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The internal organization of cells is largely determined by the architecture and orientation of the microtubule network. Microtubules serve as polar tracks for the selective transport of specific molecular motors toward either their plus or minus ends. How both motors reciprocally move microtubules and organize the network's arrangement and polarity is unknown. Here, we combined experiments on reconstituted systems and theory to study the interaction of microtubules with both plus-and minus-end directed motors bound to a fluid membrane. Depending on motor concentrations, the system could lead either to the constant transport of microtubules or to their alignment, stacking, and immobilization in regular bands that separate motors into domains of opposite polarities. In bands, microtubules shared the same polarity and segregated the two opposing motors accordingly. These regular patterns resulted from the balance of forces produced by the two motors as they walked in opposite directions along microtubules. The system was maintained in a dynamic steady state in which the directional transport of microtubule-bound motors compensates for the random diffusion of lipid-bound motors. The size of motor domains depended on their respective concentrations. The constant flow of motors allowed the system to respond to variations in motor concentrations by moving microtubules to adapt to the new force balance. The polar sorting and linear arrangement of microtubules associated with the segregation of motors of opposite polarity are typical of cellular architectures, which these data may help to better understand. [ABSTRACT FROM AUTHOR]

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein–protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5′-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials. [ABSTRACT FROM AUTHOR]

Cytoskeletal active nematics exhibit striking nonequilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold, the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale nonequilibrium dynamics of active nematics.

Simulations can help unravel the complicated ways in which molecular structure determines function. Here, we use molecular simulations to show how slight alterations of a molecular motor's structure can cause the motor's typical dynamical behavior to reverse directions. Inspired by autonomous synthetic catenane motors, we study the molecular dynamics of a minimal motor model, consisting of a shuttling ring that moves along a track containing interspersed binding sites and catalytic sites. The binding sites attract the shuttling ring while the catalytic sites speed up a reaction between molecular species, which can be thought of as fuel and waste. When that fuel and waste are held in nonequilibrium steady-state concentrations, the free energy from the reaction drives directed motion of the shuttling ring along the track. Using this model and nonequilibrium molecular dynamics, we show that the shuttling ring's direction can be reversed by simply adjusting the spacing between binding and catalytic sites on the track. We present a steric mechanism behind the current reversal, supported by kinetic measurements from the simulations. These results demonstrate how molecular simulation can guide future development of artificial molecular motors. [ABSTRACT FROM AUTHOR]

V-ATPases are rotary motor proteins that convert the chemical energy of ATP into the electrochemical potential of ions across cell membranes. V-ATPases consist of two rotary motors, Vo and V1, and Enterococcus hirae V-ATPase (EhVoV1) actively transports Na+ in Vo (EhVo) by using torque generated by ATP hydrolysis in V1 (EhV1). Here, we observed ATP-driven stepping rotation of detergent-solubilized EhVoV1 wildtype, aE634A, and BR350K mutants under various Na+ and ATP concentrations ([Na+] and [ATP], respectively) by using a 40-nm gold nanoparticle as a low-load probe. When [Na+] was low and [ATP] was high, under the condition that only Na+ binding to EhVo is rate limiting, wild-type and aE634A exhibited 10 pausing positions reflecting 10-fold symmetry of the EhVo rotor and almost no backward steps. Duration time before the forward steps was inversely proportional to [Na+], confirming that Na+ binding triggers the steps. When both [ATP] and [Na+] were low, under the condition that both Na+ and ATP bindings are rate limiting, aE634A exhibited 13 pausing positions reflecting 10- and 3-fold symmetries of EhVo and EhV1, respectively. The distribution of duration time before the forward step was fitted well by the sum of two exponential decay functions with distinct time constants. Furthermore, occasional backward steps smaller than 36° were observed. Small backward steps were also observed during three long ATP cleavage pauses of BR350K. These results indicate that EhVo and EhV1 do not share pausing positions, Na+ and ATP bindings occur at different angles, and the coupling between EhVo and EhV1 has a rigid component. [ABSTRACT FROM AUTHOR]

The bacterial flagellar motor (BFM) is responsible for driving bacterial locomotion and chemotaxis, fundamental processes in pathogenesis and biofilm formation. In the BFM, torque is generated at the interface between transmembrane proteins (stators) and a rotor. It is well established that the passage of ions down a transmembrane gradient through the stator complex provides the energy for torque generation. However, the physics involved in this energy conversion remain poorly understood. Here we propose a mechanically specific model for torque generation in the BFM. In particular, we identify roles for two fundamental forces involved in torque generation: electrostatic and steric. We propose that electrostatic forces serve to position the stator, whereas steric forces comprise the actual "power stroke." Specifically, we propose that ion-induced conformational changes about a proline "hinge" residue in a stator α-helix are directly responsible for generating the power stroke. Our model predictions fit well with recent experiments on a single-stator motor. The proposed model provides a mechanical explanation for several fundamental properties of the flagellar motor, including torque-speed and speed-ion motive force relationships, backstepping, variation in step sizes, and the effects of key mutations in the stator.

