Force generation in kinesin hinges on cover-neck bundle formation

In kinesin motors, a fundamental question concerns the mechanism by which ATP binding generates the force required for walking. Analysis of available structures combined with molecular dynamics simulations demonstrates that the conformational change of the neck linker involves the nine-residue-long N-terminal region, the cover strand, as an element that is essential for force generation. Upon ATP binding, it forms a beta sheet with the neck linker, the cover-neck bundle, which induces the forward motion of the neck linker, followed by a latch-type binding to the motor head. The estimated stall force and anisotropic response to external loads calculated from the model agree with force-clamp measurements. The proposed mechanism for force generation by the cover-neck bundle formation appears to apply to several kinesin families. It also elucidates the design principle of kinesin as the smallest known processive motor.     

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.     

Walking motion of an overdamped active particle in a ratchet potential

An active particle can convert its internal energy into mechanical work. We study a generalized energy-depot model of an overdamped active particle in a ratchet potential. Using well-known biological parameters for kinesin-1 and modeling ATP influx as a pulsed energy supply, we apply our model to the molecular motor system. We find that our simple model can capture the essential properties of the kinesin motor such as forward stepping, stalling, backward stepping, dependence on ATP concentration, and stall force. Our model might be quite universal in the sense that it is able to describe dynamics of various types of motors as long as realistic parameters for each motor species are adopted.     

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.     

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.     

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.     

Docking and rolling, a model of how the mitotic motor Eg5 works

Whereas kinesin I is designed to transport cargoes long distances in isolation, a closely related kinesin motor, Eg5, is designed to generate a sustained opposing force necessary for proper mitotic spindle formation. Do the very different roles for these evolutionarily related motors translate into differences in how they generate movement? We have addressed this question by examining when in the ATPase cycle the Eg5 motor domain and neck linker move through the use of a series of novel spectroscopic probes utilizing fluorescence resonance energy transfer, and we have compared our results to kinesin I. Our results are consistent with a model in which movement in Eg5 occurs in two sequential steps, an ATP-dependent docking of the neck linker, followed by a rotation or "rolling" of the entire motor domain on the microtubule surface that occurs with ATP hydrolysis. These two forms of movement are consistent with the functions of a motor designed to generate sustained opposing force, and hence, our findings support the argument that the mechanochemical features of a molecular motor are shaped more by the demands placed on it than by its particular family of origin.     

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。     

Irrelevance of the Power Stroke for the Directionality,Stopping Force,and Optimal Efficiency of Chemically Driven Molecular Machines

A simple model for a chemically driven molecular walker shows that the elastic energy stored by the molecule and released during the conformational change known as the power-stroke (i.e., the free-energy difference between the pre- and post-power-stroke states) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Further, the apportionment of the dependence on the externally applied force between the forward and reverse rate constants of the power-stroke (or indeed among all rate constants) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Arguments based on the principle of microscopic reversibility demonstrate that this result is general for all chemically driven molecular machines, and even more broadly that the relative energies of the states of the motor have no role in determining the directionality, stopping force, or optimal efficiency of the machine. Instead, the directionality, stopping force, and optimal efficiency are determined solely by the relative heights of the energy barriers between the states. Molecular recognition—the ability of a molecular machine to discriminate between substrate and product depending on the state of the machine—is far more important for determining the intrinsic directionality and thermodynamics of chemo-mechanical coupling than are the details of the internal mechanical conformational motions of the machine. In contrast to the conclusions for chemical driving, a power-stroke is very important for the directionality and efficiency of light-driven molecular machines and for molecular machines driven by external modulation of thermodynamic parameters.     

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.     

Force-dependent stepping kinetics of myosin-V

Myosin-V is a processive two-headed actin-based motor protein involved in many intracellular transport processes. A key question for understanding myosin-V function and the communication between its two heads is its behavior under load. Since in vivo myosin-V colocalizes with other much stronger motors like kinesins, its behavior under superstall forces is especially relevant. We used optical tweezers with a long-range force feedback to study myosin-V motion under controlled external forward and backward loads over its full run length. We find the mean step size remains constant at approximately 36 nm over a wide range of forces from 5 pN forward to 1.5 pN backward load. We also find two force-dependent transitions in the chemomechanical cycle. The slower ADP-release is rate limiting at low loads and depends only weakly on force. The faster rate depends more strongly on force. The stronger force dependence suggests this rate represents the diffusive search of the leading head for its binding site. In contrast to kinesin motors, myosin-V's run length is essentially independent of force between 5 pN of forward to 1.5 pN of backward load. At superstall forces of 5 pN, we observe continuous backward stepping of myosin-V, indicating that a force-driven reversal of the power stroke is possible.     

