Kinesin: a molecular motor with a spring in its step

A key step in the processive motion of two-headed kinesin along a microtubule is the 'docking' of the neck linker that joins each kinesin head to the motor's dimerized coiled-coil neck. This process is similar to the folding of a protein beta-hairpin, which starts in a highly mobile unfolded state that has significant entropic elasticity and finishes in a more rigid folded state. We therefore suggest that neck-linker docking is mechanically equivalent to the thermally activated shortening of a spring that has been stretched by an applied load. This critical tension-dependent step utilizes Brownian motion and it immediately follows the binding of ATP, the hydrolysis of which provides the free energy that drives the kinesin cycle. A simple three-state model incorporating neck-linker docking can account quantitatively for both the kinesin force-velocity relation and the unusual tension-dependence of its Michaelis constant. However, we find that the observed randomness of the kinesin motor requires a more detailed four-state model. Monte Carlo simulations of single-molecule stepping with this model illustrate the possibility of sub-8 nm steps, the size of which is predicted to vary linearly with the applied load.     

The role of thermal activation in motion and force generation by molecular motors

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.     

Stepping behavior of two-headed kinesin motors

The stepping behavior of the dimeric kinesin is studied by using our model based on previous biochemical, X-ray crystallography and cryo-electron microscopy studies. It is shown that, when a Pi is released from the trailing head, a forward step is made under a backward load smaller than the stall force; while when a Pi is released from the leading head, no stepping is made under a forward load or no load, and a backward step is made under a backward load. The forward stepping time, i.e., the time from the release of Pi in the trailing head to the binding of the ADP head to next binding site, is much smaller than the dwell time even under the backward load near the stall force. Thus the movement velocity of the kinesin dimer can be considered to be only dependent on ATPase rates of the two heads. The duration of the rising phase, i.e., the actual time taken by the ADP head to transit from the trailing to leading positions, is on the time scale of microseconds under any backward load smaller than the stall force. This is consistent with available experimental results.     

Stepping behavior of two-headed kinesin motors

The stepping behavior of the dimeric kinesin is studied by using our model based on previous biochemical, X-ray crystallography and cryo-electron microscopy studies. It is shown that, when a Pi is released from the trailing head, a forward step is made under a backward load smaller than the stall force; while when a Pi is released from the leading head, no stepping is made under a forward load or no load, and a backward step is made under a backward load. The forward stepping time, i.e., the time from the release of Pi in the trailing head to the binding of the ADP head to next binding site, is much smaller than the dwell time even under the backward load near the stall force. Thus the movement velocity of the kinesin dimer can be considered to be only dependent on ATPase rates of the two heads. The duration of the rising phase, i.e., the actual time taken by the ADP head to transit from the trailing to leading positions, is on the time scale of microseconds under any backward load smaller than the stall force. This is consistent with available experimental results.     

Mechanics of single kinesin molecules measured by optical trapping nanometry.

We have analyzed the mechanics of individual kinesin molecules by optical trapping nanometry. A kinesin molecule was adsorbed onto a latex bead, which was captured by an optical trap and brought into contact with an axoneme that was bound to a glass surface. The displacement of kinesin during force generation was determined by measuring the position of the beads with nanometer accuracy. As the displacement of kinesin was attenuated because of the compliance of the kinesin-to-bead and kinesin-to-microtubule linkages, the compliance was monitored during force generation and was used to correct the displacement of kinesin. Thus the velocity and the unitary steps could be obtained accurately over a wide force range. The force-velocity curves were linear from 0 to a maximum force at 10 microM and 1 mM ATP, and the maximum force was approximately 7 pN, which is larger by approximately 30% than values previously reported. Kinesin exhibited forward and occasionally backward stepwise displacements with a size of approximately 8 nm. The histograms of step dwell time show a monotonic decrease with time. Model calculations indicate that each kinesin head steps by 16-nm, whereas kinesin molecule steps by 8-nm.     

