A New Cooperation Mechanism of Kinesin Motors when Extracting Membrane Tube

Membrane tubes are important functional elements for living cells. Experiments have found that membrane tubes can be extracted from giant lipid vesicles by groups of kinesin. How these motors cooperate in extracting the membrane tube is a very important issue but still unclear so far. In this paper, we propose a cooperation mechanism called two-track-dumbbell model, in which kinesin is regarded as a dumbbell with an end (tail domain) tethered on the fluid-like membrane and the other end (head domain) stepping on the microtubule. Taking account of the elasticity of kinesin molecule and the excluded volume effect of both the head domain and the tail domain of kinesin, which are not considered in previous models, we simulate the growth process of the membrane tube pulled by kinesin motors. Our results indicate that in the case of strong or moderate exclusion of motor tails, the average number of motors pulling the tube can be as high as 9 and thus motors moving along a single microtubule protofilament can generate enough force to extract membrane tubes from vesicles. This result is different from previous studies and may be tested by future experiments.     

A New Cooperation Mechanism of Kinesin Motors when Extracting Membrane Tube

Membrane tubes are important functional elements for riving cells. Experiments have found that membrane tubes can be extracted from giant lipid vesicles by groups of kinesin. How these motors cooperate in extracting the membrane tube is a very important issue but still unclear so far. In this paper, we propose a cooperation mechanism called two-track-dumbbell model, in which kinesin is regarded as a dumbbell with an end （tail domain） tethered on the fluid-like membrane and the other end （head domain） stepping on the microtubule. Taking account of the elasticity of kinesin molecule and the excluded volume effect of both the head domain and the tail domain of kinesin, which are not considered in previous models, we simulate the growth process of the membrane tube pulled by kinesin motors. Our results indicate that in the case of strong or moderate exclusion of motor tails, the average number of motors pulling the tube can be as high as 9 and thus motors moving along a single microtubule protofilament can generate enough force to extract membrane tubes from vesicles. This result is different from previous studies and may be tested by future experiments.     

驱动蛋白单向运动机理

驱动蛋白马达在实验和理论上已被进行了广泛的研究. 然而, 其行进运动的微观机理仍未确定. 在本文中我们基于化学、力学和电学耦合提出了一个交臂模型来描述这种行进运动. 在该模型中，驱动蛋白两个头的ATP水解化学反应速率由作用在其颈上的力（包括内部弹性力和外部负荷）来调控. 在低外部负荷情况下, 驱动蛋白的后头的ATP水解化学反应速率远大于前头的速率, 因而两个头在ATP水解化学反应和力学周期循环中是协调的且马达以每步消耗一个ATP的方式的行走. 在大的前向负荷情况下, 两个头的ATP水解化学反应速率变得可比拟, 因而两个头在ATP水解化学反应和力学周期循环中不再很好地协调. 该模型与驱动蛋白的结构研究结果以及ATP水解化学反应路径一致. 利用此模型所估算的驱动力（约5.8 pN）与实验结果（5~7.5 pN）一致. 所估算的每步中的运动时间（约10）也与实验测量值（0~50）符合. 解释了已观察到的每步（8nm）分为两个半步的现象. 所得到的运动速度-负荷曲线与已有的实验结果一致.     

Initiation Mechanism of Kinesin's Neck Linker Docking Process

The neck linker(NL) docking to the motor domain is the key force generation process of a kinesin motor. In the initiation step of NL docking the first three residues(LYS325, THR326 and ILE327 in 2 KIN) of the NL must form an 'extra turn', thus the other parts of the NL could dock to the motor domain. How the extra turn is formed remains elusive. We investigate the extra turn formation mechanism using structure-based mechanical analysis via molecular dynamics simulation. We find that the motor head rotation induced by ATP binding first drives ILE327 to move towards a hydrophobic pocket on the motor domain. The driving force, together with the hydrophobic interaction of ILE327 with the hydrophobic pocket, then causes a clockwise rotation of THR326,breaks the locking of LYS325, and finally drives the extra turn formation. This extra turn formation mechanism provides a clear pathway from ATP binding to NL docking of kinesin.     

