Myosin learns to walk

A particle size threshold governs diffusion and segregation of PAR-3 during cell polarization

The actomyosin cortex regulates the localization and function of proteins at the plasma membrane. Here, we study how membrane binding, cortical movements, and diffusion determine membrane protein distribution. In Caenorhabditis elegans zygotes, actomyosin flows transport PAR polarity proteins to establish the anterior-posterior axis. Oligomerization of a key scaffold protein, PAR-3, is required for polarization. PAR-3 oligomers are a heterogeneous population of many different sizes, and it remains unclear how oligomer size affects PAR-3 segregation. To address this question, we engineered PAR-3 to defined sizes. We report that PAR-3 trimers are necessary and sufficient for PAR-3 function during polarization and later embryo development. Quantitative analysis of PAR-3 diffusion shows that a threshold size of three subunits allows PAR-3 clusters to stably bind the membrane, where they are corralled and transported by the actomyosin cortex. Our study provides a quantitative model for size-dependent protein transportation of peripheral membrane proteins by cortical flow.

The actomyosin cytoskeleton is a major regulator of cellular organization. Chang and Dickinson develop protein-engineering and particle-tracking tools to study how clustered membrane-bound proteins are transported by actomyosin contractions in vivo. Data-driven modeling reveals how membrane binding, diffusion, and collisions with F-actin contribute to protein movement.

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.

An Arginine Finger Regulates the Sequential Action of Asymmetrical Hexameric ATPase in the Double-Stranded DNA Translocation Motor

Biological motors are ubiquitous in living systems. Currently, how the motor components coordinate the unidirectional motion is elusive in most cases. Here, we report that the sequential action of the ATPase ring in the DNA packaging motor of bacteriophage ϕ29 is regulated by an arginine finger that extends from one ATPase subunit to the adjacent unit to promote noncovalent dimer formation. Mutation of the arginine finger resulted in the interruption of ATPase oligomerization, ATP binding/hydrolysis, and DNA translocation. Dimer formation reappeared when arginine mutants were mixed with other ATPase subunits that can offer the arginine to promote their interaction. Ultracentrifugation and virion assembly assays indicated that the ATPase was presenting as monomers and dimer mixtures. The isolated dimer alone was inactive in DNA translocation, but the addition of monomer could restore the activity, suggesting that the hexameric ATPase ring contained both dimer and monomers. Moreover, ATP binding or hydrolysis resulted in conformation and entropy changes of the ATPase with high or low DNA affinity. Taking these observations together, we concluded that the arginine finger regulates sequential action of the motor ATPase subunit by promoting the formation of the dimer inside the hexamer. The finding of asymmetrical hexameric organization is supported by structural evidence of many other ATPase systems showing the presence of one noncovalent dimer and four monomer subunits. All of these provide clues for why the asymmetrical hexameric ATPase gp16 of ϕ29 was previously reported as a pentameric configuration by cryo-electron microscopy (cryo-EM) since the contact by the arginine finger renders two adjacent ATPase subunits closer than other subunits. Thus, the asymmetrical hexamer would appear as a pentamer by cryo-EM, a technology that acquires the average of many images.

Detachment, futile cycling, and nucleotide pocket collapse in myosin-V stepping

Myosin-V is a highly processive dimeric protein that walks with 36-nm steps along actin tracks, powered by coordinated adenosine triphosphate (ATP) hydrolysis reactions in the two myosin heads. No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run length with adenosine diphosphate (ADP), ATP and external forcing. In particular, a result that has eluded all theoretical studies based upon rigorous physical chemistry is that run length decreases with both increasing [ADP] and [ATP]. We systematically analyze which mechanisms in existing models reproduce which experimental trends and use this information to guide the development of models that can reproduce them all. We formulate models as reaction networks between distinct mechanochemical states with energetically determined transition rates. For each network architecture, we compare predictions for velocity and run length to a subset of experimentally measured values, and fit unknown parameters using a bespoke Monte Carlo simulated annealing optimization routine. Finally we determine which experimental trends are replicated by the best-fit model for each architecture. Only two models capture them all: one involving [ADP]-dependent mechanical detachment, and another including [ADP]-dependent futile cycling and nucleotide pocket collapse. Comparing model-predicted and experimentally observed kinetic transition rates favors the latter.

Finding of widespread viral and bacterial revolution dsDNA translocation motors distinct from rotation motors by channel chirality and size

Background

Double-stranded DNA translocation is ubiquitous in living systems. Cell mitosis, bacterial binary fission, DNA replication or repair, homologous recombination, Holliday junction resolution, viral genome packaging and cell entry all involve biomotor-driven dsDNA translocation. Previously, biomotors have been primarily classified into linear and rotational motors. We recently discovered a third class of dsDNA translocation motors in Phi29 utilizing revolution mechanism without rotation. Analogically, the Earth rotates around its own axis every 24 hours, but revolves around the Sun every 365 days.

