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.     

Use of Stopped-Flow Fluorescence and Labeled Nucleotides to Analyze the ATP Turnover Cycle of Kinesins

The kinesin superfamily of microtubule associated motor proteins share a characteristic motor domain which both hydrolyses ATP and binds microtubules. Kinesins display differences across the superfamily both in ATP turnover and in microtubule interaction. These differences tailor specific kinesins to various functions such as cargo transport, microtubule sliding, microtubule depolymerization and microtubule stabilization. To understand the mechanism of action of a kinesin it is important to understand how the chemical cycle of ATP turnover is coupled to the mechanical cycle of microtubule interaction. To dissect the ATP turnover cycle, one approach is to utilize fluorescently labeled nucleotides to visualize individual steps in the cycle. Determining the kinetics of each nucleotide transition in the ATP turnover cycle allows the rate-limiting step or steps for the complete cycle to be identified. For a kinesin, it is important to know the rate-limiting step, in the absence of microtubules, as this step is generally accelerated several thousand fold when the kinesin interacts with microtubules. The cycle in the absence of microtubules is then compared to that in the presence of microtubules to fully understand a kinesin’s ATP turnover cycle. The kinetics of individual nucleotide transitions are generally too fast to observe by manually mixing reactants, particularly in the presence of microtubules. A rapid mixing device, such as a stopped-flow fluorimeter, which allows kinetics to be observed on timescales of as little as a few milliseconds, can be used to monitor such transitions. Here, we describe protocols in which rapid mixing of reagents by stopped-flow is used in conjunction with fluorescently labeled nucleotides to dissect the ATP turnover cycle of a kinesin.     

Alternating site ATPase pathway of rat conventional kinesin

The pathway of ATP hydrolysis by rat kinesin was established by pre-steady-state kinetic methods. A 406-residue long N-terminal fragment was shown by sedimentation equilibrium analysis to form a dimer with a K(d) of 46 nm. The pathway of ATP hydrolysis follows the Gilbert-Johnson pathway determined previously for a similarsized N-terminal fragment of Drosophila conventional kinesin. However, the rates of ADP release were at least 3-fold faster, and ATP hydrolysis was approximately 5-fold faster. Paralleling our previous mechanistic data, these results support an alternating site ATPase pathway, including a captive head state as an intermediate in the kinesin ATPase cycle. The kinetic data presented in this report once again point to the importance of the captive head state and argue against a pathway that short-circuits this key intermediate. In addition, several unique aspects of the rat kinesin kinetics reveal new aspects of the ATPase-coupling mechanism. These studies provide a baseline set of kinetic parameters against which future studies of rat kinesin mutants may be evaluated and directly correlated with the structure of the dimeric kinesin.     

The kinesin-13 MCAK has an unconventional ATPase cycle adapted for microtubule depolymerization

Unlike other kinesins, members of the kinesin-13 subfamily do not move directionally along microtubules but, instead, depolymerize them. To understand how kinesins with structurally similar motor domains can have such dissimilar functions, we elucidated the ATP turnover cycle of the kinesin-13, MCAK. In contrast to translocating kinesins, ATP cleavage, rather than product release, is the rate-limiting step for ATP turnover by MCAK; unpolymerized tubulin and microtubules accelerate this step. Further, microtubule ends fully activate the ATPase by accelerating the exchange of ADP for ATP. This tuning of the cycle adapts MCAK for its depolymerization activity: lattice-stimulated ATP cleavage drives MCAK into a weakly bound nucleotide state that reaches microtubule ends by diffusion, and end-specific acceleration of nucleotide exchange drives MCAK into a strongly bound state that promotes depolymerization. This altered cycle accounts well for the different mechanical behaviour of this kinesin, which depolymerizes microtubules from their ends, compared to translocating kinesins that walk along microtubules. Thus, the kinesin motor domain is a nucleotide-dependent engine that can be differentially tuned for transport or depolymerization functions.     

The role of thermal activation in motion and force generation by molecular motors

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.     

Kinesin's biased stepping mechanism: amplification of neck linker zippering

A physically motivated model of kinesin's motor function is developed within the framework of rectified Brownian motion. The model explains how the amplification of neck linker zippering arises naturally through well-known formulae for overdamped dynamics, thereby providing a means to understand how weakly-favorable zippering leads to strongly favorable plus-directed binding of a free kinesin head to microtubule. Additional aspects of kinesin's motion, such as head coordination and rate-limiting steps, are directly related to the force-dependent inhibition of ATP binding to a microtubule bound head. The model of rectified Brownian motion is presented as an alternative to power stroke models and provides an alternative interpretation for the significance of ATP hydrolysis in the kinesin stepping cycle.     

Phenomenological analysis of ATP dependence of motor proteins

In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, I found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motors can be well approximated by a Michaelis-Menten like formula V = [ATP]k(F)L([ATP] + K(M)), with L the step size, and k(F) the external load F dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant K(M) for substall, superstall and negative external load indicates, the configurations at which ATP molecule can bind to motor heads for these three cases might be different, though the expression of k(F) as a function of F might be unchanged for any external load F. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data.     

