Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

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.     

Processive movement of single kinesins on crowded microtubules visualized using quantum dots

Kinesin-1 is a processive molecular motor transporting cargo along microtubules. Inside cells, several motors and microtubule-associated proteins compete for binding to microtubules. Therefore, the question arises how processive movement of kinesin-1 is affected by crowding on the microtubule. Here we use total internal reflection fluorescence microscopy to image in vitro the runs of single quantum dot-labelled kinesins on crowded microtubules under steady-state conditions and to measure the degree of crowding on a microtubule at steady-state. We find that the runs of kinesins are little affected by high kinesin densities on a microtubule. However, the presence of high densities of a mutant kinesin that is not able to step efficiently reduces the average speed of wild-type kinesin, while hardly changing its processivity. This indicates that kinesin waits in a strongly bound state on the microtubule when encountering an obstacle until the obstacle unbinds and frees the binding site for kinesin's next step. A simple kinetic model can explain quantitatively the behaviour of kinesin under both crowding conditions.     

Processive kinesins require loose mechanical coupling for efficient collective motility

Processive motor proteins are stochastic steppers that perform actual mechanical steps for only a minor fraction of the time they are bound to the filament track. Motors usually work in teams and therefore the question arises whether the stochasticity of stepping can cause mutual interference when motors are mechanically coupled. We used biocompatible surfaces to immobilize processive kinesin-1 motors at controlled surface densities in a mechanically well-defined way. This helped us to study quantitatively how mechanical coupling between motors affects the efficiency of collective microtubule transport. We found that kinesin-1 constructs that lack most of the non-motor sequence slow each other down when collectively transporting a microtubule, depending on the number of interacting motors. This negative interference observed for a motor ensemble can be explained quantitatively by a mathematical model using the known physical properties of individual molecules of kinesin-1. The non-motor extension of kinesin-1 reduces this mutual interference, indicating that loose mechanical coupling between motors is required for efficient transport by ensembles of processive motors.     

Productive Cooperation among Processive Motors Depends Inversely on Their Mechanochemical Efficiency

Subcellular cargos are often transported by teams of processive molecular motors, which raises questions regarding the role of motor cooperation in intracellular transport. Although our ability to characterize the transport behaviors of multiple-motor systems has improved substantially, many aspects of multiple-motor dynamics are poorly understood. This work describes a transition rate model that predicts the load-dependent transport behaviors of multiple-motor complexes from detailed measurements of a single motor's elastic and mechanochemical properties. Transition rates are parameterized via analyses of single-motor stepping behaviors, load-rate-dependent motor-filament detachment kinetics, and strain-induced stiffening of motor-cargo linkages. The model reproduces key signatures found in optical trapping studies of structurally defined complexes composed of two kinesin motors, and predicts that multiple kinesins generally have difficulties in cooperating together. Although such behavior is influenced by the spatiotemporal dependence of the applied load, it appears to be directly linked to the efficiency of kinesin's stepping mechanism, and other types of less efficient and weaker processive motors are predicted to cooperate more productively. Thus, the mechanochemical efficiencies of different motor types may determine how effectively they cooperate together, and hence how motor copy number contributes to the regulation of cargo motion.     

Cargo surface fluidity can reduce inter-motor mechanical interference,promote load-sharing and enhance processivity in teams of molecular motors

In cells, multiple molecular motors work together as teams to carry cargoes such as vesicles and organelles over long distances to their destinations by stepping along a network of cytoskeletal filaments. How motors that typically mechanically interfere with each other, work together as teams is unclear. Here we explored the possibility that purely physical mechanisms, such as cargo surface fluidity, may potentially enhance teamwork, both at the single motor and cargo level. To explore these mechanisms, we developed a three dimensional simulation of cargo transport along microtubules by teams of kinesin-1 motors. We accounted for cargo membrane fluidity by explicitly simulating the Brownian dynamics of motors on the cargo surface and considered both the load and ATP dependence of single motor functioning. Our simulations show that surface fluidity could lead to the reduction of negative mechanical interference between kinesins and enhanced load sharing thereby increasing the average duration of single motors on the filament. This, along with a cooperative increase in on-rates as more motors bind leads to enhanced collective processivity. At the cargo level, surface fluidity makes more motors available for binding, which can act synergistically with the above effects to further increase transport distances though this effect is significant only at low ATP or high motor density. Additionally, the fluid surface allows for the clustering of motors at a well defined location on the surface relative to the microtubule and the fluid-coupled motors can exert more collective force per motor against loads. Our work on understanding how teamwork arises in cargo-coupled motors allows us to connect single motor properties to overall transport, sheds new light on cellular processes, reconciles existing observations, encourages new experimental validation efforts and can also suggest new ways of improving the transport of artificial cargo powered by motor teams.     

