Cooperative cargo transport by several molecular motors

Effectiveness of a dynein team in a tug of war helped by reduced load sensitivity of detachment: evidence from the study of bidirectional endosome transport in D. discoideum

Bidirectional cargo transport by molecular motors in cells is a complex phenomenon in which the cargo (usually a vesicle) alternately moves in retrograde and anterograde directions. In this case, teams of oppositely pulling motors (e.g., kinesin and dynein) bind to the cargo, simultaneously, and 'coordinate' their activity such that the motion consists of spells of positively and negatively directed segments, separated by pauses of varying duration. A set of recent experiments have analyzed the bidirectional motion of endosomes in the amoeba D. discoideum in detail. It was found that in between directional switches, a team of five to six dyneins stall a cargo against a stronger kinesin in a tug of war, which lasts for almost a second. As the mean detachment time of a kinesin under its stall load was also observed to be ∼1 s, we infer that the collective detachment time of the dynein assembly must also be similar. Here, we analyze this inference from a modeling perspective, using experimentally measured single-molecule parameters as inputs. We find that the commonly assumed exponential load-dependent detachment rate is inconsistent with observations, as it predicts that a five-dynein assembly will detach under its combined stall load in less than a hundredth of a second. A modified model where the load-dependent unbinding rate is assumed to saturate at stall-force level for super-stall loads gives results which are in agreement with experimental data. Our analysis suggests that the load-dependent detachment of a dynein in a team is qualitatively different at sub-stall and super-stall loads, a conclusion which is likely to have implications in other situations involving collective effects of many motors.

Collective dynamics of elastically coupled myosin V motors

Characterization of the collective behaviors of different classes of processive motor proteins has become increasingly important to understand various intracellular trafficking and transport processes. This work examines the dynamics of structurally-defined motor complexes containing two myosin Va (myoVa) motors that are linked together via a molecular scaffold formed from a single duplex of DNA. Dynamic changes in the filament-bound configuration of these complexes due to motor binding, stepping, and detachment were monitored by tracking the positions of different color quantum dots that report the position of one head of each myoVa motor on actin. As in studies of multiple kinesins, the run lengths produced by two myosins are only slightly larger than those of single motor molecules. This suggests that internal strain within the complexes, due to asynchronous motor stepping and the resultant stretching of motor linkages, yields net negative cooperative behaviors. In contrast to multiple kinesins, multiple myosin complexes move with appreciably lower velocities than a single-myosin molecule. Although similar trends are predicted by a discrete state stochastic model of collective motor dynamics, these analyses also suggest that multiple myosin velocities and run lengths depend on both the compliance and the effective size of their cargo. Moreover, it is proposed that this unique collective behavior occurs because the large step size and relatively small stalling force of myoVa leads to a high sensitivity of motor stepping rates to strain.

Molecular spiders on a plane

Synthetic biomolecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counterintuitive behavior-the more spiders are slowed down on unvisited sites, the more motile they become.

Distinct transport regimes for two elastically coupled molecular motors

Cooperative cargo transport by two molecular motors involves an elastic motor-motor coupling, which can reduce the motors' velocity and/or enhance their unbinding from the filament. We show theoretically that these interference effects lead, in general, to four distinct transport regimes. In addition to a weak coupling regime, kinesin and dynein motors are found to exhibit a strong coupling and an enhanced unbinding regime, whereas myosin motors are predicted to attain a reduced velocity regime. All of these regimes, which we derive by explicit calculations and general time scale arguments, can be explored experimentally by varying the elastic coupling strength.

Stochastic force generation by small ensembles of myosin II motors

Forces in the actin cytoskeleton are generated by small groups of nonprocessive myosin II motors for which stochastic effects are highly relevant. Using a cross-bridge model with the assumptions of fast power-stroke kinetics and equal load sharing between equivalent states, we derive a one-step master equation for the activity of a finite-sized ensemble of mechanically coupled myosin II motors. For constant external load, this approach yields analytical results for duty ratio and force-velocity relation as a function of ensemble size. We find that stochastic effects cannot be neglected for ensemble sizes below 15. The one-step master equation can be used also for efficient computer simulations with linear elastic external load and reveals the sequence of buildup of force and ensemble rupture that is characteristic for reconstituted actomyosin contractility.

Molecular crowding creates traffic jams of kinesin motors on microtubules

Despite the crowdedness of the interior of cells, microtubule-based motor proteins are able to deliver cargoes rapidly and reliably throughout the cytoplasm. We hypothesize that motor proteins may be adapted to operate in crowded environments by having molecular properties that prevent them from forming traffic jams. To test this hypothesis, we reconstituted high-density traffic of purified kinesin-8 motor protein, a highly processive motor with long end-residency time, along microtubules in a total internal-reflection fluorescence microscopy assay. We found that traffic jams, characterized by an abrupt increase in the density of motors with an associated abrupt decrease in motor speed, form even in the absence of other obstructing proteins. To determine the molecular properties that lead to jamming, we altered the concentration of motors, their processivity, and their rate of dissociation from microtubule ends. Traffic jams occurred when the motor density exceeded a critical value (density-induced jams) or when motor dissociation from the microtubule ends was so slow that it resulted in a pileup (bottleneck-induced jams). Through comparison of our experimental results with theoretical models and stochastic simulations, we characterized in detail under which conditions density- and bottleneck-induced traffic jams form or do not form. Our results indicate that transport kinesins, such as kinesin-1, may be evolutionarily adapted to avoid the formation of traffic jams by moving only with moderate processivity and dissociating rapidly from microtubule ends.