Kinesins are responsible for a wide variety of microtubule-based, ATP-dependent functions. Their motor domain drives these activities, but the molecular adaptations that specify these diverse and essential cellular activities are poorly understood. It has been assumed that the first identified kinesin--the transport motor kinesin-1--is the mechanistic paradigm for the entire superfamily, but accumulating evidence suggests otherwise. To address the deficits in our understanding of the molecular basis of functional divergence within the kinesin superfamily, we studied kinesin-5s, which are essential mitotic motors whose inhibition blocks cell division. Using cryo-electron microscopy and determination of structure at subnanometer resolution, we have visualized conformations of microtubule-bound human kinesin-5 motor domain at successive steps in its ATPase cycle. After ATP hydrolysis, nucleotide-dependent conformational changes in the active site are allosterically propagated into rotations of the motor domain and uncurling of the drug-binding loop L5. In addition, the mechanical neck-linker element that is crucial for motor stepping undergoes discrete, ordered displacements. We also observed large reorientations of the motor N terminus that indicate its importance for kinesin-5 function through control of neck-linker conformation. A kinesin-5 mutant lacking this N terminus is enzymatically active, and ATP-dependent neck-linker movement and motility are defective, although not ablated. All these aspects of kinesin-5 mechanochemistry are distinct from kinesin-1. Our findings directly demonstrate the regulatory role of the kinesin-5 N terminus in collaboration with the motor's structured neck-linker and highlight the multiple adaptations within kinesin motor domains that tune their mechanochemistries according to distinct functional requirements.

Motility is important for the survival and dispersal of many bacteria, and it often plays a role during infections. Regulation of bacterial motility by chemical stimuli is well studied, but recent work has added a new dimension to the problem of motility control. The bidirectional flagellar motor of the bacterium Escherichia coli recruits or releases torque-generating units (stator units) in response to changes in load. Here, we show that this mechanosensitive remodeling of the flagellar motor is independent of direction of rotation. Remodeling rate constants in clockwise rotating motors and in counterclockwise rotating motors, measured previously, fall on the same curve if plotted against torque. Increased torque decreases the off rate of stator units from the motor, thereby increasing the number of active stator units at steady state. A simple mathematical model based on observed dynamics provides quantitative insight into the underlying molecular interactions. The torque-dependent remodeling mechanism represents a robust strategy to quickly regulate output (torque) in response to changes in demand (load). [ABSTRACT FROM AUTHOR]

Conventional kinesin, responsible for directional transport of cellular vesicles, takes multiple nearly uniform 8.2-nm steps by consuming one ATP molecule per step as it walks toward the plus end of the microtubule (MT). Despite decades of intensive experimental and theoretical studies, there are gaps in the elucidation of key steps in the catalytic cycle of kinesin. How the motor waits for ATP to bind to the leading head is controversial. Two experiments using a similar protocol have arrived at different conclusions. One asserts that kinesin waits for ATP in a state with both the heads bound to the MT, whereas the other shows that ATP binds to the leading head after the trailing head detaches. To discriminate between the 2 scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observable quantities (the distribution of run length, the distribution of velocity [P(v)], and the randomness parameter) as a function of an external resistive force (F) and ATP concentration ([T]). The differences in the predicted bimodality in P(v) as a function of F between the 2 models may be amenable to experimental testing. Most importantly, we predict that the F and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of F and [T] can be quantitatively measured from stepping trajectories with very little prejudice in data analysis. Therefore, an accurate measurement of the randomness parameter and the velocity distribution as a function of load and nucleotide concentration could resolve the apparent controversy. [ABSTRACT FROM AUTHOR]

Myosins form a class of actin-based, ATPase motor proteins that mediate important cellular functions such as cargo transport and cell motility. Their functional cycle involves two large-scale swings of the lever arm: the force-generating powerstroke, which takes place on actin, and the recovery stroke during which the lever arm is reprimed into an armed configuration. Previous analyses of the prerecovery (postrigor) and postrecovery (prepowerstroke) states predicted that closure of switch II in the ATP binding site precedes the movement of the converter and the lever arm. Here, we report on a crystal structure of myosin VI, called pretransition state (PTS), which was solved at 2.2 Å resolution. Structural analysis and all-atom molecular dynamics simulations are consistent with PTS being an intermediate along the recovery stroke, where the Relay/SH1 elements adopt a postrecovery conformation, and switch II remains open. In this state, the converter appears to be largely uncoupled from the motor domain and explores an ensemble of partially reprimed configurations through extensive, reversible fluctuations. Moreover, we found that the free energy cost of hydrogen-bonding switch II to ATP is lowered by more than 10 kcal/mol compared with the prerecovery state. These results support the conclusion that closing of switch II does not initiate the recovery stroke transition in myosin VI. Rather, they suggest a mechanism in which lever arm repriming would be mostly driven by thermal fluctuations and eventually stabilized by the switch II interaction with the nucleotide in a ratchet-like fashion. [ABSTRACT FROM AUTHOR]

Cholesteric liquid crystal (CLC) droplets exhibit nontrivial topological features, which are controlled by the ratio between the cholesteric pitch and the droplet radius. The radial spherical structure (RSS) is of particular interest, as it reveals an onion-like concentric organization of the cholesteric helices, leading to the expression of spherical Bragg microcavities. Using an overcrowded alkene-based unidirectional molecular motor as a dopant, we show that the topological defect structure in the droplet can be activated by illumination. By using appropriate molecular motor concentrations, light can either break the symmetry of topological defects (as observed for the bent-twisted bipolar structure), or it can induce inversion of handedness in an onion-like organization (in the case of RSS). This latter feature may pave the way toward alternative activation modes of lasers based on cholesteric droplets. By also studying CLC droplets once they have reached full photoconversion at photostationary state (PSS), we highlight that the strong influence of confinement on the droplets structure occurs to the same extent after the helix inversion event. Our results are interpreted in terms of numerical simulations of the droplets' structure, which shed light on the major role played by curvature close to the droplets' center, this latter one becoming dominant when the droplet radius is small. [ABSTRACT FROM AUTHOR]

