Force-velocity curves of motor proteins cooperating in vivo

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

Inferring Subsystem Efficiencies in Bipartite Molecular Machines

Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here, we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the F_{o} and F_{1} subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

Horizontal Magnetic Tweezers to Directly Measure the Force-Velocity Relationship for Multiple Kinesin Motors

Transport of intracellular cargo along cytoskeletal filaments is often achieved by the concerted action of multiple motor molecules. While single-molecule studies have provided profound insight into the mechano-chemical principles and force generation of individual motors, studies on multi-motor systems are less advanced. Here, a horizontal magnetic-tweezers setup is applied, capable of producing up to 150 pN of horizontal force onto 2.8 µm superparamagnetic beads, to motor-propelled cytoskeletal filaments. It is found that kinesin-1 driven microtubules decorated with individual beads display frequent transitions in their gliding velocities which we attribute to dynamic changes in the number of engaged motors. Applying defined temporal force-ramps the force-velocity relationship is directly measured for multi-motor transport. It is found that the stall forces of individual motors are approximately additive and collective backward motion of the transport system under super-stall forces is observed. The magnetic-tweezers apparatus is expected to be readily applicable to a wide range of molecular and cellular motility assays.

Cooperation and competition in the collective drive by motor proteins: mean active force, fluctuations, and self-load

We consider the dynamics of a bio-filament under the collective drive of motor proteins. They are attached irreversibly to a substrate and undergo stochastic attachment-detachment with the filament to produce a directed force on it. We establish the dependence of the mean directed force and force correlations on the parameters describing the individual motor proteins using analytical theory and direct numerical simulations. The effective Langevin description for the filament motion gives mean-squared displacement, asymptotic diffusion constant, and mobility leading to an effective temperature. Finally, we show how competition between motor protein extensions generates a self-load, describable in terms of the effective temperature, affecting the filament motion.

Dynamic and Thermodynamic Bounds for Collective Motor-Driven Transport

Molecular motors work collectively to transport cargo within cells, with anywhere from one to several hundred motors towing a single cargo. For a broad class of collective-transport systems, we use tools from stochastic thermodynamics to derive a new lower bound for the entropy production rate which is tighter than the second law. This implies new bounds on the velocity, efficiency, and precision of general transport systems and a set of analytic Pareto frontiers for identical motors. In a specific model, we identify conditions for saturation of these Pareto frontiers.

Toward a flow-dependent phase-stability criterion: Osmotic pressure in sticky flowing suspensions

Equilibrium phase instability of colloids is robustly predicted by the Vliegenthart-Lekkerkerker (VL) critical value of the second virial efficient, but no such general criterion has been established for suspensions undergoing flow. A transition from positive to negative osmotic pressure is one mechanical hallmark of a change in phase stability in suspensions and provides a natural extension of the equilibrium osmotic pressure encoded in the second virial coefficient. Here, we propose to study the non-Newtonian rheology of an attractive colloidal suspension using the active microrheology framework as a model for focusing on the pair trajectories that underlie flow stability. We formulate and solve a Smoluchowski relation to understand the interplay between attractions, hydrodynamics, Brownian motion, and flow on particle microstructure in a semi-dilute suspension and utilize the results to study the viscosity and particle-phase osmotic pressure. We find that an interplay between attractions and hydrodynamics leads to dramatic changes in the nonequilibrium microstructure, which produces a two-stage flow-thinning of viscosity and leads to pronounced flow-induced negative osmotic pressure. We summarize these findings with an osmotic pressure heat map that predicts where hydrodynamic enhancement of attractive bonds encourages flow-induced aggregation or phase separation. We identify a critical isobar-a flow-induced critical pressure consistent with phase instability and a nonequilibrium extension of the VL criterion.

Effects of dynein inhibitor on the number of motor proteins transporting synaptic cargos

Synaptic cargo transport by kinesin and dynein in hippocampal neurons was investigated by noninvasively measuring the transport force based on nonequilibrium statistical mechanics. Although direct physical measurements such as force measurement using optical tweezers are difficult in an intracellular environment, the noninvasive estimations enabled enumerating force-producing units (FPUs) carrying a cargo comprising the motor proteins generating force. The number of FPUs served as a barometer for stable and long-distance transport by multiple motors, which was then used to quantify the extent of damage to axonal transport by dynarrestin, a dynein inhibitor. We found that dynarrestin decreased the FPU for retrograde transport more than for anterograde transport. This result indicates the applicability of the noninvasive force measurements. In the future, these measurements may be used to quantify damage to axonal transport resulting from neuronal diseases, including Alzheimer's, Parkinson's, and Huntington's diseases.

