Dwell Time Distributions of the Molecular Motor Myosin V

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.     

Myosin II Filament Dynamics in Actin Networks Revealed with Interferometric Scattering Microscopy

The plasma membrane and the underlying cytoskeletal cortex constitute active platforms for a variety of cellular processes. Recent work has shown that the remodeling acto-myosin network modifies local membrane organization, but the molecular details are only partly understood because of difficulties with experimentally accessing the relevant time and length scales. Here, we use interferometric scattering microscopy to investigate a minimal acto-myosin network linked to a supported lipid bilayer membrane. Using the magnitude of the interferometric contrast, which is proportional to molecular mass, and fast acquisition rates, we detect and image individual membrane-attached actin filaments diffusing within the acto-myosin network and follow individual myosin II filament dynamics. We quantify myosin II filament dwell times and processivity as functions of ATP concentration, providing experimental evidence for the predicted ensemble behavior of myosin head domains. Our results show how decreasing ATP concentrations lead to both increasing dwell times of individual myosin II filaments and a global change from a remodeling to a contractile state of the acto-myosin network.     

A kinetic mechanism for the fast movement of Chara myosin

Endoplasmic streaming of characean cells of Nitella or Chara is known to be in the range 30-100 microm/second. The Chara myosin extracted from the cells and fixed onto a glass surface was found to move muscle actin filaments at a velocity of 60 microm/second. This is ten times faster than that of skeletal muscle myosin (myosin II). In this study, the displacement caused by single Chara myosin molecules was measured using optical trapping nanometry. The step size of Chara myosin was approximately 19nm. This step size is longer than that of skeletal muscle myosin but shorter than that of myosin V. The dwell time of the steps was relatively long, and this most likely resulted from two rate-limiting steps, the dissociation of ADP and the binding of ATP. The rate of ADP release from Chara myosin after the completion of the force-generation step was similar to that of myosin V, but was considerably slower than that of skeletal muscle myosin. The 19nm step size and the dwell time obtained could not explain the fast movement. The fast movement could be explained by the load-dependent release of ADP. As the load imposed on the myosin decreased, the rate of ADP release increased. We propose that the interaction of Chara myosin with an actin filament resulted in a negative load being imposed on other myosin molecules interacting with the same actin filament. This resulted in an accelerated release of ADP and the fast sliding movement.     

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.     

Extracting dwell time sequences from processive molecular motor data

Processive molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. Single-molecule recordings of motor position along a substrate polymer appear as a stochastic staircase. Recordings of other single molecules, such as F1-ATPase, RNA polymerase, or topoisomerase, have the same appearance. We present a maximum likelihood algorithm that extracts the dwell time sequence from noisy data, and estimates state transition probabilities and the distribution of the motor step size. The algorithm can handle models with uniform or alternating step sizes, and reversible or irreversible kinetics. A periodic Markov model describes the repetitive chemistry of the motor, and a Kalman filter allows one to include models with variable step size and to correct for baseline drift. The data are optimized recursively and globally over single or multiple data sets, making the results objective over the full scale of the data. Local binary algorithms, such as the t-test, do not represent the behavior of the whole data set. Our method is model-based, and allows rapid testing of different models by comparing the likelihood scores. From data obtained with current technology, steps as small as 8 nm can be resolved and analyzed with our method. The kinetic consequences of the extracted dwell sequence can be further analyzed in detail. We show results from analyzing simulated and experimental kinesin and myosin motor data. The algorithm is implemented in the free QuB software.     

肌球蛋白Ⅵ定向运动的蒙特卡罗模拟

根据myosin Ⅵ分子马达头部核苷的变化建立一个四态循环,然后利用蒙特卡罗方法模拟分子马达的动力学性质,讨论了myosin Ⅵ速度、滞留时间与溶液中ATP浓度、ADP浓度和负载力F的关系。模拟得到：myosin Ⅵ会在轨道微丝上进行梯跳运动并且每次在微丝上的滞留时间并不相同;另外,myosin Ⅵ的速度会随着ATP浓度的增加而增大,随着ADP浓度和负载力的增加而减小;负载力对myosin Ⅵ在胞内执行输运还是连接功能起一定的调节作用。     

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.     

Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin

We have estimated the step size of the myosin cross-bridge (d, displacement of an actin filament per one ATP hydrolysis) in an in vitro motility assay system by measuring the velocity of slowly moving actin filaments over low densities of heavy meromyosin on a nitrocellulose surface. In previous studies, only filaments greater than a minimum length were observed to undergo continuous sliding movement. These filaments moved at the maximum speed (Vo), while shorter filaments dissociated from the surface. We have now modified the assay system by including 0.8% methylcellulose in the ATP solution. Under these conditions, filaments shorter than the previous minimum length move, but significantly slower than Vo, as they are propelled by a limited number of myosin heads. These data are consistent with a model that predicts that the sliding velocity (v) of slowly moving filaments is determined by the product of vo and the fraction of time when at least one myosin head is propelling the filament, that is, v = vo [1-(1-ts/tc)N], where ts is the time the head is strongly bound to actin, tc is the cycle time of ATP hydrolysis, and N is the average number of myosin heads that can interact with the filament. Using this equation, the optimum value of ts/tc to fit the measured relationship between v and N was calculated to be 0.050. Assuming d = vots, the step size was then calculated to be between 10nm and 28 nm per ATP hydrolyzed, the latter value representing the upper limit. This range is within that of geometric constraint for conformational change imposed by the size of the myosin head, and therefore is not inconsistent with the swinging cross-bridge model tightly coupled with ATP hydrolysis.     

Nanometer localization of single green fluorescent proteins: evidence that myosin V walks hand-over-hand via telemark configuration

Myosin V is a homodimeric motor protein involved in trafficking of vesicles in the cell. It walks bipedally along actin filaments, moving cargo approximately 37 nm per step. We have measured the step size of individual myosin heads by fusing an enhanced green fluorescent protein (eGFP) to the N-terminus of one head of the myosin dimer and following the motion with nanometer precision and subsecond resolution. We find the average step size to be 74.1 nm with 9.4 nm (SD) and 0.3 nm (SE). Our measurements demonstrate nanometer localization of single eGFPs, confirm the hand-over-hand model of myosin V procession, and when combined with previous data, suggest that there is a kink in the leading lever arm in the waiting state of myosin V. This kink, or "telemark skier" configuration, may cause strain, which, when released, leads to the powerstroke of myosin, throwing the rear head forward and leading to unidirectional motion.     

Geometrical correspondence identified and a new interaction unit suggested in striated muscle

It has long been believed that the periodic structure of the myosin helix is a consequence only of compressing the actin-myosin interaction sites. Here, we identify a length correspondence between the smallest helical unit on the thick filament and the helical pitch of the actin filaments in two different contractile muscles. This suggests a rotation/swing of the filaments that creates a new interaction unit in addition to the single interaction between an actin filament and a myosin head. Numerical characteristics of the single interaction are estimated from discussion about an in vivo interaction utilizing the new unit. The estimated twisted angle of the actin filaments is consistent with that calculated from its torsion rigidity and the evaluated step sizes per cross-bridge can be performed by a single bend of a myosin head. By comparing our evaluated step sizes with experimental results, we conclude that the most plausible mechanism at the force-recovery stage involves swings or rotations of both filaments in the same direction (clockwise).     

Myosin head mechanical performance under different conformational change mechanisms