Homodimeric KIF17 and heterotrimeric KIF3AB are processive, kinesin-2 family motors that act jointly to carry out anterograde intraflagellar transport (IFT), ferrying cargo along microtubules (MTs) toward the tips of cilia. How IFT trains attain speeds that exceed the unloaded rate of the slower, KIF3AB motor remains unknown. By characterizing the motility properties of kinesin-2 motors as a function of load we find that the increase in KIF3AB velocity, elicited by forward loads from KIF17 motors, cannot alone account for the speed of IFT trains in vivo. Instead, higher IFT velocities arise from an increased likelihood that KIF3AB motors dissociate from the MT, resulting in transport by KIF17 motors alone, unencumbered by opposition from KIF3AB. The rate of transport is therefore set by an equilibrium between a faster state, where only KIF17 motors move the train, and a slower state, where at least one KIF3AB motor on the train remains active in transport. The more frequently the faster state is accessed, the higher the overall velocity of the IFT train. We conclude that IFT velocity is governed by (i) the absolute numbers of each motor type on a given train, (ii) how prone KIF3AB is to dissociation from MTs relative to KIF17, and (iii) how prone both motors are to dissociation relative to binding MTs. [ABSTRACT FROM AUTHOR]

The detailed dynamics of the cycle of myosin-V are explored by simulation approaches, examining the nature of the energy-driven motion. Our study started with Langevin dynamics (LD) simulations on a very coarse landscape with a single rate-limiting barrier and reproduced the stall force and the hand-over-hand dynamics. We then considered a more realistic landscape and used time-dependent Monte Carlo (MC) simulations that allowed trajectories long enough to reproduce the force/velocity characteristic sigmoidal correlation, while also reproducing the hand-over-hand motion. Overall, our study indicated that the notion of a downhill lever-up to lever-down process (popularly known as the powerstroke mechanism) is the result of the energetics of the complete myosin-V cycle and is not the source of directional motion or force generation on its own. The present work further emphasizes the need to use well-defined energy landscapes in studying molecular motors in general and myosin in particular. [ABSTRACT FROM AUTHOR]

In eukaryotic cells, membranous vesicles and organelles are transported by ensembles of motor proteins. These motors, such as kinesin-1, have been well characterized in vitro as single molecules or as ensembles rigidly attached to nonbiological substrates. However, the collective transport by membrane-anchored motors, that is, motors attached to a fluid lipid bilayer, is poorly understood. Here, we investigate the influence of motors' anchorage to a lipid bilayer on the collective transport characteristics. We reconstituted "membrane-anchored" gliding motility assays using truncated kinesin- 1 motors with a streptavidin-binding peptide tag that can attach to streptavidin-loaded, supported lipid bilayers. We found that the diffusing kinesin-1 motors propelled the microtubules in the presence of ATP. Notably, we found the gliding velocity of the microtubules to be strongly dependent on the number of motors and their diffusivity in the lipid bilayer. The microtubule gliding velocity increased with increasing motor density and membrane viscosity, reaching up to the stepping velocity of single motors. This finding is in contrast to conventional gliding motility assays where the density of surfaceimmobilized kinesin-1 motors does not influence the microtubule velocity overawide range. We reason that the transport efficiency of membrane-anchored motors is reduced because of their slippage in the lipid bilayer, an effect that we directly observed using singlemolecule fluorescence microscopy. Our results illustrate the importance of motor-cargo coupling, which potentially provides cells with an additional means of regulating the efficiency of cargo transport. [ABSTRACT FROM AUTHOR]

The combinatorial nature ofmany importantmathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecularmotor- propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NPcomplete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology. [ABSTRACT FROM AUTHOR]

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. [ABSTRACT FROM AUTHOR]

Unraveling the molecular nature of the conversion of chemical energy (ATP hydrolysis in the α/β-subunits) to mechanical energy and torque (rotation of the γ-subunit) in F1-ATPase is very challenging. A major part of the challenge involves understanding the rotary-chemical coupling by a nonphenomenological structure-energy description, while accounting for the observed torque generated on the γ-subunit and its change due to mutation of this unit. Here we extend our previous study that used a coarse-grained model of the F1-ATPase to generate a structure-based free energy landscape of the rotary-chemical process. Our quantitative analysis of the landscape reproduced the observed torque for the wild-type enzyme. In doing so, we found that there are several possibilities of torque generation from landscapes with various shapes and demonstrated that a downhill slope along the chemical coordinate could still result in negligible torque, due to ineffective coupling of the chemistry to the γ-subunit rotation. We then explored the relationship between the functionality and the underlying sequence through systematic examination of the effect of various parts of the γ-subunit on free energy surfaces of F1-ATPase. Furthermore, by constructing several types of γ-deletion systems and calculating the corresponding torque generation, we gained previously unknown insights into the molecular nature of the F1-ATPase rotary motor. Significantly, our results are in excellent agreement with recent experimental findings and indicate that the rotary-chemical coupling is primarily established through electrostatic effects, although specific contacts through γ-ionizable residue side chains are not essential for establishing the basic features of the coupling. [ABSTRACT FROM AUTHOR]