Flexible light-chain and helical structure of F-actin explain the movement and step size of myosin-VI

Myosin-VI is a dimeric isoform of unconventional myosins. Single molecule experiments indicate that myosin-VI and myosin-V are processive molecular motors, but travel toward opposite ends of filamentous actin. Structural studies show several differences between myosin-V and VI, including a significant difference in the light-chain domain connecting the motor domains. Combining the measured kinetics of myosin-VI with the elasticity of the light chains, and the helical structure of F-actin, we compare and contrast the motility of myosin-VI with myosin-V. We show that the elastic properties of the light-chain domain control the stepping behavior of these motors. Simple models incorporating the motor elastic energy can quantitatively capture most of the observed data. Implications of our result for other processive motors are discussed.     

Single-molecule behavior of monomeric and heteromeric kinesins

Conventional kinesin is capable of long-range, processive movement along microtubules, a property that has been assumed to be important for its role in membrane transport. Here we have investigated whether the Caenorhabditis elegans monomeric kinesin unc104 and the sea urchin heteromeric kinesin KRP85/95, two other members of the kinesin superfamily that function in membrane transport, are also processive. Both motors were fused to green fluorescent protein, and the fusion proteins were tested for processive ability using a single-molecule fluorescence imaging microscope. Neither unc104-GFP nor KRP85/95-GFP exhibited processive movement (detection limit approximately 40 nm), although both motors were functional in multiple motor microtubule gliding assays (v = 1760 +/- 540 and 202 +/- 37 nm/s, respectively). Moreover, the ATP turnover rates (5.5 and 3.1 ATPs per motor domain per second, respectively) are too low to give rise to the observed microtubule gliding velocities, if only a single motor were driving transport with an 8 nm step per ATPase cycle. Instead, the results suggest that these motors have low duty cycles and that high processivity may not be required for efficient vesicle transport. Conventional kinesin's unusual processivity may be required for efficient transport of protein complexes that cannot carry multiple motors.     

Two single-headed myosin V motors bound to a tetrameric adapter protein form a processive complex

Myo4p, one of two class V myosins in budding yeast, continuously transports messenger RNA (mRNA) cargo in the cell but is nonprocessive when characterized in vitro. The adapter protein She3p tightly binds to the Myo4p rod, forming a single-headed motor complex. In this paper, we show that two Myo4p-She3p motors are recruited by the tetrameric mRNA-binding protein She2p to form a processive double-headed complex. The binding site for She3p was mapped to a single α helix that protrudes at right angles from She2p. Processive runs of several micrometers on yeast actin-tropomyosin filaments were observed only in the presence of She2p, and, thus, motor activity is regulated by cargo binding. While moving processively, each head steps ~72 nm in a hand-over-hand motion. Coupling two high-duty cycle monomeric motors via a common cargo-binding adapter protein creates a complex with transport properties comparable with a single dimeric processive motor such as vertebrate myosin Va.     

A potential role for isothermal calorimetry in studies of the effects of thermodynamic non-ideality in enzyme-catalyzed reactions

Attention is drawn to the feasibility of using isothermal calorimetry for the characterization of enzyme reactions under conditions bearing greater relevance to the crowded biological environment, where kinetic parameters are likely to differ significantly from those obtained by classical enzyme kinetic studies in dilute solution. An outline of the application of isothermal calorimetry to the determination of enzyme kinetic parameters is followed by considerations of the nature and consequences of crowding effects in enzyme catalysis. Some of those effects of thermodynamic non-ideality are then illustrated by means of experimental results from calorimetric studies of the effect of molecular crowding on the kinetics of catalysis by rabbit muscle pyruvate kinase. This review concludes with a discussion of the potential of isothermal calorimetry for the experimental determination of kinetic parameters for enzymes either in biological environments or at least in media that should provide reasonable approximations of the crowded conditions encountered in vivo.     