The present paper puts forward a mathematical approach to model the conformational changes of the myosin head due to ATP hydrolysis, which determine the head swinging and consequent sliding of the actin filament. Our aim is to provide a simple but effective model simulating myosin head performance to be integrated into the overall model of sarcomere mechanics under development at our Laboratory (J. Biomech. 34 (2001) 1607). We began by exploring myosin head mechanics in recent findings about myosin ultrastructure, morphology and energetics in order to calculate the working stroke distance (WS) and the force transmitted to the actin filament during muscle contraction. Two different working stroke mechanisms were investigated, assuming that the swinging of the myosin head occurs either as a consequence of purely conformational changes (Science 261 (1993a) 58) or by thermally driven motion (ratchet mechanism) followed by conformational changes (Cell 99 (1999) 421). Our results show that force and WS values vary markedly between the two models. The maximum force generated is about 10 pN for the first model and 31 pN for the second model, and the WSs are about 13 and 4 nm, respectively. These results are then discussed and compared with published data. The experimental data used for comparison are scarce and non-homogeneous; hence, the final remarks do not lead to definite conclusions. In any event, relatively speaking, the first model is more coherent with experimental findings.     

A unique ATP hydrolysis mechanism of single-headed processive myosin, myosin IX

Recent studies have revealed that myosin IX is a single-headed processive myosin, yet it is unclear how myosin IX can achieve the processive movement. Here we studied the mechanism of ATP hydrolysis cycle of actomyosin IXb. We found that myosin IXb has a rate-limiting ATP hydrolysis step unlike other known myosins, thus populating the prehydrolysis intermediate (M.ATP). M.ATP has a high affinity for actin, and, unlike other myosins, the dissociation of M.ATP from actin was extremely slow, thus preventing myosin from dissociating away from actin. The ADP dissociation step was 10-fold faster than the overall ATP hydrolysis cycle rate and thus not rate-limiting. We propose the following model for single-headed processive myosin. Upon the formation of the M.ATP intermediate, the tight binding of actomyosin IX at the interface is weakened. However, the head is kept in close proximity to actin due to the tethering role of loop 2/large unique insertion of myosin IX. There is enough freedom for the myosin head to find the next location of the binding site along with the actin filament before complete dissociation from the filament. After ATP hydrolysis, Pi is quickly released to form a strong actin binding form, and a power stroke takes place.     

Myosin cross-bridge mechanics: geometrical determinants for continuous sliding

Advances in experimental techniques have provided new details on the molecular mechanisms governing the cross-bridge kinetics. Nevertheless, the issue of micromechanics of sliding is still debated. In particular, uncertainty exists regarding the myosin filament arrangement and structure and the mechanics of the myosin head with respect to the working stroke distance (WS) and the duty ratio (r), i.e. the fraction of the ATPase cycle time the myosin head is attached to the actin filament. The object of the present work is to provide a theoretical framework to correlate different features of cross-bridge mechanics; the main hypothesis is that the attachment between the actin filament and the surrounding myosin filaments has to be continuous through the sliding (continuous sliding hypothesis) in order to maximise the effect of the myosin head performance. A 3-D model of the sliding mechanism based on a geometrical approach is presented, which is able to identify the architectures that accomplish the continuous sliding under unloaded conditions. About 200 different configurations have been simulated by changing the myosin head binding range, i.e. its ability to reach an actin binding site from its rest position, WS, the myosin head orientation and the actin filament orientation. Only few configurations were consistent with the continuous sliding hypothesis. Depending on the parameter set adopted, the percentage of attached heads (%AH) calculated ranges between 4% and 28%, r between 0.08 and 0.02 s⁻¹, and the sliding velocity between 0.7 and 10.6 μm/s. In all the cases, results were not affected by the WS value.     

Myosin VI steps via a hand-over-hand mechanism with its lever arm undergoing fluctuations when attached to actin

Myosin VI is a reverse direction myosin motor that, as a dimer, moves processively on actin with an average center-of-mass movement of approximately 30 nm for each step. We labeled myosin VI with a single fluorophore on either its motor domain or on the distal of two calmodulins (CaMs) located on its putative lever arm. Using a technique called FIONA (fluorescence imaging with one nanometer accuracy), step size was observed with a standard deviation of <1.5 nm, with 0.5-s temporal resolution, and observation times of minutes. Irrespective of probe position, the average step size of a labeled head was approximately 60 nm, strongly supporting a hand-over-hand model of motility and ruling out models in which the unique myosin VI insert comes apart. However, the CaM probe displayed large spatial fluctuations (presence of ATP but not ADP or no nucleotide) around the mean position, whereas the motor domain probe did not. This supports a model of myosin VI motility in which the lever arm is either mechanically uncoupled from the motor domain or is undergoing reversible isomerization for part of its motile cycle on actin.     

