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.     

Investigation of the structural and dynamic basis of kinesin dissociation from microtubule by atomistic molecular dynamics simulations

Kinesin is a molecular motor that can step processively on microtubules via the hydrolysis of ATP molecules. An important factor characterizing the processivity of the kinesin motor is its dissociation from the microtubule. Here, using all-atom molecular dynamics simulations, we studied the dissociation process of the kinesin head in weak-microtubule-binding or ADP state from tubulin on the basis of the available high-resolution structural data for the head and tubulin. By analyzing the simulated snapshots of the structure of the head-tubulin complex we provided detailed structural and dynamic information for the dissociation process. We found that the dissociation of the head along different directions relative to the tubulin exhibits very different dynamic behaviors. Moreover, the potential forms or energy landscapes of the interaction between the head and tubulin along different directions were determined. The studies have important implications for the detailed molecular mechanism of the dissociation of the kinesin motor and thus are critical to the mechanism of its processivity.     

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.     

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.     

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.     

Dynamic concentration of motors in microtubule arrays

We present experimental and theoretical studies of the dynamics of molecular motors in microtubule arrays and asters. By solving a convection-diffusion equation we find that the density profile of motors in a two-dimensional aster is characterized by continuously varying exponents. Simulations are used to verify the assumptions of the continuum model. We observe the concentration profiles of kinesin moving in quasi-two-dimensional artificial asters by fluorescent microscopy and compare with our theoretical results.     

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.     

Monte Carlo Simulation of Kinesin Movement with a Lattice Model

Kinesin is a processive double-headed molecular motor that moves along a microtubule by taking about 8nm steps. It generally hydrolyzes one ATP molecule for taking each forward step. The processive movement of the kinesin molecular motors is numerically simulated with a lattice model. The motors are considered as Brownian particles and the ATPase processes of both heads are taken into account. The Monte Carlo simulation results agree well with recent experimental observations, especially on the relation of velocity versus ATP and ADP concentrations.     

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.     

Moving striations in tapered discharge tube

Moving striations in the tapered tube with smoothly changing radius are studied experimentally. The frequency depends on local tube radius by nature and increases toward the narrow end of the tube, independent of direction and magnitude of the discharge current. Radius-frequency versus radius-pressure is compatible with the similarity law for striations in cylindrical tubes. When there appears synchronization, the frequency becomes apparently constant throughout the tube column. The wavelength shows different dependences on radius without and with the synchronization. An important role is played by the feedback through an electric circuit. Also, direction and magnitude of the current have influence on the phenomena. Steady states in the tubes are compared with those in cylindrical tubes. An attempt is made to explain the observed synchronizations and then the remarkable discrepancies between the previous experiments can be eliminated.     

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.     

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.     

Possible role of phospholipid nanotubes in directed transport of membrane vesicles

We indicate that membrane nanotubes may have an important role in directed transport of membrane vesicles between different membrane-enclosed compartments in cells. We present experimental evidence that small blebs of phospholipid nanotube may travel along the nanotube and act as vehicles for transporting the enclosed solution. We have also observed similar small membrane blebs of a long membrane tube in red blood cells. In both cases the small vesicles seem to be a distended integral part of the membrane tube and not independent vesicles entrapped within the tube.     

Dynamics of cooperative transport by multiple kinesin motors and diffusing microtubule-associated proteins

In eukaryote cells, cargos are often transported cooperatively by kinesin motors and nonmotor microtubule-associated proteins (MAPs). The prior in vitro experimental data showed that the velocity of the cargo transported by kinesin motors and Ndc80 (a member of MAP) proteins of truncated coiled-coil stalks decreases sensitively with the increase of the ratio of Ndc80 to motor number. However, the underlying mechanism of Ndc80 affecting sensitively the cooperative cargo transport by kinesin motors is unclear. To understand the mechanism, here we study numerically the cooperative cargo transport by kinesin motors and Ndc80 proteins. Our results showed that for the case of the motors and Ndc80 proteins with truncated short stalks, as used in the experiments, the calculated results reproduce quantitatively the prior experimental data. The mechanism of the cargo velocity decreasing sensitively with the ratio of Ndc80 to motor number is revealed. By contrast, for the case of the motors and Ndc80 proteins with full-length long stalks, the velocity of the cargo decreases slowly with the increase in the ratio of Ndc80 to kinesin number. Our results thus give an explanation of why the kinesin motors working in the cell have long stalks.     

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.     

Intracellular transport of single-headed molecular motors KIF1A

Motivated by experiments on single-headed kinesin KIF1A, we develop a model of intracellular transport by interacting molecular motors. It captures explicitly not only the effects of adenosine triphosphate hydrolysis, but also the ratchet mechanism which drives individual motors. Our model accounts for the experimentally observed single-molecule properties in the low-density limit and also predicts a phase diagram that shows the influence of hydrolysis and Langmuir kinetics on the collective spatiotemporal organization of the motors. Finally, we provide experimental evidence for the existence of domain walls in our in vitro experiment with fluorescently labeled KIF1A.     

Spicules and the effect of rigid rods on enclosing membrane tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force f exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between f approximately square root of (sigma) and f approximately sigma as the membrane tension sigma increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.     

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     

Effects of rebinding rate and asymmetry in unbinding rate on cargo transport by multiple kinesin motors

Many intracellular transports are performed by multiple molecular motors in a cooperative manner.Here,we use stochastic simulations to study the cooperative transport by multiple kinesin motors,focusing mainly on effects of the form of unbinding rate versus force and the rebinding rate of single motors on the cooperative transport.We consider two forms of the unbinding rate.One is the symmetric form with respect to the force direction,which is obtained according to Kramers theory.The other is the asymmetric form,which is obtained from the prior studies for the single kinesin motor.With the asymmetric form the simulated results of both velocity and run length of the cooperative transport by two identical motors and those by a kinesin-1 motor and a kinesin-2 motor are in quantitative agreement with the available experimental data,whereas with the symmetric form the simulated results are inconsistent with the experimental data.For the cooperative transport by a faster motor and a much slower motor,the asymmetric form can give both larger velocity and longer run length than the symmetric form,giving an explanation for why kinesin adopts the asymmetric form of the unbinding rate rather than the symmetric form.For the cooperative transport by two identical motors,while the velocity is nearly independent of the rebinding rate,the run length increases linearly with the rebinding rate.For the cooperative transport by two different motors,the increase of the rebinding rate of one motor also enhances the run length of the cooperative transport.The dynamics of transport by N(N=3,4,5,6,7 and 8)motors is also studied.     

Monomer depletion, pressure difference, and membrane tube radius reduction due to fiber polymerization in microspikes

In many processes vital to life, the growth of biological fibers outwards from a membrane surface naturally produces membrane tube tethers or microspikes in biological cells. Here, we investigate the novel effect of pressure difference (due to monomer depletion) on the polymerization dynamics of biological fibers within long membrane tubes. We crucially find that fiber monomers become depleted close to the growing tip as the fiber polymerizes, thus reducing the local pressure, and hence decreasing the membrane tube radius at the tip. This process is found to slow the growth of the fiber, a process which becomes important when we go on to construct a dynamical theory for biopolymer growth in long, narrow tubes. Our result is interesting in that it emphasizes how "passive" biological transport mechanisms such as via pressure differences may play an important role in cell movements.