Substeps within the 8-nm step of the ATPase cycle of single kinesin molecules

Kinesin is a molecular motor that moves processively by regular 8-nm steps along microtubules. The processivity of this movement is explained by a hand-over-hand model in which the two heads of kinesin work in a coordinated manner. One head remains bound to the microtubule while the other steps from the alphabeta-tubulin dimer behind the attached head to the dimer in front. The overall movement is 8 nm per ATPase cycle. To investigate elementary processes within the 8-nm step, we have developed a new assay that resolves nanometre displacements of single kinesin molecules with microsecond accuracy. Our data show that the 8-nm step can be resolved into fast and slow substeps, each corresponding to a displacement of approximately 4 nm. The substeps are most probably generated by structural changes in one head of kinesin, leading to rectified forward thermal motions of the partner head. It is also possible that the kinesin steps along the 4-nm repeat of tubulin monomers.     

Kinetics of ADP dissociation from the trail and lead heads of actomyosin V following the power stroke

Myosin V is a cellular motor protein, which transports cargos along actin filaments. It moves processively by 36-nm steps that require at least one of the two heads to be tightly bound to actin throughout the catalytic cycle. To elucidate the kinetic mechanism of processivity, we measured the rate of product release from the double-headed myosin V-HMM using a new ATP analogue, 3'-(7-diethylaminocoumarin-3-carbonylamino)-3'-deoxy-ATP (deac-aminoATP), which undergoes a 20-fold increase in fluorescence emission intensity when bound to the active site of myosin V (Forgacs, E., Cartwright, S., Kovács, M., Sakamoto, T., Sellers, J. R., Corrie, J. E. T., Webb, M. R., and White, H. D. (2006) Biochemistry 45, 13035-13045). The kinetics of ADP and deac-aminoADP dissociation from actomyosin V-HMM, following the power stroke, were determined using double-mixing stopped-flow fluorescence. These used either deac-aminoATP as the substrate with ADP or ATP chase or alternatively ATP as the substrate with either a deac-aminoADP or deac-aminoATP chase. Both sets of experiments show that the observed rate of ADP or deac-aminoADP dissociation from the trail head of actomyosin V-HMM is the same as from actomyosin V-S1. The dissociation of ADP from the lead head is decreased by up to 250-fold.     

Model for kinetics of myosin-V molecular motors

A hand-over-hand model is presented for the processive movement of myosin-V based on previous biochemical experimental results and structural observations of nucleotide-dependent conformational changes of single-headed myosins. The model shows that the ADP-release rate of the trailing head is much higher than that of the leading head, thus giving a 1 : 1 mechanochemical coupling for the processive movement of the motor. It explains well the previous finding that some 36-nm steps consist of two substeps, while other 36-nm steps consist of no substeps. Using the model, the calculated kinetic behaviors of myosin-V such as the main and intermediate dwell time distributions, the load dependence of the average main and intermediate dwell time and the load dependence of occurrence frequency of the intermediate state under various nucleotide conditions show good quantitative agreement with previous experimental results.     

Mechanism of nucleotide binding to actomyosin VI: evidence for allosteric head-head communication

We have examined the kinetics of nucleotide binding to actomyosin VI by monitoring the fluorescence of pyrene-labeled actin filaments. ATP binds single-headed myosin VI following a two-step reaction mechanism with formation of a low affinity collision complex (1/K(1)' = 5.6 mm) followed by isomerization (k(+2)' = 176 s-1) to a state with weak actin affinity. The rates and affinity for ADP binding were measured by kinetic competition with ATP. This approach allows a broader range of ADP concentrations to be examined than with fluorescent nucleotide analogs, permitting the identification and characterization of transiently populated intermediates in the pathway. ADP binding to actomyosin VI, as with ATP binding, occurs via a two-step mechanism. The association rate constant for ADP binding is approximately five times greater than for ATP binding because of a higher affinity in the collision complex (1/K(5b)' = 2.2 mm) and faster isomerization rate constant (k(+5a)' = 366 s(-1)). By equilibrium titration, both heads of a myosin VI dimer bind actin strongly in rigor and with bound ADP. In the presence of ATP, conditions that favor processive stepping, myosin VI does not dwell with both heads strongly bound to actin, indicating that the second head inhibits strong binding of the lead head to actin. With both heads bound strongly, ATP binding is accelerated 2.5-fold, and ADP binding is accelerated >10-fold without affecting the rate of ADP release. We conclude that the heads of myosin VI communicate allosterically and accelerate nucleotide binding, but not dissociation, when both are bound strongly to actin.     