Asymptotic analysis of microtubule-based transport by multiple identical molecular motors

We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: (1) highly viscous in vivo transport and (2) dynamics when multiple identical motors are attached to the cargo and microtubule.

A stochastic model of kinetochore-microtubule attachment accurately describes fission yeast chromosome segregation

In fission yeast, erroneous attachments of spindle microtubules to kinetochores are frequent in early mitosis. Most are corrected before anaphase onset by a mechanism involving the protein kinase Aurora B, which destabilizes kinetochore microtubules (ktMTs) in the absence of tension between sister chromatids. In this paper, we describe a minimal mathematical model of fission yeast chromosome segregation based on the stochastic attachment and detachment of ktMTs. The model accurately reproduces the timing of correct chromosome biorientation and segregation seen in fission yeast. Prevention of attachment defects requires both appropriate kinetochore orientation and an Aurora B-like activity. The model also reproduces abnormal chromosome segregation behavior (caused by, for example, inhibition of Aurora B). It predicts that, in metaphase, merotelic attachment is prevented by a kinetochore orientation effect and corrected by an Aurora B-like activity, whereas in anaphase, it is corrected through unbalanced forces applied to the kinetochore. These unbalanced forces are sufficient to prevent aneuploidy.

Cargo distributions differentiate pathological axonal transport impairments

Axonal transport is an essential process in neurons, analogous to shipping goods, by which energetic and cellular building supplies are carried downstream (anterogradely) and wastes are carried upstream (retrogradely) by molecular motors, which act as cargo porters. Impairments in axonal transport have been linked to devastating and often lethal neurodegenerative diseases, such as Amyotrophic Lateral Sclerosis, Huntington's, and Alzheimer's. Axonal transport impairment types include a decrease in available motors for cargo transport (motor depletion), the presence of defective or non-functional motors (motor dilution), and the presence of increased or larger cargos (protein aggregation). An impediment to potential treatment identification has been the inability to determine what type(s) of axonal transport impairment candidates that could be present in a given disease. In this study, we utilize a computational model and common axonal transport experimental metrics to reveal the axonal transport impairment general characteristics or "signatures" that result from three general defect types of motor depletion, motor dilution, and protein aggregation. Our results not only provide a means to discern these general impairments types, they also reveal key dynamic and emergent features of axonal transport, which potentially underlie multiple impairment types. The identified characteristics, as well as the analytical method, can be used to help elucidate the axonal transport impairments observed in experimental and clinical data. For example, using the model-predicted defect signatures, we identify the defect candidates, which are most likely to be responsible for the axonal transport impairments in the G93A SOD1 mouse model of ALS.

Long-range transport of giant vesicles along microtubule networks

We report on a minimal system to mimic intracellular transport of membrane-bounded, vesicular cargo. In a cell-free assay, purified kinesin-1 motor proteins were directly anchored to the membrane of giant unilamellar vesicles, and their movement studied along two-dimensional microtubule networks. Motion-tracking of vesicles with diameters of 1-3 μm revealed traveling distances up to the millimeter range. The transport velocities were identical to velocities of cargo-free motors. Using total internal reflection fluorescence (TIRF) microscopy, we were able to estimate the number of GFP-labeled motors involved in the transport of a single vesicle. We found that the vesicles were transported by the cooperative activity of typically 5-10 motor molecules. The presented assay is expected to open up further applications in the field of synthetic biology, aiming at the in vitro reconstitution of sub-cellular multi-motor transport systems. It may also find applications in bionanotechnology, where the controlled long-range transport of artificial cargo is a promising means to advance current lab-on-a-chip systems.

Cooperative responses of multiple kinesins to variable and constant loads

Microtubule-dependent transport is most often driven by collections of kinesins and dyneins that function in either a concerted fashion or antagonistically. Several lines of evidence suggest that cargo transport may not be influenced appreciably by the combined action of multiple kinesins. Yet, as in previous optical trapping experiments, the forces imposed on cargos will vary spatially and temporally in cells depending on a number of local environmental factors, and the influence of these conditions has been largely overlooked. Here, we characterize the dynamics of structurally defined complexes containing multiple kinesins under the controlled loads of an optical force clamp. While demonstrating that there are generic kinetic barriers that restrict the ability of multiple kinesins to cooperate productively, the spatial and temporal properties of applied loads is found to play an important role in the collective dynamics of multiple motor systems. We propose this dependence has implications for intracellular transport processes, especially for bidirectional transport.

Tug of war of molecular motors: the effects of uneven load sharing

We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature: a quite widespread model which assumes equal force sharing, here referred to as the mean field model (MFM), and a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations, the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be the consequences of the load sharing assumptions and can be interpreted in terms of the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness, while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin-1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins.

