Theoretical formalism for kinesin motility I. Bead movement powered by single one-headed kinesins

The directional movement on a microtubule of a plastic bead connected elastically to a single one-headed kinesin motor is studied theoretically. The kinesin motor can bind and unbind to periodic binding sites on the microtubule and undergo conformational changes while catalyzing the hydrolysis of ATP. An analytic formalism relating the dynamics of the bead and the ATP hydrolysis cycle of the motor is derived so that the calculation of the average velocity of the bead can be easily carried out. The formalism was applied to a simple three-state biochemical model to investigate how the velocity of the bead movement is affected by the external load, the diffusion coefficient of the bead, and the stiffness of the elastic element connecting the bead and the motor. The bead velocity was found to be critically dependent on the diffusion coefficient of the bead and the stiffness of the elastic element. A linear force-velocity relation was found for the model no matter whether the bead velocity was modulated by the diffusion coefficient of the bead or by the externally applied load. The formalism should be useful in modeling the mechanisms of chemimechanical coupling in kinesin motors based on in vitro motility data.     

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.     

The bidirectional depolymerizer MCAK generates force by disassembling both microtubule ends

During cell division the replicated chromosomes are segregated precisely towards the spindle poles. Although many cellular processes involving motility require ATP-fuelled force generation by motor proteins, most models of the chromosome movement invoke the release of energy stored at strained (owing to GTP hydrolysis) plus ends of microtubules. This energy is converted into chromosome movement through passive couplers, whereas the role of molecular motors is limited to the regulation of microtubule dynamics. Here we report, that the microtubule-depolymerizing activity of MCAK (mitotic centromere-associated kinesin), the founding member of the kinesin-13 family, is accompanied by the generation of significant tension-remarkably, at both microtubule ends. An MCAK-decorated bead strongly attaches to the microtubule side, but readily slides along it in either direction under weak external loads and tightly captures and disassembles both microtubule ends. We show that the depolymerization force increases with the number of interacting MCAK molecules and is ～1?pN per motor. These results provide a simple model for the generation of driving force and the regulation of chromosome segregation by the activity of MCAK at both kinetochores and spindle poles through a 'side-sliding, end-catching' mechanism.     

A bidirectional kinesin motor in live Drosophila embryos

Spindle assembly and elongation involve poleward and away-from-the-pole forces produced by microtubule dynamics and spindle-associated motors. Here, we show that a bidirectional Drosophila Kinesin-14 motor that moves either to the microtubule plus or minus end in vitro unexpectedly causes only minor spindle defects in vivo. However, spindles of mutant embryos are longer than wild type, consistent with increased plus-end motor activity. Strikingly, suppressing spindle dynamics by depriving embryos of oxygen causes the bidirectional motor to show increased accumulation at distal or plus ends of astral microtubules relative to wild type, an effect not observed for a mutant motor defective in motility. Increased motor accumulation at microtubule plus ends may be due to increased slow plus-end movement of the bidirectional motor under hypoxia, caused by perturbation of microtubule dynamics or inactivation of the only other known Drosophila minus-end spindle motor, cytoplasmic dynein. Negative-stain electron microscopy images are consistent with highly cooperative motor binding to microtubules, and gliding assays show dependence on motor density for motility. Mutant effects of the bidirectional motor on spindle function may be suppressed under normal conditions by motor: motor interactions and minus-end movement induced by spindle dynamics. These forces may also bias wild-type motor movement toward microtubule minus ends in live cells. Our findings link motor : motor interactions to function in vivo by showing that motor density, together with cellular dynamics, may influence motor function in live cells.     