Load and Pi control flux through the branched kinetic cycle of myosin V

Myosin V is a processive actin-based motor protein that takes multiple 36-nm steps to deliver intracellular cargo to its destination. In the laser trap, applied load slows myosin V heavy meromyosin stepping and increases the probability of backsteps. In the presence of 40 mm phosphate (P(i)), both forward and backward steps become less load-dependent. From these data, we infer that P(i) release commits myosin V to undergo a highly load-dependent transition from a state in which ADP is bound to both heads and its lead head trapped in a pre-powerstroke conformation. Increasing the residence time in this state by applying load increases the probability of backstepping or detachment. The kinetics of detachment indicate that myosin V can detach from actin at two distinct points in the cycle, one of which is turned off by the presence of P(i). We propose a branched kinetic model to explain these data. Our model includes P(i) release prior to the most load-dependent step in the cycle, implying that P(i) release and load both act as checkpoints that control the flux through two parallel pathways.     

Strain-dependent cross-bridge cycle for muscle. II. Steady-state behavior.

Quantitative predictions of steady-state muscle properties from the strain-dependent cross-bridge for muscle are presented. With a stiffness of 5.4 x 10(-4) N/m per head, a throw distance of 11 nm, and three allowed actin sites/head, isometric properties and their dependence on phosphate and nucleotide levels are well described if the tension-generating step occurs before phosphate release. At very low ATP levels, rigorlike states with negative strain are predicted. The rate-limiting step for cycling and ATP consumption is strain-blocked ADP release for isometric and slowly shortening muscle. Under rapid shortening, ATP hydrolysis on detached heads is the rate-limiting step, and the ratio of bound ATP to bound ADP.Pi increases by a factor of 7. At large positive strains, bound heads must be forcibly detached from actin to account for tension in rapid extension, but forced detachment in shortening has no effect without destroying isometric attached states. Strain-blocked phosphate release as proposed produces modest inhibition of the ATPase rate under rapid shortening, sufficient to give a maximum for one actin site per helix turn. Alternative cross-bridge models are discussed in the light of these predictions.     

RNA Unwinding by NS3 Helicase: A Statistical Approach

The study of double-stranded RNA unwinding by helicases is a problem of basic scientific interest. One such example is provided by studies on the hepatitis C virus (HCV) NS3 helicase using single molecule mechanical experiments. HCV currently infects nearly 3% of the world population and NS3 is a protein essential for viral genome replication. The objective of this study is to model the RNA unwinding mechanism based on previously published data and study its characteristics and their dependence on force, ATP and NS3 protein concentration. In this work, RNA unwinding by NS3 helicase is hypothesized to occur in a series of discrete steps and the steps themselves occurring in accordance with an underlying point process. A point process driven change point model is employed to model the RNA unwinding mechanism. The results are in large agreement with findings in previous studies. A gamma distribution based renewal process was found to model well the point process that drives the unwinding mechanism. The analysis suggests that the periods of constant extension observed during NS3 activity can indeed be classified into pauses and subpauses and that each depend on the ATP concentration. The step size is independent of external factors and seems to have a median value of 11.37 base pairs. The steps themselves are composed of a number of substeps with an average of about 4 substeps per step and an average substep size of about 3.7 base pairs. An interesting finding pertains to the stepping velocity. Our analysis indicates that stepping velocity may be of two kinds- a low and a high velocity.     

Differential labeling of myosin V heads with quantum dots allows direct visualization of hand-over-hand processivity

The double-headed myosin V molecular motor carries intracellular cargo processively along actin tracks in a hand-over-hand manner. To test this hypothesis at the molecular level, we observed single myosin V molecules that were differentially labeled with quantum dots having different emission spectra so that the position of each head could be identified with approximately 6-nm resolution in a total internal reflectance microscope. With this approach, the individual heads of a single myosin V molecule were observed taking 72-nm steps as they alternated positions on the actin filament during processive movement. In addition, the heads were separated by 36 nm during pauses in motion, suggesting attachment to actin along its helical repeat. The 36-nm interhead spacing, the 72-nm step size, and the observation that heads alternate between leading and trailing positions on actin are obvious predictions of the hand-over-hand model, thus confirming myosin V's mode of walking along an actin filament.     