Results

Single-channel DNA translocation conductance assay combined with structure inspections of motor channels on bacteriophages P22, SPP1, HK97, T7, T4, Phi29, and other dsDNA translocation motors such as bacterial FtsK and eukaryotic mimiviruses or vaccinia viruses showed that revolution motor is widespread. The force generation mechanism for revolution motors is elucidated. Revolution motors can be differentiated from rotation motors by their channel size and chirality. Crystal structure inspection revealed that revolution motors commonly exhibit channel diameters larger than 3 nm, while rotation motors that rotate around one of the two separated DNA strands feature a diameter smaller than 2 nm. Phi29 revolution motor translocated double- and tetra-stranded DNA that occupied 32% and 64% of the narrowest channel cross-section, respectively, evidencing that revolution motors exhibit channel diameters significantly wider than the dsDNA. Left-handed oriented channels found in revolution motors drive the right-handed dsDNA via anti-chiral interaction, while right-handed channels observed in rotation motors drive the right-handed dsDNA via parallel threads. Tethering both the motor and the dsDNA distal-end of the revolution motor does not block DNA packaging, indicating that no rotation is required for motors of dsDNA phages, while a small-angle left-handed twist of dsDNA that is aligned with the channel could occur due to the conformational change of the phage motor channels from a left-handed configuration for DNA entry to a right-handed configuration for DNA ejection for host cell infection.

Conclusions

The revolution motor is widespread among biological systems, and can be distinguished from rotation motors by channel size and chirality. The revolution mechanism renders dsDNA void of coiling and torque during translocation of the lengthy helical chromosome, thus resulting in more efficient motor energy conversion.

BMP-2 overexpression augments vascular smooth muscle cell motility by upregulating myosin Va via Erk signaling

Background. The disruption of physiologic vascular smooth muscle cell (VSMC) migration initiates atherosclerosis development. The biochemical mechanisms leading to dysfunctional VSMC motility remain unknown. Recently, cytokine BMP-2 has been implicated in various vascular physiologic and pathologic processes. However, whether BMP-2 has any effect upon VSMC motility, or by what manner, has never been investigated. Methods. VSMCs were adenovirally transfected to genetically overexpress BMP-2. VSMC motility was detected by modified Boyden chamber assay, confocal time-lapse video assay, and a colony wounding assay. Gene chip array and RT-PCR were employed to identify genes potentially regulated by BMP-2. Western blot and real-time PCR detected the expression of myosin Va and the phosphorylation of extracellular signal-regulated kinases 1/2 (Erk1/2). Immunofluorescence analysis revealed myosin Va expression locale. Intracellular Ca²⁺ oscillations were recorded. Results. VSMC migration was augmented in VSMCs overexpressing BMP-2 in a dose-dependent manner. siRNA-mediated knockdown of myosin Va inhibited VSMC motility. Both myosin Va mRNA and protein expression significantly increased after BMP-2 administration and were inhibited by Erk1/2 inhibitor U0126. BMP-2 induced Ca²⁺ oscillations, generated largely by a “cytosolic oscillator”. Conclusion. BMP-2 significantly increased VSMCs migration and myosin Va expression, via the Erk signaling pathway and intracellular Ca²⁺ oscillations. We provide additional insight into the pathophysiology of atherosclerosis, and inhibition of BMP-2-induced myosin Va expression may represent a potential therapeutic strategy.

Engineering myosins for long-range transport on actin filaments

Cytoskeletal motors act as cargo transporters in cells and may be harnessed for directed transport applications in molecular detection and diagnostic devices. High processivity, the ability to take many steps along a track before dissociating, is often a desirable characteristic because it allows nanoscale motors to transport cargoes over distances on the scale of micrometres, in vivo and in vitro. Natural processive myosins are dimeric and use internal tension to coordinate the detachment cycles of the two heads. Here, we show that processivity can be enhanced in engineered myosins using two non-natural strategies designed to optimize the effectiveness of random, uncoordinated stepping: (1) the formation of three-headed and four-headed myosins and (2) the introduction of flexible elements between heads. We quantify improvements using systematic single-molecule characterization of a panel of engineered motors. To test the modularity of our approach, we design a controllably bidirectional myosin that is robustly processive in both forward and backward directions, and also produce the fastest processive cytoskeletal motor measured so far, reaching a speed of 10 µm s(-1).

