Stepping, strain gating, and an unexpected force-velocity curve for multiple-motor-based transport

BACKGROUND: Intracellular transport via processive kinesin, dynein, and myosin molecular motors plays an important role in maintaining cell structure and function. In many cases, cargoes move distances longer than expected for single motors; there is significant evidence that this increased travel is in part due to multiple motors working together to move the cargoes. Although we understand single motors experimentally and theoretically, our understanding of multiple motors working together is less developed. RESULTS: We theoretically investigate how multiple kinesin motors function. Our model includes stochastic fluctuations of each motor as it proceeds through its enzymatic cycle. Motors dynamically influence each other and function in the presence of thermal noise and viscosity. We test the theory via comparison with the experimentally observed distribution of step sizes for two motors moving a cargo, and by predicting slightly subadditive stalling force for two motors relative to one. In the presence of load, our predictions for travel distances and mean velocities are different from the steady-state model: with high motor-motor coupling, we predict a form of strain-gating, where-because of the underlying motor's dynamics-the motors share load unevenly, leading to increased mean travel distance of the multiple-motor system under load. Surprisingly, we predict that in the presence of small load, two-motor cargoes move slightly slower than do single-motor cargoes. Unpublished data from G.T. Shubeita, B.C. Carter, and S.P.G. confirm this prediction in vivo. CONCLUSIONS: When only a few motors are active, fluctuations and unequal load sharing between motors can result in significant alterations of ensemble function.     

Cargo properties play a critical role in myosin Va-driven cargo transport along actin filaments

High-resolution experiments revealed that a single myosin-Va motor can transport micron-sized cargo on actin filaments in a stepwise manner. However, intracellular cargo transport is mediated through the dense actin meshwork by a team of myosin Va motors. The mechanism of how motors interact mechanically to bring about efficient cargo transport is still poorly understood. This study describes a stochastic model where a quantitative understanding of the collective behaviors of myosin Va motors is developed based on cargo stiffness. To understand how cargo properties affect the overall cargo transport, we have designed a model in which two myosin Va motors were coupled by wormlike chain tethers with persistence length ranging from 10 to 80 nm and contour length from 100 to 200 nm, and predicted distributions of velocity, run length, and tether force. Our analysis showed that these parameters are sensitive to both the contour and persistence length of cargo. While the velocity of two couple motors is decreased compared to a single motor (from 531 ± 251 nm/s to as low as 318 ± 287 nm/s), the run length (716 ± 563 nm for a single motor) decreased for short, rigid tethers (to as low as 377 ± 187 μm) and increased for long, flexible tethers (to as high as 1.74 ± 1.50 μm). The sensitivity of processive properties to tether rigidity (persistence length) was greatest for short tethers, which caused the motors to exhibit close, yet anti-cooperative coordination. Motors coupled by longer tethers stepped more independently regardless of tether rigidity. Therefore, the properties of the cargo or linkage must play an essential role in motor-motor communication and cargo transport.     

On the use of in vivo cargo velocity as a biophysical marker

Molecular motors move many intracellular cargos along microtubules. Recently, it has been hypothesized that in vivo cargo velocity can be used to determine the number of engaged motors. We use theoretical and experimental approaches to investigate these assertions, and find that this hypothesis is inconsistent with previously described motor behavior, surveyed and re-analyzed in this paper. Studying lipid droplet motion in Drosophila embryos, we compare transport in a mutant, Delta(halo), with that in wild-type embryos. The minus-end moving cargos in the mutant appear to be driven by more motors (based on in vivo stall force observations). Periods of minus-end motion are indeed longer than in wild-type embryos but the corresponding velocities are not higher. We conclude that velocity is not a definitive read-out of the number of motors propelling a cargo.     

Motor proteins: kinesin can replace Myosin

Directional transport of specific cargos is tuned to specific molecular motors and specific cytoskeletal tracks. Myosin V transports its cargo on actin cables, whereas kinesin or dynein transport their cargo on microtubules. A recent study shows that an engineered kinesin can substitute for myosin V and its cargo-specific transport and subsequent cellular functions.     

