The Winch Model Can Explain both Coordinated and Uncoordinated Stepping of Cytoplasmic Dynein

Cytoplasmic dynein moves processively along microtubules, but the mechanism of how its heads use the energy from ATP hydrolysis, coupled to a linker swing, to achieve directed motion, is still unclear. In this article, we present a theoretical model based on the winch mechanism in which the principal direction of the linker stroke is toward the microtubule-binding domain. When mechanically coupling two identical heads (each with postulated elastic properties and a minimal ATPase cycle), the model reproduces stepping with 8-nm steps (even though the motor itself is much larger), interhead coordination, and processivity, as reported for mammalian dyneins. Furthermore, when we loosen the elastic connection between the heads, the model still shows processive directional stepping, but it becomes uncoordinated and the stepping pattern shows a greater variability, which reproduces the properties of yeast dyneins. Their slower chemical kinetics allows processive motility and a high stall force without the need for coordination.     

Asymmetry in kinesin walking

Several lines of experimental evidence suggest that the conventional kinesin 1 walks by an asymmetric hand-over-hand mechanism, although it is a homodimer. In the previous study, we examined several important force-dependent features of the hand-over-hand mechanism of kinesin. In this study, we focus on the asymmetry in the hand-over-hand mechanism. We show that the experimentally observed kinesin limping can be explained in our model by the variation of the neck linker lengths in the kinesin stepping (which has also been suggested earlier by others). We also study the experimentally observed processive motion of a mutant heterodimer of kinesin, in which only one of the two heads has the capability of ATP hydrolysis, as well as the walking of wild-type kinesin in the presence of both ATP and its analogue AMPPNP. We show that the possible processive walking of the heterodimeric kinesin can be explained by introducing a force-generating intermediate, the kinesin-ATP complex, which is different from the posthydrolytic species, kinesin-ADP/Pi.     

The Orphan Kinesin PAKRP2 Achieves Processive Motility via a Noncanonical Stepping Mechanism

Phragmoplast-associated kinesin-related protein 2 (PAKRP2) is an orphan kinesin in Arabidopsis thaliana that is thought to transport vesicles along phragmoplast microtubules for cell plate formation. Here, using single-molecule fluorescence microscopy, we show that PAKRP2 is the first orphan kinesin to exhibit processive plus-end-directed motility on single microtubules as individual homodimers. Our results show that PAKRP2 processivity is achieved despite having an exceptionally long (32 residues) neck linker. Furthermore, using high-resolution nanoparticle tracking, we find that PAKRP2 steps via a hand-over-hand mechanism that includes frequent side steps, a prolonged diffusional search of the tethered head, and tight coupling of the ATP hydrolysis cycle to the forward-stepping cycle. Interestingly, truncating the PAKRP2 neck linker to 14 residues decreases the run length of PAKRP2; thus, the long neck linker enhances the processive behavior. Based on the canonical model of kinesin stepping, such a long neck linker is expected to decrease the processivity and disrupt the coupling of ATP hydrolysis to forward stepping. Therefore, we conclude that PAKRP2 employs a noncanonical strategy for processive motility, wherein a long neck linker is coupled with a slow ATP hydrolysis rate to allow for an extended diffusional search during each step without sacrificing processivity or efficiency.     

Productive Cooperation among Processive Motors Depends Inversely on Their Mechanochemical Efficiency

Subcellular cargos are often transported by teams of processive molecular motors, which raises questions regarding the role of motor cooperation in intracellular transport. Although our ability to characterize the transport behaviors of multiple-motor systems has improved substantially, many aspects of multiple-motor dynamics are poorly understood. This work describes a transition rate model that predicts the load-dependent transport behaviors of multiple-motor complexes from detailed measurements of a single motor's elastic and mechanochemical properties. Transition rates are parameterized via analyses of single-motor stepping behaviors, load-rate-dependent motor-filament detachment kinetics, and strain-induced stiffening of motor-cargo linkages. The model reproduces key signatures found in optical trapping studies of structurally defined complexes composed of two kinesin motors, and predicts that multiple kinesins generally have difficulties in cooperating together. Although such behavior is influenced by the spatiotemporal dependence of the applied load, it appears to be directly linked to the efficiency of kinesin's stepping mechanism, and other types of less efficient and weaker processive motors are predicted to cooperate more productively. Thus, the mechanochemical efficiencies of different motor types may determine how effectively they cooperate together, and hence how motor copy number contributes to the regulation of cargo motion.     

