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.     

The basic mechanism of ATP powered motor proteins

The ability of ATP powered motor proteins to convert chemical free energy into the mechanical work required to move intra-cellular organelles is discussed in terms of the molecular and dynamic fundamentals involved in producing such movements. This is carried out in detail for muscle contraction with the result that in order for a myosin head to act as a motor protein, it is necessary for it to be able to impose a unique series of impacts on an actin filament. It is further shown that these impacts can be generated when a single water molecule is transiently attached to the ADP formed during one step of an ATP cycle in the myosin head. This analysis leads to the conclusion that muscle must be a type of heat machine which has the capability of attaining mechanochemical efficiencies that approach 100%. An extension of ATP powered motor proteins in general is made with the finding that they must share the same motor mechanism of the transiently attached water molecule. A possible application of these considerations to the problem of the active transport of ions is also pointed out.     

Nucleotide binding induces global and local structural changes of myosin head in muscle fibres.

Thermal stability and internal dynamics of myosin heads in fiber bundles from rabbit psoas muscle has been studied by electron paramagnetic resonance (EPR) spectroscopy and differential scanning calorimetry (DSC). Using ADP, ATP and orthovanadate (V(i)), three intermediate states of the ATP hydrolysis cycle were simulated in glycerinated muscle fibers. DSC transitions contained three overlapping endotherms in each state. Deconvolution showed that the transition temperature of 58.4 degrees C was almost independent of the intermediate state of myosin, while nucleotide binding shifted the melting temperatures of 54.0 and 62.3 degrees C, and changed the enthalpies. These changes suggest global rearrangements of the internal structure in myosin head. In the presence of ADP and ADP plus V(i), the conventional EPR spectra showed changes in the ordering of the probe molecules, suggesting local conformational and motional changes in the internal structure of myosin heads. Saturation transfer EPR measurements reported increased rotational mobility of spin labels in the presence of ATP plus orthovanadate corresponding to a weakly binding state of myosin to actin.     

Kinesin's moonwalk

Kinesin-1 is a single-molecule walking machine, driven by ATP turnover. Recent optical trapping experiments show that pulling backwards on a walking kinesin-1 molecule causes the mechanical walking action to reverse, while the coupled chemical cycle of ATP turnover continues, apparently, to run forwards -- kinesin can moonwalk. Individual forward- and back-steps are fast, and each appears to be a single event, complete in a few tens of microseconds, with no substeps. Between steps, kinesin pauses, waiting for the next ATP to arrive. Several lines of evidence indicate that during these between-step dwells, only one of the two heads is strongly attached to the microtubule. The position of the other head during the dwells is less certain, and more controversial.     

Resolution of conformational states of spin-labeled myosin during steady-state ATP hydrolysis

We have measured the conventional electron paramagnetic resonance (EPR) spectrum of spin-labeled myosin filaments as a function of the nucleotide occupancy of the active site of the enzyme. The probe used was 4-(2-iodoacetamido)-2,2,6,6-tetramethylpiperidine-1-oxyl (IASL), which reacts specifically with sulfhydryl 1 of the myosin head. In the absence of nucleotide, the probe remains strongly immobilized (rigidly attached to the myosin head) so that no nanosecond rotational motions are detectable. When MgADP is added to IASL-labeled myosin filaments (T = 20 degrees C), the probe mobility increases slightly. During steady-state MgADP hydrolysis (T = 20 degrees C), the probe undergoes large-amplitude nanosecond rotational motion. These results are consistent with previous studies of myosin monomers, heavy meromyosin, and myosin subfragment 1. Isoclinic points observed in overlays of sequential EPR spectra recorded during ATP hydrolysis strongly suggest that the probes fall into two motional classes, separated by approximately an order of magnitude in effective rotational correlation time. Both of the observed states are distinct from the conformation of myosin in the absence of nucleotides, and the spectrum of the less mobile population is indistinguishable from that observed in the presence of MgADP. The addition of ADP and vanadate to IASL-myosin gives rise to two motional classes virtually identical with those observed in the presence of ATP, but the relative concentrations of the spin populations are significantly different. We have quantitated the percentage of myosin in each motional state during ATP hydrolysis. The result agrees well with the predicted percentages in the two predominant chemical states in the myosin ATPase cycle. Spectra obtained in the presence of nucleotide analogues permit us to assign the conformational states to specific chemical states. We propose that the two motional classes represent two distinct local conformations of myosin that are in exchange with one another during the ATP hydrolysis reaction cycle.     

