All-atom molecular dynamics simulations reveal how kinesin transits from one-head-bound to two-heads-bound state

Effects of stalk orientation and size of trapped bead on force-velocity relation of kinesin motor determined using single molecule optical trapping methods

Conventional kinesin protein is a prototypical biological molecular motor that can step processively on microtubules towards the plus end by hydrolyzing ATP molecules, performing the biological function of intracellular transports. An important characteristic of the kinesin is the load dependence of its velocity, which is usually measured by using the single molecule optical trapping method with a large-sized bead attached to the motor stalk. Puzzlingly, even for the same kinesin, some experiments showed that the velocity is nearly independent of the forward load whereas others showed that the velocity decreases evidently with the increase in the magnitude of the forward load. Here, a theoretical explanation is provided of why different experiments give different dependencies of the velocity on the forward load. It is shown that both the stalk orientation and bead size play a critical role in the different dependencies. Additionally, the reason why the optical trapping experiments with the movable trap usually gave a sigmoid form of the velocity versus backward load whereas with the fixed trap gave a nearly linear form is also explained theoretically. The study is not only critical to the understanding of the response of the motor to the load but also provides strong insights into the coupling mechanism of the motor.

Modeling study of kinesin-13 MCAK microtubule depolymerase

Mitotic centromere-associated kinesin (MCAK) motor protein is a typical member of the kinesin-13 family, which can depolymerize microtubules from both plus and minus ends. A critical issue for the MCAK motor is how it performs the depolymerase activity. To address the issue, the pathway of the MCAK motor moving on microtubules and depolymerizing the microtubules is presented here. On the basis of the pathway, the dynamics of both the wild-type and mutant MCAK motors is studied theoretically, which include the full-length MCAK, the full-length MCAK with mutations in the α4-helix of the motor domain, the mutant full-length MCAK with a neutralized neck, the monomeric MCAK and the mutant monomeric MCAK with a neutralized neck. The studies show that a single dimeric MCAK motor can depolymerize microtubules in a processive manner, with either one tubulin or two tubulins being removed per times. The theoretical results are in agreement with the available experimental data. Moreover, predicted results are provided.

Binding patterns of inhibitors to different pockets of kinesin Eg5

The kinesin-5 family member, Eg5, plays very important role in the mitosis. As a mitotic protein, Eg5 is the target of various mitotic inhibitors. There are two targeting pockets in the motor domain of Eg5, which locates in the α2/L5/α3 region and the α4/α6 region respectively. We investigated the interactions between the different inhibitors and the two binding pockets of Eg5 by using all-atom molecular dynamics method. Combined the conformational analysis with the free-energy calculation, the binding patterns of inhibitors to the two binding pockets are shown. The α2/L5/α3 pocket can be divided into 4 regions. The structures and binding conformations of inhibitors in region 1 and 2 are highly conserved. The shape of α4/α6 pocket is alterable. The space of this pocket in ADP-binding state of Eg5 is larger than that in ADP·Pi-binding state due to the limitation of a hydrogen bond formed in the ADP·Pi-binding state. The results of this investigation provide the structural basis of the inhibitor-Eg5 interaction and offer a reference for the Eg5-targeted drug design.

ATP Concentration-Dependent Fractions of One-Head-Bound and Two-Head-Bound States of the Kinesin Motor during Its Chemomechanical Coupling Cycle

Kinesin is a typical motor protein that can use the chemical energy of ATP hydrolysis to step processively on microtubules, alternating between one-head-bound and two-head-bound states. Some published experimental results showed that the duration of the one-head-bound state increases greatly with a decrease in ATP concentration, whereas the duration of the two-head-bound state is independent of ATP concentration, indicating that ATP binding occurs in the one-head-bound state. On the contrary, other experimental results showed that the duration of the two-head-bound state increases greatly with a decrease in ATP concentration, whereas the duration of the one-head-bound state increases slightly with a decrease in ATP concentration, indicating that ATP binding occurs mainly in the two-head-bound state. Here, we explain consistently and quantitatively these contradictory experimental results, resolving the controversy that is critical to the chemomechanical coupling mechanism of the kinesin motor.

Effect of small molecular crowders on dynamics of kinesin molecular motors

Kinesin is a motor protein that can convert chemical energy of ATP hydrolysis into mechanical energy of moving processively on microtubules. Apart from the load and ATP concentration affecting the dynamics of the motor such as velocity, run length, dissociation rate, etc., the increase of solution viscosity by supplementing crowding agents of low molecular weight into the buffer can also affect the dynamics. Here, based on our proposed model for the chemomechanical coupling of the kinesin motor, a systematically theoretical study of the motor dynamics under the variation of the viscosity and load is presented. Both the load on the motor's stalk and that on one of the two heads are considered. The theoretical results provide a consistent explanation of the available contradictory experimental results, with some showing that increasing viscosity decreases sensitively the velocity whereas others showing that increasing viscosity has little effect on the velocity. The theoretical results reproduce quantitatively the puzzling experimental data showing that under different directions of the load on the stalk, increasing viscosity has very different effects on the change of run length or dissociation rate. The theoretical results predict that in both the pure and crowded buffers the dependence of the run length on the load acting one of the two heads has very different feature from that on the load acting on the stalk.