Effect of fuel concentration and force on collective transport by a team of dynein motors

Motor proteins are essential components of intracellular transport inside eukaryotic cells. These protein molecules use chemical energy obtained from hydrolysis of ATP to produce mechanical forces required for transporting cargos inside cells, from one location to another, in a directed manner. Of these motors, cytoplasmic dynein is structurally more complex than other motor proteins involved in intracellular transport, as it shows force and fuel (ATP) concentration dependent step‐size. Cytoplasmic dynein motors are known to work in a team during cargo transport and force generation. Here, we use a complete Monte‐Carlo model of single dynein constrained by in vitro experiments, which includes the effect of both force and ATP on stepping as well as detachment of motors under force. We then use our complete Monte‐Carlo model of single dynein motor to understand collective cargo transport by a team of dynein motors, such as dependence of cargo travel distance and velocity on applied force and fuel concentration. In our model, cargos pulled by a team of dynein motors do not detach rapidly under higher forces, confirming the experimental observation of longer persistence time of dynein team on microtubule under higher forces.     

Assessing the Impact of Electrostatic Drag on Processive Molecular Motor Transport

The bidirectional movement of intracellular cargo is usually described as a tug-of-war among opposite-directed families of molecular motors. While tug-of-war models have enjoyed some success, recent evidence suggests underlying motor interactions are more complex than previously understood. For example, these tug-of-war models fail to predict the counterintuitive phenomenon that inhibiting one family of motors can decrease the functionality of opposite-directed transport. In this paper, we use a stochastic differential equations modeling framework to explore one proposed physical mechanism, called microtubule tethering, that could play a role in this “co-dependence” among antagonistic motors. This hypothesis includes the possibility of a trade-off: weakly bound trailing molecular motors can serve as tethers for cargoes and processing motors, thereby enhancing motor–cargo run lengths along microtubules; however, this introduces a cost of processing at a lower mean velocity. By computing the small- and large-time mean-squared displacement of our theoretical model and comparing our results to experimental observations of dynein and its “helper protein” dynactin, we find some supporting evidence for microtubule tethering interactions. We extrapolate these findings to predict how dynein–dynactin might interact with the opposite-directed kinesin motors and introduce a criterion for when the trade-off is beneficial in simple systems.     

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.     

Bidirectional Transport by Molecular Motors: Enhanced Processivity and Response to External Forces

Intracellular transport along cytoskeletal filaments is often mediated by two teams of molecular motors that pull on the same cargo and move in opposite directions along the filaments. We have recently shown theoretically that this bidirectional transport can be understood as a stochastic tug-of-war between the two motor teams. Here, we further develop our theory to investigate the experimentally accessible dynamic behavior of cargos transported by strong motors such as kinesin-1 or cytoplasmic dynein. By studying the run and binding times of such a cargo, we show that the properties of biological motors, such as the large ratio of stall/detachment force and the small ratio of superstall backward/forward velocity, are favorable for bidirectional cargo transport, leading to fast motion and enhanced diffusion. In addition, cargo processivity is shown to be strongly enhanced by transport via several molecular motors even if these motors are engaged in a tug-of-war. Finally, we study the motility of a bidirectional cargo under force. Frictional forces arising, e.g., from the viscous cytoplasm, lead to peaks in the velocity distribution, while external forces as exerted, e.g., by an optical trap, lead to hysteresis effects. Our results, in particular our explicit expressions for the cargo binding time and the distance of the peaks in the velocity relation under friction, are directly accessible to in vitro as well as in vivo experiments.     

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.     