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles' cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.

The Impact of Rate Formulations on Stochastic Molecular Motor Dynamics

Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active transport is necessary to organize large structures on the short timescales necessary for biological function. The main mechanism of this transport is by cargo attachment to motors which walk in a directed fashion along intracellular filaments. There are a number of models which seek to describe the motion of motors with attached cargo, from detailed microscopic to coarse phenomenological descriptions. We focus on the intermediate-detailed discrete stochastic hopping models, and explore how cargo transport changes depending on the number of motors, motor interaction, system constraints and rate formulations, which are derived from common thermodynamic assumptions. We find that, despite obeying the same detailed balance constraint, the choice of rate formulation considerably affects the characteristics of the overall motion of the system, with one rate formulation exhibiting novel behavior of loaded motor groups moving faster than a single unloaded motor.

Investigation of multiple-dynein transport of melanosomes by non-invasive force measurement using fluctuation unit χ

Pigment organelles known as melanosomes disperse or aggregate in a melanophore in response to hormones. These movements are mediated by the microtubule motors kinesin-2 and cytoplasmic dynein. However, the force generation mechanism of dynein, unlike that of kinesin, is not well understood. In this study, to address this issue, we investigated the dynein-mediated aggregation of melanosomes in zebrafish melanophores. We applied the fluctuation theorem of non-equilibrium statistical mechanics to estimate forces acting on melanosomes during transport by dynein, given that the energy of a system is related to its fluctuation. Our results demonstrate that multiple force-producing units cooperatively transport a single melanosome. Since the force is generated by dynein, this suggests that multiple dyneins carry a single melanosome. Cooperative transport has been reported for other organelles; thus, multiple-motor transport may be a universal mechanism for moving organelles within the cell.

A Quantitative Model for BicD2/Cargo Interactions

Dynein adaptor proteins such as Bicaudal D2 (BicD2) are integral components of the dynein transport machinery, as they recognize cargoes for cell cycle-specific transport and link them to the motor complex. Human BicD2 switches from selecting secretory and Golgi-derived vesicles for transport in G1 and S phase (by recognizing Rab6^GTP), to selecting the nucleus for transport in G2 phase (by recognizing nuclear pore protein Nup358), but the molecular mechanisms governing this switch are elusive. Here, we have developed a quantitative model for BicD2/cargo interactions that integrates affinities, oligomeric states, and cellular concentrations of the reactants. BicD2 and cargo form predominantly 2:2 complexes. Furthermore, the affinity of BicD2 toward its cargo Nup358 is higher than that toward Rab6^GTP. Based on our calculations, an estimated 1000 BicD2 molecules per cell would be recruited to the nucleus through Nup358 in the absence of regulation. Notably, RanGTP is a negative regulator of the Nup358/BicD2 interaction that weakens the affinity by a factor of 10 and may play a role in averting dynein recruitment to the nucleus outside of the G2 phase. However, our quantitative model predicts that an additional negative regulator remains to be identified. In the absence of negative regulation, the affinity of Nup358 would likely be sufficient to recruit BicD2 to the nucleus in G2 phase. Our quantitative model makes testable predictions of how cellular transport events are orchestrated. These transport processes are important for brain development, cell cycle control, signaling, and neurotransmission at synapses.

Application of the fluctuation theorem for noninvasive force measurement in living neuronal axons

Although its importance is recently widely accepted, force measurement has been difficult in living biological systems, mainly due to the lack of the versatile noninvasive force measurement methods. The fluctuation theorem, which represents the thermodynamic properties of small fluctuating nonequilibrium systems, has been applied to the analysis of the thermodynamic properties of motor proteins in vitro. Here we extend it to the axonal transport (displacement) of endosomes. The distribution of the displacement fluctuation had three or four distinct peaks around multiples of a unit value, which the fluctuation theorem can convert into the drag force exerted on the endosomes. The results demonstrated that a single cargo vesicle is conveyed by one to three or four units of force production.

Single-molecule analysis of endogenous β-actin mRNA trafficking reveals a mechanism for compartmentalized mRNA localization in axons

De novo protein synthesis in neuronal axons plays important roles in neural circuit formation, maintenance, and disease. Key to the selectivity of axonal protein synthesis is whether an mRNA is present at the right place to be translated, but the mechanisms behind axonal mRNA localization remain poorly understood. In this work, we quantitatively analyze the link between axonal β-actin mRNA trafficking and its localization patterns. By developing a single-molecule approach to live-image β-actin mRNAs in axons, we explore the biophysical drivers behind β-actin mRNA motion and uncover a mechanism for generating increased density at the axon tip by differences in motor protein-driven transport speeds. These results provide mechanistic insight into the control of local translation through mRNA trafficking.