Kinetics: a tool to study molecular motors

Molecular motors are enzymes that couple the energy from nucleoside triphosphate hydrolysis to movement along a filament lattice. The three cytoskeletal motor superfamilies include myosin, dynein, and kinesin. However, in the last decade it has become apparent that the nucleic acid-based enzymes (DNA and RNA polymerases as well as the DNA helicases) share a number of mechanistic features in common with the microtubule and actin motors despite the fact that their cellular functions are so different. This review addresses the mechanistic approaches that have been used to study molecular motors. We discuss the basic biochemical techniques used to characterize a protein preparation, including active site determination and steady-state kinetics. In addition, we present the transient-state kinetic approaches used to define a mechanochemical cycle. We attempt to integrate the information obtained from kinetic studies within the context of motility results to provide a better understanding of the contribution of each approach for dissecting unidirectional force generation.     

Microtubule motors in spindle and chromosome motility.

Many of the kinesin microtubule motor proteins discovered during the past 8-9 years have roles in spindle assembly and function or chromosome movement during meiosis or mitosis. The discovery of kinesin motor proteins with a clear involvement in spindle and chromosome motility, together with recent evidence that cytoplasmic dynein plays a role in chromosome distribution, has attracted great interest. The identification of microtubule motors that function in chromosome distribution represents a major advance in understanding the forces that underlie chromosome and spindle movements during cell division.     

An automated two-dimensional optical force clamp for single molecule studies

We constructed a next-generation optical trapping instrument to study the motility of single motor proteins, such as kinesin moving along a microtubule. The instrument can be operated as a two-dimensional force clamp, applying loads of fixed magnitude and direction to motor-coated microscopic beads moving in vitro. Flexibility and automation in experimental design are achieved by computer control of both the trap position, via acousto-optic deflectors, and the sample position, using a three-dimensional piezo stage. Each measurement is preceded by an initialization sequence, which includes adjustment of bead height relative to the coverslip using a variant of optical force microscopy (to +/-4 nm), a two-dimensional raster scan to calibrate position detector response, and adjustment of bead lateral position relative to the microtubule substrate (to +/-3 nm). During motor-driven movement, both the trap and stage are moved dynamically to apply constant force while keeping the trapped bead within the calibrated range of the detector. We present details of force clamp operation and preliminary data showing kinesin motor movement subject to diagonal and forward loads.     

Myosin-IXb is a single-headed and processive motor.

Class IX myosins are unique among the many classes of known actin-based motors in that the tail region of these myosins contains a GTPase-activating protein domain for the small GTP-binding protein, Rho. Previous studies on human myosin-IXb indicate that this myosin is mechanochemically active and exhibits actin-binding properties similar to the processive motor, myosin-Va. Motility analysis of antibody-tethered myosin-IXb performed using the sliding actin filament assay indicates that this myosin does exhibit properties characteristic of a processive motor. Like myosin-Va, the velocity of myosin-IXb remains constant (38.2 +/- 1.2 nm/s) even at single motor/filament densities. At low motor densities, filaments can be seen passing through and pivoting about single points on the motility surface. Analysis of filament landing rates as a function of motor density also indicates that a single motor is sufficient for filament movement. However, in contrast to myosin-Va, which uses coordinated motion of its two heads to move processively along the filament, hydrodynamic and chemical cross-linking studies indicate that under the conditions tested, myosin-IXb is a single-headed motor consisting of a single heavy chain and associated light chains.     

On tracks and locomotives: the long route of DNA to the nucleus

Molecular motors have prominent functions in organelle transport, cytoskeletal organization, division and motility. The dyneins are one of the three families of cytoskeleton-based molecular motors and they travel along the cytoplasmic microtubule network towards the minus end of the microtubule. This directed movement is used by DNA viruses to deliver their infectious genome and proteins to the host cell nucleus. In recent studies, it has been hypothesized that Agrobacterium species use a similar pathway to deliver their infectious unit--a large complex between single-stranded DNA and proteins--to the host cell nucleus and that a karyophilic protein carrier that can deliver synthetic DNA to the nucleus is also driven by a dynein motor. These studies shed light on the mechanism of Agrobacterium-mediated genetic transformation and could lead to new methods for the efficient transfection of synthetic DNA.     

Directional loading of the kinesin motor molecule as it buckles a microtubule.