Temperature dependent measurements reveal similarities between muscle and non-muscle myosin motility

We examined the temperature dependence of muscle and non-muscle myosin (heavy meromyosin, HMM) with in vitro motility and actin-activated ATPase assays. Our results indicate that myosin V (MV) has a temperature dependence that is similar in both ATPase and motility assays. We demonstrate that skeletal muscle myosin (SK), smooth muscle myosin (SM), and non-muscle myosin IIA (NM) have different temperature dependence in ATPase compared to in vitro motility assays. In the class II myosins we examined (SK, SM, and NM) the rate-limiting step in ATPase assays is thought to be attachment to actin or phosphate release, while for in vitro motility assays it is controversial. In MV the rate-limiting step for both in vitro motility and ATPase assays is known to be ADP release. Consequently, in MV the temperature dependence of the ADP release rate constant is similar to the temperature dependence of in vitro motility. Interestingly, the temperature dependence of the ADP release rate constant of SM and NM was shifted toward the in vitro motility temperature dependence. Our results suggest that the rate-limiting step in SK, SM, and NM may shift from attachment-limited in solution to detachment limited in the in vitro motility assay. Internal strain within the myosin molecule or by neighboring myosin motors may slow ADP release which becomes rate-limiting in the in vitro motility assay. Within this small subset of myosins examined, the in vitro sliding velocity correlates reasonably well with actin-activated ATPase activity, which was suggested by the original study by Barany (J Gen Physiol 50:197-218, 1967).

Calcineurin homologous protein: a multifunctional Ca2+-binding protein family

The calcineurin homologous protein (CHP) belongs to an evolutionarily conserved Ca(2+)-binding protein subfamily. The CHP subfamily is composed of CHP1, CHP2, and CHP3, which in vertebrates share significant homology at the protein level with each other and between other Ca(2+)-binding proteins. The CHP structure consists of two globular domains containing from one to four EF-hand structural motifs (calcium-binding regions composed of two helixes, E and F, joined by a loop), the myristoylation, and nuclear export signals. These structural features are essential for the function of the three members of the CHP subfamily. Indeed, CHP1-CHP3 have multiple and diverse essential functions, ranging from the regulation of the plasma membrane Na(+)/H(+) exchanger protein function, to carrier vesicle trafficking and gene transcription. The diverse functions attributed to the CHP subfamily rendered an understanding of its action highly complex and often controversial. This review provides a comprehensive and organized examination of the properties and physiological roles of the CHP subfamily with a view to revealing a link between CHP diverse functions.

Optical traps to study properties of molecular motors

In vitro motility assays enabled the analysis of coupling between ATP hydrolysis and movement of myosin along actin filaments or kinesin along microtubules. Single-molecule assays using laser trapping have been used to obtain more detailed information about kinesins, myosins, and processive DNA enzymes. The combination of in vitro motility assays with laser-trap measurements has revealed detailed dynamic structural changes associated with the ATPase cycle. This article describes the use of optical traps to study processive and nonprocessive molecular motor proteins, focusing on the design of the instrument and the assays to characterize motility.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.

Multiscale modeling of structural dynamics underlying force generation and product release in actomyosin complex

To decrypt the mechanistic basis of myosin motor function, it is essential to probe the conformational changes in actomyosin with high spatial and temporal resolutions. In a computational effort to meet this challenge, we have performed a multiscale modeling of the allosteric couplings and transition pathway of actomyosin complex by combining coarse-grained modeling of the entire complex with all-atom molecular dynamics simulations of the active site. Our modeling of allosteric couplings at the pre-powerstroke state has pinpointed key actin-activated couplings to distant myosin parts which are critical to force generation and the sequential release of phosphate and ADP. At the post-powerstroke state, we have identified isoform-dependent couplings which underlie the reciprocal coupling between actin binding and nucleotide binding in fast Myosin II, and load-dependent ADP release in Myosin V. Our modeling of transition pathway during powerstroke has outlined a clear sequence of structural events triggered by actin binding, which lead to subsequent force generation, twisting of central beta-sheet, and the sequential release of phosphate and ADP. Finally we have performed atomistic simulations of active-site dynamics based on an on-path "transition-state" myosin conformation, which has revealed significantly weakened coordination of phosphate by Switch II, and a disrupted key salt bridge between Switch I and II. Meanwhile, the coordination of MgADP by Switch I and P loop is less perturbed. As a result, the phosphate can be released prior to MgADP. This study has shed new lights on the controversy over the structural mechanism of actin-activated phosphate release and force generation in myosin motor.

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.