Effect of the Neck Linker on Processive Stepping of Kinesin Motor

Kinesin motor protein, which is composed of two catalytic domains connected together by a long coiled-coil stalk via two flexible neck linkers (NLs), can step processively on a microtubule towards the plus end by hydrolyzing adenosine triphosphate (ATP) molecules. To understand what the role is that the NL plays in the processive stepping, the dynamics of the kinesin motor are studied theoretically here by considering the mutation or deletion of an N-terminal cover strand that contributes to the docking of the NL in kinesin-1, the extension of the NL in kinesin-1, the mutation of the NL in kinesin-1, the swapping of the NL of kinesin-2 with that of kinesin-1, the joining of the stalk and neck of Ncd that moves towards the minus end of MT to the catalytic domain of kinesin-1, the replacement of catalytic domain of kinesin-1 with that of Ncd, and so on. The theoretical results give a consistent and quantitative explanation of various available experimental results about the effects of these mutations on motor dynamics and, moreover, provide predicted results. Additionally, the processive motility of kinesin-6 MKLP2 without NL docking is also explained. The available experimental data about the effect of NL mutations on the dynamics of the bi-directional kinesin-5 Cin8 are also explained. The studies are critically implicative to the mechanism of the stepping of the kinesin motor.

Dynamics of kinesin motor proteins under longitudinal and sideways loads

The available single-molecule data showed that different species of N-terminal kinesin molecular motors have very different features on dependences of run length and dissociation rate upon longitudinal load acting on stalks of the motors. The prior single-molecule data for Loligo pealei kinesin-1 indicated that the sideways load has only a weak effect on the velocity, but even a small sideways load can cause a large reduction in the run length. However, these puzzling experimental data remain to be explained and the underlying physical mechanisms are unclear. Here, based on our proposed model we study analytically the dynamics of the N-terminal kinesin motors such as Loligo pealei kinesin-1, Drosophila kinesin-1, truncated kinesin-5/Eg5, truncated kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB dimers under both longitudinal and sideways loads. The theoretical results explain quantitatively the available experimental data and provide predictions. The physical mechanism of different kinesin species showing very different features on the load-dependent dynamics and the physical mechanism of the effect of the sideways load on the dynamics are revealed.

Molecular Mechanism of Processive Stepping of Kinesin Motors

Kinesin-1 is a motor protein that can step processively on microtubule by hydrolyzing ATP molecules, playing an essential role in intracellular transports. To better understand the mechanochemical coupling of the motor stepping cycle, numerous structural, biochemical, single molecule, theoretical modeling and numerical simulation studies have been undertaken for the kinesin-1 motor. Recently, a novel ultraresolution optical trapping method was employed to study the mechanics of the kinesin-1 motor and new results were supplemented to its stepping dynamics. In this commentary, the new single molecule results are explained well theoretically with one of the models presented in the literature for the mechanochemical coupling of the kinesin-1 motor. With the model, various prior experimental results for dynamics of different families of N-terminal kinesin motors have also been explained quantitatively.

Modeling processive motion of kinesin-13 MCAK and kinesin-14 Cik1-Kar3 molecular motors

Kinesin-13 MCAK, which is composed of two identical motor domains, can undergo unbiased one-dimensional diffusion on microtubules. Kinesin-14 Cik1-Kar3, which is composed of a Kar3 motor domain and a Cik1 motor homology domain with no ATPase activity, can move processively toward the minus end of microtubules. Here, we present a model for the diffusion of MCAK homodimer and a model for the processive motion of Cik1-Kar3 heterodimer. Although the two dimeric motors show different domain composition, in the models it is proposed that the two motors use the similar physical mechanism to move processively. With the models, the dynamics of the two dimers is studied analytically. The theoretical results for MCAK reproduce quantitatively the available experimental data about diffusion constant and lifetime of the motor bound to microtubule in different nucleotide states. The theoretical results for Cik1-Kar3 reproduce quantitatively the available experimental data about load dependence of velocity and explain consistently the available experimental data about effects of the exchange and mutation of the motor homology domain on the velocity of the heterodimer. Moreover, predicted results for other aspects of the dynamics of the two dimers are provided.

