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.     

Motor proteins transporting cargos

Processive motor proteins such as kinesin and myosin-V are enzymes that use the energy of ATP hydrolysis to travel along polar cytoskeletal filaments. One of the functions of these proteins is the transport of vesicles and protein complexes that are linked to the light chains of the motors. Modeling the light chain by a linear elastic spring, and using the two-state model for one- and two-headed molecular motors, we study the influence of thermal fluctuations of the cargo on the motion of the motor-cargo complex. We solve numerically the Fokker-Planck equations of motor motion, and find that the mean velocity of the motor-cargo complex decreases monotonously as the spring becomes softer. This effect is due to the random force of thermal fluctuations of the cargo disrupting the operation of the motor. Increasing the size (thus, the friction coefficient) of the cargo also decreases the velocity. Surprisingly, we find that for a given size of the cargo, the velocity has a maximum for a certain friction of the motor. We explain this effect by the interplay between the characteristic length of thermal fluctuations of the cargo on a spring, the motor diffusion length, and the filament period. Our results may be relevant for the interpretation of single-molecule experiments with molecular motors (bead assays), where the motor motion is observed by tracking of a bead attached to the motor.     

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.     

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.     

Experimental studies of the myosin-actin motor

The mechanical processes generated by the molecular motors, myosin and actin, were measured using single molecule imaging, manipulation, and nanometry techniques. It was shown that the mechanical events of myosin are not tightly coupled with the ATP hydrolysis reaction and that myosin molecules move stochastically. These results indicate that the movement of myosin is driven by thermal motion rather than structural changes occurring in the myosin molecules. Thermal Brownian motion must be biased using the energy released from the hydrolysis of ATP. Thus, the molecular motors can harness thermal energy to perform mechanical work efficiently. Received: 20 November 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

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.     

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.     

Bursting Ca2+ Oscillations and Synchronization in Coupled Cells

A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntracellulax bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca^2＋ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point cycle type.     

Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Dufling oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dufl~ng oscillators coupled linearly, the transition to the synchronization generally consists of two steps： Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.     

Different Types of Synchronization in Time-Delayed Systems

We investigate different types of synchronization between two unidirectionally nonlinearly coupled identical delay- differential systems related to optical bistable or hybrid optical bistable devices. This system can represent some kinds of delay-differential models, i.e. Ikeda model, Vall~e model, sine-square model, Mackey Glass model, and so on. We find existence and sufficient stability conditions by theoretical analysis and test the correctness by＂ numerical simulations. Lag, complete and anticipating synchronization are observed, respectively. It is found that the time-delay system can be divided into two parts~ one is the instant term and the other is the delay term. Synchronization between two identical chaotic systems can be derived by adding a coupled term to the delay term in the driven system.     

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.     

Stochastic synchronization of coupled neural networks with intermittent control

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.     

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.     

Effect of kinesin velocity distribution on slow axonal transport

The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.     

The effects of viscoelastic fluid on kinesin transport

Kinesins are molecular motors which transport various cargoes in the cytoplasm of cells and are involved in cell division. Previous models for kinesins have only targeted their in vitro motion. Thus, their applicability is limited to kinesin moving in a fluid with low viscosity. However, highly viscoelastic fluids have considerable effects on the movement of kinesin. For example, the high viscosity modifies the relation between the load and the speed of kinesin. While the velocity of kinesin has a nonlinear dependence with respect to the load in environments with low viscosity, highly viscous forces change that behavior. Also, the elastic nature of the fluid changes the velocity of kinesin. The new mechanistic model described in this paper considers the viscoelasticity of the fluid using subdiffusion. The approach is based on a generalized Langevin equation and fractional Brownian motion. Results show that a single kinesin has a maximum velocity when the ratio between the viscosity and elasticity is about 0.5. Additionally, the new model is able to capture the transient dynamics, which allows the prediction of the motion of kinesin under time varying loads.     

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.     

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.     

Rhythm Synchronization of Coupled Neurons with Temporal Coding Scheme

Encoding information by firing patterns is one of the basic neural functions, and synchronization is important collective behaviour of a group of coupled neurons. Taking account of two schemes for encoding information （that is, rate coding and temporal coding）, rhythm synchronization of coupled neurons is studied. There are two types of rhythm synchronization of neurons： spike and burst synchronizations. Firstly, it is shown that the spike synchronization is equivalent to the phase synchronization for coupled neurons. Secondly, the similarity function of the slow variables of neurons, which have relevant to the bursting process, is proposed to judge the burst synchronization. It is also found that the burst synchronization can be achieved more easily than the spike synchronization, whatever the firing patterns of the neurons are. Hence the temporal encoding scheme, which is closely related to both the spike and burst synchronizations, is more comprehensive than the rate coding scheme in essence.     

A random walker on a ratchet

We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet that are represented as two particles coupled nonlinearly through a bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics, where the ordering of the particles can alternate during the walking. The transitions between the two stable states on the bistable potential correspond to a walking with alternating particles. We distinguish between two main walking styles: alternating and no alternating, resembling the hand-over-hand and the inchworm walking in motor proteins, respectively. When the equilibrium distance between the two particles divided by the periodicity of the ratchet is an integer, we obtain a maximum for the current, indicating optimal transport.