Kinesin-microtubule binding depends on both nucleotide state and loading direction

Competition between physical search and a weak-to-strong transition rate-limits kinesin binding times

The self-organization of cells relies on the profound complexity of protein-protein interactions. Challenges in directly observing these events have hindered progress toward understanding their diverse behaviors. One notable example is the interaction between molecular motors and cytoskeletal systems that combine to perform a variety of cellular functions. In this work, we leverage theory and experiments to identify and quantify the rate-limiting mechanism of the initial association between a cargo-bound kinesin motor and a microtubule track. Recent advances in optical tweezers provide binding times for several lengths of kinesin motors trapped at varying distances from a microtubule, empowering the investigation of competing models. We first explore a diffusion-limited model of binding. Through Brownian dynamics simulations and simulation-based inference, we find this simple diffusion model fails to explain the experimental binding times, but an extended model that accounts for the ADP state of the molecular motor agrees closely with the data, even under the scrutiny of penalizing for additional model complexity. We provide quantification of both kinetic rates and biophysical parameters underlying the proposed binding process. Our model suggests that a typical binding event is limited by ADP state rather than physical search. Lastly, we predict how these association rates can be modulated in distinct ways through variation of environmental concentrations and physical properties.

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.

Theoretical analysis of cargo transport by catch bonded motors in optical trapping assays

Dynein motors exhibit catch bonding, where the unbinding rate of the motors from microtubule filaments decreases with increasing opposing load. The implications of this catch bond on the transport properties of dynein-driven cargo are yet to be fully understood. In this context, optical trapping assays constitute an important means of accurately measuring the forces generated by molecular motor proteins. We investigate, using theory and stochastic simulations, the transport properties of cargo transported by catch bonded dynein molecular motors - both singly and in teams - in a harmonic potential, which mimics the variable force experienced by cargo in an optical trap. We estimate the biologically relevant measures of first passage time - the time during which the cargo remains bound to the microtubule and detachment force - the force at which the cargo unbinds from the microtubule, using both two-dimensional and one-dimensional force balance frameworks. Our results suggest that even for cargo transported by a single motor, catch bonding may play a role depending on the force scale which marks the onset of the catch bond. By comparing with experimental measurements on single dynein-driven transport, we estimate realistic bounds of this catch bond force scale. Generically, catch bonding results in increased persistent motion, and can also generate non-monotonic behaviour of first passage times. For cargo transported by multiple motors, emergent collective effects due to catch bonding can result in non-trivial re-entrant phenomena wherein average first passage times and detachment forces exhibit non-monotonic behaviour as a function of the stall force and the motor velocity.

ADP release can explain spatially-dependent kinesin binding times

The self-organization of cells relies on the profound complexity of protein-protein interactions. Challenges in directly observing these events have hindered progress toward understanding their diverse behaviors. One notable example is the interaction between molecular motors and cytoskeletal systems that combine to perform a variety of cellular functions. In this work, we leverage theory and experiments to identify and quantify the rate-limiting mechanism of the initial association between a cargo-bound kinesin motor and a microtubule track. Recent advances in optical tweezers provide binding times for several lengths of kinesin motors trapped at varying distances from a microtubule, empowering the investigation of competing models. We first explore a diffusion-limited model of binding. Through Brownian dynamics simulations and simulation-based inference, we find this simple diffusion model fails to explain the experimental binding times, but an extended model that accounts for the ADP state of the molecular motor agrees closely with the data, even under the scrutiny of penalizing for additional model complexity. We provide quantification of both kinetic rates and biophysical parameters underlying the proposed binding process. Our model suggests that most but not every motor binding event is limited by their ADP state. Lastly, we predict how these association rates can be modulated in distinct ways through variation of environmental concentrations and spatial distances.

Fast backward steps and detachment of single kinesin molecules measured under a wide range of loads

To understand force generation under a wide range of loads, the stepping of single kinesin molecules was measured at loads from -20 to 42 pN by optical tweezers with high temporal resolution. The optical trap has been improved to halve positional noise and increase bandwidth by using 200-nm beads. The step size of the forward and backward steps was 8.2 nm even over a wide range of loads. Histograms of the dwell times of backward steps and detachment fit well to two independent exponential equations with fast (~0.4 ms) and slow (>3 ms) time constants, indicating the existence of a fast step in addition to the conventional slow step. The dwell times of the fast steps were almost independent of the load and ATP concentration, while those of the slow backward steps and detachment depended on those. We constructed the kinetic model to explain the fast and slow steps under a wide range of loads.

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.

Calculating the force-dependent unbinding rate of biological macromolecular bonds from force-ramp optical trapping assays

The non-covalent biological bonds that constitute protein–protein or protein–ligand interactions play crucial roles in many cellular functions, including mitosis, motility, and cell–cell adhesion. The effect of external force (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F$$\end{document}F) on the unbinding rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{\text{off}}\left(F\right)$$\end{document}koffF) of macromolecular interactions is a crucial parameter to understanding the mechanisms behind these functions. Optical tweezer-based single-molecule force spectroscopy is frequently used to obtain quantitative force-dependent dissociation data on slip, catch, and ideal bonds. However, analyses of this data using dissociation time or dissociation force histograms often quantitatively compare bonds without fully characterizing their underlying biophysical properties. Additionally, the results of histogram-based analyses can depend on the rate at which force was applied during the experiment and the experiment’s sensitivity. Here, we present an analytically derived cumulative distribution function-like approach to analyzing force-dependent dissociation force spectroscopy data. We demonstrate the benefits and limitations of the technique using stochastic simulations of various bond types. We show that it can be used to obtain the detachment rate and force sensitivity of biological macromolecular bonds from force spectroscopy experiments by explicitly accounting for loading rate and noisy data. We also discuss the implications of our results on using optical tweezers to collect force-dependent dissociation data.