Regular gaits and optimal velocities for motor proteins

It has been observed in numerical experiments that adding a cargo to a motor protein can regularize its gait. Here we explain these results via asymptotic analysis on a general stochastic motor protein model. This analysis permits a computation of various observables (e.g., the mean velocity) of the motor protein and shows that the presence of the cargo also makes the velocity of the motor nonmonotone in certain control parameters (e.g., ATP concentration). As an example, we consider the case of a single myosin-V protein transporting a cargo and show that, at realistic concentrations of ATP, myosin-V operates in the regime which maximizes motor velocity. Our analysis also suggests an experimental regimen which can test the efficacy of any specific motor protein model to a greater degree than was heretofore possible.

A kinetic model of coordinated myosin V

We present a kinetic model for the walking of myosin V on actin under conditions of zero external force. The model includes three pathways and the termination of the processivity. Experimentally measured kinetic parameters are used in the model to obtain quantitative results. Using the model and associated parameters, we compute the proportion of the pathway containing an intermediate state, as well as the walking velocities and run lengths at various concentrations of ATP and ADP. The resulting trends agree with experimental data. The model explains the surprising experimental finding that myosin walks at a faster speed but for a shorter distance as the ATP concentration increases in the absence of ADP. It also suggests that under physiological condition ([ADP] approximately 12-50 microM), myosin walks with a higher speed and for longer distances when ATP is more abundant.

Molecular Motors: A Theorist's Perspective

Individual molecular motors, or motor proteins, are enzymatic molecules that convert chemical energy, typically obtained from the hydrolysis of ATP (adenosine triphosphate), into mechanical work and motion. Processive motor proteins, such as kinesin, dynein, and certain myosins, step unidirectionally along linear tracks, specifically microtubules and actin filaments, and play a crucial role in cellular transport processes, organization, and function. In this review some theoretical aspects of motor-protein dynamics are presented in the light of current experimental methods that enable the measurement of the biochemical and biomechanical properties on a single-molecule basis. After a brief discussion of continuum ratchet concepts, we focus on discrete kinetic and stochastic models that yield predictions for the mean velocity, V(F, [ATP], ...), and other observables as a function of an imposed load force F, the ATP concentration, and other variables. The combination of appropriate theory with single-molecule observations should help uncover the mechanisms underlying motor-protein function.

Kinetic mechanism of human myosin IIIA

Myosin IIIA is specifically expressed in photoreceptors and cochlea and is important for the phototransduction and hearing processes. In addition, myosin IIIA contains a unique N-terminal kinase domain and C-terminal tail actin-binding motif. We examined the kinetic properties of baculovirus expressed human myosin IIIA containing the kinase, motor, and two IQ domains. The maximum actin-activated ATPase rate is relatively slow (k(cat) = 0.77 +/- 0.08 s(-1)), and high actin concentrations are required to fully activate the ATPase rate (K(ATPase) = 34 +/- 11 microm). However, actin co-sedimentation assays suggest that myosin III has a relatively high steady-state affinity for actin in the presence of ATP (K(actin) approximately 7 microm). The rate of ATP binding to the motor domain is quite slow both in the presence and absence of actin (K(1)k(+2) = 0.020 and 0.001 microm(-1).s(-1), respectively). The rate of actin-activated phosphate release is more than 100-fold faster (85 s(-1)) than the k(cat), whereas ADP release in the presence of actin follows a two-step mechanism (7.0 and 0.6 s(-1)). Thus, our data suggest a transition between two actomyosin-ADP states is the rate-limiting step in the actomyosin III ATPase cycle. Our data also suggest the myosin III motor spends a large fraction of its cycle in an actomyosin ADP state that has an intermediate affinity for actin (K(d) approximately 5 microm). The long lived actomyosin-ADP state may be important for the ability of myosin III to function as a cellular transporter and actin cross-linker in the actin bundles of sensory cells.

Identification of the Single Specific IQ Motif of Myosin V from Which Calmodulin Dissociates in the Presence of Ca2+

Each heavy chain of dimeric chick brain myosin V (BMV) has a neck domain consisting of six IQ motifs with different amino acid sequences. The six IQ motifs form binding sites for five calmodulin (CaM) molecules and one essential light chain (either 17 or 23 kDa). When the calcium concentration is high, a small fraction of the 10 total CaM molecules dissociates from one molecule of BMV, resulting in loss of actin-based motor activity. At low Ca2+ concentrations, two molecules of exogenous CaM associate with one molecule of CaM-released BMV. This suggests that there is a single specific IQ motif responsible for the calcium-induced dissociation of CaM. In this study, we identify the specific IQ motif to be IQ2, the second IQ motif when counted from the N-terminal end of the neck domain. In addition, we showed that the essential light chains do not reside on IQ1 and IQ2. These findings were derived from proteolysis of BMV at high Ca2+ concentrations specifically at the neck region and SDS-PAGE analyses of the digests.