Viral DNA packaging motors are among the most powerful molecular motors known. A variety of structural, biochemical, and single-molecule biophysical approaches have been used to understand their mechanochemistry. However, packaging initiation has been diffkult to analyze because of its transient and highly dynamic nature. Here, we developed a single-molecule fluorescence assay that allowed visualization of packaging initiation and reinitiation in real time and quantification of motor assembly and initiation kinetics. We observed that a single bacteriophage T4 packaging machine can package multiple DNA molecules in bursts of activity separated by long pauses, suggesting that it switches between active and quiescent states. Multiple initiation pathways were discovered including, unexpectedly, direct DNA binding to the capsid portal followed by recruitment of motor subunits. Rapid succession of ATP hydrolysis was essential for efficient initiation. These observations have implications for the evolution of icosahedral viruses and regulation of virus assembly. [ABSTRACT FROM AUTHOR]

Kinesin-1 is a dimeric motor protein, central to intracellular transport, that steps hand-over-hand toward the microtubule (MT) plus-end, hydrolyzing one ATP molecule per step. Its remarkable processivity is critical for ferrying cargo within the cell: over 100 successive steps are taken, on average, before dissociation from the MT. Despite considerable work, it is not understood which features coordinate, or "gate," the mechanochemical cycles of the two motor heads. Here, we show that kinesin dissociation occurs subsequent to, or concomitant with, phosphate (Pi) release following ATP hydrolysis. In optical trapping experiments, we found that increasing the steady-state population of the posthydrolysis ADPPi state (by adding free Pi) nearly doubled the kinesin run length, whereas reducing either the ATP binding rate or hydrolysis rate had no effect. The data suggest that, during processive movement, tethered-head binding occurs subsequent to hydrolysis, rather than immediately after ATP binding, as commonly suggested. The structural change driving motility, thought to be neck linker docking, is therefore completed only upon hydrolysis, and not ATP binding. Our results offer additional insights into gating mechanisms and suggest revisions to prevailing models of the kinesin reaction cycle. [ABSTRACT FROM AUTHOR]

Understanding the basis for the action of myosin motors and related molecular machines requires a quantitative energy-based description of the overall functional cycle. Previous theoretical attempts to do so have provided interesting insights on parts of the cycle but could not generate a structure-based free energy landscape for the complete cycle of myosin. In particular, a nonphenomenological structure/energy-based understanding of the unidirectional motion is still missing. Here we use a coarse-grained model of myosin V and generate a structure-based free energy surface of the largest conformational change, namely the transition from the post- to prepowerstroke movement. We also couple the observed energetics of ligand binding/hydrolysis and product release to that of the conformational surface and reproduce the energetics of the complete mechanochemical cycle. It is found that the release in electrostatic free energy upon changing the conformation of the lever arm and the convertor domain from its postto prepowerstroke state provides the necessary energy to bias the system towards the unidirectional movement of myosin V on the actin filament. The free energy change of 11 kcal is also in the range of ∼2–3 pN, which is consistent with the experimentally observed stalling force required to stop the motor completely on its track. The conformational-chemical coupling generating a successful powerstroke cycle is believed to be conserved among most members of the myosin family, thus highlighting the importance of the previously unknown role of electrostatics free energy in guiding the functional cycle in other actin-based myosin motors. [ABSTRACT FROM AUTHOR]

Terminase enzymes are viral motors that package DNA into a preformed capsid and are of interest both therapeutically and as potential nano-machines. The enzymes excise a single genome from a concatemeric precursor (genome maturation) and then package the duplex to near-crystalline density (genome packaging). The functional motors are oligomers of protomeric subunits and are the most powerful motors currently known. Here, we present mechanistic studies on the terminase motor from bacteriophage λ. We identify a mutant (K76R) that is specifically deficient in packaging activity. Biochemical analysis of this enzyme provides insight into the linkage between ATP hydrolysis and motor translocation. We further use this mutant to assemble chimeric motors with WT enzyme and characterize the catalytic activity of the complexes. The data demonstrate that strong coordination between the motor protomers is required for DNA packaging and that incorporation of even a single mutant protomer poisons motor activity. Significant coordination is similarly observed in the genome maturation reaction; however, although the motor is composed of a symmetric tetramer of protomers, the maturation complex is better described as a "dimer-of-dimers" with half-site reactivity. We describe a model for how the motor alternates between a stable genome maturation complex and a dynamic genome packaging complex. The fundamental features of coordinated ATP hydrolysis, DNA movement, and tight association between the motor and the duplex during translocation are recapitulated in all of the viral motors. This work is thus of relevance to all terminase enzymes, both prokaryotic and eukaryotic. [ABSTRACT FROM AUTHOR]

Kinesin and dynein are fundamental components of intracellular transport, but their interactions when simultaneously present on cargos are unknown. We built an optical trap that can be calibrated in vivo during data acquisition for each individual cargo to measure forces in living cells. Comparing directional stall forces in vivo and in vitro, we found evidence that cytoplasmic dynein is active during minus- and plus-end directed motion, whereas kinesin is only active in the plus direction. In vivo, we found outward (~plus-end) stall forces range from 2 to 7 pN, which is significantly less than the 5-to 7-pN stall force measured in vitro for single kinesin molecules. In vitro measurements on beads with kinesin-1 and dynein bound revealed a similar distribution, implying that an interaction between opposite polarity motors causes this difference. Finally, inward (~minus-end) stalls in vivo were 2-3 pN, which is higher than the 1.1-pN stall force of a single dynein, implying multiple active dynein. [ABSTRACT FROM AUTHOR]