COOPERATIVE TRANSPORT BY SMALL TEAMS OF MOLECULAR MOTORS

Molecular motors power directed transport of cargoes within cells. Even if a single motor is sufficient to transport a cargo, motors often cooperate in small teams. We discuss the cooperative cargo transport by several motors theoretically and explore some of its properties. In particular we emphasize how motor teams can drag cargoes through a viscous environment.

ACTIVE BIO-SYSTEMS: FROM SINGLE MOTOR MOLECULES TO COOPERATIVE CARGO TRANSPORT

Living cells contain a large number of molecular motors that convert the chemical energy released from nucleotide hydrolysis into mechanical work. This review focusses on stepping motors that move along cytoskeletal filaments. The behavior of these motors involves three distinct nonequilibrium processes that cover a wide range of length and time scales: (i) Directed stepping of single motors bound to a filament; (ii) Composite motor walks of single motors consisting of directed stepping interrupted by diffusive motion; and (iii) Cooperative transport by teams of several motors. On the molecular scale, the energy conversion of these motors leads to single steps along the filaments with a step size of about 10 nm. The corresponding chemomechanical coupling is governed by several distinct motor cycles, which represent the dominant pathways for different values of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses the direction of its motion. Because of thermal noise, the stepping motors unbind from the filaments after a certain run time and run length. For kinesin, the run time is about 1 s and the run length is about 1 μm for high ATP concentration and low load force. On length scales that are large compared to the run length, a single motor undergoes composite walks consisting of directed stepping interrupted by diffusive motion. The relative importance of bound and unbound motor states depends on the binding and unbinding rates of the motors. The effective transport velocity and diffusion coefficient of the motors are determined by the geometry of the compartments, in which the motors move. The effective diffusion coefficient can be enhanced by several orders of magnitude if the motors undergo active diffusion by interacting with certain filament patterns. In vivo, stepping motors are responsible for the transport of vesicles and other types of intracellular cargo particles that shuttle between the different cell compartments. This cargo transport is usually performed by teams of motors. If all motors belong to the same molecular species, the cooperative action of the motors leads to uni-directional transport with a strongly increased run length and to a characteristic force dependence of the velocity distributions. If two antagonistic species of motors pull on the cargo, they perform a stochastic tug-of-war, which is characterized by a subtle force balance between the two motor teams and leads to seven distinct patterns of uni- and bi-directional transport. So far, all experimental observations on bi-directional transport are consistent with such a tug-of-war. Finally, the traffic of interacting motors is also briefly discussed. Depending on their mutual interactions and the compartment geometry, the motors form various spatio-temporal patterns such as traffic jams, and undergo nonequilibrium phase transitions between such transport patterns.

Mechanical stochastic tug-of-war models cannot explain bidirectional lipid-droplet transport

Intracellular transport via the microtubule motors kinesin and dynein plays an important role in maintaining cell structure and function. Often, multiple kinesin or dynein motors move the same cargo. Their collective function depends critically on the single motors' detachment kinetics under load, which we experimentally measure here. This experimental constraint--combined with other experimentally determined parameters--is then incorporated into theoretical stochastic and mean-field models. Comparison of modeling results and in vitro data shows good agreement for the stochastic, but not mean-field, model. Many cargos in vivo move bidirectionally, frequently reversing course. Because both kinesin and dynein are present on the cargos, one popular hypothesis explaining the frequent reversals is that the opposite-polarity motors engage in unregulated stochastic tugs-of-war. Then, the cargos' motion can be explained entirely by the outcome of these opposite-motor competitions. Here, we use fully calibrated stochastic and mean-field models to test the tug-of-war hypothesis. Neither model agrees well with our in vivo data, suggesting that, in addition to inevitable tugs-of-war between opposite motors, there is an additional level of regulation not included in the models.

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.

Co-operative transport by molecular motors

Intracellular transport is often driven co-operatively by several molecular motors, which may belong to one or several motor species. Understanding how these motors interact and what co-ordinates and regulates their movements is a central problem in studies of intracellular transport. A general theoretical framework for the analysis of such transport processes is described, which enables us to explain the behaviour of intracellular cargos by the transport properties of individual motors and their interactions. We review recent advances in the theoretical description of motor co-operativity and discuss related experimental results.

Conformational changes, diffusion and collective behavior in monomeric kinesin-based motility

Molecular motors convert chemical energy into mechanical motion and power the transport of material within living cells; the motion of a motor is thought to be influenced by stochastic chemical state transitions of the molecule as well as intramolecular diffusion of one motor head seeking the next binding site. Existing models for the motility of single-headed monomeric motors that map the system to a simplified two-state Brownian ratchet have some predictive power, but in general are unable to elucidate the contributions of different molecular level processes to the overall effective parameters. In this work, we build a detailed molecular level model of monomeric kinesin motility that naturally incorporates conformational changes (power strokes) and biased diffusion. Our results predict that mean velocity is most sensitive to the power stroke size, while run length distribution is sensitive primarily to the strength of the microtubule bias potential with a weak dependence on power stroke that can be tuned by the strength of an applied load. In addition, we demonstrate that motor pairs attached to the same cargo can cooperatively function to increase motility in both the plus- and minus-end directions. These findings illustrate the importance of a detailed mechanochemical model for dissecting the contributions of microscopic parameters to monomeric kinesin dynamics.