Motors and Their Tethers: The Role of Secondary Binding Sites in Processive Motility

Cytoskeletal motors convert the energy from binding and hydrolyzing ATP into conformational changes that direct movement along a cytoskeletal polymer substrate. These enzymes utilize different mechanisms to generate long-range motion on the order of a micron or more that is required for functions ranging from muscle contraction to transport of growth factors along a nerve axon. Several of the individual cytoskeletal motors are processive, meaning that they have the ability to take sequential steps along their polymer substrate without dissociating from the polymer. This ability to maintain contact with the polymer allows individual motors to move cargos quickly from one cellular location to another. Many of the processive motors have now been found to utilize secondary binding sites that aid in motor processivity.     

Motor Reattachment Kinetics Play a Dominant Role in Multimotor-Driven Cargo Transport

Kinesin-based cargo transport in cells frequently involves the coordinated activity of multiple motors, including kinesins from different families that move at different speeds. However, compared to the progress at the single-molecule level, mechanisms by which multiple kinesins coordinate their activity during cargo transport are poorly understood. To understand these multimotor coordination mechanisms, defined pairs of kinesin-1 and kinesin-2 motors were assembled on DNA scaffolds and their motility examined in vitro. Although less processive than kinesin-1 at the single-molecule level, addition of kinesin-2 motors more effectively amplified cargo run lengths. By applying the law of total expectation to cargo binding durations in ADP, the kinesin-2 microtubule reattachment rate was shown to be fourfold faster than that of kinesin-1. This difference in microtubule binding rates was also observed in solution by stopped-flow. High-resolution tracking of a gold-nanoparticle-labeled motor with 1 ms and 2 nm precision revealed that kinesin-2 motors detach and rebind to the microtubule much more frequently than does kinesin-1. Finally, compared to cargo transported by two kinesin-1, cargo transported by two kinesin-2 motors more effectively navigated roadblocks on the microtubule track. These results highlight the importance of motor reattachment kinetics during multimotor transport and suggest a coordinated transport model in which kinesin-1 motors step effectively against loads whereas kinesin-2 motors rapidly unbind and rebind to the microtubule. This dynamic tethering by kinesin-2 maintains the cargo near the microtubule and enables effective navigation along crowded microtubules.     

Nonprocessive Motor Dynamics at the Microtubule Membrane Tube Interface

Key cellular processes such as cell division, membrane compartmentalization, and intracellular transport rely on motor proteins. Motors have been studied in detail on the single motor level such that information on their step size, stall force, average run length, and processivity are well known. However, in vivo, motors often work together, so that the question of their collective coordination has raised great interest. Here, we specifically attach motors to giant vesicles and examine collective motor dynamics during membrane tube formation. Image correlation spectroscopy reveals directed motion as processive motors walk at typical speeds (≤500 nm/s) along an underlying microtubule and accumulate at the tip of the growing membrane tube. In contrast, nonprocessive motors exhibit purely diffusive behavior, decorating the entire length of a microtubule lattice with diffusion constants at least 1000 times smaller than a freely-diffusing lipid-motor complex in a lipid bilayer (1 μm²/s); fluorescence recovery after photobleaching experiments confirm the presence of the slower-moving motor population at the microtubule-membrane tube interface. We suggest that nonprocessive motors dynamically bind and unbind to maintain a continuous interaction with the microtubule. This dynamic and continuous interaction is likely necessary for nonprocessive motors to mediate bidirectional membrane tube dynamics reported previously.     