Pathway of ADP-stimulated ADP release and dissociation of tethered kinesin from microtubules. Implications for the extent of processivity

Kinesin binds to microtubules with half-site ADP release to form a tethered intermediate with one attached head without nucleotide and one tethered head that retains its bound ADP. For DKH405 containing amino acid residues 1-405 of Drosophila kinesin, release of the remaining ADP from the tethered head is slow (0.05 s(-1)), but release is accelerated by added ADP or ATP. The maximum rate of ADP-stimulated dissociation of tethered DKH405 from the microtubule is approximately 12 s(-1) as determined by turbidity. Parallel measurements of ADP-stimulated release of 2'(3')-O-(N-methylanthraniloyl)-ADP (mantADP) from the tethered intermediate by fluorescence indicate that the reaction is biphasic with a fast phase that occurs at a rate that is similar to dissociation. The rate of the slow phase is dependent on the concentrations of salt and microtubules and is equal in each case to the rate for bimolecular stimulation of ADP release by microtubules as measured independently. These results are consistent with a scheme in which the fast phase, with approximately one-third of the total amplitude change, is due to ADP-stimulated release of mantADP from the tethered intermediate at approximately 6 s(-1). This direct release of mantADP continues until terminated by dissociation of DKH405 from the microtubule at approximately 12 s(-1). The majority of the amplitude change thus occurs through bimolecular recombination of DKH405.mantADP with microtubules following initial dissociation. Analysis of a simple scheme indicates that hydrolysis of ATP at the attached head before the tethered head can release its ADP and become tightly bound may be the principal limitation to processivity.     

An alternative reaction pathway of F1-ATPase suggested by rotation without 80 degrees/40 degrees substeps of a sluggish mutant at low ATP

F(1)-ATPase, a water-soluble portion of F(o)F(1)-ATP synthase, is a rotary motor driven by ATP hydrolysis. The central gamma-subunit rotates in the alpha(3)beta(3) cylinder by repeating four stages of rotation: ATP-binding dwell, rapid 80 degrees substep rotation, catalytic dwell, and rapid 40 degrees substep rotation. In the catalytic dwell, at least two catalytic reactions occur-cleavage of the enzyme-bound ATP and presumably release of the hydrolyzed product(s) from the enzyme-but we found that a slow ATP cleavage mutant of F(1)-ATPase from thermophilic Bacillus PS3 rotates at low ATP concentration without substeps and the catalytic dwell. Analysis indicates that in this alternative reaction pathway the two catalytic reactions occur during the preceding long ATP-binding dwell. Thus, F(1)-ATPase can operate through (at least) two competing reaction pathways, not necessarily through a simple consecutive reaction.     

Detection of the swings of the lever arm of a myosin motor by fluorescence resonance energy transfer of green and blue fluorescent proteins

The "lever-arm" model of a myosin motor predicts that the lever-arm domain in the myosin head tilts and swings against the catalytic domain during ATP hydrolysis, resulting in force generation. To investigate if this "swing" of the lever arm really occurs during the hydrolysis of ATP, we employed fluorescence resonance energy transfer (FRET) between two fluorescent proteins [green (GFP) and blue (BFP)] fused to the N and C termini of the Dictyostelium myosin-motor domain. FRET measurements showed that the C-terminal BFP in the fusion protein first swings against the N-terminal GFP at the isomerization step of the ATP hydrolysis cycle and then swings back at the phosphate-release step. Because the C-terminal BFP mimics the motion of the lever arm, the result indicates that the lever arm swings at the specific steps of the ATP hydrolysis cycle, i.e., at the isomerization and phosphate-release steps. The latter swing may correspond to the power stroke of myosin, while the former may be related to the recovery stroke.     

Asymmetry in the F1-ATPase and its implications for the rotational cycle

ATP synthase uses a rotary mechanism to carry out its cellular function of manufacturing ATP. The central gamma-shaft rotates inside a hexameric cylinder composed of alternating alpha- and beta-subunits. When operating in the hydrolysis direction under high frictional loads and low ATP concentrations, a coordinated mechanochemical cycle in the three catalytic sites of the beta-subunits rotates the gamma-shaft in three 120 degrees steps. At low frictional loads, the 120 degrees steps alternate with three ATP-independent substeps separated by approximately 30 degrees. We present a quantitative model that accounts for these substeps and show that the observed pauses are due to 1), the asymmetry of the F(1) hexamer that produces a propeller-like motion of the power-stroke and 2), the relatively tight binding of ADP to the catalytic sites.     