An elastically tethered viscous load imposes a regular gait on the motion of myosin-V. Simulation of the effect of transient force relaxation on a stochastic process

Myosin-V is a processive molecular motor that moves membrane vesicles along actin tracks. In the simple model for motor and cargo motion investigated here, an elastic connection between motor and cargo transiently absorbs the abrupt mechanical transitions of the motor, and allows smooth relaxation of the cargo to a new position. We use a stochastic description to model motor stepping, with kinetics that depends on the instantaneous force exerted on the motor through the elastic connection. Tether relaxation is modelled as a continuous process, in which the rate is determined by the viscous drag of the cargo and the stiffness profile of the connection. Quantitative combined stochastic-continuous simulation of the dynamics of this system shows that bulky loads can impose a highly regular gait on the motor. If the characteristics of the elastic connection are similar to those of the myosin-II coiled-coil domain, the myosin-V motor, tether and cargo form a true escapement, in which the motor only escapes from its current position after one or more force thresholds have been crossed. Multiple thresholds limit the variation in tether length to values below that of the total step size.

Myosin at work: motor adaptations for a variety of cellular functions

Cells have evolved multiple mechanisms to overcome the effects of entropy and diffusion to create a highly ordered environment. For cells to function properly, some components must be anchored to provide a framework or structure. Others must be rapidly transported over long distances to generate asymmetries in cell morphology and composition. To accomplish long-range transport, cells cannot rely on diffusion alone as many large organelles and macromolecular complexes are essentially immobilized by the dense meshwork of the cytosol. One strategy used by cells to overcome diffusion is to harness the free energy liberated by ATP hydrolysis through molecular motors. Myosins are a family of actin based molecular motors that have evolved a variety of ways to contribute to cellular organization through numerous modifications to the manner they convert that free energy into mechanical work.

A kinetic model describing the processivity of myosin-V

The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.

Myosin-V is a mechanical ratchet

Myosin-V is a linear molecular motor that hydrolyzes ATP to move processively toward the plus end of actin filaments. Motion of this motor under low forces has been studied recently in various single-molecule assays. In this paper we show that myosin-V reacts to high forces as a mechanical ratchet. High backward loads can induce rapid and processive backward steps along the actin filament. This motion is completely independent of ATP binding and hydrolysis. In contrast, forward forces cannot induce ATP-independent forward steps. We can explain this pronounced mechanical asymmetry by a model in which the strength of actin binding of a motor head is modulated by the lever arm conformation. Knowledge of the complete force-velocity dependence of molecular motors is important to understand their function in the cellular environment.

Renewal processes and fluctuation analysis of molecular motor stepping

We present a systematic method of analysis of experiments performed with single motor proteins. The use of such a method should allow a more detailed description of the motor's chemical cycle through the precise fitting of the experimental data. We model the dynamics of a processive or rotary molecular motor using a renewal process, in line with the work initiated by Svoboda, Mitra and Block. We apply a functional technique to compute different types of multiple-time correlation function of the renewal process, which have applications to bead-assay experiments performed both with processive molecular motors, such as myosin V and kinesin, and rotary motors, such as F1-ATPase.

A force-dependent state controls the coordination of processive myosin V

Myosin V is an efficient processive molecular motor. Recent experiments have shown how the structure and kinetics of myosin V are specialized to produce a highly processive motor capable of taking multiple 36-nm steps on an actin filament track. Here, we examine how two identical heads coordinate their activity to produce efficient hand-over-hand stepping. We have used a modified laser-trap microscope to apply a approximately 2-pN forward or backward force on a single-headed myosin V molecule, hypothesized to simulate forces experienced by the rear or lead head, respectively. We found that pulling forward produces only a small change in the kinetics, whereas pulling backward induces a large reduction in the cycling of the head. These results support a model in which the coordination of myosin V stepping is mediated by strain-generated inhibition of the lead head.

