Theoretical Analysis of Dynamics of Kinesin Molecular Motors

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.

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.

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.

Determinant factors for residence time of kinesin motors at microtubule ends

Kinesins constitute a superfamily of microtubule (MT)-based motor proteins, which can perform diverse biological functions in cells such as transporting vesicle, regulating MT dynamics, and segregating chromosome. Some motors such as kinesin-1, kinesin-2, and kinesin-3 do the activity mainly on the MT lattice, while others such as kinesin-7 and kinesin-8 do the activity mainly at the MT plus end. To perform the different functions, it is required that the former motors can reside on the MT lattice for longer times than at the end, while the latter motors can reside at the MT plus end for long times. Here, a simple but general theory of the MT-end residence time of the kinesin motor is presented, with which the factors dictating the residence time are determined. The theory is further used to study specifically the MT-end residence times of Drosophila kinesin-1, kinesin-2/KIF3AB, kinesin-3/Unc104, kinesin-5/Eg5, kinesin-7/CENP-E, and kinesin-8/Kip3 motors, with the theoretical results being in agreement with the available experimental data.

Optimizing dynamical functions for speed with stochastic paths

Living systems are built from microscopic components that function dynamically; they generate work with molecular motors, assemble and disassemble structures such as microtubules, keep time with circadian clocks, and catalyze the replication of DNA. How do we implement these functions in synthetic nanostructured materials to execute them before the onset of dissipative losses? Answering this question requires a quantitative understanding of when we can improve performance and speed while minimizing the dissipative losses associated with operating in a fluctuating environment. Here, we show that there are four modalities for optimizing dynamical functions that can guide the design of nanoscale systems. We analyze Markov models that span the design space: a clock, ratchet, replicator, and self-assembling system. Using stochastic thermodynamics and an exact expression for path probabilities, we classify these models of dynamical functions based on the correlation of speed with dissipation and with the chosen performance metric. We also analyze random networks to identify the model features that affect their classification and the optimization of their functionality. Overall, our results show that the possible nonequilibrium paths can determine our ability to optimize the performance of dynamical functions, despite ever-present dissipation, when there is a need for speed.

Impact of noise on the regulation of intracellular transport of intermediate filaments

Noise affects all biological processes from molecules to cells, organisms and populations. Although the effect of noise on these processes is highly variable, evidence is accumulating which shows natural stochastic fluctuations (noise) can facilitate biological functions. Herein, we investigate the effect of noise on the transport of intermediate filaments in cells by comparing the stochastic and deterministic formalizations of the bidirectional transport of intermediate filaments, long elastic polymers transported along microtubules by antagonistic motor proteins Dallon et al., 2019; Portet et al., 2019. By numerically exploring discrepancies in timescales and attractors between both formalizations, we characterize the impact of stochastic fluctuations on the individual and ensemble transport. Biologically, we find that noise promotes the collective movement of intermediate filaments and increases the efficiency of its regulation by the biochemical properties of motor-cargo interactions. While stochastic fluctuations reduce the impact of the initial distributions of motor proteins in cells, the number of binding sites and the affinity of motor-cargo interactions are the key parameters controlling transport efficiency and efficacy.

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.

Diffusion Biased by a Soft Neck Linker Regulates Kinesin Stepping

Conventional kinesin is a high-performance motor that moves primarily toward the plus end of microtubules and occasionally toward the opposite direction. The physical mechanism of this directional stepping remains unclear. Here we develop a kinetic two-cycle model incorporating kinesin forward and backward stepping, in which the neck linker zippering and ATP catalysis process are conserved in backward steps. This model is quantitatively validated by a variety of experimental data, including load dependence of velocity, stepping ratio, and dwell time. The physical mechanism of kinesin stepping regulated by a biased diffusion process is identified by analyzing the load dependence and relevant thermodynamic properties of the model. Furthermore, the model suggests the kinesin directionality is optimized resulting from fulfilling a thermodynamic constraint. Our modeling provides a chemomechanical coupling mechanism that connects the flexibility of the neck linker zippering effect for direction rectification and the measured performance into a consistent frame.

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.

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.