Motor Dynamics Underlying Cargo Transport by Pairs of Kinesin-1 and Kinesin-3 Motors

Intracellular cargo transport by kinesin family motor proteins is crucial for many cellular processes, particularly vesicle transport in axons and dendrites. In a number of cases, the transport of specific cargo is carried out by two classes of kinesins that move at different speeds and thus compete during transport. Despite advances in single-molecule characterization and modeling approaches, many questions remain regarding the effect of intermotor tension on motor attachment/reattachment rates during cooperative multimotor transport. To understand the motor dynamics underlying multimotor transport, we analyzed the complexes of kinesin-1 and kinesin-3 motors attached through protein scaffolds moving on immobilized microtubules in vitro. To interpret the observed behavior, simulations were carried out using a model that incorporated motor stepping, attachment/detachment rates, and intermotor force generation. In single-molecule experiments, isolated kinesin-3 motors moved twofold faster and had threefold higher landing rates than kinesin-1. When the positively charged loop 12 of kinesin-3 was swapped with that of kinesin-1, the landing rates reversed, indicating that this “K-loop” is a key determinant of the motor reattachment rate. In contrast, swapping loop 12 had negligible effects on motor velocities. Two-motor complexes containing one kinesin-1 and one kinesin-3 moved at different speeds depending on the identity of their loop 12, indicating the importance of the motor reattachment rate on the cotransport speed. Simulations of these loop-swapped motors using experimentally derived motor parameters were able to reproduce the experimental results and identify best fit parameters for the motor reattachment rates for this geometry. Simulation results also supported previous work, suggesting that kinesin-3 microtubule detachment is very sensitive to load. Overall, the simulations demonstrate that the transport behavior of cargo carried by pairs of kinesin-1 and -3 motors are determined by three properties that differ between these two families: the unloaded velocity, the load dependence of detachment, and the motor reattachment rate.     

Transport Properties of Melanosomes along Microtubules Interpreted by a Tug-of-War Model with Loose Mechanical Coupling

In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent cargo-motor linkers and stepping motion for the motors. It has been recently proposed that the stiffness of the motor plays an important role when multiple motors collectively transport a cargo. Therefore, we considered in our model the recently reported values for the stiffness of the cargo-motor linker determined in living cells (～0.01 pN/nm, [1]) which is significantly lower than the motor stiffness obtained in in vitro assays and used in previous studies. Our model could reproduce the multimodal velocity distributions and typical trajectory characteristics including the properties of the reversions in the overall direction of motion observed during melanosome transport along microtubules in Xenopus laevis melanophores. Moreover, we explored the contribution of the different motility states of the cargo-motor system to the different modes of the velocity distributions and could identify the microscopic mechanisms of transport leading to trajectories compatible with those observed in living cells. Finally, by changing the attachment and detachment rates, the model could reproduce the different velocity distributions observed during melanosome transport along microtubules in Xenopus laevis melanophores stimulated for aggregation and dispersion. Our analysis suggests that active tug-of-war processes with loose mechanical coupling can account for several aspects of cargo transport along microtubules in living cells.     

How molecular motors are arranged on a cargo is important for vesicular transport

The spatial organization of the cell depends upon intracellular trafficking of cargos hauled along microtubules and actin filaments by the molecular motor proteins kinesin, dynein, and myosin. Although much is known about how single motors function, there is significant evidence that cargos in vivo are carried by multiple motors. While some aspects of multiple motor function have received attention, how the cargo itself--and motor organization on the cargo--affects transport has not been considered. To address this, we have developed a three-dimensional Monte Carlo simulation of motors transporting a spherical cargo, subject to thermal fluctuations that produce both rotational and translational diffusion. We found that these fluctuations could exert a load on the motor(s), significantly decreasing the mean travel distance and velocity of large cargos, especially at large viscosities. In addition, the presence of the cargo could dramatically help the motor to bind productively to the microtubule: the relatively slow translational and rotational diffusion of moderately sized cargos gave the motors ample opportunity to bind to a microtubule before the motor/cargo ensemble diffuses out of range of that microtubule. For rapidly diffusing cargos, the probability of their binding to a microtubule was high if there were nearby microtubules that they could easily reach by translational diffusion. Our simulations found that one reason why motors may be approximately 100 nm long is to improve their 'on' rates when attached to comparably sized cargos. Finally, our results suggested that to efficiently regulate the number of active motors, motors should be clustered together rather than spread randomly over the surface of the cargo. While our simulation uses the specific parameters for kinesin, these effects result from generic properties of the motors, cargos, and filaments, so they should apply to other motors as well.     