Kinesin assembly and movement in cells

Long-distance transport in eukaryotic cells is driven by molecular motors that move along microtubule tracks. Molecular motors of the kinesin superfamily contain a kinesin motor domain attached to family-specific sequences for cargo binding, regulation, and oligomerization. The biochemical and biophysical properties of the kinesin motor domain have been widely studied, yet little is known about how kinesin motors work in the complex cellular environment. We discuss recent studies on the three major families involved in intracellular transport (kinesin-1, kinesin-2, and kinesin-3) that have begun to bridge the gap in knowledge between the in vitro and in vivo behaviors of kinesin motors. These studies have increased our understanding of how kinesin subunits assemble to produce a functional motor, how kinesin motors are affected by biochemical cues and obstacles present on cellular microtubules, and how multiple motors on a cargo surface can work collectively for increased force production and travel distance.

Time-dependent motor properties of multipedal molecular spiders

Molecular spiders are synthetic biomolecular walkers that use the asymmetry resulting from cleavage of their tracks to bias the direction of their stepping motion. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the dependence of the biased motion of molecular spiders, along with binding time and processivity, on tunable experimental parameters, such as number of legs, span between the legs, and unbinding rate of a leg from a substrate site. We find that an increase in the number of legs increases the spiders' processivity and binding time but not their mean velocity. However, we can increase the mean velocity of spiders with simultaneous tuning of the span and the unbinding rate of a spider leg from a substrate site. To study the efficiency of molecular spiders, we introduce a time-dependent expression for the thermodynamic efficiency of a molecular motor, allowing us to account for the behavior of spider populations as a function of time. Based on this definition, we find that spiders exhibit transient motor function over time scales of many hours and have a maximum efficiency on the order of 1%, weak compared to other types of molecular motors.

Kinesin-3 and dynein cooperate in long-range retrograde endosome motility along a nonuniform microtubule array

The polarity of microtubules (MTs) determines the motors for intracellular motility, with kinesins moving to plus ends and dynein to minus ends. In elongated cells of Ustilago maydis, dynein is thought to move early endosomes (EEs) toward the septum (retrograde), whereas kinesin-3 transports them to the growing cell tip (anterograde). Occasionally, EEs run up to 90 μm in one direction. The underlying MT array consists of unipolar MTs at both cell ends and antipolar bundles in the middle region of the cell. Cytoplasmic MT-organizing centers, labeled with a γ-tubulin ring complex protein, are distributed along the antipolar MTs but are absent from the unipolar regions. Dynein colocalizes with EEs for 10-20 μm after they have left the cell tip. Inactivation of temperature-sensitive dynein abolishes EE motility within the unipolar MT array, whereas long-range motility is not impaired. In contrast, kinesin-3 is continuously present, and its inactivation stops long-range EE motility. This indicates that both motors participate in EE motility, with dynein transporting the organelles through the unipolar MT array near the cell ends, and kinesin-3 taking over at the beginning of the medial antipolar MT array. The cooperation of both motors mediates EE movements over the length of the entire cell.

Force-velocity relationship for multiple kinesin motors pulling a magnetic bead

Although the velocity of single kinesin motors against an opposing force F of 0-10 pN is well known, the behavior of multiple kinesin motors working to overcome a larger load is still poorly understood. We have carried out gliding assays in which 3-7 Drosophila kinesin-1 motors moved a microtubule at 200-700 μm/s against a 0-31 pN load at saturating [ATP]. The load F was generated by applying a spatially uniform magnetic field gradient to a superparamagnetic bead attached to the (+) end of the microtubule. When F was scaled by the average number of motors [Symbol: see text]n[Symbol: see text], the force-velocity relationship for multiple motors was similar to the force-velocity relationship for a single motor, supporting a minimal load-sharing model. The velocity distribution at low load has a single mode consistent with rapid fluctuations of n. However, against a load of 2.5-4.7 pN/motor, additional modes appeared at lower velocity. These observations support the Klumpp-Lipowsky model of multimotor transport [Proc Natl Acad Sci USA 102. 17284-17289 (2005)].

Modelling active transport in Drosophila unipolar motor neurons

This paper develops a model for simulating organelle transport in Drosophila unipolar motor neurons. The paper is motivated by a recent experimental investigation by Stone et al. (Microtubules have opposite orientation in axons and dendrites of Drosophila neurons. Mol Biol Cell.19:4122-4129) who proposed a map of microtubule (MT) orientation in Drosophila neurons, and explained why dynein mutations selectively impede dendritic growth without having much effect on axonal growth. Two different approaches to modelling the effect of dynein mutations are utilised: one through assuming a reduced average velocity of a dynein mutant motor and the other through assuming its decreased processivity (an increased detachment rate from MTs). Modified Smith-Simmons equations are used for developing a continuum model of the process. Distributions of organelle concentrations as well as distributions of diffusion, motor-driven and total organelle fluxes are simulated.