A flexible domain is essential for the large step size and processivity of myosin VI

Myosin VI moves processively along actin with a larger step size than expected from the size of the motor. Here, we show that the proximal tail (the approximately 80-residue segment following the IQ domain) is not a rigid structure but, rather, a flexible domain that permits the heads to separate. With a GCN4 coiled coil inserted in the proximal tail, the heads are closer together in electron microscopy (EM) images, and the motor takes shorter processive steps. Single-headed myosin VI S1 constructs take nonprocessive 12 nm steps, suggesting that most of the processive step is covered by a diffusive search for an actin binding site. Based on these results, we present a mechanical model that describes stepping under an applied load.     

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.     

Processivity and Velocity for Motors Stepping on Periodic Tracks

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism, the trailing motor detaches from the track and binds the filament again in the leading position. This requires fuel consumption in the form of ATP hydrolysis and coordination of the catalytic cycles between the leading and the trailing heads. Alternate stepping pathways also exist, including inchworm-like movements, backward steps, and foot stomps. Whether all the pathways are coupled to ATP hydrolysis remains to be determined. Here, to establish the principles governing the dynamics of processive movement, we present a theoretical framework that includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head and the experimentally measurable quantities such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions that hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model quantitatively reproduces various observables of myosin VI motility reported by four experimental groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration.     

Strain through the neck linker ensures processive runs: a DNA‐kinesin hybrid nanomachine study

The motor protein kinesin has two heads and walks along microtubules processively using energy derived from ATP. However, how kinesin heads are coordinated to generate processive movement remains elusive. Here we created a hybrid nanomachine (DNA‐kinesin) using DNA as the skeletal structure and kinesin as the functional module. Single molecule imaging of DNA‐kinesin hybrid allowed us to evaluate the effects of both connect position of the heads (N, C‐terminal or Mid position) and sub‐nanometer changes in the distance between the two heads on motility. Our results show that although the native structure of kinesin is not essential for processive movement, it is the most efficient. Furthermore, forward bias by the power stroke of the neck linker, a 13‐amino‐acid chain positioned at the C‐terminus of the head, and internal strain applied to the rear of the head through the neck linker are crucial for the processive movement. Results also show that the internal strain coordinates both heads to prevent simultaneous detachment from the microtubules. Thus, the inter‐head coordination through the neck linker facilitates long‐distance walking.     

Kinesins with Extended Neck Linkers: A Chemomechanical Model for Variable-Length Stepping

We develop a stochastic model for variable-length stepping of kinesins engineered with extended neck linkers. This requires that we consider the separation in microtubule binding sites between the heads of the motor at the beginning of a step. We show that this separation is stationary and can be included in the calculation of standard experimental quantities. We also develop a corresponding matrix computational framework for conducting computer experiments. Our matrix approach is more efficient computationally than large-scale Monte Carlo simulation. This efficiency greatly eases sensitivity analysis, an important feature when there is considerable uncertainty in the physical parameters of the system. We demonstrate the application and effectiveness of our approach by showing that the worm-like chain model for the neck linker can explain recently published experimental data. While we have focused on a particular scenario for kinesins, these methods could also be applied to myosin and other processive motors.     

Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Mechanical Characterization of One-Headed Myosin-V Using Optical Tweezers

Class V myosin (myosin-V) is a cargo transporter that moves along an actin filament with large (∼36-nm) successive steps. It consists of two heads that each includes a motor domain and a long (23 nm) neck domain. One of the more popular models describing these steps, the hand-over-hand model, assumes the two-headed structure is imperative. However, we previously succeeded in observing successive large steps by one-headed myosin-V upon optimizing the angle of the acto-myosin interaction. In addition, it was reported that wild type myosin-VI and myosin-IX, both one-headed myosins, can also generate successive large steps. Here, we describe the mechanical properties (stepsize and stepping kinetics) of successive large steps by one-headed and two-headed myosin-Vs. This study shows that the stepsize and stepping kinetics of one-headed myosin-V are very similar to those of the two-headed one. However, there was a difference with regards to stability against load and the number of multisteps. One-headed myosin-V also showed unidirectional movement that like two-headed myosin-V required 3.5 k_BT from ATP hydrolysis. This value is also similar to that of smooth muscle myosin-II, a non-processive motor, suggesting the myosin family uses a common mechanism for stepping regardless of the steps being processive or non-processive. In this present paper, we conclude that one-headed myosin-V can produce successive large steps without following the hand-over-hand mechanism.     

Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Stochastic simulation of processive and oscillatory sliding using a two-headed model for axonemal dynein

Computer simulations have been used in an attempt to understand experimental observations of processive and oscillatory sliding by one or a few axonemal dyneins. A simple two-headed model has been examined using stochastic simulation methods. To explain the experimental observations, the model must be capable of taking backward steps, as well as forward steps, and there must be hysteresis in switching between forward or backward stepping. When the effects of Brownian movement on motor strain are included, it is not possible to obtain oscillations as regular as the experimental records by using motor strain to regulate switching between forward or backward stepping.     

Directed binding

We propose a novel physical mechanism to describe the mode of processive propagation of twoheaded kinesin motor proteins along microtubule (MT) filaments. Binding and unbinding of the kinesin heads to and from the MT filament play a crucial role in producing movement. The chemical energy of adenosine triphosphate hydrolysis is used in large part for the unbinding process of kinesin from the MT filament. Importantly, in our model, the binding of each head is to be directionally oriented to the MT filament. Therefore, we treat the two motor domains (heads) as extended objects that are connected with each other by a neck region that contains the kinesin dimerization domain. The head domains recognize tubulin binding sites by feeling the two-dimensional periodic potential from the MT surface and are also subjected to thermal noise. Using experimentally determined results regarding physical parameters of the walk, we develop a simple mathematical and mechanical model in which directed binding of the heads to tubulin results in a directed twist of the molecule, probably in the neck linker region, away from its relaxed state. Unbinding of the head from the filament relaxes the twist and defines the propagation direction. We showed that there must be at least two torsional springs (one for every head) involved that can store elastic energy. Consequently, in our model, it is the internal structure both of the relaxed and tensed-up state and the transition mode between them that define the walking direction of kinesin. We present calculations based on the model that are in good quantitative agreement with experimental observations for kinesin.     

Flexible light-chain and helical structure of F-actin explain the movement and step size of myosin-VI

Myosin-VI is a dimeric isoform of unconventional myosins. Single molecule experiments indicate that myosin-VI and myosin-V are processive molecular motors, but travel toward opposite ends of filamentous actin. Structural studies show several differences between myosin-V and VI, including a significant difference in the light-chain domain connecting the motor domains. Combining the measured kinetics of myosin-VI with the elasticity of the light chains, and the helical structure of F-actin, we compare and contrast the motility of myosin-VI with myosin-V. We show that the elastic properties of the light-chain domain control the stepping behavior of these motors. Simple models incorporating the motor elastic energy can quantitatively capture most of the observed data. Implications of our result for other processive motors are discussed.     

Dissection of Kinesin's Processivity

The protein family of kinesins contains processive motor proteins that move stepwise along microtubules. This mechanism requires the precise coupling of the catalytic steps in the two heads, and their precise mechanical coordination. Here we show that these functionalities can be uncoupled in chimera of processive and non-processive kinesins. A chimera with the motor domain of Kinesin-1 and the dimerization domain of a non-processive Kinesin-3 motor behaves qualitatively as conventional kinesin and moves processively in TIRF and bead motility assays, suggesting that spatial proximity of two Kinein-1 motor domains is sufficient for processive behavior. In the reverse chimera, the non-processive motor domains are unable to step along microtubules, despite the presence of the Kinesin-1 neck coiled coil. Still, ATP-binding to one head of these chimera induces ADP-release from the partner head, a characteristic feature of alternating site catalysis. These results show that processive movement of kinesin dimers requires elements in the motor head that respond to ADP-release and induce stepping, in addition to a proper spacing of the motor heads via the neck coiled coil.     

Dynamics of myosin-V processivity

Myosin-V is an actin-associated processive molecular motor. Single molecule experiments revealed that myosin-V walks in a stepwise fashion with occasional backward steps. By combining the mechanical structure of the motor with the ATP hydrolysis kinetics, we construct a dynamical model that accounts for the stepwise processivity. The molecular properties of the protein chains connecting the myosin heads are important. A simple elastic model demonstrates that the stress transmitted from the leading head to the trailing head leads to net forward motion. The step-sizes are non-uniform. We also predict there are several substeps. The translational speed and step-size distributions are computed for several different conditions. The computed force-versus-velocity curve shows that under an external load, myosin-V slows down. However, the sizes of the steps remain the same.     