Engineered Tug‐of‐War Between Kinesin and Dynein Controls Direction of Microtubule Based Transport In Vivo

Bidirectional transport of membrane organelles along microtubules (MTs) is driven by plus‐end directed kinesins and minus‐end directed dynein bound to the same cargo. Activities of opposing MT motors produce bidirectional movement of membrane organelles and cytoplasmic particles along MT transport tracks. Directionality of MT‐based transport might be controlled by a protein complex that determines which motor type is active at any given moment of time, or determined by the outcome of a tug‐of‐war between MT motors dragging cargo organelles in opposite directions. However, evidence in support of each mechanisms of regulation is based mostly on the results of theoretical analyses or indirect experimental data. Here, we test whether the direction of movement of membrane organelles in vivo can be controlled by the tug‐of‐war between opposing MT motors alone, by attaching a large number of kinesin‐1 motors to organelles transported by dynein to minus‐ends of MTs. We find that recruitment of kinesin significantly reduces the length and velocity of minus‐end‐directed dynein‐dependent MT runs, leading to a reversal of the overall direction of dynein‐driven organelles in vivo. Therefore, in the absence of external regulators tug‐of‐war between opposing MT motors alone is sufficient to determine the directionality of MT transport in vivo.      

Bidirectional transport of organelles: unity and struggle of opposing motors

Bidirectional transport along microtubules is ensured by opposing motor proteins: cytoplasmic dynein that drives cargo to the minus-ends and various kinesins that generally move to the plus-ends of microtubules. Regulation of motor proteins that are simultaneously bound to the same organelle is required to maintain directional transport and prevent pausing of cargo pulled away by motors of opposite polarity. Debates of the recent decade have been focused on two possible mechanisms of such regulation: (i) coordination, which implies that only one type of motors is active at a given time, and (ii) tug-of-war, which assumes that both motors are active at the same time and that direction of transport depends on the outcome of motor's confrontation. The initial idea of coordination has been challenged by observations of simultaneous activity of plus- and minus-end-directed motors applied to the same cargo. Analysis of the available data indicates that coordination and tug-of-war theories rather complement than contradict each other: cargo interacts with two teams of active motors, the resulting direction and the winner team are determined by coordination complexes, but the activity of the loser team is never completely inhibited and remains at some background level. Such persisting activity might enhance the overall efficiency of transport by increasing processivity or helping to overcome the obstacles on microtubule track.     

Filament-Filament Switching Can Be Regulated by Separation Between Filaments Together with Cargo Motor Number

How intracellular transport controls the probability that cargos switch at intersections between filaments is not well understood. In one hypothesis some motors on the cargo attach to one filament while others attach to the intersecting filament, and the ensuing tug-of-war determines which filament is chosen. We investigate this hypothesis using 3D computer simulations, and discover that switching at intersections increases with the number of motors on the cargo, but is not strongly dependent on motor number when the filaments touch. Thus, simply controlling the number of active motors on the cargo cannot account for in vivo observations that found reduced switching with increasing motor number, suggesting additional mechanisms of regulation. We use simulations to show that one possible way to regulate switching is by simultaneously adjusting the separation between planes containing the crossing filaments and the total number of active motors on the cargo. Heretofore, the effect of filament-filament separation on switching has been unexplored. We find that the switching probability decreases with increasing filament separation. This effect is particularly strong for cargos with only a modest number of motors. As the filament separation increases past the maximum head-to-head distance of the motor, individual motors walking along a filament will be unable to reach the intersecting filament. Thus, any switching requires that other motors on the cargo attach to the intersecting filament and haul the cargo along it, while motor(s) engaged on the original filament detach. Further, if the filament separation is large enough, the cargo can have difficulty proceeding along the initial filament because the engaged motors can walk underneath the intersecting filament, but the cargo itself cannot fit between the filaments. Thus, the cargo either detaches entirely from the original filament, or must dip to the side of the initial filament and then pass below the crossing filament.     