Dynein arm substructure and the orientation of arm-microtubule attachments

In the presence of AMP-PCP (beta, gamma-methyleneadenosine 5'-triphosphate), a non-hydrolyzable analog of ATP, negative stain images of increased morphological detail indicate that the dynein arm, attached to ciliary doublet microtubules, is composed of subunits including a cape, an elongated body and a head. The arrangement of these subunits makes it possible to distinguish A from B subfiber binding sites on a single arm and to demonstrate that the head of an extended arm on subfiber A of one ciliary doublet is capable of binding to subfiber B of an adjacent doublet in a specific orientation, which supports a key step in a current model of the mechanochemical cycle by which the arm produces microtubule sliding in the ciliary axoneme.     

Structural characterization of the binding of Myosin*ADP*Pi to actin in permeabilized rabbit psoas muscle

When myosin is attached to actin in a muscle cell, various structures in the filaments are formed. The two strongly bound states (A*M*ADP and A*M) and the weakly bound A*M*ATP states are reasonably well understood. The orientation of the strongly bound myosin heads is uniform ("stereospecific" attachment), and the attached heads exhibit little spatial fluctuation. In the prehydrolysis weakly bound A*M*ATP state, the orientations of the attached myosin heads assume a wide range of azimuthal and axial angles, indicating considerable flexibility in the myosin head. The structure of the other weakly bound state, A*M*ADP*P(i), however, is poorly understood. This state is thought to be the critical pre-power-stroke state, poised to make the transition to the strongly binding, force-generating states, and hence it is of particular interest for understanding the mechanism of contraction. However, because of the low affinity between myosin and actin in the A*M*ADP*P(i) state, the structure of this state has eluded determination both in isolated form and in muscle cells. With the knowledge recently gained in the structures of the weakly binding M*ATP, M*ADP*P(i) states and the weakly attached A*M*ATP state in muscle fibers, it is now feasible to delineate the in vivo structure of the attached state of A*M*ADP*P(i). The series of experiments presented in this article were carried out under relaxing conditions at 25 degrees C, where approximately 95% of the myosin heads in the skinned rabbit psoas muscle contain the hydrolysis products. The affinity for actin is enhanced by adding polyethylene glycol (PEG) or by lowering the ionic strength in the bathing solution. Solution kinetics and binding constants were determined in the presence and in the absence of PEG. When the binding between actin and myosin was increased, both the myosin layer lines and the actin layer lines increased in intensity, but the intensity profiles did not change. The configuration (mode) of attachment in the A*M*ADP*P(i) state is thus unique among the intermediate attached states of the cross-bridge ATP hydrolysis cycle. One of the simplest explanations is that both myosin filaments and actin filaments are stabilized (e.g., undergo reduced spatial fluctuations) by the attachment. The alignment of the myosin heads in the thick filaments and the alignment of the actin monomers in the thin filaments are improved as a result. The compact atomic structure of M*ADP*P(i) with strongly coupled domains may contribute to the unique attachment configuration: the "primed" myosin heads may function as "transient struts" when attached to the thin filaments.     

Direct visualization by electron microscopy of the weakly bound intermediates in the actomyosin adenosine triphosphatase cycle.