The molecular origin of the action of the F0 proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challen-ging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F0-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunita. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems. [ABSTRACT FROM AUTHOR]

Duplication of double-stranded DNA (dsDNA) requires a fine-tuned coordination between the DNA replication and unwinding reactions. Using optical tweezers, we probed the coupling dynamics between these two activities when they are simultaneously carried out by individual Phi29 DNA polymerase molecules replicating a dsDNA hairpin. We used the wild-type and an unwinding deficient polymerase variant and found that mechanical tension applied on the DNA and the DNA sequence modulate in different ways the replication, unwinding rates, and pause kinetics of each polymerase. However, incorporation of pause kinetics in a model to quantify the unwinding reaction reveals that both polymerases destabilize the fork with the same active mechanism and offers insights into the topological strategies that could be used by the Phi29 DNA polymerase and other DNA replication systems to couple unwinding and replication reactions. [ABSTRACT FROM AUTHOR]

In cells, many vital processes involve myosin-driven motility that actively remodels the actin cytoskeleton and changes cell shape. Here we study how the collective action of myosin motors organizes actin filaments into contractile structures in a simplified model system devoid of biochemical regulation. We show that this self-organization occurs through an active multistage coarsening process. First, motors form dense foci by moving along the actin network structure followed by coalescence. Then the foci accumulate actin filaments in a shell around them. These actomyosin condensates eventually cluster due to motor-driven coalescence. We propose that the physical origin of this multistage aggregation is the highly asymmetric load response of actin filaments: they can support large tensions but buckle easily under piconewton compressive loads. Because the motor-generated forces well exceed this threshold, buckling is induced on the connected actin network that resists motor-driven filament sliding. We show how this buckling can give rise to the accumulation of actin shells around myosin foci and subsequent coalescence of foci into superaggregates. This new physical mechanism provides an explanation for the formation and contractile dynamics of disordered condensed actomyosin states observed in vivo. [ABSTRACT FROM AUTHOR]

The implementation of multiconfigurational quantum chemistry methods into a quantum-mechanics/molecular-mechanics protocol has allowed the construction of a realistic computer model for the sensory rhodopsin of the cyanobacterium Anabaena PCC 7120. The model, which reproduces the absorption spectra of both the all-trans and 13-cis forms of the protein and their associated K and L intermediates, is employed to investigate the light-driven steps of the photochromic cycle exhibited by the protein. It is found that the photoisomerizations of the all-trans and 13-cis retinal chromophores occur through unidirectional, counterclockwise 180° rotations of the =C14-C15= moiety with respect to the Lys2l0- linked end of the chromophore axis. Thus, the sequential interconversions of the all-trans and 1 3-cis forms during a single photochromic cycle yield a complete (360°) unidirectional rotation of the =C14-C15= moiety. This finding implies that Anabaena sensory rhodopsin is a biological realization of a light-driven molecular rotor. [ABSTRACT FROM AUTHOR]

The time it takes an enzyme to complete its reaction is a stochastic quantity governed by thermal fluctuations. With the advent of high-resolution methods of single-molecule manipulation and detection, it is now possible to observe directly this natural variation in the enzymatic cycle completion time and extract kinetic information from the statistics of its fluctuations. To this end, the inverse of the squared coefficient of variation, which we term nmin, is a useful measure of fluctuations because it places a strict lower limit on the number of kinetic states in the enzymatic mechanism. Here we show that there is a single general expression for the substrate dependence of nmin for a wide range of kinetic models. This expression is governed by three kinetic parameters, which we term NL, NS, and a. These parameters have simple geometric interpretations and provide clear constraints on possible kinetic mechanisms. As a demonstration of this analysis, we fit the fluctuations in the dwell times of the packaging motor of the bacteriophage φ29, revealing additional features of the nucleotide loading process in this motor. Because a diverse set of kinetic models display the same substrate dependence for their fluctuations, the expression for this general dependence may prove of use in the characterization and study of the dynamics of a wide range of enzymes. [ABSTRACT FROM AUTHOR]

Cilia are microtubute-based protrusions of the plasma membrane found on most eukaryotic cells. Their assembly is mediated through the conserved intraflagellar transport mechanism. One class of motor proteins involved in intraflagellar transport, kinesin-2, is unique among kinesin motors in that some of its members are composed of two distinct polypeptides. However, the biological reason for heterodimerization has remained elusive. Here we provide several interdependent reasons for the heterodimerization of the kinesin-2 motor KLP11/KLP20 of Caenorhabditis elegans cilia. One motor domain is unprocessive as a homodimer, but heterodimerization with a processive partner generates processivity. The "unprocessive" subunit is kept in this partnership as it mediates an asymmetric autoregulation of the motor activity. Finally, heterodimerization is necessary to bind KAP1, the in vivo link between motor and cargo. [ABSTRACT FROM AUTHOR]