Load‐dependent detachment kinetics plays a key role in bidirectional cargo transport by kinesin and dynein

Bidirectional cargo transport along microtubules is carried out by opposing teams of kinesin and dynein motors. Despite considerable study, the factors that determine whether these competing teams achieve net anterograde or retrograde transport in cells remain unclear. The goal of this work is to use stochastic simulations of bidirectional transport to determine the motor properties that most strongly determine overall cargo velocity and directionality. Simulations were carried out based on published optical tweezer characterization of kinesin‐1 and kinesin‐2, and for available data for cytoplasmic dynein and the dynein‐dynactin‐BicD2 (DDB) complex. By varying dynein parameters and analyzing cargo trajectories, we find that net cargo transport is predicted to depend minimally on the dynein stall force, but strongly on dynein load‐dependent detachment kinetics. In simulations, dynein is dominated by kinesin‐1, but DDB and kinesin‐1 are evenly matched, recapitulating recent experimental work. Kinesin‐2 competes less well against dynein and DDB, and overall, load‐dependent motor detachment is the property that most determines a motor's ability to compete in bidirectional transport. It follows that the most effective intracellular regulators of bidirectional transport are predicted to be those that alter motor detachment kinetics rather than motor velocity or stall force.      

CRMP-2 directly binds to cytoplasmic dynein and interferes with its activity

The active transport of proteins and organelles is critical for cellular organization and function in eukaryotic cells. A substantial portion of long-distance transport depends on the opposite polarity of the kinesin and dynein family molecular motors to move cargo along microtubules. It is increasingly clear that many cargo molecules are moved bi-directionally by both sets of motors; however, the regulatory mechanism that determines the directionality of transport remains unclear. We previously reported that collapsin response mediator protein-2 (CRMP-2) played key roles in axon elongation and neuronal polarization. CRMP-2 was also found to associate with the anterograde motor protein Kinesin-1 and was transported with other cargoes toward the axon terminal. In this study, we investigated the association of CRMP-2 with a retrograde motor protein, cytoplasmic dynein. Immunoprecipitation assays showed that CRMP-2 interacted with cytoplasmic dynein heavy chain. Dynein heavy chain directly bound to the N-terminus of CRMP-2, which is the distinct side of CRMP-2's kinesin light chain-binding region. Furthermore, over-expression of the dynein-binding fragments of CRMP-2 prevented dynein-driven microtubule transport in COS-7 cells. Given that CRMP-2 is a key regulator of axon elongation, this interference with cytoplasmic dynein function by CRMP-2 might have an important role in axon formation, and neuronal development.     

A Biophysical Analysis of Mitochondrial Movement: Differences Between Transport in Neuronal Cell Bodies Versus Processes

There is an increasing interest in factors that can impede cargo transport by molecular motors inside the cell. Although potentially relevant (Yi JY, Ori‐McKenney KM, McKenney RJ, Vershinin M, Gross SP, Vallee RB. High‐resolution imaging reveals indirect coordination of opposite motors and a role for LIS1 in high‐load axonal transport. J Cell Biol 2011;195:193–201), the importance of cargo size and subcellular location has received relatively little attention. Here we address these questions taking advantage of the fact that mitochondria – a common cargo – in Drosophila neurons exhibit a wide distribution of sizes. In addition, the mitochondria can be genetically marked with green fluorescent protein (GFP) making it possible to visualize and compare their movement in the cell bodies and in the processes of living cells. Using total internal reflection microscopy coupled with particle tracking and analysis, we quantified the transport properties of GFP‐positive mitochondria as a function of their size and location. In neuronal cell bodies, we find little evidence for significant opposition to motion, consistent with a previous study on lipid droplets (Shubeita GT, Tran SL, Xu J, Vershinin M, Cermelli S, Cotton SL, Welte MA, Gross SP. Consequences of motor copy number on the intracellular transport of kinesin‐1‐driven lipid droplets. Cell 2008;135:1098–1107). However, in the processes, we observe an inverse relationship between the mitochondrial size and velocity and the run distances. This can be ameliorated via hypotonic treatment to increase process size, suggesting that motor‐mediated movement is impeded in this more‐confined environment. Interestingly, we also observe local mitochondrial accumulations in processes but not in cell bodies. Such accumulations do not completely block the transport but do increase the probability of mitochondria–mitochondria interactions. They are thus particularly interesting in relation to mitochondrial exchange of elements.