We used a novel stopped-flow/rapid-freezing machine to prepare the transient intermediates in the actin-myosin adenosine triphosphatase (ATPase) cycle for direct observation by electron microscopy. We focused on the low affinity complexes of myosin-adenosine triphosphate (ATP) and myosin-adenosine diphosphate (ADP)-Pi with actin filaments since the transition from these states to the high affinity actin-myosin-ADP and actin-myosin states is postulated to generate the molecular motion that drives muscle contraction and other types of cellular movements. After rapid freezing and metal replication of mixtures of myosin subfragment-1, actin filaments, and ATP, the structure of the weakly bound intermediates is indistinguishable from nucleotide-free rigor complexes. In particular, the average angle of attachment of the myosin head to the actin filament is approximately 40 degrees in both cases. At all stages in the ATPase cycle, the configuration of most of the myosin heads bound to actin filaments is similar, and the part of the myosin head preserved in freeze-fracture replicas does not tilt by more than a few degrees during the transition from the low affinity to high affinity states. In contrast, myosin heads chemically cross-linked to actin filaments differ in their attachment angles from ordered at 40 degrees without ATP to nearly random in the presence of ATP when viewed by negative staining (Craig, R., L.E. Greene, and E. Eisenberg. 1985. Proc. Natl. Acad. Sci. USA. 82:3247-3251, and confirmed here), freezing in vitreous ice (Applegate, D., and P. Flicker. 1987. J. Biol. Chem. 262:6856-6863), and in replicas of rapidly frozen samples. This suggests that many of the cross-linked heads in these preparations are dissociated from but tethered to the actin filaments in the presence of ATP. These observations suggest that the molecular motion produced by myosin and actin takes place with the myosin head at a point some distance from the actin binding site or does not involve a large change in the shape of the myosin head.     

Electron cryomicroscopy of acto-myosin-S1 during steady-state ATP hydrolysis.

The structure of the complex of actin and myosin subfragment-1 (S1) during steady-state ATP hydrolysis has been examined by electron microscopy. This complex is normally dissociated by ATP in vitro but was stabilized here by low ionic strength. Optimal conditions for attachment were established by light-scattering experiments that showed that approximately 70% of S1 could be bound in the presence of ATP. Micrographs of the unstained complex in vitreous water suggest that S1 attaches to actin in a variety of configurations in ATP; this contrasts with the single attached configuration seen in the presence of ADP. The data are therefore compatible with the idea that a change in attached configuration of the myosin cross-bridge is the origin of muscle force. In control experiments where ATP was allowed to hydrolyze completely the binding of the S1 seemed cooperative.     

The post-rigor structure of myosin VI and implications for the recovery stroke

Myosin VI has an unexpectedly large swing of its lever arm (powerstroke) that optimizes its unique reverse direction movement. The basis for this is an unprecedented rearrangement of the subdomain to which the lever arm is attached, referred to as the converter. It is unclear at what point(s) in the myosin VI ATPase cycle rearrangements in the converter occur, and how this would effect lever arm position. We solved the structure of myosin VI with an ATP analogue (ADP.BeF3) bound in its nucleotide-binding pocket. The structure reveals that no rearrangement in the converter occur upon ATP binding. Based on previously solved myosin structures, our structure suggests that no reversal of the powerstroke occurs during detachment of myosin VI from actin. The structure also reveals novel features of the myosin VI motor that may be important in maintaining the converter conformation during detachment from actin, and other features that may promote rapid rearrangements in the structure following actin detachment that enable hydrolysis of ATP.     

Electron microscopic evidence for the myosin head lever arm mechanism in hydrated myosin filaments using the gas environmental chamber

Muscle contraction results from an attachment–detachment cycle between the myosin heads extending from myosin filaments and the sites on actin filaments. The myosin head first attaches to actin together with the products of ATP hydrolysis, performs a power stroke associated with release of hydrolysis products, and detaches from actin upon binding with new ATP. The detached myosin head then hydrolyses ATP, and performs a recovery stroke to restore its initial position. The strokes have been suggested to result from rotation of the lever arm domain around the converter domain, while the catalytic domain remains rigid. To ascertain the validity of the lever arm hypothesis in muscle, we recorded ATP-induced movement at different regions within individual myosin heads in hydrated myosin filaments, using the gas environmental chamber attached to the electron microscope. The myosin head were position-marked with gold particles using three different site-directed antibodies. The amplitude of ATP-induced movement at the actin binding site in the catalytic domain was similar to that at the boundary between the catalytic and converter domains, but was definitely larger than that at the regulatory light chain in the lever arm domain. These results are consistent with the myosin head lever arm mechanism in muscle contraction if some assumptions are made.     