The direction of rotation of the Escherichia coli flagellum is controlled by an assembly called the switch complex formed from multiple subunits of the proteins FliG, FliM, and FliN. Structurally, the switch complex corresponds to a drum-shaped feature at the bottom of the basal body, termed the C-ring. Stimulus-regulated reversals in flagellar motor rotation are the basis for directed movement such as chemotaxis. In E. coli, the motors turn counterclockwise (CCW) in their default state, allowing the several filaments on a cell to join together in a bundle and propel the cell smoothly forward. In response to the chemotaxis signaling molecule phospho-CheY (CheYP), the motors can switch to clockwise (CW) rotation, causing dissociation of the filament bundle and reorientation of the cell. CheYP has previously been shown to bind to a conserved segment near the N terminus of FliM. Here, we show that this interaction serves to capture CheYP and that the switch to CW rotation involves the subsequent interaction of CheYP with FliN. FliN is located at the bottom of the C-ring, in close association with the C-terminal domain of FliM (FliMC), and the switch to CW rotation has been shown to involve relative movement of FliN and FliMC. Using a recently developed structural model for the FliN/FliMC array, and the CheYP-binding site here identified on FliN, we propose a mechanism by which CheYP binding could induce the conformational switch to CW rotation. [ABSTRACT FROM AUTHOR]

The actomyosin molecular motor, the motor composed of myosin II and actin filament, is responsible for muscle contraction, converting chemical energy into mechanical work. Although recent single molecule and structural studies have shed new light on the energy-converting mechanism, the physical basis of the molecular-level mechanism remains unclear because of the experimental limitations. To provide a clue to resolve the controversy between the lever-arm mechanism and the Brownian ratchet-like mechanism, we here report an in silico single molecule experiment of an actomyosin motor. When we placed myosin on an actin filament and allowed myosin to move along the filament, we found that myosin exhibits a unidirectional Brownian motion along the filament. This unidirectionality was found to arise from the combination of a nonequilibrium condition realized by coupling to the ATP hydrolysis and a ratchet-like energy landscape inherent in the actin-myosin interaction along the filament, indicating that a Brownian ratchet-like mechanism contributes substantially to the energy conversion of this molecular motor. [ABSTRACT FROM AUTHOR]

The powerstroke of the myosin motor is the basis of cell division and bodily movement, but has eluded empirical description due to the short lifetime and low abundance of intermediates during force generation. To gain insight into this process, we used well-established single-tryptophan and pyrene fluorescent sensors and electron microscopy to characterize the structural and kinetic properties of myosin complexed with ADP and blebbistatin, a widely used inhibitor. We found that blebbistatin does not weaken the tight actin binding of myosin.ADP, but unexpectedly it induces lever priming, a process for which the gamma-phosphate of ATP (or its analog) had been thought necessary. The results indicate that a significant fraction of. the myosin.ADP.blebbistatin complex populates a previously inaccessible conformation of myosin resembling the start of the powerstroke. [ABSTRACT FROM AUTHOR]

Myosin II is a molecular motor that converts chemical to mechanical energy and enables muscle operations. After a power stroke, a recovery transition completes the cycle and returns the molecular motor to its prestroke state. Atomically detailed simulations in the framework of the Milestoning theory are used to calculate kinetics and mechanisms of the recovery stroke. Milestoning divides the process into transitions between hyper-surfaces (Milestones) along a reaction coordinate. Decorrelation of dynamics between sequential Milestones is assumed, which speeds up the atomically detailed simulations by a factor of millions. Two hundred trajectories of myosin with explicit water solvation are used to sample transitions between sequential pairs of Milestones. Collective motions of hundreds of atoms are described at atomic resolution and at the millisecond time scale. The experimentally measured transition time of about a millisecond is in good agreement with the computed time. The simulations support a sequential mechanism. In the first step the P-loop and switch 2 close on the ATP and in the second step the mechanical relaxation is induced via the relay and the SH1 helices. We propose that the entropy of switch 2 helps to drive the power stroke. Secondary structure elements are progressing through a small number of discrete states in a network of activated transitions and are assisted by side chain flips between rotameric states. The few-state sequential mechanism is likely to enhance the efficiency of the relaxation reducing the probability of off-pathway intermediates. [ABSTRACT FROM AUTHOR]

We study the role of microtubule movement in bidirectional organelle transport in Drosophila S2 cells and show that EGFP- tagged peroxisomes in cells serve as sensitive probes of motor induced, noisy cytoskeletal motions. Multiple peroxisomes move in unison over large time windows and show correlations with microtubule tip positions, indicating rapid microtubule fluctuations in the longitudinal direction. We report the first high-resolution measurement of longitudinal microtubule fluctuations per- formed by tracing such pairs of co-moving peroxisomes. The resulting picture shows that motor-dependent longitudinal micro- tubule oscillations contribute significantly to cargo movement along microtubules. Thus, contrary to the conventional view. organelle transport cannot be described solely in terms of cargo movement along stationary microtubule tracks, but instead includes a strong contribution from the movement of the tracks. [ABSTRACT FROM AUTHOR]