Multiscale Coarse-Grained Model for the Stepping of Molecular Motors with Application to Kinesin

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps toward the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin, there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multiscale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with a focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted, allowing the step to be completed in tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full three-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

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.

Highly-Parallel Microfluidics-Based Force Spectroscopy on Single Cytoskeletal Motors

Cytoskeletal motors transform chemical energy into mechanical work to drive essential cellular functions. Optical trapping experiments have provided crucial insights into the operation of these molecular machines under load. However, the throughput of such force spectroscopy experiments is typically limited to one measurement at a time. Here, a highly-parallel, microfluidics-based method that allows for rapid collection of force-dependent motility parameters of cytoskeletal motors with two orders of magnitude improvement in throughput compared to currently available methods is introduced. Tunable hydrodynamic forces to stepping kinesin-1 motors via DNA-tethered beads and utilize a large field of view to simultaneously track the velocities, run lengths, and interaction times of hundreds of individual kinesin-1 molecules under varying resisting and assisting loads are applied. Importantly, the 16 µm long DNA tethers between the motors and the beads significantly reduces the vertical component of the applied force pulling the motors away from the microtubule. The approach is readily applicable to other molecular systems and constitutes a new methodology for parallelized single-molecule force studies on cytoskeletal motors.

Cutting-Edge Single-Molecule Technologies Unveil New Mechanics in Cellular Biochemistry

Single-molecule technologies have expanded our ability to detect biological events individually, in contrast to ensemble biophysical technologies, where the result provides averaged information. Recent developments in atomic force microscopy have not only enabled us to distinguish the heterogeneous phenomena of individual molecules, but also allowed us to view up to the resolution of a single covalent bond. Similarly, optical tweezers, due to their versatility and precision, have emerged as a potent technique to dissect a diverse range of complex biological processes, from the nanomechanics of ClpXP protease-dependent degradation to force-dependent processivity of motor proteins. Despite the advantages of optical tweezers, the time scales used in this technology were inconsistent with physiological scenarios, which led to the development of magnetic tweezers, where proteins are covalently linked with the glass surface, which in turn increases the observation window of a single biomolecule from minutes to weeks. Unlike optical tweezers, magnetic tweezers use magnetic fields to impose torque, which makes them convenient for studying DNA topology and topoisomerase functioning. Using modified magnetic tweezers, researchers were able to discover the mechanical role of chaperones, which support their substrate proteinsby pulling them during translocation and assist their native folding as a mechanical foldase. In this article, we provide a focused review of many of these new roles of single-molecule technologies, ranging from single bond breaking to complex chaperone machinery, along with the potential to design mechanomedicine, which would be a breakthrough in pharmacological interventions against many diseases.

CYK4 relaxes the bias in the off-axis motion by MKLP1 kinesin-6

Centralspindlin, a complex of the MKLP1 kinesin-6 and CYK4 GAP subunits, plays key roles in metazoan cytokinesis. CYK4-binding to the long neck region of MKLP1 restricts the configuration of the two MKLP1 motor domains in the centralspindlin. However, it is unclear how the CYK4-binding modulates the interaction of MKLP1 with a microtubule. Here, we performed three-dimensional nanometry of a microbead coated with multiple MKLP1 molecules on a freely suspended microtubule. We found that beads driven by dimeric MKLP1 exhibited persistently left-handed helical trajectories around the microtubule axis, indicating torque generation. By contrast, centralspindlin, like monomeric MKLP1, showed similarly left-handed but less persistent helical movement with occasional rightward movements. Analysis of the fluctuating helical movement indicated that the MKLP1 stochastically makes off-axis motions biased towards the protofilament on the left. CYK4-binding to the neck domains in MKLP1 enables more flexible off-axis motion of centralspindlin, which would help to avoid obstacles along crowded spindle microtubules.

Analysing the 3D movement of MKLP1 motors, Maruyama et al. find that dimeric C. elegans MKLP1 drives a left-handed helical motion around the microtubule with minimum protofilament switching to the right side whereas less persistent motions are driven by monomers or by heterotetramers with CYK4. These findings suggest how obstacles along crowded spindle microtubules may be avoided by CYK4 binding to MKLP1.

Backstepping Mechanism of Kinesin-1

Kinesin-1 is an ATP-driven molecular motor that transports cellular cargo along microtubules. At low loads, kinesin-1 almost always steps forward, toward microtubule plus ends, but at higher loads, it can also step backward. Backsteps are usually 8 nm but can be larger. These larger backward events of 16 nm, 24 nm, or more are thought to be slips rather than steps because they are too fast to consist of multiple, tightly coupled 8-nm steps. Here, we propose that not only these larger backsteps, but all kinesin-1 backsteps, are slips. We show first that kinesin waits before forward steps for less time than before backsteps and detachments; second, we show that kinesin waits for the same amount of time before backsteps and detachments; and third, we show that by varying the microtubule type, we can change the ratio of backsteps to detachments without affecting forward stepping. Our findings indicate that backsteps and detachments originate from the same state and that this state arises later in the mechanochemical cycle than the state that gives rise to forward steps. To explain our data, we propose that, in each cycle of ATP turnover, forward kinesin steps can only occur before Pi release, whereas backslips and detachments can only occur after Pi release. In the scheme we propose, Pi release gates access to a weak binding K⋅ADP-K⋅ADP state that can slip back along the microtubule, re-engage, release ADP, and try again to take an ATP-driven forward step. We predict that this rescued detachment pathway is key to maintaining kinesin processivity under load.

