processivity of two-headed molecular motors

The processive motion of two-headed molecular motors is studied theoretically by introducing a model that takes into account the coordinated motion of the constituent heads and the detachment process of heads from linear molecular tracks. The mean velocity, the mean run length, and the mean run time of the motor along the track are calculated numerically based on the Langevin equation. It turns out that the model, with appropriate choice of model parameters, can explain qualitatively the dependence of these quantities on the external load and adenosin triphosphate concentration observed experimentally for kinesin motors. Furthermore, we discuss how the motility and processivity of the motor are affected by various model parameters, which may be tested by experiments.

Single-particle tracking image microscopy

The techniques of single particle tracking (SPT) and optical force microscopy (OFM) as described above allow direct imaging of the motion of molecules in the membrane of live cells, and provide a means of controlling the movement by an almost noninvasive method. Combination of these techniques with other single-molecule methods, such as single-fluorophore imaging, allows direct comparison of motion at video rate (because faster than video rate imaging of fluorophore is still not generally feasible) to determine any effect due to the attached colloidal gold particle. Also, simultaneous use of the two techniques allows for monitoring two molecules, one at high time resolution. As such, the system can then be used in conjunction with green fluorescent protein (GFP) transfection to watch simultaneously the motion of an internal component of, say, a signaling pathway while seeing the motion of the transmembrane signaling receptor.

Loading direction regulates the affinity of ADP for kinesin

Kinesin is an ATP-driven molecular motor that moves processively along a microtubule. Processivity has been explained as a mechanism that involves alternating single- and double-headed binding of kinesin to microtubules coupled to the ATPase cycle of the motor. The internal load imposed between the two bound heads has been proposed to be a key factor regulating the ATPase cycle in each head. Here we show that external load imposed along the direction of motility on a single kinesin molecule enhances the binding affinity of ADP for kinesin, whereas an external load imposed against the direction of motility decreases it. This coupling between loading direction and enzymatic activity is in accord with the idea that the internal load plays a key role in the unidirectional and cooperative movement of processive motors.

Higher plant myosin XI moves processively on actin with 35 nm steps at high velocity

High velocity cytoplasmic streaming is found in various plant cells from algae to angiosperms. We characterized mechanical and enzymatic properties of a higher plant myosin purified from tobacco bright yellow-2 cells, responsible for cytoplasmic streaming, having a 175 kDa heavy chain and calmodulin light chains. Sequence analysis shows it to be a class XI myosin and a dimer with six IQ motifs in the light chain-binding domains of each heavy chain. Electron microscopy confirmed these predictions. We measured its ATPase characteristics, in vitro motility and, using optical trap nanometry, forces and movement developed by individual myosin XI molecules. Single myosin XI molecules move processively along actin with 35 nm steps at 7 micro m/s, the fastest known processive motion. Processivity was confirmed by actin landing rate assays. Mean maximal force was approximately 0.5 pN, smaller than for myosin IIs. Dwell time analysis of beads carrying single myosin XI molecules fitted the ATPase kinetics, with ADP release being rate limiting. These results indicate that myosin XI is highly specialized for generation of fast processive movement with concomitantly low forces.

Probing the kinesin reaction cycle with a 2D optical force clamp

With every step it takes, the kinesin motor undergoes a mechanochemical reaction cycle that includes the hydrolysis of one ATP molecule, ADPP(i) release, plus an unknown number of additional transitions. Kinesin velocity depends on both the magnitude and the direction of the applied load. Using specialized apparatus, we subjected single kinesin molecules to forces in differing directions. Sideways and forward loads up to 8 pN exert only a weak effect, whereas comparable forces applied in the backward direction lead to stall. This strong directional bias suggests that the primary working stroke is closely aligned with the microtubule axis. Sideways loads slow the motor asymmetrically, but only at higher ATP levels, revealing the presence of additional, load-dependent transitions late in the cycle. Fluctuation analysis shows that the cycle contains at least four transitions, and confirms that hydrolysis remains tightly coupled to stepping. Together, our findings pose challenges for models of kinesin motion.