Crystal structure of the mitotic spindle kinesin Eg5 reveals a novel conformation of the neck-linker

Success of mitosis depends upon the coordinated and regulated activity of many cellular factors, including kinesin motor proteins, which are required for the assembly and function of the mitotic spindle. Eg5 is a kinesin implicated in the formation of the bipolar spindle and its movement prior to and during anaphase. We have determined the crystal structure of the Eg5 motor domain with ADP-Mg bound. This structure revealed a new intramolecular binding site of the neck-linker. In other kinesins, the neck-linker has been shown to be a critical mechanical element for force generation. The neck-linker of conventional kinesin is believed to undergo an ordered-to-disordered transition as it translocates along a microtubule. The structure of Eg5 showed an ordered neck-linker conformation in a position never observed previously. The docking of the neck-linker relies upon residues conserved only in the Eg5 subfamily of kinesin motors. Based on this new information, we suggest that the neck-linker of Eg5 may undergo an ordered-to-ordered transition during force production. This ratchet-like mechanism is consistent with the biological activity of Eg5.     

Intramolecular strain coordinates kinesin stepping behavior along microtubules

Kinesin advances 8 nm along a microtubule per ATP hydrolyzed, but the mechanism responsible for coordinating the enzymatic cycles of kinesin's two identical motor domains remains unresolved. Here, we have tested whether such coordination is mediated by intramolecular tension generated by the "neck linkers," mechanical elements that span between the motor domains. When tension is reduced by extending the neck linkers with artificial peptides, the coupling between ATP hydrolysis and forward stepping is impaired and motor's velocity decreases as a consequence. However, speed recovers to nearly normal levels when external tension is applied by an optical trap. Remarkably, external load also induces bidirectional stepping of an immotile kinesin that lacks its mechanical element (neck linker) and fuel (ATP). Our results indicate that the kinesin motor domain senses and responds to strain in a manner that facilitates its plus-end-directed stepping and communication between its two motor domains.     

A Brownian Dynamics Model of Kinesin in Three Dimensions Incorporating the Force-Extension Profile of the Coiled-Coil Cargo Tether

The kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers can probe individual molecules, there has been an increasing interest in understanding the mechanisms by which motor proteins convert chemical energy into mechanical work. Here we present a mathematical model for the chemistry and three dimensional mechanics of the kinesin motor protein which captures many of the force dependent features of the motor. For the elasticity of the tether that attaches cargo to the motor we develop a method for deriving the non-linear force-extension relationship from optical trap data. For the kinesin heads, cargo, and microscope stage we formulate a three dimensional Brownian Dynamics model that takes into account excluded volume interactions. To efficiently compute statistics from the model, an algorithm is proposed which uses a two step protocol that separates the simulation of the mechanical features of the model from the chemical kinetics of the model. Using this approach for a bead transported by the motor, the force dependent average velocity and randomness parameter are computed and compared with the experimental 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.     

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.     

Limping of homodimeric kinesin motors

Conventional kinesin, a homodimeric motor protein that transports cargo in various cells, walks limpingly along microtubule. Here, based on our previously proposed partially coordinated hand-over-hand model, we present a new mechanism for the limping behaviors of both wild-type and mutant kinesin homodimers. The limping is caused by different vertical forces acting on the heads in two successive steps during the processive movement of the dimer. From the model, various theoretical results, such as the dependences of the mean dwell time and dwell time ratio on the coiled-coil length and on the external load as well as the effect of vertical force on velocity, are in good agreement with previous experimental results. We predict that a high degree of limping will correlate strongly with a high sensitivity of ATP turnover rate to upwards force.     

Crystal structure of kinesin regulated by Ca(2+)-calmodulin

Kinesins orchestrate cell division by controlling placement of chromosomes. Kinesins must be precisely regulated or else cell division fails. Calcium, a universal second messenger in eukaryotes, and calmodulin regulate some kinesins by causing the motor to dissociate from its biological track, the microtubule. Our focus was the mechanism of calcium regulation of kinesin at atomic resolution. Here we report the crystal structure of kinesin-like calmodulin-binding protein (KCBP) from potato, which was resolved to 2.3 A. The structure reveals three subdomains of the regulatory machinery located at the C terminus extension of the kinesin motor. Calmodulin that is activated by Ca2+ ions binds to an alpha-helix positioned on the microtubule-binding face of kinesin. A negatively charged segment following this helix competes with microtubules. A mimic of the conventional kinesin neck, connecting the calmodulin-binding helix to the KCBP motor core, links the regulatory machine to the kinesin catalytic cycle. Together with biochemical data, the crystal structure suggests that Ca(2+)-calmodulin inhibits the binding of KCBP to microtubules by blocking the microtubule-binding sites on KCBP.     

Three phase model of the processive motor protein 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. So far, the physical mechanism underlying the unidirectional bias of the kinesin is not fully understood. Recently, Martin Bier have provided a stepper model [Martin Bier, 2003, Processive motor protein as an overdamped Brownian stepper, Phys. Rev. Lett. 91, 148104], in which the stepping cycle of kinesin includes two distinguished phases: (i) a power stroke phase and (ii) a ratcheted diffusion phase which is characterized as a "random diffusional search". At saturating ATP level, this model can fit the experimental results accurately. In this paper, we'll provide a modified Brownian stepper model, in which the dependence of ATP concentration is considered. In our model, the stepping cycle of kinesin is distinguished into three phases: an ATP-binding phase, a power stroke phase and a ratcheted diffusion phase. This modified model can reconstruct most of the experimental results accurately.