A chemically reversible Brownian motor: application to kinesin and Ncd.

Kinesin and nonclaret disjunctional protein (ncd) are two microtubule-based molecular motors that use energy from ATP hydrolysis to drive motion in opposite directions. They are structurally very similar and bind with similar orientations on microtubule. What is the origin of the different directionality? Is it some subtle feature of the structure of the motor domains, not apparent in x-ray diffraction studies, or possibly some difference near the neck regions far from the microtubule binding site? Perhaps because the motors function as dimers, the explanation involves differences in the strength of the interaction between the two motor monomers themselves. Here we present another possibility, based on a Brownian ratchet, in which the direction of motion of the motor is controlled by the chemical mechanism of ATP hydrolysis and is an inherent property of a single head. In contrast to conventional power stroke models, dissociation of the individual heads is not obligatory in the chemomechanical cycle, and the steps during which motion and force generation occurs are best described as one-dimensional thermally activated transitions that take place while both heads are attached to the microtubule. We show that our model is consistent with experiments on kinesin in which the velocity is measured as a function of external force and with the observed stiochiometry of one ATP/8-nm step at low load. Further, the model provides a way of understanding recent experiments on the ATP dependence of the variance (randomness) of the distance moved in a given time.     

Stoichiometry and affinity of nucleotide binding to P-glycoprotein during the catalytic cycle

Drug transport mediated by P-glycoprotein (Pgp) is driven by hydrolysis of ATP at the two cytosolic nucleotide binding domains. However, little is currently known concerning the stoichiometry of nucleotide binding and how both stoichiometry and binding affinity change during the catalytic cycle of the transporter. To address this issue, we used fluorescence techniques to measure both the number of nucleotides bound to P-glycoprotein during various stages of the catalytic cycle and the affinity of nucleotide binding. Results showed that resting state P-glycoprotein bound two molecules of the fluorescent nucleotide derivative, 2'(3')-O-(2,4,6-trinitrophenyl)adenosine 5'-triphosphate (TNP-ATP), whereas the vanadate-trapped transition state bound only one nucleotide molecule. Both resting and transition state P-glycoprotein showed similar affinity for TNP-ATP/TNP-ADP and unlabeled ATP/ADP. Following binding of various drugs, resting state P-glycoprotein displayed a higher affinity for nucleotides, up to 4-fold depending on the compound used. In contrast, the transition state showed substantially lower (up to 3-fold) nucleotide binding affinity when the drug binding site(s) is/are occupied. These results indicate that both nucleotide binding domains of P-glycoprotein are likely to be occupied with either ATP (or ADP) in the resting state and the transition state in the absence of transport substrates. Drugs alter the binding affinity to favor association of ATP with P-glycoprotein at the start of the catalytic cycle and release of ADP from the transition state following nucleotide hydrolysis.     

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.     

Feedback of the kinesin-1 neck-linker position on the catalytic site

Kinesin-1 motor proteins step along microtubules by a mechanism in which the heads cycle through microtubule-bound and unbound states in an interlaced fashion. An important contribution to head-head coordination arises from the action of the neck-linker that docks onto the core motor domain upon ATP binding. We show here that the docked neck-linker not only guides the microtubule-unbound head to the next microtubule binding site but also signals its position to the head to which it is attached. Cross-linking studies on mutated kinesin constructs reveal that residues at the interface motor core/docked neck-linker, among them most importantly a conserved tyrosine, are involved in this feedback. The primary effect of the docked neck-linker is a reduced microtubule binding affinity in the ADP state.     

A chemically driven fluctuating ratchet model for actomyosin interaction

With reference to the experimental observations by Yanagida and his co-workers on actomyosin interaction, a Brownian motor of fluctuating ratchet kind is designed with the aim to describe the interaction between a Myosin II head and a neighboring actin filament. Our motor combines the dynamics of the myosin head with a chemical external system related to the ATP cycle, whose role is to provide the energy supply necessary to bias the motion. Analytical expressions for the duration of the ATP cycle, for the Gibbs free energy and for the net displacement of the myosin head are obtained. Finally, by exploiting a method due to Sekimoto [J. Phys. Soc. Jpn. 66 (1997) 1234], a formula is worked out for the amount of energy consumed during the ATP cycle.     