Structure of the light chain-binding domain of myosin V

Myosin V is a double-headed molecular motor involved in organelle transport. Two distinctive features of this motor, processivity and the ability to take extended linear steps of approximately 36 nm along the actin helical track, depend on its unusually long light chain-binding domain (LCBD). The LCBD of myosin V consists of six tandem IQ motifs, which constitute the binding sites for calmodulin (CaM) and CaM-like light chains. Here, we report the 2-A resolution crystal structure of myosin light chain 1 (Mlc1p) bound to the IQ2-IQ3 fragment of Myo2p, a myosin V from Saccharomyces cerevisiae. This structure, combined with FRET distance measurements between probes in various CaM-IQ complexes, comparative sequence analysis, and the previously determined structures of Mlc1p-IQ2 and Mlc1p-IQ4, allowed building a model of the LCBD of myosin V. The IQs of myosin V are distributed into three pairs. There appear to be specific cooperative interactions between light chains within each IQ pair, but little or no interaction between pairs, providing flexibility at their junctions. The second and third IQ pairs each present a light chain, whether CaM or a CaM-related molecule, bound in a noncanonical extended conformation in which the N-lobe does not interact with the IQ motif. The resulting free N-lobes may engage in protein-protein interactions. The extended conformation is characteristic of the single IQ of myosin VI and is common throughout the myosin superfamily. The model points to a prominent role of the LCBD in the function, regulation, and molecular interactions of myosin V.

Statistical kinetics of macromolecular dynamics

Fluctuations in biochemical processes can provide insights into the underlying kinetics beyond what can be gleaned from studies of average rates alone. Historically, analysis of fluctuating transmembrane currents supplied information about ion channel conductance states and lifetimes before single-channel recording techniques emerged. More recently, fluctuation analysis has helped to define mechanochemical pathways and coupling ratios for the motor protein kinesin as well as to probe the contributions of static and dynamic disorder to the kinetics of single enzymes. As growing numbers of assays are developed for enzymatic or folding behaviors of single macromolecules, the range of applications for fluctuation analysis increases. To evaluate specific biochemical models against experimental data, one needs to predict analytically the distribution of times required for completion of each reaction pathway. Unfortunately, using traditional methods, such calculations can be challenging for pathways of even modest complexity. Here, we derive an exact expression for the distribution of completion times for an arbitrary pathway with a finite number of states, using a recursive method to solve algebraically for the appropriate moment-generating function. To facilitate comparisons with experiments on processive motor proteins, we develop a theoretical formalism for the randomness parameter, a dimensionless measure of the variance in motor output. We derive the randomness for motors that take steps of variable sizes or that move on heterogeneous substrates, and then discuss possible applications to enzymes such as RNA polymerase, which transcribes varying DNA sequences, and to myosin V and cytoplasmic dynein, which may advance by variable increments.

Analysis of biological motors via multidimensional fractionation: a strategy

Past strategies for the analysis of ATP-fueled motors include single-motor analysis. Single-motor analysis bypasses limitations caused by motor asynchrony during the traditional ensemble averaging analysis. The present communication describes revised ensemble averaging analysis that also can bypass asynchrony-derived limitations. This revised analysis makes measurements of one motor variable dependent on the others. One example is nondenaturing gel electrophoresis with more than one dimension. Each dimension measures one of the motor variables. This multidimensional procedure is used to obtain the values of "conformational" motor variables as a function of a "clock" motor variable. In theory, the cycle of the motor can be analyzed from a single multidimensional analysis of a collection of asynchronous motors sampled at only one time. That is to say, motor asynchrony becomes an asset, rather than a liability.

Interhead distance measurements in myosin VI via SHRImP support a simplified hand-over-hand model

Myosin VI walks in a hand-over-hand fashion with an average step size of 30 nm, which is much larger than its 10 nm lever arm. Recent experiments suggest that the myosin VI structure has an unfolded and flexible region in the proximal tail which makes such a large step possible. In addition, cryoelectron microscopy images of actomyosin VI show the two heads bound to the actin monomers with a broad distribution of distances, including some as close as a few nanometers. This observation, when combined with the existence of a flexible region in the structure, which takes part in stepping, challenged the hand-over-hand model. In the hand-over-hand model, the lever arm is considered to be rigid and the interhead separation should not be very different from 30 nm. We considered an alternative model in which myosin VI heads sequentially take 60 nm steps whereas the interhead separation alternates between a large and small value (x and 60 - x, where x < 30). To clarify these issues, we used a new technique, SHRImP, to measure the interhead distance of nearly rigor myosin VI molecules. Our data show a single peak at 29.3 +/- 0.7 nm, in agreement with the straightforward hand-over-hand model.