During embryonic nervous system assembly, mRNA localization is precisely regulated in growing axons, affording subcellular autonomy by allowing controlled protein expression in space and time. Different sets of mRNAs exhibit different localization patterns across the axon. However, little is known about how mRNAs move in axons or how these patterns are generated. Here, we couple molecular beacon technology with highly inclined and laminated optical sheet microscopy to image single molecules of identified endogenous mRNA in growing axons. By combining quantitative single-molecule imaging with biophysical motion models, we show that β-actin mRNA travels mainly as single copies and exhibits different motion-type frequencies in different axonal subcompartments. We find that β-actin mRNA density is fourfold enriched in the growth cone central domain compared with the axon shaft and that a modicum of directed transport is vital for delivery of mRNA to the axon tip. Through mathematical modeling we further demonstrate that directional differences in motor-driven mRNA transport speeds are sufficient to generate β-actin mRNA enrichment at the growth cone. Our results provide insight into how mRNAs are trafficked in axons and a mechanism for generating different mRNA densities across axonal subcompartments.

ER-endosome contact sites in endosome positioning and protrusion outgrowth

The endoplasmic reticulum (ER) makes abundant contacts with endosomes, and the numbers of contact sites increase as endosomes mature. It is already clear that such contact sites have diverse compositions and functions, but in this mini-review we will focus on two particular types of ER-endosome contact sites that regulate endosome positioning. Formation of ER-endosome contact sites that contain the cholesterol-binding protein oxysterol-binding protein-related protein 1L (ORP1L) is coordinated with loss of the minus-end-directed microtubule motor Dynein from endosomes. Conversely, formation of ER-endosome contact sites that contain the Kinesin-1-binding protein Protrudin results in transfer of the plus-end-directed microtubule motor Kinesin-1 from ER to endosomes. We discuss the possibility that formation of these two types of contact sites is coordinated as a 'gear-shift' mechanism for endosome motility, and we review evidence that Kinesin-1-mediated motility of late endosomes (LEs) to the cell periphery promotes outgrowth of neurites and other protrusions.

Cooperative protofilament switching emerges from inter-motor interference in multiple-motor transport

Within living cells, the transport of cargo is accomplished by groups of molecular motors. Such collective transport could utilize mechanisms which emerge from inter-motor interactions in ways that are yet to be fully understood. Here we combined experimental measurements of two-kinesin transport with a theoretical framework to investigate the functional ramifications of inter-motor interactions on individual motor function and collective cargo transport. In contrast to kinesin's low sidestepping frequency when present as a single motor, with exactly two kinesins per cargo, we observed substantial motion perpendicular to the microtubule. Our model captures a surface-associated mode of kinesin, which is only accessible via inter-motor interference in groups, in which kinesin diffuses along the microtubule surface and rapidly “hops” between protofilaments without dissociating from the microtubule. Critically, each kinesin transitions dynamically between the active stepping mode and this weak surface-associated mode enhancing local exploration of the microtubule surface, possibly enabling cellular cargos to overcome macromolecular crowding and to navigate obstacles along microtubule tracks without sacrificing overall travel distance.

Motor coupling through lipid membranes enhances transport velocities for ensembles of myosin Va

Myosin Va is an actin-based molecular motor responsible for transport and positioning of a wide array of intracellular cargoes. Although myosin Va motors have been well characterized at the single-molecule level, physiological transport is carried out by ensembles of motors. Studies that explore the behavior of ensembles of molecular motors have used nonphysiological cargoes such as DNA linkers or glass beads, which do not reproduce one key aspect of vesicular systems--the fluid intermotor coupling of biological lipid membranes. Using a system of defined synthetic lipid vesicles (100- to 650-nm diameter) composed of either 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) (fluid at room temperature) or 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) (gel at room temperature) with a range of surface densities of myosin Va motors (32-125 motors per μm(2)), we demonstrate that the velocity of vesicle transport by ensembles of myosin Va is sensitive to properties of the cargo. Gel-state DPPC vesicles bound with multiple motors travel at velocities equal to or less than vesicles with a single myosin Va (∼450 nm/s), whereas surprisingly, ensembles of myosin Va are able to transport fluid-state DOPC vesicles at velocities significantly faster (>700 nm/s) than a single motor. To explain these data, we developed a Monte Carlo simulation that suggests that these reductions in velocity can be attributed to two distinct mechanisms of intermotor interference (i.e., load-dependent modulation of stepping kinetics and binding-site exclusion), whereas faster transport velocities are consistent with a model wherein the normal stepping behavior of the myosin is supplemented by the preferential detachment of the trailing motor from the actin track.