Delineating elastic properties of kinesin linker and their sensitivity to point mutations

We analyze free energy estimators from simulation trials mimicking single-molecule pulling experiments on a neck linker of a kinesin motor. For that purpose, we have performed a version of steered molecular dynamics (SMD) calculations. The sample trajectories have been analyzed to derive distribution of work done on the system. In order to induce stretching of the linker, we have applied a constant pulling force to the molecule and allowed for a subsequent relaxation of its structure. The use of fluctuation relations (FR) relevant to non-equilibrium systems subject to thermal fluctuations allows us to assess the difference in free energy between stretched and relaxed conformations. To further understand effects of potential mutations on elastic properties of the linker, we have performed similar in silico studies on a structure formed of a polyalanine sequence (Ala-only) and on three other structures, created by substituting selected types of amino acid residues in the linker’s sequence with alanine (Ala) ones. The results of SMD simulations indicate a crucial role played by the Asparagine (Asn) and Lysine (Lys) residues in controlling stretching and relaxation properties of the linker domain of the motor.

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.

A Generalized Kinetic Model for Coupling between Stepping and ATP Hydrolysis of Kinesin Molecular Motors

A general kinetic model is presented for the chemomechanical coupling of dimeric kinesin molecular motors with and without extension of their neck linkers (NLs). A peculiar feature of the model is that the rate constants of ATPase activity of a kinesin head are independent of the strain on its NL, implying that the heads of the wild-type kinesin dimer and the mutant with extension of its NLs have the same force-independent rate constants of the ATPase activity. Based on the model, an analytical theory is presented on the force dependence of the dynamics of kinesin dimers with and without extension of their NLs at saturating ATP. With only a few adjustable parameters, diverse available single molecule data on the dynamics of various kinesin dimers, such as wild-type kinesin-1, kinesin-1 with mutated residues in the NLs, kinesin-1 with extension of the NLs and wild-type kinesin-2, under varying force and ATP concentration, can be reproduced very well. Additionally, we compare the power production among different kinesin dimers, showing that the mutation in the NLs reduces the power production and the extension of the NLs further reduces the power production.

Complex nearly immotile behaviour of enzymatically driven cargos

We report a minimal microtubule-based motile system displaying signatures of unconventional diffusion. The system consists of a single model cargo driven by an ensemble of N340K NCD motors along a single microtubule. Despite the absence of cytosolic or cytoskeleton complexity, the system shows complex behavior, characterized by sub-diffusive motion for short time lag scales and linear mean squared displacement dependence for longer time lags. The latter is also shown to have non-Gaussian character and cannot be ascribed to a canonical diffusion process. We use single particle tracking and analysis at varying temperatures and motor concentrations to identify the origin of these behaviors as enzymatic activity of mutant NCD. Our results show that signatures of non-Gaussian diffusivities can arise as a result of an active process and suggest that some immotility of cargos observed in cells may reflect the ensemble workings of mechanochemical enzymes and need not always reflect the properties of the cytoskeletal network or the cytosol.

ATP-Concentration- and Force-Dependent Chemomechanical Coupling of Kinesin Molecular Motors

A model is presented for the chemomechanical coupling of kinesin motors, which proposes that the rate constants of the chemical reaction are independent of the external force. On the basis of the model, we study theoretically the movement dynamics of the motors under varying external force and ATP concentration, such as the forward to backward stepping ratio, velocity, dwell time between two mechanical steps, stall force, and so on. The theoretical results reproduce quantitatively the diverse and even contradictory available single-molecule experimental data for different species of the motors. Furthermore, we study the dependence of the chemomechanical coupling ratio on ATP concentration and external force, with both ATP concentration and external force having large effects on the chemomechanical coupling.

Step Sizes and Rate Constants of Single-headed Cytoplasmic Dynein Measured with Optical Tweezers

A power stroke of dynein is thought to be responsible for the stepping of dimeric dynein. However, the actual size of the displacement driven by a power stroke has not been directly measured. Here, the displacements of single-headed cytoplasmic dynein were measured by optical tweezers. The mean displacement of dynein interacting with microtubule was ~8 nm at 100 µM ATP, and decreased sigmoidally with a decrease in the ATP concentration. The ATP dependence of the mean displacement was explained by a model that some dynein molecules bind to microtubule in pre-stroke conformation and generate 8-nm displacement, while others bind in the post-stroke one and detach without producing a power stroke. Biochemical assays showed that the binding affinity of the post-stroke dynein to a microtubule was ~5 times higher than that of pre-stroke dynein, and the dissociation rate was ~4 times lower. Taking account of these rates, we conclude that the displacement driven by a power stroke is 8.3 nm. A working model of dimeric dynein driven by the 8-nm power stroke was proposed.

Investigating role of conformational changes of microtubule in regulating its binding affinity to kinesin by all-atom molecular dynamics simulation

Changes of affinity of kinesin head to microtubule regulated by changes in the nucleotide state are essential to processive movement of kinesin on microtubule. Here, using all-atom molecular dynamics simulations we show that besides the nucleotide state, large conformational changes of microtubule-tubulin heterodimers induced by strong interaction with the head in strongly binding state are also indispensable to regulate the affinity of the head to the tubulin. In strongly binding state the high affinity of the head to microtubule arises largely from mutual conformational changes of the microtubule and head induced by the specific interaction between them via an induced-fit mechanism. Moreover, the ADP-head has a much weaker affinity to the local microtubule-tubulin, whose conformation is largely altered by the interaction with the head in strongly binding state, than to other unperturbed tubulins. This indicates that upon Pi release the ADP-head temporarily has a much weaker affinity to the local tubulin than to other tubulins.

Dynamics of Allosteric Transitions in Dynein

Cytoplasmic dynein, whose motor domain belongs to the AAA+ family, walks on microtubules toward the minus end. Using the available structures in different nucleotide states, we performed simulations of a coarse-grained model to elucidate the dynamics of allosteric transitions. Binding of ATP closes the cleft between the AAA1 and AAA2 domains, triggering conformational changes in the rest of the motor domain, thus forming the pre-power stroke state. Interactions with the microtubule, modeled implicitly, enhance ADP release rate, and the formation of the post-power stroke state. The dynamics of the linker (LN), which reversibly changes from a straight to a bent state, is heterogeneous. Persistent interactions between the LN and the insert loops in the AAA2 domain prevent the formation of pre-power stroke state when ATP is bound to AAA3, thus locking dynein in a repressed non-functional state. Application of mechanical force to the LN restores motility in the repressed state.