Adenosine diphosphate and strain sensitivity in myosin motors

The release of adenosine diphosphate (ADP) from the actomyosin cross-bridge plays an important role in the adenosine-triphosphate-driven cross-bridge cycle. In fast contracting muscle fibres, the rate at which ADP is released from the cross-bridge correlates with the maximum shortening velocity of the muscle fibre, and in some models the rate of ADP release defines the maximum shortening velocity. In addition, it has long been thought that the rate of ADP release could be sensitive to the load on the cross-bridge and thereby provide a molecular explanation of the Fenn effect. However, direct evidence of a strain-sensitive ADP-release mechanism has been hard to come by for fast muscle myosins. The recently published evidence for a strain-sensing mechanism involving ADP release for slower muscle myosins, and in particular non-muscle myosins, is more compelling and can provide the mechanism of processivity for motors such as myosin V. It is therefore timely to examine the evidence for this strain-sensing mechanism. The evidence presented here will argue that a strain-sensitive mechanism of ADP release is universal for all myosins but the basic mechanism has evolved in different ways for different types of myosin. Furthermore, this strain-sensing mechanism provides a way of coordinating the action of multiple myosin motor domains in a single myosin molecule, or in complex assemblies of myosins over long distances without invoking a classic direct allosteric or cooperative communication between motors.

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.

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.

Molecular Motors: Strategies to Get Along

The majority of active transport in the cell is driven by three classes of molecular motors: the kinesin and dynein families that move toward the plus-end and minus-end of microtubules, respectively, and the unconventional myosin motors that move along actin filaments. Each class of motor has different properties, but in the cell they often function together. In this review we summarize what is known about their single-molecule properties and the possibilities for regulation of such properties. In view of new results on cytoplasmic dynein, we attempt to rationalize how these different classes of motors might work together as part of the intracellular transport machinery. We propose that kinesin and myosin are robust and highly efficient transporters, but with somewhat limited room for regulation of function. Because cytoplasmic dynein is less efficient and robust, to achieve function comparable to the other motors it requires a number of accessory proteins as well as multiple dyneins functioning together. This necessity for additional factors, as well as dynein's inherent complexity, in principle allows for greatly increased control of function by taking the factors away either singly or in combination. Thus, dynein's contribution relative to the other motors can be dynamically tuned, allowing the motors to function together differently in a variety of situations.

Actin-based metallic nanowires as bio-nanotransporters

The synthesis of conductive nanowires or patterned conductive nanoelements is a challenging goal for the future fabrication of nanoscale circuitry. Similarly, the realization of nanoscale mechanics might introduce a new facet to the area of nanobiotechnology. Here we report on the design of conductive and patterned actin-based gold nanowires, and on the ATP-driven motility of the nano-objects. The polymerization of G-actin labelled with Au nanoparticles, followed by the catalytic enlargement of the nanoparticles, yields gold wires (1-4 microm long and 80-200 nm high) exhibiting high electrical conductivity. The polymerization of the Au nanoparticle/G-actin monomer followed by the polymerization of free G-actin, or alternatively the polymerization of the Au-nanoparticle-labelled G-actin on polymerized F-actin followed by the catalytic enlargement of the particles, yields patterned actin-Au wire-actin or Au wire-actin-Au wire nanostructures, respectively. We demonstrate the ATP-fuelled motility of the actin-Au wire-actin filaments on a myosin interface. These actin-based metallic wires and their nanotransporting funcionality introduce new concepts for developing biological/inorganic hybrid devices.

Free energy transduction in a chemical motor model

Motor enzymes catalyse chemical reactions, like the hydrolysis of ATP, and in the process they also perform work. Recent studies indicate that motor enzymes perform work with specific biochemical steps in their catalysed reactions, challenging the classical view that work can only be performed within a biochemical state. To address these studies an alternative class of models, often referred to as chemical motor models, has emerged in which motors perform work with biochemical transitions. In this paper, I develop a novel, self-consistent framework for chemical motor models, which accommodates multiple pathways for free energy transfer, predicts rich behaviors from the simplest multi-motor systems, and provides important new insights into muscle and motor function.

A model of myosin V processivity

Cytoplasmic transport is mediated by a group of molecular motors that typically work in isolation, under conditions where they must move their cargos long distances without dissociating from their tracks. This processive behavior requires specific adaptations of motor enzymology to meet these unique physiologic demands. One of these involves the ability of the two heads of a processive motor to communicate their structural states to each other. In this study, we examine a processive motor from the myosin superfamily myosin V. We have measured the kinetics of nucleotide release, of phosphate release, and of the weak-to-strong transition, as this motor interacts with actin, and we have used these studies to develop a model of how myosin V functions as a transport motor. Surprisingly, both heads release phosphate rapidly upon the initial encounter with an actin filament, suggesting that there is little or no intramolecular strain associated with this step. However, ADP release can be affected by both forward and rearward strain, and under steady-state conditions it is essentially prevented in the lead head until the rear head detaches. Many of these features are remarkably like those underlying the processive movement of kinesin on microtubules, supporting our hypothesis that different molecular motors satisfy the requirement for processive movement in similar ways, regardless of their particular family of origin.

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.

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.

