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

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 of Chemomechanical Coupling of Cytoplasmic Dynein Motors

Cytoplasmic dynein homodimer is a motor protein that can step processively on microtubules (MTs) toward the minus end by hydrolyzing ATP molecules. Some dynein motors show a complicated stepping behavior with variable step sizes and having both hand-overhand and inchworm steps, while some mammalian dynein motors show simplistic stepping behavior with a constant step size and having only hand-overhand steps. Here, a model for the chemomechanical coupling of the dynein is presented, based on which an analytical theory is given on the dynamics of the motor. The theoretical results explain consistently and quantitatively the available experimental data on various aspects of the dynamics of dynein with complicated stepping behavior and the dynamics of dynein with simplistic stepping behavior. The very differences in the dynamic behavior between the two motors are due solely to different elastic coefficients of the linkage connecting the two dynein heads, with the dynein motors of the complicated and simplistic stepping behaviors having small and large coefficients, respectively. Moreover, it is analyzed that the ATPase rate of the dynein head with a docked linker being larger than that with an undocked linker is indispensable for the unidirectional motility of the motor, and the small free energy change for the linker docking in the strong MT-binding state facilitates the unidirectional motility.

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.

Modeling Studies of the Mechanism of Context-Dependent Bidirectional Movements of Kinesin-14 Motors

Kinesin-14s, a subfamily of the large superfamily of kinesin motor proteins, function mainly in spindle assembly and maintenance during mitosis and meiosis. KlpA from Aspergillus nidulans and GiKIN14a from Giardia intestinalis are two types of kinesin-14s. Available experimental results puzzlingly showed that while KlpA moves preferentially toward the minus end in microtubule-gliding setups and inside parallel microtubule overlaps, it moves preferentially toward the plus end on single microtubules. More puzzlingly, the insertion of an extra polypeptide linker in the central region of the neck stalk switches the motility direction of KlpA on single microtubules to the minus end. Prior experimental results showed that GiKIN14a moves preferentially toward the minus end on single microtubules in either tailless or full-length forms. The tail not only greatly enhances the processivity but also accelerates the ATPase rate and velocity of GiKIN14a. The insertion of an extra polypeptide linker in the central region of the neck stalk reduces the ATPase rate of GiKIN14a. However, the underlying mechanism of these puzzling dynamical features for KlpA and GiKIN14a is unclear. Here, to understand this mechanism, the dynamics of KlpA and GiKIN14a were studied theoretically on the basis of the proposed model, incorporating potential changes between the kinesin head and microtubule, as well as the potential between the tail and microtubule. The theoretical results quantitatively explain the available experimental results and provide predicted results. It was found that the elasticity of the neck stalk determines the directionality of KlpA on single microtubules and affects the ATPase rate and velocity of GiKIN14a on single microtubules.

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.

Molecular mechanism of interaction between kinesin motors affecting their residence times on microtubule lattice and end

Kinesin superfamily can be classified into 14 subfamilies. Some families of kinesin motors such as kinesin-1 are responsible for long-distance intracellular transports and thus the motors are required to reside on the microtubule (MT) lattice for a longer time than at the end. Some families such as kinesin-8 Kip3 and kinesin-5 Eg5 are responsible for the regulation of MT length by depolymerizing or polymerizing the MT from the plus end and thus the motors are required to reside at the MT end for a long time. Under the crowded condition of the motors, it was found experimentally that the residence times of the kinesin-8 Kip3 and kinesin-5 Eg5 at the MT end are reduced greatly compared to the single-motor case. However, the underlying mechanism of different families of kinesin motors having different MT-end residence times is unknown. The molecular mechanism by which the interaction between the two motors greatly reduces the residence time of the motor at the MT end is elusive. In addition, during the processive stepping on the MT lattice, when two kinesin motors meet it is unknown how the interaction between them affects their dissociation rates. To address the above unclear issues, here we make a consistent and theoretical study of the residence times of the kinesin-1, kinesin-8 Kip3 and kinesin-5 Eg5 motors on the MT lattice and at the end under both the single-motor condition and multiple-motors or crowded condition.

Causes, costs and consequences of kinesin motors communicating through the microtubule lattice

Microtubules are critical for a variety of important functions in eukaryotic cells. During intracellular trafficking, molecular motor proteins of the kinesin superfamily drive the transport of cellular cargoes by stepping processively along the microtubule surface. Traditionally, the microtubule has been viewed as simply a track for kinesin motility. New work is challenging this classic view by showing that kinesin-1 and kinesin-4 proteins can induce conformational changes in tubulin subunits while they are stepping. These conformational changes appear to propagate along the microtubule such that the kinesins can work allosterically through the lattice to influence other proteins on the same track. Thus, the microtubule is a plastic medium through which motors and other microtubule-associated proteins (MAPs) can communicate. Furthermore, stepping kinesin-1 can damage the microtubule lattice. Damage can be repaired by the incorporation of new tubulin subunits, but too much damage leads to microtubule breakage and disassembly. Thus, the addition and loss of tubulin subunits are not restricted to the ends of the microtubule filament but rather, the lattice itself undergoes continuous repair and remodeling. This work leads to a new understanding of how kinesin motors and their microtubule tracks engage in allosteric interactions that are critical for normal cell physiology.

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.

Modeling Study of the Dynamics of Kinesin-14 Molecular Motors

Kinesin-14s constitute a subfamily of the large superfamily of adenosine triphosphate-dependent microtubule-based motor proteins. Kinesin-14s have the motor domain at the C-terminal end of the peptide, playing key roles during spindle assembly and maintenance. Some of them are nonprocessive motors, whereas others can move processively on microtubules. Here, we take budding yeast Cik1-Kar3 and human HSET as examples to study theoretically the dynamics of the processive kinesin-14 motor moving on the single microtubule under load, the dynamics of the motor coupled with an Ndc80 protein moving on the single microtubule, the dynamics of the motor moving in microtubule arrays, and so on. The dynamics of the nonprocessive Drosophila Ncd motor is also discussed. The studies explain well the available experimental data and, moreover, provide predicted results. We show that the processive kinesin-14 motors can move efficiently in microtubule arrays toward the minus ends, and after reaching the minus ends, they can stay there stably, thus performing the function of organizing the microtubules in the bipolar spindle into polar arrays at the spindle poles.

Effect of varying load in moving period of a step on dynamics of molecular motors

During the processive stepping of a molecular motor on its polar track, a step consists of a long dwell period and a very short moving period. In single molecule optical trapping experiments to determine the load dependence of the motor dynamics, although the motor experiences a constant load during the dwell period, it experiences a varying load during the moving period. However, in previous theoretical studies to explain the single molecule optical trapping data, it was simply assumed that the motor experiences a constant load during both the dwell period and the following moving period. Thus, an important but unclear issue is whether the assumption is appropriate in the theoretical studies. Here, we take kinesin and myosin-V as examples to study theoretically the motor dynamics with the consideration of the varying load during the moving period and compare with that with the assumption of the constant load. The studies show that in the optical trapping experiments employed in the literature, for the kinesin with a small step size of about 8 nm it is a good approximation to make the theoretical studies by assuming that the motor experiences the constant load during the moving period. For the myosin-V with a large step size of about 36 nm, there are small but noticeable deviations of the results obtained by considering that the motor experiences the varying load during the moving period from those by assuming that the motor experiences the constant load. .

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.