How occasional backstepping can speed up a processive motor protein

Fueled by the hydrolysis of ATP, the motor protein kinesin literally walks on two legs along the biopolymer microtubule. The number of accidental backsteps that kinesin takes appears to be much larger than what one would expect given the amount of free energy that ATP hydrolysis makes available. This indicates that backsteps are not simply the forward stepping cycle run backwards. We propose here a simple effective model that consistently includes the backstep transition. Using this model, we show how more backstepping increases the entropy of the final state, and probably also the activation state, thus reducing their free energy. This free energy reduction of the activation state (related to backstepping) speeds up the catalytic cycle of the kinesin, making both forward and backward steps more frequent. As a consequence, maximal net forward speed is achieved at nonzero backstep percentage. In addition, the optimal backstep percentage coincides with the backstep percentage measured for kinesin. This result suggests that, through natural selection, kinesin could have evolved to maximal speed.     

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.     

Kinesin has three nucleotide-dependent conformations. Implications for strain-dependent release

Although crystallographic information is available on several nucleotide-induced states in myosin, little is known about the corresponding structural changes in kinesin, since a crystallographic model is only available for the kinesin:ADP complex. This makes it difficult to characterize at a molecular level the structural changes that occur in this motor through the course of its ATPase cycle. In this study, we report on the production of a series of single tryptophan mutants of a monomeric human kinesin motor domain, which demonstrate nucleotide-dependent changes in microtubule affinity that are similar to wild type. We have used these mutations to measure intramolecular distances in both strong and weak binding states, using fluorescence resonance energy transfer. This work provides direct evidence that movement of the switch II loop and helix are essential to mediate communication between the catalytic and microtubule binding sites, evidence that is supported as well by molecular modeling. Kinetic studies of fluorescent nucleotide binding to these mutants are consistent with these distance changes, and demonstrate as well that binding of ADP produces two structural transitions, neither of which are identical to that produced by the binding of ATP. This study provides a basis for understanding current structural models of the kinesin mechanochemical cycle.     

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.     

驱动蛋白结构与运动机制

驱动蛋白是一类能够利用ATP水解释放的化学能驱动其所携带的“货物”分子沿着微管（microtubule,MT）定向运动的分子马达,在细胞器运输、有丝分裂、轴突运输等方面有着重要的生理作用。随着驱动蛋白结合ADP、ATP和未结合核苷酸（APO）三种特征状态的晶体结构的解析,驱动蛋白构象变化的研究得到了进一步发展,而在力产生机制和运动模型方面仍然存在较大争议。本文以kinesin-1家族为例,分析了驱动蛋白三种特征状态结构的特点、状态结构间的构象转变,论述了驱动蛋白的力产生机制和整个迈步过程。并探讨了驱动蛋白的运动模型,同时采用分子动力学模拟比较了驱动蛋白的两种迈步方式,为深入研究驱动蛋白提供了一定的理论计算。最后,基于本课题组对复杂体系的研究,对驱动蛋白体系的控制机制提出了新的假设,并对未来的研究方向进行了展望。     

Load and Pi control flux through the branched kinetic cycle of myosin V

Myosin V is a processive actin-based motor protein that takes multiple 36-nm steps to deliver intracellular cargo to its destination. In the laser trap, applied load slows myosin V heavy meromyosin stepping and increases the probability of backsteps. In the presence of 40 mm phosphate (P(i)), both forward and backward steps become less load-dependent. From these data, we infer that P(i) release commits myosin V to undergo a highly load-dependent transition from a state in which ADP is bound to both heads and its lead head trapped in a pre-powerstroke conformation. Increasing the residence time in this state by applying load increases the probability of backstepping or detachment. The kinetics of detachment indicate that myosin V can detach from actin at two distinct points in the cycle, one of which is turned off by the presence of P(i). We propose a branched kinetic model to explain these data. Our model includes P(i) release prior to the most load-dependent step in the cycle, implying that P(i) release and load both act as checkpoints that control the flux through two parallel pathways.     

Modification of the microtubule-binding and ATPase activities of kinesin by N-ethylmaleimide (NEM) suggests a role for sulfhydryls in fast axonal transport

N-Ethylmaleimide, an agent which alkylates free sulfhydryls in proteins, has been used to probe the role of sulfhydryls in kinesin, a motor protein for the movement of membrane-bounded organelles in fast axonal transport. When squid axoplasm is perfused with concentrations of NEM higher than 0.5 mM, organelle movements in both the anterograde and retrograde directions cease, and the vesicles remain attached to microtubules. Incubation of highly purified bovine brain kinesin with similar concentrations of NEM modifies the enzyme's microtubule-stimulated ATPase activity and promotes the binding of kinesin to microtubules in the presence of ATP. These results suggest that alkylation of sulfhydryls on kinesin alters the conformation of the protein in a manner that profoundly affects its interactions with ATP and microtubules. The NEM-sensitive sulfhydryls, therefore, may provide a valuable tool for the dissection of functional domains of the kinesin molecule and for understanding the mechanochemical cycle of this enzyme.     