Processivity of dimeric kinesin-1 molecular motors

Kinesin‐1 is a homodimeric motor protein that can move along microtubule filaments by hydrolyzing ATP with a high processivity. How the two motor domains are coordinated to achieve such high processivity is not clear. To address this issue, we computationally studied the run length of the dimer with our proposed model. The computational data quantitatively reproduced the puzzling experimental data, including the dramatically asymmetric character of the run length with respect to the direction of external load acting on the coiled‐coil stalk, the enhancement of the run length by addition of phosphate, and the contrary features of the run length for different types of kinesin‐1 with extensions of their neck linkers compared with those without extension of the neck linker. The computational data on other aspects of the movement dynamics such as velocity and durations of one‐head‐bound and two‐head‐bound states in a mechanochemical coupling cycle were also in quantitative agreement with the available experimental data. Moreover, predicted results are provided on dependence of the run length upon external load acting on one head of the dimer, which can be easily tested in the future using single‐molecule optical trapping assays.

Kif15 functions as an active mechanical ratchet

Kif15 is a kinesin-12 that contributes critically to bipolar spindle assembly in humans. Here we use force-ramp experiments in an optical trap to probe the mechanics of single Kif15 molecules under hindering or assisting loads and in a variety of nucleotide states. While unloaded Kif15 is established to be highly processive, we find that under hindering loads, Kif15 takes <∼10 steps. As hindering load is increased, Kif15 forestep:backstep ratio decreases exponentially, with stall occurring at 6 pN. In contrast, under assisting loads, Kif15 detaches readily and rapidly, even from its AMPPNP state. Kif15 mechanics thus depend markedly on the loading direction. Kif15 interacts with a binding partner, Tpx2, and we show that Tpx2 locks Kif15 to microtubules under both hindering and assisting loads. Overall, our data predict that Kif15 in the central spindle will act as a mechanical ratchet, supporting spindle extension but resisting spindle compression.

Parsing the roles of neck-linker docking and tethered head diffusion in the stepping dynamics of kinesin

Kinesin walks processively on microtubules (MTs) in an asymmetric hand-over-hand manner consuming one ATP molecule per 16-nm step. The individual contributions due to docking of the approximately 13-residue neck linker to the leading head (deemed to be the power stroke) and diffusion of the trailing head (TH) that contributes in propelling the motor by 16 nm have not been quantified. We use molecular simulations by creating a coarse-grained model of the MT-kinesin complex, which reproduces the measured stall force as well as the force required to dislodge the motor head from the MT, to show that nearly three-quarters of the step occurs by bidirectional stochastic motion of the TH. However, docking of the neck linker to the leading head constrains the extent of diffusion and minimizes the probability that kinesin takes side steps, implying that both the events are necessary in the motility of kinesin and for the maintenance of processivity. Surprisingly, we find that during a single step, the TH stochastically hops multiple times between the geometrically accessible neighboring sites on the MT before forming a stable interaction with the target binding site with correct orientation between the motor head and the [Formula: see text] tubulin dimer.

Vinculin forms a directionally asymmetric catch bond with F-actin

Vinculin is an actin-binding protein thought to reinforce cell-cell and cell-matrix adhesions. However, how mechanical load affects the vinculin-F-actin bond is unclear. Using a single-molecule optical trap assay, we found that vinculin forms a force-dependent catch bond with F-actin through its tail domain, but with lifetimes that depend strongly on the direction of the applied force. Force toward the pointed (-) end of the actin filament resulted in a bond that was maximally stable at 8 piconewtons, with a mean lifetime (12 seconds) 10 times as long as the mean lifetime when force was applied toward the barbed (+) end. A computational model of lamellipodial actin dynamics suggests that the directionality of the vinculin-F-actin bond could establish long-range order in the actin cytoskeleton. The directional and force-stabilized binding of vinculin to F-actin may be a mechanism by which adhesion complexes maintain front-rear asymmetry in migrating cells.

Design principles governing chemomechanical coupling of kinesin

A systematic chemomechanical network model for the molecular motor kinesin is presented in this report. The network model is based on the nucleotide-dependent binding affinity of the heads to an microtubule (MT) and the asymmetries and similarities between the chemical transitions caused by the intramolecular strain between the front and rear heads. The network model allows for multiple chemomechanical cycles and takes into account all possible mechanical transitions between states in which one head is strongly bound and the other head is weakly bound to an MT. The results obtained from the model show the ATP-concentration dependence of the dominant forward stepping cycle and support a gated rear head mechanism in which the forward step is controlled by ATP hydrolysis and the resulting ADP-bound state of the rear head when the ATP level is saturated. When the ATP level is saturated, the energy from ATP hydrolysis is used to concentrate the chemical transition flux to a force-generating state that can produce the power stroke. In contrast, when the ATP level is low, the hydrolysis energy is consumed to avoid states in which the leading head is weakly bound to an MT and to inhibit frequent backward steps upon loading.

Crystal structure of Zen4 in the apo state reveals a missing conformation of kinesin

Kinesins hydrolyse ATP to transport intracellular cargoes along microtubules. Kinesin neck linker (NL) functions as the central mechano-chemical coupling element by changing its conformation through the ATPase cycle. Here we report the crystal structure of kinesin-6 Zen4 in a nucleotide-free, apo state, with the NL initial segment (NIS) adopting a backward-docked conformation and the preceding α6 helix partially melted. Single-molecule fluorescence resonance energy transfer (smFRET) analyses indicate the NIS of kinesin-1 undergoes similar conformational changes under tension in the two-head bound (2HB) state, whereas it is largely disordered without tension. The backward-docked structure of NIS is essential for motility of the motor. Our findings reveal a key missing conformation of kinesins, which provides the structural basis of the stable 2HB state and offers a tension-based rationale for an optimal NL length to ensure processivity of the motor.