Resource Letter: LBOT-1: Laser-based optical tweezers

This Resource Letter provides a guide to the literature on optical tweezers, also known as laser-based, gradient-force optical traps. Journal articles and books are cited for the following main topics: general papers on optical tweezers, trapping instrument design, optical detection methods, optical trapping theory, mechanical measurements, single molecule studies, and sections on biological motors, cellular measurements and additional applications of optical tweezers.

A simple kinetic model describes the processivity of myosin-v

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness-a quantitative measure of the stochastic deviations from uniform, constant-speed motion-with ATP concentration under both resisting and assisting loads, and indicates a substep of size d(0) approximately 13-14 nm (from the ATP-binding state) that appears to accord with independent observations.

Single fungal kinesin motor molecules move processively along microtubules

Conventional kinesins are two-headed molecular motors that move as single molecules micrometer-long distances on microtubules by using energy derived from ATP hydrolysis. The presence of two heads is a prerequisite for this processive motility, but other interacting domains, like the neck and K-loop, influence the processivity and are implicated in allowing some single-headed kinesins to move processively. Neurospora kinesin (NKin) is a phylogenetically distant, dimeric kinesin from Neurospora crassa with high gliding speed and an unusual neck domain. We quantified the processivity of NKin and compared it to human kinesin, HKin, using gliding and fluorescence-based processivity assays. Our data show that NKin is a processive motor. Single NKin molecules translocated microtubules in gliding assays on average 2.14 micro m (N = 46). When we tracked single, fluorescently labeled NKin motors, they moved on average 1.75 micro m (N = 182) before detaching from the microtubule, whereas HKin motors moved shorter distances (0.83 micro m, N = 229) under identical conditions. NKin is therefore at least twice as processive as HKin. These studies, together with biochemical work, provide a basis for experiments to dissect the molecular mechanisms of processive movement.

Equilibrium and transition between single- and double-headed binding of kinesin as revealed by single-molecule mechanics

Kinesin is a processive motor protein that "walks" on a microtubule toward its plus end. We reported previously that the distribution of unbinding force and elastic modulus for a single kinesin-microtubule complex was either unimodal or bimodal depending on the nucleotide states of the kinesin heads, hence showing that the kinesin may bind the microtubule either with one head or with both heads at once. Here, we found that the shape of the unbinding-force distribution depends both on the loading rate and on the manner of loading not only in the presence of AMP-PNP but also in the absence of nucleotides. Irrespective of the nucleotide state and the loading conditions examined here, the unbinding force obtained by loading directed toward the minus end of microtubule was 45% greater than that for plus end-directed loading. These results could be explained by a model in which equilibrium exists between single- and double-headed binding and the load (F) dependence of lifetime, tau(F), of each binding is expressed by tau(F) = tau(0)exp(-Fd/k(B)T), where tau(0) is the lifetime without external load and d a characteristic distance, both of which depend on single- or double-headed binding, k(B), the Boltzmann constant and T, the absolute temperature. The model analysis showed that the forward and backward rates of transition from single- to double-headed binding are 2 and 0.2/s for the AMP-PNP state, and 70 and 7/s for the nucleotide-free state. Moreover, in the presence of AMP-PNP, we detected the moment of transition from single- to double-headed binding through an abrupt increase in the elastic modulus and estimated the transition rate to be approximately 1/s, which is consistent with the model analysis.

Coordination of kinesin's two heads studied with mutant heterodimers

A conventional kinesin molecule has two identical catalytic domains (heads) and is thought to use them alternately to move processively, with 8-nm steps. To clarify how each head contributes to the observed steps, we have constructed heterodimeric kinesins that consist of two distinct heads. The heterodimers in which one of the heads is mutated in a microtubule-binding loop moved processively, even when the parent mutant homodimers bound too weakly to retain microtubules in microtubule-gliding assays. The velocities of the heterodimers were only slightly higher than those of the mutant homodimers, although mixtures of these weak-binding mutant homodimers and the WT dimers moved microtubules at a velocity similar to the WT. Thus, the mutant head affects the motility of the WT head only when they are in the same molecule. The maximum force a single heterodimer produced in optical trapping nanometry was intermediate between the WT and mutant homodimers, indicating that both heads contribute to the maximum force at the same time. These results demonstrate close collaboration of kinesin's two heads in producing force and motility.