Reconceptualizing kinesin’s working cycle as separate chemical and mechanical processes

The biomolecular motor kinesin uses chemical energy released from a fuel reaction to generate directional movement and produce mechanical work. The underlying physical mechanism is not fully understood yet. To analyze the energetics of the motor, we reconceptualize its chemomechanical cycle in terms of separate fuel reaction and work production processes and introduce a thermodynamic constraint to optimize the cycle. The model predicts that the load dependences of the motor’s velocity, stepping ratio, and dwell time are determined by the mechanical parameters of the motor–track system rather than the fuel reaction rate. This behavior is verified using reported experimental data from wild-type and elongated kinesins. The fuel reaction and work production processes indicate that kinesin is driven by switching between two chemical states, probably following a general pattern for molecular motors. The comparison with experimental data indicates that the fuel reaction processes are close to adiabatic, which is important for efficient operation of the motor. The model also suggests that a soft, short neck linker is important for the motor to maintain its load transport velocity.     

Model for processive movement of myosin V and myosin VI

Myosin V and myosin VI are two classes of two-headed molecular motors of the myosin superfamily that move processively along helical actin filaments in opposite directions. Here we present a hand-over-hand model for their processive movements. In the model, the moving direction of a dimeric molecular motor is automatically determined by the relative orientation between its two heads at free state and its head‘s binding orientation on track filament.This determines that myosin V moves toward the barbed end and myosin VI moves toward the pointed end of actin.During the moving period in one step, one head remains bound to actin for myosin V whereas two heads are detached for myosin VI: the moving manner is determined by the length of neck domain. This naturally explains the similar dynamic behaviours but opposite moving directions of myosin VI and mutant myosin V (the neck of which is truncated to only one-sixth of the native length). Because of different moving manners, myosin VI and mutant myosin V exhibit significantly broader step-size distribution than native myosin V. However, all the three motors give the same mean step size of -36nm (the pseudo-repeat of actin helix). All these theoretical results are in agreement with previous experimental ones.     

Detectable states,cycle fluxes,and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.     

A non-Markov ratchet model of molecular motors：processive movement of single-headed kinesin KIF1A

A fluctuating ratchet model of non-Markov process is presented to describe the processive movement of molecular motors of single-headed kinesin KIF1A,where the fluctuation perturbation to the local potential is introduced and the detailed ATPase pathway of the motor is included. The theoretical results show good quantitative agreement with the previous experimental ones.     

Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering

Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into the coordinated mechanical movement of the entire motor protein. In this paper, we propose two combined nonlinear mechanisms for this particular functional activity and suggest the application of neutron scattering assays to experimentally determine the incoherent dynamic structure factor S(q,ω). We argue that this type of experiment is not only feasible but it could offer significant insights into the mechanism of MP function at a molecular level.     

The neck linker of kinesin 1 seems optimally designed to approach the largest stepping velocity: a simulation study of an ideal model

The neck linker is widely believed to play a critical role in the hand-over-hand walking of conventional kinesin 1. Experiments have shown that change of the neck linker length will significantly change the stepping velocity of the motor. In this paper, we studied this length effect based on a highly simplified chemically powered ratchet model. In this model, we assume that the chemical steps (ATP hydrolysis, ADP and P(i) release, ATP binding, neck linker docking) are fast enough under conditions far from equilibrium and the mechanical steps (detachment, diffusional search and re-attachment of the free head) are rate-limiting in kinesin walking. According to this model, and regarding the neck linker as a worm-like-chain polypeptide, we can calculate the steady state stepping velocity of the motor for different neck linker lengths. Our results show, under the actual values of binding energy between kinesin head and microtubule (~15k(B)T) and the persistence length of neck linker (~0.5 nm), that there is an optimal neck linker length (~14-16 a.a.) corresponding to the maximal velocity, which implies that the length of the wild-type neck linker (~15 a.a.) might be optimally designed for kinesin 1 to approach the largest stepping velocity.     