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the “Driven by Detachment (DbD)” mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.     

Muscle contraction: a mechanism of energy transduction

A mechanism of muscle contraction is presented in which energy from the hydrolysis of MgATP is transferred directly to conformational strain in a flexible segment of the myosin head. That segment is proximal to both the active site and the subfragment 1—subfragment 2 hinge (the portion of the myosin molecule that connects each of its two enzymatically active globular heads to the long thin helical body). This proximity allows configurational changes at the active site, which are an intrinsic part of the enzymatic mechanism, to impose a localized strain, or distortion, near the hinge. The energy, trapped in the protein this way, is subsequently used for mechanical work when other enzymatically-induced conformational changes free the strained segment of the myosin head to unbend. As this happens, the head rotates and the distal end (opposite the hinge) attaches to the actin filament and pulls on it. In this mechanism, actin interacts with myosin in two different ways: (1) at the active site where it activates a step in the hydrolysis of MgATP that frees the head to rotate; (2) at the distal end of myosin, where it forms the grip through which the rotating head pulls on the actin filament. The first interaction allows actin to initiate primary movement of the myosin head; the second directs the force and allows the movement of the head to be used for the sliding motion of the actin and myosin filaments during contraction. In this model, there are also two different energy transfers: one occurs in the transduction process itself when energy from hydrolysis is trapped as conformational distortion in the hinge region; the other occurs, reversibly, when actin and myosin form and then break the distal grip; in this second transfer there is no net energy change in the course of a cycle. A chemical mechanism is suggested to explain actin-activation of hydrolysis at the active site-hinge region.     

Velocity, Processivity, and Individual Steps of Single Myosin V Molecules in Live Cells

We report the tracking of single myosin V molecules in their natural environment, the cell. Myosin V molecules, labeled with quantum dots, are introduced into the cytoplasm of living HeLa cells and their motion is recorded at the single molecule level with high spatial and temporal resolution. We perform an intracellular measurement of key parameters of this molecular transporter: velocity, processivity, step size, and dwell time. Our experiments bridge the gap between in vitro single molecule assays and the indirect measurements of the motor features deduced from the tracking of organelles in live cells.     

Single-molecule tracking of myosins with genetically engineered amplifier domains

We combined protein engineering and single molecule measurements to directly record the step size of a series of myosin constructs with shortened and elongated artificial neck domains. Our results show that the step size has a clear linear dependence on the length of the neck domain and we also established that mechanical amplification in the myosin motor is based on a rotation of the neck domain relative to the actin-bound head. For all our constructs, including those with artificial necks, the magnitude of the neck rotation concurrent with the displacement step was approximately 30 degrees. The engineered change in the step size of myosin marks a significant advance in our ability to selectively modify the functional properties of molecular motors.     

Along the road not taken: how many myosin heads act on a single actin filament at any instant in working muscle?

We reconsider the use of stiffness measurements to estimate N, the number of myosin heads acting (working at any instant to produce tension) on a single actin filament in vertebrate striated muscle, and give reasons for our rejection of numbers produced from such measurements. We go on to present a different approach to the problem, citing and extending a model bearing on the value of N which is derived from other physiological and biochemical data and which offers insight into the fundamental actin-myosin contractile event as an impulsive force. New experimental data accumulating over the past decade support this model, in which the myosin heads act sequentially along the actin filament (this is an example of Conformational Spread). In this model only a single myosin head acts on a single actin filament to produce an impulse at any given instant in normally-contracting muscle, either in the isometric or the isotonic mode, so N?=?1. However, extra impulses occur within the same time frame after quick release of length or tension. The predictions of this sequential model are in striking agreement with a large body of recent detailed biophysical and biochemical evidence. We suggest that this warrants further in-depth experimental work, specifically to explore and test the sequential model and its implications.