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.

The spatial organization of living cells depends upon a transportation system consisting of molecular motor proteins that act like porters carrying cargos along filaments that are analogous to roads. The breakdown of this transportation system has been associated with neurodegenerative diseases such as Alzheimer's and Huntington's disease. In living cells, cargos are typically carried by multiple motors. While some aspects of multiple motor function have received attention, how the cargo itself affects transport has not been considered. To address this, we developed a three-dimensional computer simulation of motors transporting a spherical cargo subject to fluctuations produced when small molecules in the intracellular environment buffet the cargo. These fluctuations can cause the cargo to pull on the motors, slowing them down and making them detach from the filament (road). This effect increases as the cargo size and viscosity of the medium increase. We also found that the presence of the cargo helped the motors to bind to a filament before it drifted away. If other filaments were present, then the cargo could bind to one of them. Our results also indicated that it is better to group the motors on the cargo rather than spread them randomly over the surface.

Two kinesins transport cargo primarily via the action of one motor: implications for intracellular transport

The number of microtubule motors attached to vesicles, organelles, and other subcellular commodities is widely believed to influence their motile properties. There is also evidence that cells regulate intracellular transport by tuning the number and/or ratio of motor types on cargos. Yet, the number of motors responsible for cargo motion is not easily characterized, and the extent to which motor copy number affects intracellular transport remains controversial. Here, we examined the load-dependent properties of structurally defined motor assemblies composed of two kinesin-1 molecules. We found that a group of kinesins can produce forces and move with velocities beyond the abilities of single kinesin molecules. However, such capabilities are not typically harnessed by the system. Instead, two-kinesin assemblies adopt a range of microtubule-bound configurations while transporting cargos against an applied load. The binding arrangement of motors on their filament dictates how loads are distributed within the two-motor system, which in turn influences motor-microtubule affinities. Most configurations promote microtubule detachment and prevent both kinesins from contributing to force production. These results imply that cargos will tend to be carried by only a fraction of the total number of kinesins that are available for transport at any given time, and provide an alternative explanation for observations that intracellular transport depends weakly on kinesin number in vivo.

Controlled and stochastic retention concentrates dynein at microtubule ends to keep endosomes on track

Bidirectional transport of early endosomes (EEs) involves microtubules (MTs) and associated motors. In fungi, the dynein/dynactin motor complex concentrates in a comet-like accumulation at MT plus-ends to receive kinesin-3-delivered EEs for retrograde transport. Here, we analyse the loading of endosomes onto dynein by combining live imaging of photoactivated endosomes and fluorescent dynein with mathematical modelling. Using nuclear pores as an internal calibration standard, we show that the dynein comet consists of ∼55 dynein motors. About half of the motors are slowly turned over (T(1/2): ∼98 s) and they are kept at the plus-ends by an active retention mechanism involving an interaction between dynactin and EB1. The other half is more dynamic (T(1/2): ∼10 s) and mathematical modelling suggests that they concentrate at MT ends because of stochastic motor behaviour. When the active retention is impaired by inhibitory peptides, dynein numbers in the comet are reduced to half and ∼10% of the EEs fall off the MT plus-ends. Thus, a combination of stochastic accumulation and active retention forms the dynein comet to ensure capturing of arriving organelles by retrograde motors.

Distinct intracellular vesicle transport mechanisms are selectively modified by spastin and spastin mutations

Spastin is a microtubule severing ATPase that regulates intracellular and axonal transport of vesicles. Intracellular vesicle trafficking was analyzed in differentiated SH-SY5Y-neuroblastoma cells, transfected with spastin wild-type and three spastin mutations (ΔN, K388R, S44L) to investigate spastin-mediated effects on the velocity of vesicles, stained with LysoTracker Red®. The vesicle velocity varied considerably between mutations and detailed analysis revealed up to five distinct velocity classes. Microtubule severing by overexpressed wild-type spastin caused reduced vesicle velocity. S44L and ΔN mutations, which were functionally impaired, showed similar velocities as control cells. K388R-transfected cells exhibited an intermediate velocity profile. The results support the idea that spastin mutations not only alter axonal transport, but in addition regulate intracellular trafficking in the cell soma as well.

Kinesin recycling in stationary membrane tubes

Collections of motors dynamically organize to extract membrane tubes. These tubes grow but often pause or change direction as they traverse an underlying microtubule (MT) network. In vitro, membrane tubes also stall: they stop growing in length despite a large group of motors available at the tip to pull them forward. In these stationary membrane tubes in vitro, we find that clusters of processive kinesin motors form and reach the tip of the tube at regular time intervals. The average times between cluster arrivals depends on the time over which motors depart from the tip, suggesting that motors are recycled toward the tip. Numerical simulations of the motor dynamics in the membrane tube and on the MTs show that the presence of cooperative binding between motors quantitatively accounts for the clustering observed experimentally. Cooperative binding along the length of the MT and a nucleation point at a distance behind the tip define the recycling period. Based on comparison of the numerical results and experimental data, we estimate a cooperative binding probability and concentration regime where the recycling phenomenon occurs.