Effect of Kinesin-5 Tail Domain on Motor Dynamics for Antiparallel Microtubule Sliding

Kinesin-5 motor consists of two pairs of heads and tail domains, which are situated at the opposite ends of a common stalk. The two pairs of heads can bind to two antiparallel microtubules (MTs) and move on the two MTs independently towards the plus ends, sliding apart the two MTs, which is responsible for chromosome segregation during mitosis. Prior experimental data showed that the tails of kinesin-5 Eg5 can modulate the dynamics of single motors and are critical for multiple motors to generate high steady forces to slide apart two antiparallel MTs. To understand the molecular mechanism of the tails modulating the ability of Eg5 motors, based on our proposed model the dynamics of the single Eg5 with the tails and that without the tails moving on single MTs is studied analytically and compared. Furthermore, the dynamics of antiparallel MT sliding by multiple Eg5 motors with the tails and that without the tails is studied numerically and compared. Both the analytical results for single motors and the numerical results for multiple motors are consistent with the available experimental data.

Studies of Conformational Changes of Tubulin Induced by Interaction with Kinesin Using Atomistic Molecular Dynamics Simulations

The transition between strong and weak interactions of the kinesin head with the microtubule, which is regulated by the change of the nucleotide state of the head, is indispensable for the processive motion of the kinesin molecular motor on the microtubule. Here, using all-atom molecular dynamics simulations, the interactions between the kinesin head and tubulin are studied on the basis of the available high-resolution structural data. We found that the strong interaction can induce rapid large conformational changes of the tubulin, whereas the weak interaction cannot. Furthermore, we found that the large conformational changes of the tubulin have a significant effect on the interaction of the tubulin with the head in the weak-microtubule-binding ADP state. The calculated binding energy of the ADP-bound head to the tubulin with the large conformational changes is only about half that of the tubulin without the conformational changes.

A model of processive walking and slipping of kinesin-8 molecular motors

Kinesin-8 molecular motor can move with superprocessivity on microtubules towards the plus end by hydrolyzing ATP molecules, depolymerizing microtubules. The available single molecule data for yeast kinesin-8 (Kip3) motor showed that its superprocessive movement is frequently interrupted by brief stick-slip motion. Here, a model is presented for the chemomechanical coupling of the kinesin-8 motor. On the basis of the model, the dynamics of Kip3 motor is studied analytically. The analytical results reproduce quantitatively the available single molecule data on velocity without including the slip and that with including the slip versus external load at saturating ATP as well as slipping velocity versus external load at saturating ADP and no ATP. Predicted results on load dependence of stepping ratio at saturating ATP and load dependence of velocity at non-saturating ATP are provided. Similarities and differences between dynamics of kinesin-8 and that of kinesin-1 are discussed.

Mechanistic basis of propofol-induced disruption of kinesin processivity

Propofol is a widely used general anesthetic to induce and maintain anesthesia, and its effects are thought to occur through impact on the ligand-gated channels including the GABA_A receptor. Propofol also interacts with a large number of proteins including molecular motors and inhibits kinesin processivity, resulting in significant decrease in the run length for conventional kinesin-1 and kinesin-2. However, the molecular mechanism by which propofol achieves this outcome is not known. The structural transition in the kinesin neck-linker region is crucial for its processivity. In this study, we analyzed the effect of propofol and its fluorine derivative (fropofol) on the transition in the neck-linker region of kinesin. Propofol binds at two crucial surfaces in the leading head: one at the microtubule-binding interface and the other in the neck-linker region. We observed in both the cases the order-disorder transition of the neck-linker was disrupted and kinesin lost its signal for forward movement. In contrast, there was not an effect on the neck-linker transition with propofol binding at the trailing head. Free-energy calculations show that propofol at the microtubule-binding surface significantly reduces the microtubule-binding affinity of the kinesin head. While propofol makes pi-pi stacking and H-bond interactions with the propofol binding cavity, fropofol is unable to make a suitable interaction at this binding surface. Therefore, the binding affinity of fropofol is much lower compared to propofol. Hence, this study provides a mechanism by which propofol disrupts kinesin processivity and identifies transitions in the ATPase stepping cycle likely affected.

A common ATP-dependent stepping model for kinesin-5 and kinesin-1: Mechanism of bi-directionality of kinesin-5

Kinesin-5 and kinesin-1 proteins are two families of kinesin superfamily molecular motors that can move processively on microtubules powered by ATP hydrolysis. Kinesin-1 is a unidirectional motor. By contrast, some yeast kinesin-5 motors are bidirectional and the directionality can be switched by changing the experimental conditions. Here, on the basis of a common chemomechanical coupling model, the dynamics of kinesin-1 and in particular the dynamics of kinesin-5 is studied theoretically, explaining the available experimental data. For example, the experimental data about different movement directions under different experimental conditions for kinesin-5 are explained well. The origin of why kinesin-1 can only make unidirectional movement and kinesin-5 can make bidirectional movements is revealed. The origin of mutations or deletions of several structural elements affecting the directionality of kinesin-5 is revealed. Moreover, some predicted results for kinesin-5 are provided.