Chemomechanical coupling of the forward and backward steps of single kinesin molecules

The molecular motor kinesin travels processively along a microtubule in a stepwise manner. Here we have studied the chemomechanical coupling of the hydrolysis of ATP to the mechanical work of kinesin by analysing the individual stepwise movements according to the directionality of the movements. Kinesin molecules move primarily in the forward direction and only occasionally in the backward direction. The hydrolysis of a single ATP molecule is coupled to either the forward or the backward movement. This bidirectional movement is well described by a model of Brownian motion assuming an asymmetric potential of activation energy. Thus, the stepwise movement along the microtubule is most probably due to Brownian motion that is biased towards the forward direction by chemical energy stored in ATP molecules.     

Single molecule processes on the stepwise movement of ATP-driven molecular motors

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.     

Force-dependent stepping kinetics of myosin-V

Myosin-V is a processive two-headed actin-based motor protein involved in many intracellular transport processes. A key question for understanding myosin-V function and the communication between its two heads is its behavior under load. Since in vivo myosin-V colocalizes with other much stronger motors like kinesins, its behavior under superstall forces is especially relevant. We used optical tweezers with a long-range force feedback to study myosin-V motion under controlled external forward and backward loads over its full run length. We find the mean step size remains constant at approximately 36 nm over a wide range of forces from 5 pN forward to 1.5 pN backward load. We also find two force-dependent transitions in the chemomechanical cycle. The slower ADP-release is rate limiting at low loads and depends only weakly on force. The faster rate depends more strongly on force. The stronger force dependence suggests this rate represents the diffusive search of the leading head for its binding site. In contrast to kinesin motors, myosin-V's run length is essentially independent of force between 5 pN of forward to 1.5 pN of backward load. At superstall forces of 5 pN, we observe continuous backward stepping of myosin-V, indicating that a force-driven reversal of the power stroke is possible.     

Molecular motors: thermodynamics and the random walk

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.     

Symmetry based mechanism for hand-over-hand molecular motors

Many bio-molecular motors are dimers that move by a "hand-over-hand" mechanism along polar bio-polymeric tracks. Examples include kinesin, that "walks" on microtubule and myosin V that "walks" on actin. These molecular motors share two important symmetries. Typically the motor dimers have approximate mirror symmetry, and their tracks have translational, but not mirror, symmetry. Here we use a trajectory approach to analyze a minimal model for a generic dimeric motor that moves on a polymer track incorporating these two symmetry features. The analysis focuses of the relative probabilities of forward, reverse, backward, backward reverse trajectories and provides an experimentally accessible measure of the relative importance of a "Brownian motor" vs. "Power stroke" mechanism. Reciprocal relations, similar to those derived for the linear regime by Onsager for the fluxes (generalized velocities), hold for arbitrary magnitude forces (i.e., far from the linear regime) for the net probabilities for stepping and for chemical reaction.     

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.     

Nanometres and piconewtons: the macromolecular mechanics of kinesin

Much of our current understanding of the molecular physiology of kinesin has come from in vitro motility assays: indeed, the discovery of kinesin relied upon such assays. By marrying in vitro assays with novel instruments capable of resolving movements on the molecular scale, it has proved possible to make measurements on single motors. Such key parameters as the step size, stepping force, and force-velocity relationship for kinesin have been determined in this fashion, and should soon contribute to a molecular model for the movement of kinesin.     

Entropy rectifies the Brownian steps of kinesin

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. The physical mechanism underlying the unidirectional bias of the kinesin steps is not fully understood. Here we explored the mechanical kinetics and thermodynamics of forward and backward kinesin steps by analyzing their temperature and load dependence. Results show that the frequency asymmetry between forward and backward steps is produced by entropy. Furthermore, the magnitude of the entropic asymmetry is 6 k(B)T, more than three times greater than expected from a current model, in which a mechanical conformational change within the kinesin molecular structure directly biases the kinesin steps forward. We propose that the stepping direction of kinesin is preferably caused by an entropy asymmetry resulting from the compatibility between the kinesin and microtubule interaction based on their polar structures.     