Coordination of Kinesin motors pulling on fluid membranes

Intracellular transport relies on the action of motor proteins, which work collectively to either carry small vesicles or pull membranes tubes along cytoskeletal filaments. Although the individual properties of kinesin-1 motors have been extensively studied, little is known on how several motors coordinate their action and spatially organize on the microtubule when pulling on fluid membranes. Here we address these questions by studying, both experimentally and numerically, the growth of membrane tubes pulled by molecular motors. Our in vitro setup allows us to simultaneously control the parameters monitoring tube growth and measure its characteristics. We perform numerical simulations of membrane tube growth, using the experimentally measured values of all parameters, and analyze the growth properties of the tube considering various motor cooperation schemes. The comparison of the numerical results and the experimental data shows that motors use simultaneously several protofilaments of a microtubule to pull a single tube, as motors moving along a single protofilament cannot generate the forces required for tube extraction. In our experimental conditions, we estimate the average number of motors pulling the tube to be approximately nine, distributed over three contiguous protofilaments. Our results also indicate that the motors pulling the tube do not step synchronously.     

Molecular motors: thermodynamics and the random walk

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.     

To step or not to step? How biochemistry and mechanics influence processivity in Kinesin and Eg5

Conventional kinesin and Eg5 are essential nanoscale motor proteins. Single-molecule and presteady-state kinetic experiments indicate that both motors use similar strategies to generate movement along microtubules, despite having distinctly different in vivo functions. Single molecules of kinesin, a long-distance cargo transporter, are highly processive, binding the microtubule and taking 100 or more sequential steps at velocities of up to 700 nm/s before dissociating, whereas Eg5, a motor active in mitotic spindle assembly, is also processive, but takes fewer steps at a slower rate. By dissecting the structural, biochemical and mechanical features of these proteins, we hope to learn how kinesin and Eg5 are optimized for their specific biological tasks, while gaining insight into how biochemical energy is converted into mechanical work.     

Kinetics: a tool to study molecular motors

Molecular motors are enzymes that couple the energy from nucleoside triphosphate hydrolysis to movement along a filament lattice. The three cytoskeletal motor superfamilies include myosin, dynein, and kinesin. However, in the last decade it has become apparent that the nucleic acid-based enzymes (DNA and RNA polymerases as well as the DNA helicases) share a number of mechanistic features in common with the microtubule and actin motors despite the fact that their cellular functions are so different. This review addresses the mechanistic approaches that have been used to study molecular motors. We discuss the basic biochemical techniques used to characterize a protein preparation, including active site determination and steady-state kinetics. In addition, we present the transient-state kinetic approaches used to define a mechanochemical cycle. We attempt to integrate the information obtained from kinetic studies within the context of motility results to provide a better understanding of the contribution of each approach for dissecting unidirectional force generation.     

Myosin V from Drosophila reveals diversity of motor mechanisms within the myosin V family

Myosin V is the best characterized vesicle transporter in vertebrates, but it has been unknown as to whether all members of the myosin V family share a common, evolutionarily conserved mechanism of action. Here we show that myosin V from Drosophila has a strikingly different motor mechanism from that of vertebrate myosin Va, and it is a nonprocessive, ensemble motor. Our steady-state and transient kinetic measurements on single-headed constructs reveal that a single Drosophila myosin V molecule spends most of its mechanochemical cycle time detached from actin, therefore it has to function in processive units that comprise several molecules. Accordingly, in in vitro motility assays, double-headed Drosophila myosin V requires high surface concentrations to exhibit a continuous translocation of actin filaments. Our comparison between vertebrate and fly myosin V demonstrates that the well preserved function of myosin V motors in cytoplasmic transport can be accomplished by markedly different underlying mechanisms.     

A method for multiprotein assembly in cells reveals independent action of kinesins in complex

Teams of processive molecular motors are critical for intracellular transport and organization, yet coordination between motors remains poorly understood. Here, we develop a system using protein components to generate assemblies of defined spacing and composition inside cells. This system is applicable to studying macromolecular complexes in the context of cell signaling, motility, and intracellular trafficking. We use the system to study the emergent behavior of kinesin motors in teams. We find that two kinesin motors in complex act independently (do not help or hinder each other) and can alternate their activities. For complexes containing a slow kinesin-1 and fast kinesin-3 motor, the slow motor dominates motility in vitro but the fast motor can dominate on certain subpopulations of microtubules in cells. Both motors showed dynamic interactions with the complex, suggesting that motor–cargo linkages are sensitive to forces applied by the motors. We conclude that kinesin motors in complex act independently in a manner regulated by the microtubule track.