Monte Carlo analysis of neck linker extension in kinesin molecular motors

Kinesin stepping is thought to involve both concerted conformational changes and diffusive movement, but the relative roles played by these two processes are not clear. The neck linker docking model is widely accepted in the field, but the remainder of the step--diffusion of the tethered head to the next binding site--is often assumed to occur rapidly with little mechanical resistance. Here, we investigate the effect of tethering by the neck linker on the diffusive movement of the kinesin head, and focus on the predicted behavior of motors with naturally or artificially extended neck linker domains. The kinesin chemomechanical cycle was modeled using a discrete-state Markov chain to describe chemical transitions. Brownian dynamics were used to model the tethered diffusion of the free head, incorporating resistive forces from the neck linker and a position-dependent microtubule binding rate. The Brownian dynamics and chemomechanical cycle were coupled to model processive runs consisting of many 8 nm steps. Three mechanical models of the neck linker were investigated: Constant Stiffness (a simple spring), Increasing Stiffness (analogous to a Worm-Like Chain), and Reflecting (negligible stiffness up to a limiting contour length). Motor velocities and run lengths from simulated paths were compared to experimental results from Kinesin-1 and a mutant containing an extended neck linker domain. When tethered by an increasingly stiff spring, the head is predicted to spend an unrealistically short amount of time within the binding zone, and extending the neck is predicted to increase both the velocity and processivity, contrary to experiments. These results suggest that the Worm-Like Chain is not an adequate model for the flexible neck linker domain. The model can be reconciled with experimental data if the neck linker is either much more compliant or much stiffer than generally assumed, or if weak kinesin-microtubule interactions stabilize the diffusing head near its binding site.     

A kinetic and stochastic analysis of crossbridge-type stepping mechanisms in rotary molecular motors

The bacterial flagellar motor is generally supposed to be a stepping mechanism. The main evidence for this is based on a fluctuation analysis of experiments with tethered bacteria in which rotation frequency was varied by applying an external torque: the variance in time taken for a fixed number of revolutions was found to be essentially proportional to the inverse square of the frequency. This behavior was shown to characterize a Poissonian stepper. Here we present a rigorous kinetic and stochastic analysis of elastic crossbridge stepping in tethered bacteria. We demonstrate that Poissonian stepping is a virtually unachievable limit. To the extent that a system may approach Poissonian stepping it cannot be influenced by an externally applied torque; stepping mechanisms capable of being so influenced are necessarily non-Poissonian and exhibit an approximately inverse cubic dependence. This conclusion applies whatever the torsional characteristics of the tether may be, and contrary to claims, no perceptible relaxation of the tether following each step is found. Furthermore, the inverse square dependence is a necessary but not sufficient condition for Poissonian stepping, since a nonstepping mechanism, which closely reproduces most experimental data, also fulfills this condition. Hence the inference that crossbridge-type stepping occurs is not justified.     

Mechanochemical aspects of axonemal dynein activity studied by in vitro microtubule translocation.

We have determined the relationship between microtubule length and translocation velocity from recordings of bovine brain microtubules translocating over a Paramecium 22S dynein substratum in an in vitro assay chamber. For comparison with untreated samples, the 22S dynein has been subjected to detergent and/or to pretreatments that induce phosphorylation of an associated 29 kDa light chain. Control and treated dyneins have been used at the same densities in the translocation assays. In any given condition, translocation velocity (v) shows an initial increase with microtubule length (L) and then reaches a plateau. This situation may be represented by a hyperbola of the general form v = aL/(L+b), which is formally analogous to the Briggs-Haldane relationship, which we have used to interpret our data. The results indicate that the maximum translocation velocity Vo(= a) is increased by pretreatment, whereas the length constant KL(= b), which corresponds to Km, does not change with pretreatment, implying that the mechanochemical properties of the pretreated dyneins differ from those of control dyneins. The conclusion that KL is constant for defined in vitro assays rules out the possibility that the velocity changes seen are caused by changes in geometry in the translocation assays or by the numbers of dyneins or dynein heads needed to produce maximal translocational velocity. From our analysis, we determine that f, the fraction of cycle time during which the dynein is in the force-generating state, is small--roughly 0.01, comparable to the f determined previously for heavy meromyosin. The practical limits of these mechanochemical changes imply that the maximum possible ciliary beat frequency is about 120 Hz, and that in the physiological range of 5-60 Hz, beat frequency could be controlled by varying the numbers of phosphorylated outer arm dyneins along an axonemal microtubule.