The diffusive search mechanism of processive myosin class-V motor involves directional steps along actin subunits

It is widely accepted that the vesicle-transporter myosin-V moves processively along F-actin with large steps of approximately 36 nm using a hand-over-hand mechanism. A key question is how does the rear head of two-headed myosin-V search for the forward actin target in the forward direction. Scanning probe nanometry was used to resolve this underlying search process, which was made possible by attaching the head to a relatively large probe. One-headed myosin-V undergoes directional diffusion with approximately 5.5 nm substeps to develop an average displacement of approximately 20 nm, which was independent of the neck length (2IQ and 6IQ motifs). Two-headed myosin-V showed several approximately 5.5 nm substeps within each processive approximately 36 nm step. These results suggest that the myosin-V head searches in the forward direction for the actin target using directional diffusion on the actin subunits according to a potential slope created along the actin helix.     

Thermodynamics of nucleotide binding to actomyosin V and VI: a positive heat capacity change accompanies strong ADP binding

We have measured the energetics of ATP and ADP binding to single-headed actomyosin V and VI from the temperature dependence of the rate and equilibrium binding constants. Nucleotide binding to actomyosin V and VI can be modeled as two-step binding mechanisms involving the formation of collision complexes followed by isomerization to states with high nucleotide affinity. Formation of the actomyosin VI-ATP collision complex is much weaker and slower than for actomyosin V. A three-step binding mechanism where actomyosin VI isomerizes between two conformations, one competent to bind ATP and one not, followed by rapid ATP binding best accounts for the data. ADP binds to actomyosin V more tightly than actomyosin VI. At 25 degrees C, the strong ADP-binding equilibria are comparable for actomyosin V and VI, and the different overall ADP affinities arise from differences in the ADP collision complex affinity. The actomyosin-ADP isomerization leading to strong ADP binding is entropy driven at >15 degrees C and occurs with a large, positive change in heat capacity (DeltaC(P) degrees ) for both actomyosin V and VI. Sucrose slows ADP binding and dissociation from actomyosin V and VI but not the overall equilibrium constants for strong ADP binding, indicating that solvent viscosity dampens ADP-dependent kinetic transitions, presumably a tail swing that occurs with ADP binding and release. We favor a mechanism where strong ADP binding increases the dynamics and flexibility of the actomyosin complex. The heat capacity (DeltaC(P) degrees ) and entropy (DeltaS degrees ) changes are greater for actomyosin VI than actomyosin V, suggesting different extents of ADP-induced structural rearrangement.     

Force production by single kinesin motors

Motor proteins such as kinesin, myosin and polymerase convert chemical energy into work through a cycle that involves nucleotide hydrolysis. Kinetic rates in the cycle that depend upon load identify transitions at which structural changes, such as power strokes or diffusive motions, are likely to occur. Here we show, by modelling data obtained with a molecular force clamp, that kinesin mechanochemistry can be characterized by a mechanism in which a load-dependent isomerization follows ATP binding. This model quantitatively accounts for velocity data over a wide range of loads and ATP levels, and indicates that movement may be accomplished through two sequential 4-nm substeps. Similar considerations account for kinesin processivity, which is found to obey a load-dependent Michaelis-Menten relationship.     

ATPase cycle and DNA unwinding kinetics of RecG helicase

The superfamily 2 bacterial helicase, RecG, is a monomeric enzyme with a role in DNA repair by reversing stalled replication forks. The helicase must act specifically and rapidly to prevent replication fork collapse. We have shown that RecG binds tightly and rapidly to four-strand oligonucleotide junctions, which mimic a stalled replication fork. The helicase unwinds such DNA junctions with a step-size of approximately four bases per ATP hydrolyzed. To gain an insight into this mechanism, we used fluorescent stopped-flow and quenched-flow to measure individual steps within the ATPase cycle of RecG, when bound to a DNA junction. The fluorescent ATP analogue, mantATP, was used throughout to determine the rate limiting steps, effects due to DNA and the main states in the cycle. Measurements, when possible, were also performed with unlabeled ATP to confirm the mechanism. The data show that the chemical step of hydrolysis is the rate limiting step in the cycle and that this step is greatly accelerated by bound DNA. The ADP release rate is similar to the cleavage rate, so that bound ATP and ADP would be the main states during the ATP cycle. Evidence is provided that the main structural rearrangements, which bring about DNA unwinding, are linked to these states.     