Cargo transport by several motors

In a cell, organelles and vesicles are usually transported by cooperation of several motor proteins, including plus-end-directed motor kinesin and minus-end-directed motor dynein. In recent years, many biophysical models have been constructed to understand the mechanism of this transport; however, so far, its basic principle has not been completely understood. In this paper, we will present a model that is based on recent experimental results and existing theoretical models. In this model, each motor is regarded as a head-spring system. The head can bind to or detach from the track stochastically, and step forward or backward with a fixed step size L and force-dependent transition rates. The spring connects the head to the cargo tightly. The position of the cargo is determined by the force-balance condition. An obvious characteristic of our model is that the motors interact with each other and do not share the external load equally. Results indicate that the basic properties of the cargo, including its mean velocity and stall force (definitions are given in the text), are greatly affected by the intermotor interaction. Stated simplistically, the mean velocity and (average) stall force decrease with the intermotor interaction. Therefore, in a sense, the intermotor interaction is negative to the cooperate motion of motors. However, if the cargo is pulled by motors from the same species, its (average) stall force is usually larger than that of the single motor; this means that under external load, the velocity of cargo transported by several motors might be higher than the single-motor cases. We can infer from this that the cooperation of motors is beneficial to draw big cargoes, while it is not as beneficial as one might expect to improve motion velocity when the external load is low.

Cooperativity of self-organized Brownian motors pulling on soft cargoes

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

Coupling between motor proteins determines dynamic behaviors of motor protein assemblies

Transport of intracellular cargos by multiple microtubule motor proteins is believed to be a common and significant phenomenon in vivo, yet signatures of the microscopic dynamics of multiple motor systems are only now beginning to be resolved. Understanding these mechanisms largely depends on determining how grouping motors affect their association with microtubules and stepping rates, and hence, cargo run lengths and velocities. We examined this problem using a discrete state transition rate model of collective transport. This model accounts for the structural and mechanical properties in binding/unbinding and stepping transitions between distinct microtubule-bound configurations of a multiple motor system. In agreement with previous experiments that examine the dynamics of two coupled kinesin-1 motors, the energetic costs associated with deformations of mechanical linkages within a multiple motor assembly are found to reduce the system's overall microtubule affinity, producing attenuated mean cargo run lengths compared to cases where motors are assumed to function independently. With our present treatment, this attenuation largely stems from reductions in the microtubule binding rate and occurs even when mechanical coupling between motors is weak. Thus, our model suggests that, at least for a variety of kinesin-dependent transport processes, the net 'gains' obtained by grouping motors together may be smaller than previously expected.

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.

Lattice-gas model for active vesicle transport by molecular motors with opposite polarities

We introduce a multispecies lattice-gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargos being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process to characterize the motion of the interacting cargos, we allow for mass exchange with the environment, input, and output at filament boundaries and focus on the role of interconversion rates and how they affect the directionality of the net cargo transport. We quantify the effect of the various different competing processes in terms of nonequilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation-deposition processes, introduces qualitatively unique features in the phase diagrams. We observe regimes of three-phase coexistence, the possibility of phase re-entrance, and a significant flexibility in how the different phase boundaries shift in response to changes in control parameters. The moving steady-state solutions of this model allows for different possibilities for the spatial distribution of cargo vesicles, ranging from homogeneous distribution of vesicles to polarized distributions, characterized by inhomogeneities or shocks. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe that this minimal model will clarify the understanding of many features of collective vesicle transport, apart from serving as the basis for building more exact quantitative models for vesicle transport relevant to various in vivo situations.

Dynamics of the tug-of-war model for cellular transport

The transport of organelles and other cargoes in living cells has been described by a kinetic tug-of-war model advanced by Müller, Klumpp, and Lipowsky, in which, as a function of time, t, a team of n+ (t)=0,1,⋯,N+ molecular motors may attach a cargo to a filamentous track and pull it towards the plus end in competition with n- (t)=0,1,⋯,N- motors that pull towards the opposite end. In recent work [Y. Zhang, Phys. Rev. E 79, 061918 (2009)] this model was analyzed for N+,N->>1, establishing the existence, depending on the motor parameters and the ratio ν=N+/N-, of system states with either one, two, or three distinct stable stationary modes of motion. Here, adopting a theoretical perspective, we study the parametric and ν dependence of the transitions between these mono-, bi-, or tristable system states and examine their associated trajectories and domains of attraction in the flow space, (n+,n-), of the attached motor numbers. Various sequences of winning, losing, and "stalemate" or close-to-motionless modes are uncovered. When, as realistic, N+ and N- are of order 2 to 10, fluctuations will move the system from one of two or three modes of motion to another mode. An analysis of the associated probability fluxes demonstrates that the mean time between mode-to-mode transitions increases exponentially with N+ and N-. The overall stall force, i.e., the externally imposed load under which the mean cargo velocity vanishes, is similarly elucidated and shown to vary strongly but sublinearly with N+ and N-, as well as depending in a less than transparent manner on other model parameters beyond the stall forces of the individual + and - motors.