向生命学习新的机制

根据有关分子马达的重要实验结果,明确指出分子马达的运动过程是一个化学、电学、力学3种过程互相耦合的生物学过程。主要介绍有关kinesin的力产生机制的研究现状以及在这方面的研究。On the basis of the important experimental results of molecular motors, it was polnted out that the moving process of molecular motors is a coupling biological process of chemical-electrical-mechanical processes. This clever mechanism of energy conversion on the molecular level with several processes coupled together had never been observed before. The understanding of this new mechanism is an important step towards the understanding of life and an important content of what we can learn from life. We introduced here the status of the investigations on the mechanism for the force generation of kinesin and the studies of the authors in this field     

Processive motor protein as an overdamped brownian stepper

The two headed motor protein kinesin appears to "walk" along the biopolymer microtubule in 8 nm steps. There is ample justification for a model where the motion of the detached head to the next docking site on the biopolymer is described as ratcheted diffusion. The forward reorientation of an attached head can be conceived of as a power stroke. A model that is based on these premises can accurately predict parameters of motor protein motion.     

Dipole-Dipole Interaction and the Directional Motion of Brownian Motors

The electric field of the microtubule is calculated according to its dipole distribution. The conformationalchange of a molecular motor is described by the rotation ofa dipole which interacts with the microtubulc. The mricalsimulation for the particle current shows that this interaction helps to produce a directional motion along the microtubule.And tte average displacement executes step changes that resemble the experimental result for kinesin motors.     

Dipole—Dipole Interaction and the Directional Motion of Brownian

The electric field of the microtubule is calculated according to its dipole distribution.The conformational change of a molecular motor is described by the rotation of a dipole which interacts with the microtubule.The numerical simulation for the particle currend shows that this interaction helps to produce a directional motion along the microtubule.And the average displacement executes step changes that resemble the experimental result for kinesin motors.     

Monte Carlo simulation on backward steps of single kinesin molecule

Kinesin is a stepping molecular motor travelling along the microtubule. It moves primarily in the plus end direction of the microtubule and occasionally in the minus-end, backward, direction. Recently, the backward steps of kinesin under different loads and temperatures start to attract interests, and the relations among them are revealed. This paper aims to theoretically understand these relations observed in experiments. After introducing a backward pathway into the previous model of the ATPase cycle of kinesin movement, the dependence of the backward movement on the load and the temperature is explored through Monte Carlo simulation. Our results agree well with previous experiments.     

A general two-cycle network model of molecular motors

Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale. They convert chemical energy into mechanical work by moving along filamentous structures. In this paper, we study the velocity of two-head molecular motors in the framework of a mechanochemical network theory. The network model, a generalization of the recently work of Liepelt and Lipowsky [Steffen Liepelt, Reinhard Lipowsky, Kinesins network of chemomechanical motor cycles, Physical Review Letters 98 (25) (2007) 258102], is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for a single cycle motor [Michael E. Fisher, Anatoly B. Kolomeisky, Simple mechanochemistry describes the dynamics of kinesin molecules, Proceedings of the National Academy of Sciences 98 (14) (2001) 7748-7753], we are able to obtain an explicit formula for the velocity of a molecular motor.     

Kramers-type elastic ratchet model for ATP gating during kinesin’s mechanochemical cycle

ATP binding, acting as a gate, plays an important role in kinesin stepping. To understand the physical mechanism of the ATP gate, we propose a Kramers-type elastic ratchet model in which the free head undergoes a biased diffusive search. By first passage time analysis, we investigate the dependence of the mean dwell time on the load force for forward steps of kinesin and find that the forward dwell time varies exponentially with the backward load force which is consistent with the data of Carter and Cross, Nature 435 (2005) 308. Our work suggests that the gating mechanism triggered by ATP binding involves both Kramers-type elastic ratchet mechanism and power stroke movement.     

How kinesins walk,assemble and transport: A birds-eye-view of some unresolved questions

Eukaryotic cells contain an intricate network of microtubule filaments inside. It provides the mechanical support for maintaining cell shape as well as a railway for intracellular traffic. A special class of ATP hydrolyzing enzymes bind microtubule inside the cells and ‘walk’ along the filament. Kinesins constitute a subset of these so called ‘motor’ proteins. These are a diverse set of proteins capable of converting the chemical energy of ATP hydrolysis to mechanical force and move from one end of the cell to the other carrying a variety of different cargoes. Although the composition, structure and their force generating mechanism is understood in considerable detail, several questions regarding the mechanism of kinesin mediated transport remained unanswered. Here, in this review, I have provided a brief overview of kinesin structure and functions in different intracellular transports and highlighted some of the key unresolved issues.