Single kinesin motor molecules were observed to buckle the microtubules along which they moved in a modified in vitro gliding assay. In this assay a central portion of the microtubule was clamped to the glass substrate via biotin-streptavidin bonds, while the plus end of the microtubule was free to interact with motors adsorbed at low density to the substrate. A statistical analysis of the length of microtubules buckled by single motors showed a decreasing probability of buckling for loads greater than 4-6 pN parallel to the filament. This is consistent with kinesin stalling forces found in other experiments. A detailed analysis of some buckling events allowed us to estimate both the magnitude and direction of the loading force as it developed a perpendicular component tending to pull the motor away from the microtubule. We also estimated the motor speed as a function of this changing vector force. The kinesin motors consistently reached unexpectedly high speeds as the force became nonparallel to the direction of motor movement. Our results suggest that a perpendicular component of load does not hinder the kinesin motor, but on the contrary causes the motor to move faster against a given parallel load. Because the perpendicular force component speeds up the motor but does no net work, perpendicular force acts as a mechanical catalyst for the reaction. A simple explanation is that there is a spatial motion of the kinesin molecule during its cycle that is rate-limiting under load; mechanical catalysis results if this motion is oriented away from the surface of the microtubule.     

Kinesin velocity increases with the number of motors pulling against viscoelastic drag

Although the properties of single kinesin molecular motors are well understood, it is not clear whether multiple motors pulling a single vesicle in a cell cooperate or interfere with one another. To learn how small numbers of motors interact, microtubule gliding assays were carried out with full-length Drosophila kinesin in a novel motility medium containing xanthan, a stiff, water-soluble polysaccharide. At 2 mg/ml xanthan, the zero-shear viscosity of this medium is 1,000 times the viscosity of water, similar to cellular viscosity. To mimic the rheological drag force on the motors when attached to a vesicle in a cell, we attached a 2 μm bead to one end of the microtubule (MT). During gliding assays in our novel medium, the moving bead exerted a drag force of 4–15 pN on the kinesins pulling the MT. The velocity of MTs with an attached bead increased with MT length and with kinesin concentration. The increase with MT length arose because the number of motors is directly proportional to MT length. Our results show that small numbers of kinesins cooperate constructively when pulling against a viscoelastic drag. In the absence of a bead but still in the viscous medium, MT velocity was independent of MT length and kinesin concentration because the thin MT, like a snake moving through grass, was able to move between xanthan molecules with little resistance. A minimal shared-load model in which the number of motors is proportional to MT length fits the observed dependence of gliding velocity on MT length and kinesin concentration.     

The family-specific K-loop influences the microtubule on-rate but not the superprocessivity of kinesin-3 motors

The kinesin-3 family (KIF) is one of the largest among the kinesin superfamily and an important driver of a variety of cellular transport events. Whereas all kinesins contain the highly conserved kinesin motor domain, different families have evolved unique motor features that enable different mechanical and functional outputs. A defining feature of kinesin-3 motors is the presence of a positively charged insert, the K-loop, in loop 12 of their motor domains. However, the mechanical and functional output of the K-loop with respect to processive motility of dimeric kinesin-3 motors is unknown. We find that, surprisingly, the K-loop plays no role in generating the superprocessive motion of dimeric kinesin-3 motors (KIF1, KIF13, and KIF16). Instead, we find that the K-loop provides kinesin-3 motors with a high microtubule affinity in the motor''s ADP-bound state, a state that for other kinesins binds only weakly to the microtubule surface. A high microtubule affinity results in a high landing rate of processive kinesin-3 motors on the microtubule surface. We propose that the family-specific K-loop contributes to efficient kinesin-3 cargo transport by enhancing the initial interaction of dimeric motors with the microtubule track.     