Dimeric myosins V and VI travel long distances in opposite directions along actin filaments in cells, taking multiple steps in a "hand-over-hand" fashion. The catalytic cycles of both myosins are limited by ADP dissociation, which is considered a key step in the walking mechanism of these motors. Here, we demonstrate that external loads applied to individual actomyosin V or VI bonds asymmetrically affect ADP affinity, such that ADP binds weaker under loads assisting motility. Model-based analysis reveals that forward and backward loads modulate the kinetics of ADP binding to both myosins, although the effect is less pronounced for myosin VI. ADP dissociation is modestly accelerated by forward loads and inhibited by backward loads. Loads applied in either direction slow ADP binding to myosin V but accelerate binding to myosin VI. We calculate that the intramolecular load generated during processive stepping is ≈2 pN for both myosin V and myosin VI. The distinct load dependence of ADP binding allows these motors to perform different cellular functions. [ABSTRACT FROM AUTHOR]

RNA helicases regulate virtually all RNA-dependent cellular processes. Although much is known about helicase structures, very little is known about how they deal with barriers in RNA and the factors that affect their processivity. The hepatitis C virus encodes NS3, an RNA helicase that is essential for viral RNA replication. We have used optical tweezers to determine at the single-molecule level how the local stability of the RNA substrate affects the enzyme rate of strand separation, whether separation occurs by an active or a passive mechanism, and whether processivity is affected. We show that sequence barriers in RNA modulate NS3 activity. NS3 processivity depends on barriers ahead of the opening fork. Our results rule out a model where NS3 passively waits for the thermal fraying of double-stranded RNA. Instead, we find that NS3 destabilizes the duplex before separating the strands. Failure to do so before a strong barrier leads to helicase dissociation and limits the processivity of the enzyme. [ABSTRACT FROM AUTHOR]

Filopodia are thin, spike-like cell surface protrusions containing bundles of parallel actin filaments. So far, filopodial dynamics has mainly been studied in the context of cell motility on coverslip-adherent filopodia by using fluorescence and differential interference contrast (DIC) microscopy. In this study, we used an optical trap and interferometric particle tracking with nanometer precision to measure the three-dimensional dynamics of macrophage filopodia, which were not attached to flat surfaces. We found that filopodia act as cellular tentacles: a few seconds after binding to a particle, filopodia retract and pull the bound particle toward the cell. We observed F-actin-dependent stepwise retraction of filopodia with a mean step size of 36 nm. suggesting molecular motor activity during filopodial pulling. Remarkably, this intracellular stepping motion, which was measured at counteracting forces of up to 19 pN, was transmitted to the extracellular tracked particle via the filopodial F-actin bundle and the cell membrane. The pulling velocity depended strongly on the counteracting force and ranged between 600 nm/s at forces <1 pN and ≈40 nm/s at forces >15 pN. This result provides an explanation of the significant differences in filopodial retraction velocities previously reported in the literature. The measured filopodial retraction force-velocity relationship is in agreement with a model for force-dependent multiple motor kinetics. [ABSTRACT FROM AUTHOR]

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well defined internal mechanical motions to various initial deformations and that these motions are robust against external perturbations. We show that this behavior is not characteristic for random elastic networks. However, special network architectures with such properties can be designed by evolutionary optimization methods. Using them, an example of an artificial elastic network, operating as a cyclic machine powered by ligand binding, is constructed. [ABSTRACT FROM AUTHOR]

Intracellular active transport is driven by ATP-hydrolyzing motor proteins that move along cytoskeletal filaments. In particular, the microtubule-associated dynein motor is involved in the transport of organelles and vesicles, the maintenance of the Golgi, and mitosis. However, unlike kinesin and myosin, the mechanism by which dynein converts chemical energy into mechanical force remains largely a mystery, due primarily to the lack of a high-resolution molecular structure. Using homology modeling and normal mode analysis, we propose a complete atomic structure and a mechanism for force generation by the motor protein dynein. In agreement with very recent electron microscopy (EM) reconstructions showing dynein as a ring-shaped heptamer, our model consists of six ATPases of the AAA (ATPases associated with various cellular activities) superfamily and a C-terminal domain, which is experimentally known to control motor function. Our model shows a coiled coil spanning the diameter of the motor that accounts for previously unidentified structures in EM studies and provides a potential mechanism for long-range communication between the AAA domains. Furthermore, normal mode analysis reveals that the subunits of the motor that contain the nucleotide binding sites exhibit minimal movement, whereas the rest of the motor is very mobile. Our analysis suggests the likely domain rearrangements of the motor unit that generate its power stroke. This study provides insights into the structure and function of dynein that can guide further experimental investigations into energy transduction in dynein. [ABSTRACT FROM AUTHOR]

By applying atomic force microscope (AFM)-based force spectroscopy together with computational modeling in the form of molecular force-field simulations, we have determined quantitatively the actuation energetics of a synthetic motor-molecule. This multidisciplinary approach was performed on specifically designed, bistable, redox-controllable [2]rotaxanes to probe the steric and electrostatic interactions that dictate their mechanical switching at the single-molecule level. The fusion of experimental force spectroscopy and theoretical computational modeling has revealed that the repulsive electrostatic interaction, which is responsible for the molecular actuation, is as high as 65 kcal·mol-1, a result that is supported by ab initio calculations. [ABSTRACT FROM AUTHOR]