How Kinesin-1 Utilize the Energy of Nucleotide: The Conformational Changes and Mechanochemical Coupling in the Unidirectional Motion of Kinesin-1

Kinesin-1 is a typical motile molecular motor and the founding member of the kinesin family. The most significant feature in the unidirectional motion of kinesin-1 is its processivity. To realize the fast and processive movement on the microtubule lattice, kinesin-1 efficiently transforms the chemical energy of nucleotide binding and hydrolysis to the energy of mechanical movement. The chemical and mechanical cycle of kinesin-1 are coupled to avoid futile nucleotide hydrolysis. In this paper, the research on the mechanical pathway of energy transition and the regulating mechanism of the mechanochemical cycle of kinesin-1 is reviewed.

A common chemomechanical coupling model for orphan and conventional kinesin molecular motors

Orphan and conventional kinesin dimers represent two families of the kinesin superfamily molecular motors. Conventional kinesin, having a 14-residue neck linker (NL) in each head, can step processively on microtubule (MT), with an ATP hydrolysis being coupled with a mechanical stepping under no load. Orphan kinesin phragmoplast-associated kinesin-related protein 2 (PAKRP2) dimer, despite having a NL of 32 residues in each head, can also step processively on MT and exhibits tight chemomechanical coupling under no load. However, the dynamic properties of the wild type PAKRP2 and the mutant one with each NL truncated to 14 residues are very different from those of the wild type conventional kinesin and the mutant one with each NL being replaced by the 32-residue NL from PAKRP2. Here, based on a common chemomechanical coupling model we study computationally the dynamics of the two families of the kinesin dimers, with the simulated results explaining quantitatively the available experimental data. The large differences in the dynamics between the two families of kinesin dimers arise mainly from different rate constants of NL docking and ATPase activity and different weak affinities of the head in ADP state for MT. The studies indicate that both the orphan kinesin PAKRP2 and conventional kinesin use the same mechanism for processive motility.

Theoretical Analysis of Dynamics of Kinesin Molecular Motors

Kinesin is a typical molecular motor that can step processively on microtubules powered by hydrolysis of adenosine triphosphate (ATP) molecules, playing a critical role in intracellular transports. Its dynamical properties such as its velocity, stepping ratio, run length, dissociation rate, etc. as well as the load dependencies of these quantities have been well documented through single-molecule experimental methods. In particular, the run length shows a dramatic asymmetry with respect to the direction of the load, and the dissociation rate exhibits a slip-catch-slip bond behavior under the backward load. Here, an analytic theory was provided for the dynamics of kinesin motors under both forward and backward loads, explaining consistently and quantitatively the diverse available experimental results.

Non-tight and tight chemomechanical couplings of biomolecular motors under hindering loads

Biomolecular motors make use of free energy released from chemical reaction (typically ATP hydrolysis) to perform mechanical motion or work. An important issue is whether a molecular motor exhibits tight or non-tight chemomechanical (CM) coupling. The tight CM coupling refers to that each ATPase activity is coupled with a mechanical step, while the non-tight CM coupling refers to that an ATPase activity is not necessarily coupled with a mechanical step. Here, we take kinesin, monomeric DNA helicase, ring-shaped hexameric DNA helicase and ribosome as examples to study this issue. Our studies indicate that some motors such as kinesin, monomeric helicase and ribosome exhibit non-tight CM coupling under hindering forces, while others such as the ring-shaped hexameric helicase exhibit tight or nearly tight CM coupling under any force. For the former, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the CM coupling efficiency, while the ATPase rate is independent or nearly independent of the force. For the latter, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the ATPase rate, while the CM coupling efficiency is independent or nearly independent of the force.

Run length distribution of dimerized kinesin-3 molecular motors: comparison with dimeric kinesin-1

Kinesin-3 and kinesin-1 molecular motors are two families of the kinesin superfamily. It has been experimentally revealed that in monomeric state kinesin-3 is inactive in motility and cargo-mediated dimerization results in superprocessive motion, with an average run length being more than 10-fold longer than that of kinesin-1. In contrast to kinesin-1 showing normally single-exponential distribution of run lengths, dimerized kinesin-3 shows puzzlingly Gaussian distribution of run lengths. Here, based on our proposed model, we studied computationally the dynamics of kinesin-3 and compared with that of kinesin-1, explaining quantitatively the available experimental data and revealing the origin of superprocessivity and Gaussian run length distribution of kinesin-3. Moreover, predicted results are provided on ATP-concentration dependence of run length distribution and force dependence of mean run length and dissociation rate of kinesin-3.