Fluctuations and randomness of movement of the bead powered by a single kinesin molecule in a force-clamped motility assay: Monte Carlo simulations

The motility assay of K. Visscher, M. J. Schnitzer, and S. M. Block (Nature, 400:184-189, 1999) in which the movement of a bead powered by a single kinesin motor can be measured is a very useful tool in characterizing the force-dependent steps of the mechanochemical cycle of kinesin motors, because in this assay the external force applied to the bead can be controlled (clamped) arbitrarily. However, because the bead is elastically attached to the motor and the response of the clamp is not fast enough to compensate the Brownian motion of the bead, interpretation or analysis of the data obtained from the assay is not trivial. In a recent paper (Y. Chen and B. Yan, Biophys. Chem. 91:79-91, 2001), we showed how to evaluate the mean velocity of the bead and the motor in the motility assay for a given mechanochemical cycle. In this paper we extend the study to the evaluation of the fluctuation or the randomness of the velocity using a Monte Carlo simulation method. Similar to the mean, we found that the randomness of the velocity of the motor is also influenced by the parameters that affect the dynamic behavior of the bead, such as the viscosity of the medium, the size of the bead, the stiffness of the elastic element connecting the bead and the motor, etc. The method presented in this paper should be useful in modeling the kinetic mechanism of any processive motor (such as conventional kinesin and myosin V) based on measured force-clamp motility data.

Chemomechanical coupling of the forward and backward steps of single kinesin molecules

The molecular motor kinesin travels processively along a microtubule in a stepwise manner. Here we have studied the chemomechanical coupling of the hydrolysis of ATP to the mechanical work of kinesin by analysing the individual stepwise movements according to the directionality of the movements. Kinesin molecules move primarily in the forward direction and only occasionally in the backward direction. The hydrolysis of a single ATP molecule is coupled to either the forward or the backward movement. This bidirectional movement is well described by a model of Brownian motion assuming an asymmetric potential of activation energy. Thus, the stepwise movement along the microtubule is most probably due to Brownian motion that is biased towards the forward direction by chemical energy stored in ATP molecules.

Diffusion and directed motion in cellular transport

We study the motion of a probe driven by microtubule-associated motors within a living eukaryotic cell. The measured mean square displacement, <x(t)2> of engulfed 2 and 3 microm diameter microspheres shows enhanced diffusion scaling as t(3/2) at short times, with a clear crossover to ordinary or subdiffusive scaling, i.e., t(gamma) with gamma less than or equal to 1, at long times. Using optical tweezers we tried to move the engulfed bead within the cell in order to relate the anomalous diffusion scaling to the density of the network in which the bead is embedded. Results show that the larger beads, 2 and 3 microm diameter, must actively push the cytoskeleton filaments out of the way in order to move, whereas smaller beads of 1 microm diameter can be "rattled" within a cage. The 1 microm beads also perform an enhanced diffusion but with a smaller and less consistent exponent 1.2<gamma<1.45. We interpret the half-integer power observed with large beads based on two diverse phenomena widely studied in purified cytoskeleton filaments: (1) the motion of the intracellular probe results from random forces generated by motor proteins rather than thermal collisions for classical Brownian particles, and (2) thermal bending modes of these semiflexible polymers lead to anomalous subdiffusion of particles embedded in purified gel networks or attached to single filaments, with <x(t)2> approximately t(3/4). In the case of small beads, there may also be a Brownian contribution to the motion that results in a smaller exponent.

Surpassing the standard quantum limit for optical imaging using nonclassical multimode light

Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.