Torque is generated in the rotary motor at the base of the bacterial flagellum by ion translocating stator units anchored to the peptidoglycan cell wall. Stator units are composed of the proteins MotA and MotB in proton-driven motors, and they are composed of PomA and PomB in sodium-driven motors. Strains of Escherichia coli lacking functional stator proteins produce flagella that do not rotate, and induced expression of the missing proteins leads to restoration of motor rotation in discrete speed increments, a process known as "resurrection." Early work suggested a maxi- mum of eight units. More recent indications that WT motors may contain more than eight units, based on recovery of disrupted motors, are inconclusive. Here we demonstrate conclusively that the maximum number of units in a motor is at least 11. Using back-focal-plane interferometry of 1-µm polystyrene beads attached to flagella, we observed at least 11 distinct speed increments during resurrection with three different combinations of stator proteins in E. coli. The average torques generated by a single unit and a fully induced motor were lower than previous estimates. Speed increments at high numbers of units are smaller than those at low numbers, indicating that not all units in a fully induced motor are equivalent. [ABSTRACT FROM AUTHOR]

The role of protein flexibility in molecular motor function has previously been studied by considering a Brownian ratchet motor that is connected to its cargo by an elastic spring, with the result that the average velocity of the motor/cargo system is increased by reducing the stiffness of the linkage. Here, we extend this investigation to the case of chromosome transport during anaphase A, in which the relevant flexibility is not primarily in the motor/cargo linkage but rather in the cargo itself, i.e., in the chromosome. We model the motor mechanism as an imperfect Brownian ratchet with a built-in opposing load and the chromosome as a collection of discrete segments linked by an elastic energy function that discretizes the potential energy of an elastic rod. Thermal fluctuations are produced in the model by random forces, as in Brownian dynamics. All of the parameters that characterize the chromosome are known or can be estimated from experimental data, as can all but one of the motor parameters, which is adjusted to give the correct transport velocity of normal-length chromosomes. With the parameters so determined, we then reproduce the experimental finding of Nicklas [Nicklas, R. B. (1965) J. Cell Biol. 25, 119-135] that chromosome speed is essentially independent of chromosome length, even though our model contains no "velocity governor." We find instead that this effect is a consequence of chromosome flexibility, as it disappears when stiffer than normal chromosomes are considered. [ABSTRACT FROM AUTHOR]

Molecular motors are responsible for active transport and organization in the cell, underlying an enormous number of crucial biological processes. Dynein is more complicated in its structure and function than other motors. Recent experiments have found that unlike other motors, dynein can take different size steps along microtubules depending on load and ATP concentration. We use Monte Carlo simulations to model the molecular motor function of cytoplasmic dynein at the single-molecule level. The theory relates dynein's enzymatic properties to its mechanical force production. Our simulations reproduce the main features of recent single-molecule experiments that found a discrete distribution of dynein step sizes, depending on load and ATP concentration. The model reproduces the large steps found experimentally under high ATP and no load by assuming that the ATP binding affinities at the secondary sites decrease as the number of ATP bound to these sites increases. Additionally, to capture the essential features of the step-size distribution at very low ATP concentration and no load, the ATP hydrolysis of the primary site must be dramatically reduced when none of the secondary sites have ATP bound to them. We make testable predictions that should guide future experiments related to dynein function. [ABSTRACT FROM AUTHOR]

Dynactin is a large complex of at least nine distinct proteins that co-complexes with cytoplasmic dynein within cells, where it plays a major role as a regulator of the motors function. Owing to its large size and complexity, relatively little is known about dynactin's 3D structure or the structural basis of its function. Use of single-particle image analysis techniques has enabled us to produce the first 3D reconstruction of the dynactin complex, to a resolution of 3 nm. The actin-related protein (Arp) backbone of the filament has been clearly visualized. Fitting of models of the Arp backbone showed that it consists of 10 subunits. Additional mass, not part of the Arp backbone, was also seen. A preliminary fitting of the capping protein CapZ structure into our 3D reconstruction of the dynactin complex suggests that it is optimally placed to perform its proposed function as a stabilizer of the Arp1 backbone and gives clues as to likely interaction points between the capping protein and Arp subunits. The results provide the first detailed visualization of the dynactin complex and shed light on the mode of interaction between several of its constituent proteins and their possible functions. [ABSTRACT FROM AUTHOR]

The widespread use of molecular-level motion in key natural processes suggests that great rewards could come from bridging the gap between the present generation of synthetic molecular machines-which by and large function as switches-and the machines of the macroscopic world, which utilize the synchronized behavior of integrated components to perform more sophisticated tasks than is possible with any individual switch. Should we try to make molecular machines of greater complexity by trying to mimic machines from the macroscopic world or instead apply unfamiliar (and no doubt have to discover or invent currently unknown) mechanisms utilized by biological machines? Here we try to answer that question by exploring some of the advances made to date using bio-inspired machine mechanisms., Competing Interests: The authors declare no conflict of interest.

A prerequisite for DNA replication is the unwinding of duplex DNA catalyzed by a replicative hexameric helicase. Despite a growing body of research, key elements of helicase mechanism remain under substantial debate. In particular, the number of DNA strands encircled by the helicase ring during unwinding and the ring orientation at the replication fork completely contrast in contemporary mechanistic models. Here we use single-molecule and ensemble assays to address these questions for the papillomavirus E1 helicase. We find that E1 unwinds DNA with a strand-exclusion mechanism, with the N-terminal side of the helicase ring facing the replication fork. We show that E1 generates strikingly heterogeneous unwinding patterns stemming from varying degrees of repetitive movements, which is modulated by the DNA-binding domain. Together, our studies reveal previously unrecognized dynamic facets of replicative helicase unwinding mechanisms.