Nucleus-targeted drug delivery: theoretical optimization of nanoparticles decoration for enhanced intracellular active transport

A rational design for a nanoparticle is suggested, which will maximize its arrival efficiency from the plasma membrane to the nuclear surrounding. The design is based on grafting the particle surface with polymer spacers, each ending with a motor protein associating molecule, for example, nuclear localization signal peptide. It is theoretically shown that the spacer polymer molecular weight can be adjusted to significantly increase the effective particle processivity time. This should lead to appreciable enhancement of active transport of the nanocarrier, and consequently drug delivery, to the nucleus.

The effects of viscoelastic fluid on kinesin transport

Kinesins are molecular motors which transport various cargoes in the cytoplasm of cells and are involved in cell division. Previous models for kinesins have only targeted their in vitro motion. Thus, their applicability is limited to kinesin moving in a fluid with low viscosity. However, highly viscoelastic fluids have considerable effects on the movement of kinesin. For example, the high viscosity modifies the relation between the load and the speed of kinesin. While the velocity of kinesin has a nonlinear dependence with respect to the load in environments with low viscosity, highly viscous forces change that behavior. Also, the elastic nature of the fluid changes the velocity of kinesin. The new mechanistic model described in this paper considers the viscoelasticity of the fluid using subdiffusion. The approach is based on a generalized Langevin equation and fractional Brownian motion. Results show that a single kinesin has a maximum velocity when the ratio between the viscosity and elasticity is about 0.5. Additionally, the new model is able to capture the transient dynamics, which allows the prediction of the motion of kinesin under time varying loads.

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.

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.

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.

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.

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.

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.

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.

A protein diffusion model of the sealing effect

Water transport across the arterial endothelium is believed primarily to occur through breaks in the tight junction strands at the cell periphery between neighboring cells. Additional proteins arriving at the tight junction can close these breaks, thereby attenuating this water flux. Motivated by evidence that the diffusion of presynthesized protein from the interior of the cell to and incorporation into the cell border is the mechanism of endothelial tight junctional sealing, we develop a diffusion-limited mathematical model of intercellular gap sealing. A single endothelial cell is represented as a thin, axisymmetric disk, initially containing a uniform distribution of junctional protein that does not interact with the apical or basal cell surfaces. Upon application of a transmural pressure gradient, water flows through the junctional cleft, and tight junction remodeling begins. We assume that proteins at the junction are instantaneously incorporated into its strand, dropping the free protein concentration at the cell periphery to zero. This sets the diffusion of intracellular proteins toward the junction in motion. The solution of this one-dimensional initial value problem provides excellent fits to current and previously published experimental data over a wide variety of conditions. It yields three physically meaningful parameters for each fit, including a protein diffusivity in the cytoplasm that varies little within experimental treatments. Statistical variation of these parameters allows rational comparison of experimental runs and identification of outlier runs.

Transition to superdiffusive behavior in intracellular actin-based transport mediated by molecular motors

Intracellular transport of large cargoes, such as organelles, vesicles, or large proteins, is a complex dynamical process that involves the interplay of adenosine triphosphate-consuming molecular motors, cytoskeleton filaments, and the viscoelastic cytoplasm. In this work we investigate the motion of pigment organelles (melanosomes) driven by myosin-V motors in Xenopus laevis melanocytes using a high-spatio-temporal resolution tracking technique. By analyzing the obtained trajectories, we show that the melanosomes mean-square displacement undergoes a transition from a subdiffusive to a superdiffusive behavior. A stochastic theoretical model, which explicitly considers the collective action of the molecular motors, is introduced to generalize the interpretation of our data. Starting from a generalized Langevin equation, we derive an analytical expression for the mean square displacement, which also takes into account the experimental noise. By fitting theoretical expressions to experimental data we were able to discriminate the exponents that characterize the passive and active contributions to the dynamics and to estimate the "global" motor forces correctly. Then, our model gives a quantitative description of active transport in living cells with a reduced number of parameters.