Myosin V processivity: multiple kinetic pathways for head-to-head coordination

Myosin V, a double-headed molecular motor, transports organelles within cells by walking processively along actin, a process that requires coordination between the heads. To understand the mechanism underlying this coordination, processive runs of single myosin V molecules were perturbed by varying nucleotide content. Contrary to current views, our results show that the two heads of a myosin V molecule communicate, not through any one mechanism but through an elaborate system of cooperative mechanisms involving multiple kinetic pathways. These mechanisms introduce redundancy and safeguards that ensure robust processivity under differing physiologic demands.

Polarized distribution of intracellular components by class V myosins in Saccharomyces cerevisiae

The budding yeast Saccharomyces cerevisiae has three classes of myosins corresponding to three actin structures: class I myosin for endocytic actin structure, actin patches; class II myosin for contraction of the actomyosin contractile ring around the bud neck; and class V myosin for transport along a cable-like actin structure (actin cables), extending toward the growing cortex. Myo2p and Myo4p constitute respective class V myosins as the heavy chain and, like class V myosins in other organisms, function as actin-based motors for polarized distribution of organelles and intracellular molecules. Proper distribution of organelles is essential for autonomously replicating organelles that cannot be reproduced de novo, and is also quite important for other organelles to ensure their efficient segregation and proper positioning, even though they can be newly synthesized, such as those derived from endoplasmic reticulum. In the budding yeast, microtubule-based motors play limited roles in the distribution. Instead, the actin-based motor myosins, especially Myo2p, play a major role. Studies on Myo2p have revealed a wide variety of Myo2p cargo and Myo2p-interacting proteins and have established that Myo2p interacts with cargo and transfers it along actin cables. Moreover, recent findings suggest that Myo2p has another way to distribute cargo in that Myo2p conveys the attaching cargo along the actin track. Thus, the myosin have "dual paths" for distribution of a cargo. This dual path mechanism is proposed in the last section of this review.

Myosin-Va binds to and mechanochemically couples microtubules to actin filaments

Myosin-Va was identified as a microtubule binding protein by cosedimentation analysis in the presence of microtubules. Native myosin-Va purified from chick brain, as well as the expressed globular tail domain of this myosin, but not head domain bound to microtubule-associated protein-free microtubules. Binding of myosin-Va to microtubules was saturable and of moderately high affinity (approximately 1:24 Myosin-Va:tubulin; Kd = 70 nM). Myosin-Va may bind to microtubules via its tail domain because microtubule-bound myosin-Va retained the ability to bind actin filaments resulting in the formation of cross-linked gels of microtubules and actin, as assessed by fluorescence and electron microscopy. In low Ca2+, ATP addition induced dissolution of these gels, but not release of myosin-Va from MTs. However, in 10 microM Ca2+, ATP addition resulted in the contraction of the gels into aster-like arrays. These results demonstrate that myosin-Va is a microtubule binding protein that cross-links and mechanochemically couples microtubules to actin filaments.

The unique properties of tonic smooth muscle emerge from intrinsic as well as intermolecular behaviors of Myosin molecules

To better understand the molecular basis for some of the unique mechanical properties of tonic smooth muscle, we use a laser trap to assay the mechanochemistry of single smooth muscle heavy meromyosin molecules lacking a seven-amino acid insert in the nucleotide binding loop (minus insert). We measured a second-order ATP-induced actin dissociation rate, kT, of 2.2 x 10(6) m(-1) s(-1), an ADP release rate, k-D, of 19 s(-1), a second-order ADP binding rate, kD, of 60 x 10(5) m(-1) s(-1), and an ADP affinity, KD, of 3.2 microm, which is more than 100-fold greater than that measured for skeletal muscle myosin. By performing in vitro motility studies under nearly identical conditions, we show that the relatively slow actin velocity generated by minus-insert heavy meromyosin is significantly influenced, but not limited, by k-D. Our results support a model in which two separate intermediate steps in the actin-myosin catalyzed ATP hydrolysis reaction are energetically coupled through mechanical interactions, and we discuss this model in the context of the ability of tonic muscle to maintain high forces at low energetic cost (latch).

Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization

Myosin V is a dimeric molecular motor that moves processively on actin, with the center of mass moving approximately 37 nanometers for each adenosine triphosphate hydrolyzed. We have labeled myosin V with a single fluorophore at different positions in the light-chain domain and measured the step size with a standard deviation of <1.5 nanometers, with 0.5-second temporal resolution, and observation times of minutes. The step size alternates between 37 + 2x nm and 37 - 2x, where x is the distance along the direction of motion between the dye and the midpoint between the two heads. These results strongly support a hand-over-hand model of motility, not an inchworm model.