Tug-of-war between two elastically coupled molecular motors: a case study on force generation and force balance

Intracellular transport is performed by molecular motors that pull cargos along cytoskeletal filaments. Many cellular cargos are observed to move bidirectionally, with fast transport in both directions. This behaviour can be understood as a stochastic tug-of-war between two teams of antagonistic motors. The first theoretical model for such a tug-of-war, the Müller-Klumpp-Lipowsky (MKL) model, was based on two simplifying assumptions: (i) both motor teams move with the same velocity in the direction of the stronger team, and (ii) this velocity matching and the associated force balance arise immediately after the rebinding of an unbound motor to the filament. In this study, we extend the MKL model by including an elastic coupling between the antagonistic motors, and by allowing the motors to perform discrete motor steps. Each motor step changes the elastic interaction forces experienced by the motors. In order to elucidate the basic concepts of force balance and force fluctuations, we focus on the simplest case of two antagonistic motors, one kinesin against one dynein. We calculate the probability distribution for the spatial separation of the motors and the dependence of this distribution on the motors' unbinding rate. We also compute the probability distribution for the elastic interaction forces experienced by the motors, which determines the average elastic force 〈F〉 and the standard deviation of the force fluctuations around this average value. The average force 〈F〉 is found to decrease monotonically with increasing unbinding rate ε₀. The behaviour of the MKL model is recovered in the limit of small ε₀. In the opposite limit of large ε₀, 〈F〉 is found to decay to zero as 1/ε₀. Finally, we study the limiting case with ε₀ = 0 for which we determine both the force statistics and the time needed to attain the steady state. Our theoretical predictions are accessible to experimental studies of in vitro systems consisting of two antagonistic motors attached to a synthetic scaffold or crosslinked via DNA hybridization.

Discrete Step Sizes of Molecular Motors Lead to Bimodal Non-Gaussian Velocity Distributions under Force

Fluctuations in the physical properties of biological machines are inextricably linked to their functions. Distributions of run lengths and velocities of processive molecular motors, like kinesin-1, are accessible through single-molecule techniques, but rigorous theoretical models for these probabilities are lacking. Here, we derive exact analytic results for a kinetic model to predict the resistive force (F)-dependent velocity [P(v)] and run length [P(n)] distribution functions of generic finitely processive molecular motors. Our theory quantitatively explains the zero force kinesin-1 data for both P(n) and P(v) using the detachment rate as the only parameter. In addition, we predict the F dependence of these quantities. At nonzero F, P(v) is non-Gaussian and is bimodal with peaks at positive and negative values of v, which is due to the discrete step size of kinesin-1. Although the predictions are based on analyses of kinesin-1 data, our results are general and should hold for any processive motor, which walks on a track by taking discrete steps.

Directed Binding of Gliding Bacterium, Mycoplasma mobile, Shown by Detachment Force and Bond Lifetime

Mycoplasma mobile, a fish-pathogenic bacterium, features a protrusion that enables it to glide smoothly on solid surfaces at a velocity of up to 4.5 µm s⁻¹ in the direction of the protrusion. M. mobile glides by a repeated catch-pull-release of sialylated oligosaccharides fixed on a solid surface by hundreds of 50-nm flexible “legs” sticking out from the protrusion. This gliding mechanism may be explained by a possible directed binding of each leg with sialylated oligosaccharides, by which the leg can be detached more easily forward than backward. In the present study, we used a polystyrene bead held by optical tweezers to detach a starved cell at rest from a glass surface coated with sialylated oligosaccharides and concluded that the detachment force forward is 1.6- to 1.8-fold less than that backward, which may be linked to a catch bond-like behavior of the cell. These results suggest that this directed binding has a critical role in the gliding mechanism.

Mycoplasma species are the smallest bacteria and are parasitic and occasionally commensal, as represented by Mycoplasma pneumoniae, which causes so-called “walking pneumonia” in humans. Dozens of species glide on host tissues, always in the direction of the characteristic cellular protrusion, by novel mechanisms. The fastest species, Mycoplasma mobile, catches, pulls, and releases sialylated oligosaccharides (SOs), which are common targets among influenza viruses, by means of a specific receptor based on the energy of ATP hydrolysis. Here, force measurements made with optical tweezers revealed that the force required to detach a cell from SOs is smaller forward than backward along the gliding direction. The directed binding should be a clue to elucidate this novel motility mechanism.

Collective dynamics of processive cytoskeletal motors

Major cellular processes are supported by various biomolecular motors that usually operate together as teams. We present an overview of the collective dynamics of processive cytokeletal motor proteins based on recent experimental and theoretical investigations. Experimental studies show that multiple motors function with different degrees of cooperativity, ranging from negative to positive. This effect depends on the mechanical properties of individual motors, the geometry of their connections, and the surrounding cellular environment. Theoretical models based on stochastic approaches underline the importance of intermolecular interactions, the properties of single motors, and couplings with cellular medium in predicting the collective dynamics. We discuss several features that specify the cooperativity in motor proteins. Based on this approach a general picture of collective dynamics of motor proteins is formulated, and the future directions and challenges are discussed.