Biased transport of elastic cytoskeletal filaments with alternating polarities by molecular motors

We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with nonprocessive myosin motors. The bundle is represented as an elastic chain consisting of monomers with positive and negative polarities. The motion of the bundle is induced by the pulling forces of the underlying motors which stochastically attach to the monomers and, depending on their polarities, pull them in the right or left direction. We demonstrate that perfectly apolar chains consisting of equal numbers of monomers with positive and negative polarities may exhibit biased bidirectional motion with a nonzero drift. This effect is attributed to the elastic tension developed in the chain due to the action of the myosin motors. We also show that as a result of this tension, the attachment probability of the motors is greatly reduced and becomes strongly dependent on the length of the chain.

Motor proteins: kinesins influence each other through load

What happens when two types of kinesin transport the same cargo? Each motor experiences a load coming from the others. These loads are sufficient to explain the emergent properties of the cargo's motion.

LIS1 and NudE induce a persistent dynein force-producing state

Cytoplasmic dynein is responsible for many aspects of cellular and subcellular movement. LIS1, NudE, and NudEL are dynein interactors initially implicated in brain developmental disease but now known to be required in cell migration, nuclear, centrosomal, and microtubule transport, mitosis, and growth cone motility. Identification of a specific role for these proteins in cytoplasmic dynein motor regulation has remained elusive. We find that NudE stably recruits LIS1 to the dynein holoenzyme molecule, where LIS1 interacts with the motor domain during the prepowerstroke state of the dynein crossbridge cycle. NudE abrogates dynein force production, whereas LIS1 alone or with NudE induces a persistent-force dynein state that improves ensemble function of multiple dyneins for transport under high-load conditions. These results likely explain the requirement for LIS1 and NudE in the transport of nuclei, centrosomes, chromosomes, and the microtubule cytoskeleton as well as the particular sensitivity of migrating neurons to reduced LIS1 expression.

Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

Traffic of cytoskeletal motors with disordered attachment rates

Motivated by experimental results on the interplay between molecular motors and tau proteins, we extend lattice-based models of intracellular transport to include a second species of particle which locally influences the motor-filament attachment rate. We consider various exactly solvable limits of a stochastic multiparticle model before focusing on the low-motor-density regime. Here, an approximate treatment based on the random-walk behavior of single motors gives good quantitative agreement with simulation results for the tau dependence of the motor current. Finally, we discuss the possible physiological implications of our results.

Robust transport by multiple motors with nonlinear force-velocity relations and stochastic load sharing

Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force-velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the 'tug-of-war' of the multiple opposing motors.

A nano-needle/microtubule composite gliding on a kinesin-coated surface for target molecule transport

An alternative method of micro/nano-transport has been achieved by using motor proteins. Microtubules on a kinesin-coated surface have potential to act as a nano-transport system. When microtubules are used as carriers, either cargo or cargo linkers are attached on the microtubule surface. Such cargo attachments can significantly affect kinesin motion. To deal with the difficulty caused by molecular attachment to the microtubule surface, the cargo loading and transport mechanism should be separated. In this work, we propose to use micromachined needles as cargo carriers which then can be transported on microtubules. Because of the separation of needle functionalization and transport mechanism, functionalization of the needles can proceed without any effect on the microtubule structure, significantly increasing the possible types of cargo. We have fabricated silicon needles in mass numbers using a simple and effective method and have shown that the microtubule-needle composites are transported without affecting the kinesin activity.

Quality control in single-molecule studies of kinesins and microtubule-associated proteins

Commercial microscopes capable of single-molecule experiments have made it simple for researchers to adopt these powerful techniques. This chapter is meant to help newcomers assess whether their data is of sufficient quality to warrant time-intensive analysis. Two problems can hamper single-molecule experiments: (1) non-specific aggregation of the proteins of interest and (2) detection thresholds from a poor microscope setup. I outline four steps that researchers can take to overcome these problems and convince themselves that they are observing bona fide single molecules.

Clustering of centralspindlin is essential for its accumulation to the central spindle and the midbody

Cytokinesis in animal cells requires the central spindle and midbody, which contain prominent microtubule bundles. Centralspindlin, a heterotetrameric complex consisting of kinesin-6 and RhoGAP (Rho-family GTPase-activating protein) subunits, is essential for the formation of these structures. Centralspindlin becomes precisely localized to the central spindle, where it promotes the equatorial recruitment of important cytokinetic regulators. These include ECT2, the activator of the small GTPase RhoA, which controls cleavage furrow formation and ingression. Centralspindlin's own RhoGAP domain also contributes to furrow ingression. Finally, centralspindlin facilitates recruitment of the chromosome passenger complex and factors that control abscission. Despite the importance of localized accumulation of centralspindlin, the mechanism by which this motor protein complex suddenly concentrates to the center of interpolar microtubule bundles during anaphase is unclear. Here, we show that centralspindlin travels along central spindle microtubules as higher-order clusters. Clustering of centralspindlin is critical for microtubule bundling and motility along microtubules in vitro and for midbody formation in vivo. These data support a positive feedback loop of centralspindlin clustering and microtubule organization that may underlie its distinctive localization during cytokinesis.