A mechanistic model for Ncd directionality

Ncd is a kinesin-related protein that drives movement to the minus-end of microtubules. Pre-steady-state kinetic experiments have been employed to investigate the cooperative interactions between the motor domains of the MC1 dimer and to establish the ATPase mechanism. Our results indicate that the active sites of dimeric Ncd free in solution are not equivalent; ADP is held more tightly at one site than at the other. Upon microtubule binding, fast release of ADP from the first motor domain is stimulated at 18 s(-1), yet rate-limiting ADP release from the second motor domain occurs at 1.4 s(-1). We propose that the head with the low affinity for ADP binds the microtubule first to establish the directional bias of the microtubule.Ncd intermediate where one motor domain is bound to the microtubule with the second head detached and directed toward the minus-end of the microtubule. The force generating cycle is initiated as ATP binds to the empty site of the microtubule-bound head. ATP hydrolysis at head 1 is required for head 2 to bind to the microtubule. The kinetics indicate that two ATP molecules are required for a single step and force generation for minus-end directed movement generated by this non-processive dimeric motor.     

ATPase mechanism of Eg5 in the absence of microtubules: insight into microtubule activation and allosteric inhibition by monastrol

The ATPase mechanism of kinesin superfamily members in the absence of microtubules remains largely uncharacterized. We have adopted a strategy to purify monomeric human Eg5 (HsKSP/Kinesin-5) in the nucleotide-free state (apoEg5) in order to perform a detailed transient state kinetic analysis. We have used steady-state and presteady-state kinetics to define the minimal ATPase mechanism for apoEg5 in the absence and presence of the Eg5-specific inhibitor, monastrol. ATP and ADP binding both occur via a two-step process with the isomerization of the collision complex limiting each forward reaction. ATP hydrolysis and phosphate product release are rapid steps in the mechanism, and the observed rate of these steps is limited by the relatively slow isomerization of the Eg5-ATP collision complex. A conformational change coupled to ADP release is the rate-limiting step in the pathway. We propose that the microtubule amplifies and accelerates the structural transitions needed to form the ATP hydrolysis competent state and for rapid ADP release, thus stimulating ATP turnover and increasing enzymatic efficiency. Monastrol appears to bind weakly to the Eg5-ATP collision complex, but after tight ATP binding, the affinity for monastrol increases, thus inhibiting the conformational change required for ADP product release. Taken together, we hypothesize that loop L5 of Eg5 undergoes an "open" to "closed" structural transition that correlates with the rearrangements of the switch-1 and switch-2 regions at the active site during the ATPase cycle.     

Theoretical Analysis of the F1-ATPase Experimental Data

F₁-ATPase is a rotatory molecular motor fueled by ATP nucleotides. Different loads can be attached to the motor axis to show that it rotates in main discrete steps of 120° with substeps of ∼80° and 40°. Experimental data show the dependence on the mean rotational velocity ω with respect to the external control parameters: the nucleotide concentration [ATP] and the friction of the load γ_L. In this work we present a theoretical analysis of the experimental data whose main results are: 1), A derivation of a simple analytical formula for ω([ATP], γ_L) that compares favorably with experiments; 2), The introduction of a two-state flashing ratchet model that exhibits experimental phenomenology of a greater specificity than has been, to our knowledge, previously available; 3), The derivation of an argument to obtain the values of the substep sizes; 4), An analysis of the energy constraints of the model; and 5), The theoretical analysis of the coupling ratio between the ATP consumed and the success of a forward step. We also discuss the compatibility of our approach with recent experimental observations.     

Neck length and processivity of myosin V

Myosin V is an unconventional myosin that transports cargo such as vesicles, melanosomes, or mRNA on actin filaments. It is a two-headed myosin with an unusually long neck that has six IQ motifs complexed with calmodulin. In vitro studies have shown that myosin V moves processively on actin, taking multiple 36-nm steps that coincide with the helical repeat of actin. This allows the molecule to "walk" across the top of an actin filament, a feature necessary for moving large vesicles along an actin filament bound to the cytoskeleton. The extended neck length of the two heads is thought to be critical for taking 36-nm steps for processive movements. To test this hypothesis we have expressed myosin V heavy meromyosin-like fragments containing 6IQ motifs, as well as ones that shorten (2IQ, 4IQ) or lengthen (8IQ) the neck region or alter the spacing between 3rd and 4th IQ motifs. The step size was proportional to neck length for the 2IQ, 4IQ, 6IQ, and 8IQ molecules, but the molecule with the altered spacing took shorter than expected steps. Total internal reflection fluorescence microscopy was used to determine whether the heavy meromyosin IQ molecules were capable of processive movements on actin. At saturating ATP concentrations, all molecules except for the 2IQ mutant moved processively on actin. When the ATP concentration was lowered to 10 microm or less, the 2IQ mutant demonstrated some processive movements but with reduced run lengths compared with the other mutants. Its weak processivity was also confirmed by actin landing assays.