Kinetics of nucleotide-dependent structural transitions in the kinesin-1 hydrolysis cycle

To dissect the kinetics of structural transitions underlying the stepping cycle of kinesin-1 at physiological ATP, we used interferometric scattering microscopy to track the position of gold nanoparticles attached to individual motor domains in processively stepping dimers. Labeled heads resided stably at positions 16.4 nm apart, corresponding to a microtubule-bound state, and at a previously unseen intermediate position, corresponding to a tethered state. The chemical transitions underlying these structural transitions were identified by varying nucleotide conditions and carrying out parallel stopped-flow kinetics assays. At saturating ATP, kinesin-1 spends half of each stepping cycle with one head bound, specifying a structural state for each of two rate-limiting transitions. Analysis of stepping kinetics in varying nucleotides shows that ATP binding is required to properly enter the one-head-bound state, and hydrolysis is necessary to exit it at a physiological rate. These transitions differ from the standard model in which ATP binding drives full docking of the flexible neck linker domain of the motor. Thus, this work defines a consensus sequence of mechanochemical transitions that can be used to understand functional diversity across the kinesin superfamily.

Cytoplasmic dynein regulates its attachment to microtubules via nucleotide state-switched mechanosensing at multiple AAA domains

Cytoplasmic dynein is a homodimeric microtubule (MT) motor protein responsible for most MT minus-end-directed motility. Dynein contains four AAA+ ATPases (AAA: ATPase associated with various cellular activities) per motor domain (AAA1-4). The main site of ATP hydrolysis, AAA1, is the only site considered by most dynein motility models. However, it remains unclear how ATPase activity and MT binding are coordinated within and between dynein's motor domains. Using optical tweezers, we characterize the MT-binding strength of recombinant dynein monomers as a function of mechanical tension and nucleotide state. Dynein responds anisotropically to tension, binding tighter to MTs when pulled toward the MT plus end. We provide evidence that this behavior results from an asymmetrical bond that acts as a slip bond under forward tension and a slip-ideal bond under backward tension. ATP weakens MT binding and reduces bond strength anisotropy, and unexpectedly, so does ADP. Using nucleotide binding and hydrolysis mutants, we show that, although ATP exerts its effects via binding AAA1, ADP effects are mediated by AAA3. Finally, we demonstrate "gating" of AAA1 function by AAA3. When tension is absent or applied via dynein's C terminus, ATP binding to AAA1 induces MT release only if AAA3 is in the posthydrolysis state. However, when tension is applied to the linker, ATP binding to AAA3 is sufficient to "open" the gate. These results elucidate the mechanisms of dynein-MT interactions, identify regulatory roles for AAA3, and help define the interplay between mechanical tension and nucleotide state in regulating dynein motility.

The Mechanochemical Cycle of Mammalian Kinesin-2 KIF3A/B under Load

The response of motor proteins to external loads underlies their ability to work in teams and determines the net speed and directionality of cargo transport. The mammalian kinesin-2, KIF3A/B, is a heterotrimeric motor involved in intraflagellar transport and vesicle motility in neurons. Bidirectional cargo transport is known to result from the opposing activities of KIF3A/B and dynein bound to the same cargo, but the load-dependent properties of kinesin-2 are poorly understood. We used a feedback-controlled optical trap to probe the velocity, run length, and unbinding kinetics of mouse KIF3A/B under various loads and nucleotide conditions. The kinesin-2 motor velocity is less sensitive than kinesin-1 to external forces, but its processivity diminishes steeply with load, and the motor was observed occasionally to slip and reattach. Each motor domain was characterized by studying homodimeric constructs, and a global fit to the data resulted in a comprehensive pathway that quantifies the principal force-dependent kinetic transitions. The properties of the KIF3A/B heterodimer are intermediate between the two homodimers, and the distinct load-dependent behavior is attributable to the properties of the motor domains and not to the neck linkers or the coiled-coil stalk. We conclude that the force-dependent movement of KIF3A/B differs significantly from conventional kinesin-1. Against opposing dynein forces, KIF3A/B motors are predicted to rapidly unbind and rebind, resulting in qualitatively different transport behavior from kinesin-1.

Kinesin's front head is gated by the backward orientation of its neck linker

Kinesin-1 is a two-headed motor that takes processive 8-nm hand-over-hand steps and transports intracellular cargos toward the plus-end of microtubules. Processive motility requires a gating mechanism to coordinate the mechanochemical cycles of the two heads. Kinesin gating involves neck linker (NL), a short peptide that interconnects the heads, but it remains unclear whether gating is facilitated by the NL orientation or tension. Using optical trapping, we measured the force-dependent microtubule release rate of kinesin monomers under different nucleotide conditions and pulling geometries. We find that pulling NL in the backward direction inhibits nucleotide binding and subsequent release from the microtubule. This inhibition is independent of the magnitude of tension (2-8 pN) exerted on NL. Our results provide evidence that the front head of a kinesin dimer is gated by the backward orientation of its NL until the rear head releases from the microtubule.

Highly loaded behavior of kinesins increases the robustness of transport under high resisting loads

Kinesins are nano-sized biological motors which walk by repeating a mechanochemical cycle. A single kinesin molecule is able to transport its cargo about 1 μm in the absence of external loads. However, kinesins perform much longer range transport in cells by working collectively. This long range of transport by a team of kinesins is surprising because the motion of the cargo in cells can be hindered by other particles. To reveal how the kinesins are able to accomplish their tasks of transport in harsh intracellular circumstances, stochastic studies on the kinesin motion are performed by considering the binding and unbinding of kinesins to microtubules and their dependence on the force acting on kinesin molecules. The unbinding probabilities corresponding to each mechanochemical state of kinesin are modeled. The statistical characterization of the instants and locations of binding are captured by computing the probability of unbound kinesin being at given locations. It is predicted that a group of kinesins has a more efficient transport than a single kinesin from the perspective of velocity and run length. Particularly, when large loads are applied, the leading kinesin remains bound to the microtubule for long time which increases the chances of the other kinesins to bind to the microtubule. To predict effects of this behavior of the leading kinesin under large loads on the collective transport, the motion of the cargo is studied when the cargo confronts obstacles. The result suggests that the behavior of kinesins under large loads prevents the early termination of the transport which can be caused by the interference with the static or moving obstacles.