Mitochondria on the move

Interactions of mitochondria with the cytoskeleton are crucial for normal mitochondrial function and for localization of the organelle at its sites of action within cells. Early studies revealed a role for microtubule motors in mitochondrial motility in neurons and other cell types. Here, we describe advances in our understanding of mitochondrial movement and distribution. Specifically, we review recent studies on proteins that mediate or regulate the interaction between motor molecules and the organelle, motor-independent mechanisms for mitochondrial motility, anchorage of mitochondria at cortical sites within cells and links between mitochondria-cytoskeleton interactions and mitochondrial plasticity.     

Modulation of Kinesin’s Load-Bearing Capacity by Force Geometry and the Microtubule Track

Kinesin motors and their associated microtubule tracks are essential for long-distance transport of cellular cargos. Intracellular activity and proper recruitment of kinesins is regulated by biochemical signaling, cargo adaptors, microtubule-associated proteins, and mechanical forces. In this study, we found that the effect of opposing forces on the kinesin-microtubule attachment duration depends strongly on experimental assay geometry. Using optical tweezers and the conventional single-bead assay, we show that detachment of kinesin from the microtubule is likely accelerated by forces vertical to the long axis of the microtubule due to contact of the single bead with the underlying microtubule. We used the three-bead assay to minimize the vertical force component and found that when the opposing forces are mainly parallel to the microtubule, the median value of attachment durations between kinesin and microtubules can be up to 10-fold longer than observed using the single-bead assay. Using the three-bead assay, we also found that not all microtubule protofilaments are equivalent interacting substrates for kinesin and that the median value of attachment durations of kinesin varies by more than 10-fold, depending on the relative angular position of the forces along the circumference of the microtubule. Thus, depending on the geometry of forces across the microtubule, kinesin can switch from a fast detaching motor (median attachment duration <0.2 s) to a persistent motor that sustains attachment (median attachment duration >3 s) at high forces (5 pN). Our data show that the load-bearing capacity of the kinesin motor is highly variable and can be dramatically affected by off-axis forces and forces across the microtubule lattice, which has implications for a range of cellular activities, including cell division and organelle transport.     

Kar3Vik1, a member of the kinesin-14 superfamily, shows a novel kinesin microtubule binding pattern

Kinesin-14 motors generate microtubule minus-end-directed force used in mitosis and meiosis. These motors are dimeric and operate with a nonprocessive powerstroke mechanism, but the role of the second head in motility has been unclear. In Saccharomyces cerevisiae, the Kinesin-14 Kar3 forms a heterodimer with either Vik1 or Cik1. Vik1 contains a motor homology domain that retains microtubule binding properties but lacks a nucleotide binding site. In this case, both heads are implicated in motility. Here, we show through structural determination of a C-terminal heterodimeric Kar3Vik1, electron microscopy, equilibrium binding, and motility that at the start of the cycle, Kar3Vik1 binds to or occludes two αβ-tubulin subunits on adjacent protofilaments. The cycle begins as Vik1 collides with the microtubule followed by Kar3 microtubule association and ADP release, thereby destabilizing the Vik1-microtubule interaction and positioning the motor for the start of the powerstroke. The results indicate that head-head communication is mediated through the adjoining coiled coil.     

Plus-end motors override minus-end motors during transport of squid axon vesicles on microtubules

Plus- and minus-end vesicle populations from squid axoplasm were isolated from each other by selective extraction of the minus-end vesicle motor followed by 5'-adenylyl imidodiphosphate (AMP-PNP)- induced microtubule affinity purification of the plus-end vesicles. In the presence of cytosol containing both plus- and minus-end motors, the isolated populations moved strictly in opposite directions along microtubules in vitro. Remarkably, when treated with trypsin before incubation with cytosol, purified plus-end vesicles moved exclusively to microtubule minus ends instead of moving in the normal plus-end direction. This reversal in the direction of movement of trypsinized plus-end vesicles, in light of further observation that cytosol promotes primarily minus-end movement of liposomes, suggests that the machinery for cytoplasmic dynein-driven, minus-end vesicle movement can establish a functional interaction with the lipid bilayers of both vesicle populations. The additional finding that kinesin overrides cytoplasmic dynein when both are bound to bead surfaces indicates that the direction of vesicle movement could be regulated simply by the presence or absence of a tightly bound, plus-end kinesin motor; being processive and tightly bound, the kinesin motor would override the activity of cytoplasmic dynein because the latter is weakly bound to vesicles and less processive. In support of this model, it was found that (a) only plus-end vesicles copurified with tightly bound kinesin motors; and (b) both plus- and minus-end vesicles bound cytoplasmic dynein from cytosol.     