Interacting molecular motors: efficiency and work fluctuations

We investigate the model of "reversible ratchet" with interacting particles, presented by us earlier [F. Slanina, EPL 84, 50009 (2008)]. We further clarify the effect of efficiency enhancement due to interaction and show that it is of energetic origin, rather than a consequence of reduced fluctuations. We also show complicated structures emerging in the interaction and density dependence of the current and response function. The fluctuation properties of the work and input energy indicate in detail the far-from-equilibrium nature of the dynamics.

Mechanism of membrane nanotube formation by molecular motors

Membrane nanotubes are ubiquitous in eukaryotic cells due to their involvement in the communication between many different membrane compartments. They are very dynamical structures, which are generally extended along the microtubule network. One possible mechanism of tube formation involves the action of molecular motors, which can generate the necessary force to pull the tubes along the cytoskeleton tracks. However, it has not been possible so far to image in living organisms simultaneously both tube formation and the molecular motors involved in the process. The reasons for this are mainly technological. To overcome these limitations and to elucidate in detail the mechanism of tube formation, many experiments have been developed over the last years in cell-free environments. In the present review, we present the results, which have been obtained in vitro either in cell extracts or with purified and artificial components. In particular, we will focus on a biomimetic system, which involves Giant Unilamellar Vesicles, kinesin-1 motors and microtubules in the presence of ATP. We present both theoretical and experimental results based on fluorescence microscopy that elucidate the dynamics of membrane tube formation, growth and stalling.

Kinesin velocity increases with the number of motors pulling against viscoelastic drag

Although the properties of single kinesin molecular motors are well understood, it is not clear whether multiple motors pulling a single vesicle in a cell cooperate or interfere with one another. To learn how small numbers of motors interact, microtubule gliding assays were carried out with full-length Drosophila kinesin in a novel motility medium containing xanthan, a stiff, water-soluble polysaccharide. At 2 mg/ml xanthan, the zero-shear viscosity of this medium is 1,000 times the viscosity of water, similar to cellular viscosity. To mimic the rheological drag force on the motors when attached to a vesicle in a cell, we attached a 2 microm bead to one end of the microtubule (MT). During gliding assays in our novel medium, the moving bead exerted a drag force of 4-15 pN on the kinesins pulling the MT. The velocity of MTs with an attached bead increased with MT length and with kinesin concentration. The increase with MT length arose because the number of motors is directly proportional to MT length. Our results show that small numbers of kinesins cooperate constructively when pulling against a viscoelastic drag. In the absence of a bead but still in the viscous medium, MT velocity was independent of MT length and kinesin concentration because the thin MT, like a snake moving through grass, was able to move between xanthan molecules with little resistance. A minimal shared-load model in which the number of motors is proportional to MT length fits the observed dependence of gliding velocity on MT length and kinesin concentration.

Impact of external stimuli and cell micro-architecture on intracellular transport states

A living cell is a complex out-of-equilibrium system, in which a great variety of biochemical and physical processes have to be coordinated to ensure viability. We investigate properties of intracellular transport in single cells of the amoeba Dictyostelium discoideum, a relevant model organism due to its cytoskeleton simplicity. In the cells, vesicles undergo two types of motion: directed transport, driven by molecular motors on filaments, or thermal diffusion in a crowded active medium. We present results obtained with our recently developed TRAnSpORT algorithm, which performs a high-resolution temporal analysis of the track of endosomal superparamagnetic particles and splits intracellular transport into different motion states. It results in a two-state model, distinguishing active and passive transport phenomena. We can extract the precise effect of cellular micro- and nanoarchitecture on endosomal transport by disturbing the cytoskeleton through the use of depolymerizing drugs (Benomyl for microtubules, and Latrunculin A for F-actin). Further, we investigate how cytoskeleton filaments act together in order to maintain cell integrity, by applying external mechanical force on the magnetic particle and influencing its motion.

The mechanochemistry of integrated motor protein complexes

The assembly of molecular motor proteins into multi-unit protein complexes plays an important role in determining the intracellular transport and trafficking properties of many subcellular commodities. Yet, it is not known how proteins within these complexes interact and function collectively. Considering the established ties between motor transport and diseases, it has become increasingly important to investigate the functional properties of these essential transport 'motifs'. Doing so requires that the composite motile and force-generating properties of multi-unit motor assemblies are characterized. However, such analyses are typically confounded by a lack of understanding of the links between the structural and mechanical properties of many motor complexes. New experimental challenges also emerge when one examines motor cooperation. Distributions in the mechanical microstates available to motor ensembles must be examined in order to fully understand the transport behavior of multi-motor complexes. Furthermore, mechanisms by which motors communicate must be explored to determine whether motor groups can move cargo together in a truly cooperative fashion. Resolving these issues requires the development of experimental methods that allow the dynamics of complex systems of transport proteins to be monitored with the same precision available to single-molecule biophysical assays. Herein, we discuss key fundamental principles governing the function of motor complexes and their relation to mechanisms that regulate intracellular cargo transport. We also outline new experimental strategies to resolve these essential features of intracellular transport.