Fluorescent, acyl chain-labeled phosphatidylcholine analogs reveal novel transport pathways across the plasma membrane of yeast

Acyl chain-labeled NBD-phosphatidylcholine (NBD-PC) has been used to identify three gene products (Lem3p, Dnf1p, and Dnf2p) that are required for normal levels of inward-directed phospholipid transport (flip) across the plasma membrane of yeast. Although the head group structure of acyl chain-labeled NBD phospholipids has been shown to influence the mechanism of flip across the plasma membrane, the extent to which the acyl chain region and the associated fluorophore affect flip has not been assessed. Given the identification of these proteins required for NBD-PC flip, it is now possible to determine whether the fluorophore attached to a phospholipid acyl chain influences the mechanism of flip. Thus, flip of phosphatidylcholine molecules with three different Bodipy fluorophores (Bodipy FL, Bodipy 530, and Bodipy 581) was tested and compared with that of NBD-PC in strains carrying deletions in LEM3, DNF1, and DNF2. Deletion of these genes significantly reduced the flip of NBD-PC and Bodipy FL-PC but had no effect on that of Bodipy 581-PC and Bodipy 530-PC. These data, in combination with comparisons of the effect of ATP depletion, collapse of the proton electrochemical gradient across the plasma membrane, and culture density led to the conclusion that at least three different flip pathways exist in yeast that are selective for the structure of the fluorophore attached to the acyl chain of phosphatidylcholine molecules.     

Chemomechanical coupling in actomyosin system: An approach by in vitro movement assay and kinetic analysis of ATP hydrolysis by shortening myofibrils

On the basis of our recent studies of the sliding distance of actin filaments during one ATP cycle on the surface of myosin-coated glass surface and ATP hydrolysis by rapidly shortening myofibrils, the molecular mechanism of chemomechanical coupling is considered. We conclude that the myosin head can repeat many active cyclic interactions with actins to drive the actin filaments over a long distance during one ATP cycle, and that the distance is variable depending on the load.     

Effect of activation by calcium on the x-ray diffraction pattern from insect flight muscle.

A low-angle X-ray diffraction pattern of calcium-activated Lethocerus flight muscle was formed and the intensities of various parts of the pattern observed by means of a proportional counter. The muscle was sinusoidally oscillated in length to produce mechanical work. The resultant changes in diffraction intensity were related to the state of the muscle and to the phase of the mechanical oscillatory cycle. The measurements were interpreted in terms of a movement of the heads of the myosin molecules into contact with the actin filaments. In these terms the results showed that between 10 and 20% of the myosin heads attached to actin during work-producing oscillation of the muscle. The time-course of this attachment followed that of tension generation with a small delay. Calculation suggests that not all of the myosin molecules attached to actin at any one moment were generating tension.     

ATP-dependent exonuclease V from Micrococcus luteus. The enzyme-DNA complex, the processive mechanism, and the role of ATP

Some kinetic predictions of the proposed processive mechanism for the hydrolysis of DNA by the ATP-dependent enzyme exonuclease V have been checked. The method is to trap enzyme molecules not attached to radioactive DNA substrate with an excess of nonradioactive DNA, so that enzyme molecules attached to the radioactive substrate contribute to the liberation of radioactive products only until they dissociate from it. The experiments show that enzyme molecules remain attached to a T7 double-stranded DNA molecule, while hydrolysing it, for about 2 min under our conditions, in agreement with the predictions of the processive mechanism. However, the mechanism of degradation of single-stranded DNA is not processive. Formation of an enzyme-DNA complex is largely dependent on the presence of ATP. This formation does not appear to be synchronous. ATP analogs do not stimulate formation of, nor stabilize, the enzyme-DNA complex. EDTA causes dissociation of enzyme molecules from the DNA complex.