The coordination of protein motors and the kinetic behavior of microtubule--a computational study

Utilizing the mechanical energy converted from chemical energy through hydrolysis of ATP, motor proteins drive cytoskeleton filaments to move in various biological systems. Recent technological advance has shown the potential of the motor proteins for powering future nano-bio-mechanical systems. In order to effectively use motor proteins as a biological motor, the interaction between the protein motors and bio-filaments needs to be well clarified, since such interaction is largely influenced by many factors, such as the coordination among the motors, their dynamic behavior, physical properties of microtubules, and the viscosity of solution involved, etc. In this study, a two-dimensional model was proposed to simulate the motion of a microtubule driven by protein motors based on a dissipative particle dynamics (DPD) method with attempt to correlate the microtubule's kinetic behavior to the coordination among protein motors.     

Controlling kinesin by reversible disulfide cross-linking. Identifying the motility-producing conformational change

Conventional kinesin, a dimeric molecular motor, uses ATP-dependent conformational changes to move unidirectionally along a row of tubulin subunits on a microtubule. Two models have been advanced for the major structural change underlying kinesin motility: the first involves an unzippering/zippering of a small peptide (neck linker) from the motor catalytic core and the second proposes an unwinding/rewinding of the adjacent coiled-coil (neck coiled-coil). Here, we have tested these models using disulfide cross-linking of cysteines engineered into recombinant kinesin motors. When the neck linker motion was prevented by cross-linking, kinesin ceased unidirectional movement and only showed brief one-dimensional diffusion along microtubules. Motility fully recovered upon adding reducing agents to reverse the cross-link. When the neck linker motion was partially restrained, single kinesin motors showed biased diffusion towards the microtubule plus end but could not move effectively against a load imposed by an optical trap. Thus, partial movement of the neck linker suffices for directionality but not for normal processivity or force generation. In contrast, preventing neck coiled-coil unwinding by disulfide cross-linking had relatively little effect on motor activity, although the average run length of single kinesin molecules decreased by 30-50%. These studies indicate that conformational changes in the neck linker, not in the neck coiled-coil, drive processive movement by the kinesin motor.     

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.     

The E-hook of tubulin interacts with kinesin's head to increase processivity and speed

Kinesins are dimeric motor proteins that move processively along microtubules. It has been proposed that the processivity of conventional kinesins is increased by electrostatic interactions between the positively charged neck of the motor and the negatively charged C-terminus of tubulin (E-hook). In this report we challenge this anchoring hypothesis by studying the motility of a fast fungal kinesin from Neurospora crassa (NcKin). NcKin is highly processive despite lacking the positive charges in the neck. We present a detailed analysis of how proteolytic removal of the E-hook affects truncated monomeric and dimeric constructs of NcKin. Upon digestion we observe a strong reduction of the processivity and speed of dimeric motor constructs. Monomeric motors with truncated or no neck display the same reduction of microtubule gliding speed as dimeric constructs, suggesting that the E-hook interacts with the head only. The E-hook has no effect on the strongly bound states of NcKin as microtubule digestion does not alter the stall forces produced by single dimeric motors, suggesting that the E-hook affects the interaction site of the kinesin.ADP-head and the microtubule. In fact, kinetic and binding experiments indicate that removal of the E-hook shifts the binding equilibrium of the weakly attached kinesin.ADP-head toward a more strongly bound state, which may explain reduced processivity and speed on digested microtubules.