Model for kinetics of wild-type and mutant kinesins

A hand-over-hand model is presented for the processive movement of two-headed kinesin based on previous structural and biochemical studies. In the model, the ATPase activities of the two heads are regulated by forces, both from internal elasticity and external load, exerted on their neck linkers. The results from the model show that the two heads may be partially coordinated in their ATPase cycles: in the case of backward load or low forward load, the ATPase cycles of its two heads are well coordinated, whereas in the case of high forward load, they are no longer well coordinated. The model gives results that show good quantitative agreement with both previous biochemical and mechanical experimental results such as the limping of homodimers and the dependences of mean velocity on [ATP] and on loads (both positive and negative). Furthermore, using the model we study the kinetics of a number of mutant kinesin homodimers and heterodimers, showing that the two heads' ATPase activities of some of these molecules are not well coordinated and they move processively with low mechanochemical coupling efficiencies even under no load. The theoretical results of ATPase rate per head, moving velocity, and stall force of the motors show good quantitative agreement with the experimental ones. The puzzling dynamic behaviours of mutant homodimeric and heterodimeric kinesins become understandable.     

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.     

Kinesin's walk: Springy or gated head coordination?

Conventional kinesin (kinesin-1) is a motor protein that performs a vital function in the eukaryotic cell: it actively transports cargo to required destinations. Kinesin pulls cargo along microtubule tracks using twin linked motor domains (heads) that bind the microtubule, hydrolyse ATP, and alternately step forward. The detail of the kinesin walk has yet to be discovered but a prominent theory is that the mechanism is rectified Brownian motion (RBM) biased by linker zippering. There is evidence that an ATP binding gate coordinates the heads. The hypothesis proposed here is that the gate is unnecessary, that entropic linker strain is sufficient to enable procession. An agent-based computer simulation has been devised to explore head coordination in the RBM model. Walking was found to emerge in silico without a gate to synchronise the heads. Further investigation of the model by applying a range of hindering loads resulted in backstepping or detachment with similar characteristics to behaviour observed in vitro. It is unclear whether kinesin waits at an obstacle but adding an ATP hydrolysis gate to the model in order to force waiting resulted in the model behaving less realistically under load. It is argued here that an RBM model free of gating is a good candidate for explaining kinesin procession.     

Walking motion of an overdamped active particle in a ratchet potential

An active particle can convert its internal energy into mechanical work. We study a generalized energy-depot model of an overdamped active particle in a ratchet potential. Using well-known biological parameters for kinesin-1 and modeling ATP influx as a pulsed energy supply, we apply our model to the molecular motor system. We find that our simple model can capture the essential properties of the kinesin motor such as forward stepping, stalling, backward stepping, dependence on ATP concentration, and stall force. Our model might be quite universal in the sense that it is able to describe dynamics of various types of motors as long as realistic parameters for each motor species are adopted.     

Molecular motors: how to make models that can be used to convey the concept of molecular ratchets and thermal capture

A wide variety of cellular processes use molecular motors, including processive motors that move along some form of track (e.g., myosin with actin, kinesin or dynein with tubulin) and polymerases that move along a template (e.g., DNA and RNA polymerases, ribosomes). In trying to understand how these molecular motors actually move, many apply their understanding of how man-made motors work: the latter use some form of energy to exert a force or torque on its load. However, quite a different mechanism has been proposed to possibly account for the movement of molecular motors. Rather than hydrolyzing ATP to push or pull their load, they might use their own thermal vibrational energy as well as that of their load and their environment to move the load, capturing those movements that occur along a desired vector or axis and resisting others; ATP hydrolysis is required to make backward movements impossible. This intriguing thermal capture or Brownian ratchet model is relatively more difficult to convey to students. In this report, we describe several teaching aids that are very easily constructed using widely available household materials to convey the concept of a molecular ratchet.     

Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.     

Hopping and stalling of processive molecular motors

When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to ‘hop’ backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.