Theoretical formalism for bead movement powered by single two-headed motors in a motility assay

Kinesins and dyneins are protein motors that can use the free energy of ATP hydrolysis to carry a cargo and move uni-directionally along a microtubule filament. The purpose of this paper is to derive the formalism connecting the ATP-driven translocation reactions of these motors on microtubule filaments and the movement of the bead carried by the motor in a motility assay in which the bead is clamped at an arbitrary constant force. The formalism is thus useful in elucidating the load-dependent kinetic mechanism of the free-energy transduction of the motor using the mechanical data obtained from the motility assay. The formalism is also useful in assessing the effect on the measured motility data of various physical and hydrodynamic parameters of the assay, such as the size of the bead, the viscosity of the medium, the stiffness of the elastic element connecting the motor and the bead, etc. In a previous paper [Biophys. J. 67 (2000) 313] (hereafter referred to as paper I), we have derived the formalism for the case that the motor in the assay has only one head. In this paper we extend the derivation to the case that the motor is two-headed. The formalism is derived based on a simple two-state hand-over-hand model for the movement of the motor on microtubule, but can be easily extended to more complicated kinetic models. Effects of various hydrodynamic parameters on the velocity of the bead are studied with numerical calculations of the model. The difference between the formalism presented in this paper and the widely used "chemical" formalism, in which the movement of the kinesin and the bead is described by pure chemical reactions, is discussed.     

Molecular motors: thermodynamics and the random walk

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.     

The Orphan Kinesin PAKRP2 Achieves Processive Motility via a Noncanonical Stepping Mechanism

Phragmoplast-associated kinesin-related protein 2 (PAKRP2) is an orphan kinesin in Arabidopsis thaliana that is thought to transport vesicles along phragmoplast microtubules for cell plate formation. Here, using single-molecule fluorescence microscopy, we show that PAKRP2 is the first orphan kinesin to exhibit processive plus-end-directed motility on single microtubules as individual homodimers. Our results show that PAKRP2 processivity is achieved despite having an exceptionally long (32 residues) neck linker. Furthermore, using high-resolution nanoparticle tracking, we find that PAKRP2 steps via a hand-over-hand mechanism that includes frequent side steps, a prolonged diffusional search of the tethered head, and tight coupling of the ATP hydrolysis cycle to the forward-stepping cycle. Interestingly, truncating the PAKRP2 neck linker to 14 residues decreases the run length of PAKRP2; thus, the long neck linker enhances the processive behavior. Based on the canonical model of kinesin stepping, such a long neck linker is expected to decrease the processivity and disrupt the coupling of ATP hydrolysis to forward stepping. Therefore, we conclude that PAKRP2 employs a noncanonical strategy for processive motility, wherein a long neck linker is coupled with a slow ATP hydrolysis rate to allow for an extended diffusional search during each step without sacrificing processivity or efficiency.     

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.     

Modulation of the Kinesin ATPase Cycle by Neck Linker Docking and Microtubule Binding

Kinesin motor proteins use an ATP hydrolysis cycle to perform various functions in eukaryotic cells. Many questions remain about how the kinesin mechanochemical ATPase cycle is fine-tuned for specific work outputs. In this study, we use isothermal titration calorimetry and stopped-flow fluorometry to determine and analyze the thermodynamics of the human kinesin-5 (Eg5/KSP) ATPase cycle. In the absence of microtubules, the binding interactions of kinesin-5 with both ADP product and ATP substrate involve significant enthalpic gains coupled to smaller entropic penalties. However, when the wild-type enzyme is titrated with a non-hydrolyzable ATP analog or the enzyme is mutated such that it is able to bind but not hydrolyze ATP, substrate binding is 10-fold weaker than ADP binding because of a greater entropic penalty due to the structural rearrangements of switch 1, switch 2, and loop L5 on ATP binding. We propose that these rearrangements are reversed upon ATP hydrolysis and phosphate release. In addition, experiments on a truncated kinesin-5 construct reveal that upon nucleotide binding, both the N-terminal cover strand and the neck linker interact to modulate kinesin-5 nucleotide affinity. Moreover, interactions with microtubules significantly weaken the affinity of kinesin-5 for ADP without altering the affinity of the enzyme for ATP in the absence of ATP hydrolysis. Together, these results define the energy landscape of a kinesin ATPase cycle in the absence and presence of microtubules and shed light on the role of molecular motor mechanochemistry in cellular microtubule dynamics.     

Mechanism of processive movement of monomeric and dimeric kinesin molecules

Kinesin molecules are motor proteins capable of moving along microtubule by hydrolyzing ATP. They generally have several forms of construct. This review focuses on two of the most studied forms: monomers such as KIF1A (kinesin-3 family) and dimers such as conventional kinesin (kinesin-1 family), both of which can move processively towards the microtubule plus end. There now exist numerous models that try to explain how the kinesin molecules convert the chemical energy of ATP hydrolysis into the mechanical energy to "power" their processive movement along microtubule. Here, we attempt to present a comprehensive review of these models. We further propose a new hybrid model for the dimeric kinesin by combining the existing models and provide a framework for future studies in this subject.