A stochastic model for kinesin bidirectional stepping

In this paper, a hand-over-hand stochastic model for the dynamics of the conventional kinesin is constructed. In the model, both forward and backward motions are taken into consideration. First passage time distributions, average velocities, dwell times, and forward/backward step ratios are investigated based on the model. A good agreement between the results of the model and experimental data is achieved under a variety of external loads.

Bidirectional cargo transport: moving beyond tug of war

Vesicles, organelles and other intracellular cargo are transported by kinesin and dynein motors, which move in opposite directions along microtubules. This bidirectional cargo movement is frequently described as a 'tug of war' between oppositely directed molecular motors attached to the same cargo. However, although many experimental and modelling studies support the tug-of-war paradigm, numerous knockout and inhibition studies in various systems have found that inhibiting one motor leads to diminished motility in both directions, which is a 'paradox of co-dependence' that challenges the paradigm. In an effort to resolve this paradox, three classes of bidirectional transport models--microtubule tethering, mechanical activation and steric disinhibition--are proposed, and a general mathematical modelling framework for bidirectional cargo transport is put forward to guide future experiments.

Tension on the linker gates the ATP-dependent release of dynein from microtubules

Cytoplasmic dynein is a dimeric motor that transports intracellular cargoes towards the minus-end of microtubules (MTs). In contrast to other processive motors, stepping of the dynein motor domains (heads) is not precisely coordinated. Therefore, the mechanism of dynein processivity remains unclear. Here, by engineering the mechanical and catalytic properties of the motor, we show that dynein processivity minimally requires a single active head and a second inert MT binding domain. Processivity arises from a high ratio of MT-bound to unbound time, and not from interhead communication. Additionally, nucleotide-dependent microtubule release is gated by tension on the linker domain. Intramolecular tension sensing is observed in dynein’s stepping motion at high interhead separations. We developed a quantitative model for the stepping characteristics of dynein and its response to chemical and mechanical perturbation.

Asymmetric friction of nonmotor MAPs can lead to their directional motion in active microtubule networks

Diverse cellular processes require microtubules to be organized into distinct structures, such as asters or bundles. Within these dynamic motifs, microtubule-associated proteins (MAPs) are frequently under load, but how force modulates these proteins' function is poorly understood. Here, we combine optical trapping with TIRF-based microscopy to measure the force dependence of microtubule interaction for three nonmotor MAPs (NuMA, PRC1, and EB1) required for cell division. We find that frictional forces increase nonlinearly with MAP velocity across microtubules and depend on filament polarity, with NuMA's friction being lower when moving toward minus ends, EB1's lower toward plus ends, and PRC1's exhibiting no directional preference. Mathematical models predict, and experiments confirm, that MAPs with asymmetric friction can move directionally within actively moving microtubule pairs they crosslink. Our findings reveal how nonmotor MAPs can generate frictional resistance in dynamic cytoskeletal networks via micromechanical adaptations whose anisotropy may be optimized for MAP localization and function within cellular structures.

Oatp1a1 requires PDZK1 to traffic to the plasma membrane by selective recruitment of microtubule-based motor proteins

Previous studies identified a family of organic anion transport proteins (OATPs), many of which have C-terminal PDZ binding consensus sequences. In particular, the C-terminal four amino acids of Oatp1a1, a transporter on rat and mouse hepatocytes, comprise a consensus binding site for PDZK1. In PDZK1 knockout mice and in transfected cells where PDZK1 expression was knocked down, Oatp1a1 accumulates in intracellular vesicles. The present study tests the hypothesis that Oatp1a1 traffics to and from the cell surface in vesicles along microtubules, and that PDZK1 guides recruitment of specific motors to these vesicles. Oatp1a1-containing vesicles were prepared from wild-type and PDZK1 knockout mice. As seen by immunofluorescence, kinesin-1, a microtubule plus-end directed motor, was largely associated with vesicles from wild-type mouse liver, whereas dynein, a minus-end directed motor, was largely associated with vesicles from PDZK1 knockout mouse liver. Quantification of motility on directionally marked microtubules following addition of 50 µM ATP showed that wild-type vesicles moved equally toward the plus and minus ends whereas PDZK1 knockout vesicles moved predominantly toward the minus end, consistent with net movement toward the cell interior. These studies provide a novel mechanism by which PDZK1 regulates intracellular trafficking of Oatp1a1 by recruiting specific motors to Oatp1a1-containing vesicles. In the absence of PDZK1, Oatp1a1-containing vesicles cannot recruit kinesin-1 and associate with dynein as a predominant minus-end directed motor. Whether this is a result of direct interaction of the Oatp1a1 cytoplasmic domain with dynein or with a dynein-containing protein complex remains to be established.

Bifurcation of velocity distributions in cooperative transport of filaments by fast and slow motors

Several intracellular processes are governed by two different species of molecular motors, fast and slow ones, that both move in the same direction along the filaments but with different velocities. The transport of filaments arising from the cooperative action of these motors has been recently studied by three in vitro experiments, in which the filament velocity was measured for varying fraction of the fast motors adsorbed onto substrate surfaces in a gliding assay. As the fast motor fraction was increased, two experiments found a smooth change whereas the third one observed an abrupt increase of the filament velocity. Here, we show that all of these experimental results reflect the competition between fast and slow motors and can be understood in terms of an underlying saddle-node bifurcation. The comparison between theory and experiment leads to predictions for the detachment forces of the two motor species. Our theoretical study shows the existence of three different motility regimes: 1), fast transport with a single velocity; 2), slow transport with a single velocity; and 3), bistable transport, where the filament velocity stochastically switches between fast and slow transport. We determine the parameter regions for these regimes in terms of motility diagrams as a function of the surface fraction of fast motors and microscopic single-motor parameters. An abrupt increase of the filament velocity for an increasing fraction of fast motors is associated with the occurrence of bistable transport.

Neck-linker length dependence of processive Kinesin-5 motility

Processive motility of individual molecules is essential for the function of many kinesin motors. Processivity for kinesins relies on communication between the two heads of a dimeric molecule, such that binding strictly alternates. The main communicating elements are believed to be the two neck linkers connecting the motors' stalks and heads. A proposed mechanism for coordination is the transmission of stress through the neck linkers. It is believed that the efficiency of gating depends on the length of the neck linker. Recent studies have presented support for a simple model in which the length of the neck linker directly controls the degree of processivity. Based on a previously published Kinesin-1/Kinesin-5 chimera, Eg5Kin, we have analyzed the motility of 12 motor constructs: we have varied the length of the neck linker in the range between 9 and 21 amino acids using the corresponding native Kinesin-5 sequence (Xenopus laevis Eg5). We found, surprisingly, that neither velocity nor force generation depended on neck-linker length. We also found that constructs with short neck linkers, down to 12 amino acids, were still highly processive, while processivity was lost at a length of 9 amino acids. Run lengths were maximal with neck linkers close to the native Kinesin-5 length and decreased beyond that length. This finding generally confirms the coordinating role of the neck linker for kinesin motility but challenges the simplest model postulating a motor-type-independent optimal length. Instead, our results suggest that different kinesins might be optimized for different neck-linker lengths.

Quasiperiodic distribution of rigor cross-bridges along a reconstituted thin filament in a skeletal myofibril

Electron microscopy has shown that cross-bridges (CBs) are formed at the target zone that is periodically distributed on the thin filament in striated muscle. Here, by manipulating a single bead-tailed actin filament with optical tweezers, we measured the unbinding events of rigor CBs one by one on the surface of the A-band in rabbit skeletal myofibrils. We found that the spacings between adjacent CBs were not always the same, and instead were 36, 72, or 108 nm. Tropomyosin and troponin did not affect the CB spacing except for a relative increase in the appearance of longer spacing in the presence of Ca(2+). In addition, in an in vitro assay where myosin molecules were randomly distributed, were obtained the same spacing, i.e., a multiple of 36 nm. These results indicate that the one-dimensional distribution of CBs matches with the 36-nm half pitch of a long helical structure of actin filaments. A stereospecific model composed of three actin protomers per target zone was shown to explain the experimental results. Additionally, the unbinding force (i.e., the binding affinity) of CBs for the reconstituted thin filaments was found to be larger and smaller relative to that for actin filaments with and without Ca(2+), respectively.

Are coiled-coils of dimeric kinesins unwound during their walking on microtubule?

Dimeric kinesin motor proteins such as homodimeric kinesin-1, homodimeric Ncd and heterodimeric Kar3/Vik1are composed of two head domains which are connected together by a rod-shaped, coiled-coil stalk. Despite the extensive and intensive studies on structures, kinetics, dynamics and walking mechanism of the dimers, whether their coiled-coils are unwound or not during their walking on the microtubule is still an unclear issue. Here, we try to clarify this issue by using molecular dynamics simulations. Our simulation results showed that, for Ncd, a large change in potential of mean force is required to unwind the coiled-coil by only several pairs of residues. For both Ncd and kinesin-1, the force required to initiate the coiled-coil unwinding is larger than that required for unfolding of the single -helix that forms the coiled-coil or is larger than that required to unwind the DNA duplex, which is higher than the unbinding force of the kinesin head from the microtubule in strong microtubule-binding states. Based on these results and the comparison of the sequence between the coiled-coil of Kar3/Vik1 and those of Ncd and kinesin-1, it was deduced that the coiled-coil of the Kar3/Vik1 should also be very stable. Thus, we concluded that the coiled-coils of kinesin-1, Ncd and Kar3/Vik1 are almost impossible to unwind during their walking on the microtubule.

MICROTUBULE-KINESIN MECHANICS BY MOLECULAR MODELING

The cellular cytoskeleton contains microtubules which function both as fundamental structural elements as well as motor protein tracks. While the structural property is connected to the properties of the tubulin dimer, its interactions with surrounding dimers and the geometric organization within the microtubule, the transport track properties are related to the interactions between the tubulin dimer and kinesin.

Based on the atomistic structures of kinesin and the tubulin dimer, we used molecular modeling to examine the interaction energy and force as function of a spatial distance of separation. From the results, elastic constants describing the system stiffness are obtained. By using the results related to the structure alone, a model of a 1 μm long microtubule is constructed as a network of elastic elements, and its mechanical properties were obtained via finite element method and compared to experimental results.

Concerning microtubule-kinesin complex, the interaction strength during a complete cycle of ATP hydrolysis was investigated. As expected, the affinity between the proteins is modulated by the type of nucleotide occupying the nucleotide binding pocket of the motor protein. The work underscores how molecular modeling can provide fundamental protein information in terms of the relation between mechanical properties and structural changes.

Time-dependent motor properties of multipedal molecular spiders

Molecular spiders are synthetic biomolecular walkers that use the asymmetry resulting from cleavage of their tracks to bias the direction of their stepping motion. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the dependence of the biased motion of molecular spiders, along with binding time and processivity, on tunable experimental parameters, such as number of legs, span between the legs, and unbinding rate of a leg from a substrate site. We find that an increase in the number of legs increases the spiders' processivity and binding time but not their mean velocity. However, we can increase the mean velocity of spiders with simultaneous tuning of the span and the unbinding rate of a spider leg from a substrate site. To study the efficiency of molecular spiders, we introduce a time-dependent expression for the thermodynamic efficiency of a molecular motor, allowing us to account for the behavior of spider populations as a function of time. Based on this definition, we find that spiders exhibit transient motor function over time scales of many hours and have a maximum efficiency on the order of 1%, weak compared to other types of molecular motors.