Cooperative cargo transport by several molecular motors

Nature of barriers determines first passage times in heterogeneous media

Intuition suggests that passage times across a region increase with the number of barriers along the path. Can this fail depending on the nature of the barrier? To probe this fundamental question, we exactly solve for the first passage time in general d-dimensions for diffusive transport through a spatially patterned array of obstacles - either entropic or energetic, depending on the nature of the obstacles. For energetic barriers, we show that first passage times vary non-monotonically with the number of barriers, while for entropic barriers it increases monotonically. This non-monotonicity for energetic barriers is further reflected in the behaviour of effective diffusivity as well. We then design a simple experiment where a robotic bug navigates in a heterogeneous environment through a spatially patterned array of obstacles to validate our predictions. Finally, using numerical simulations, we show that this non-monotonic behaviour for energetic barriers is general and extends to even super-diffusive transport.

Episodic Transport of Protein Aggregates Achieves a Positive Size Selectivity in Aggresome Formation

Eukaryotic cells direct toxic misfolded proteins to various protein quality control pathways based on their chemical features and aggregation status. Aggregated proteins are targeted to selective autophagy or specifically sequestered into the "aggresome," a perinuclear inclusion at the microtubule-organizing center (MTOC). However, the mechanism for selectively sequestering protein aggregates into the aggresome remains unclear. To investigate aggresome formation, we reconstituted MTOC-directed aggregate transport in Xenopus laevis egg extract using AgDD, a chemically inducible aggregation system. High-resolution single-particle tracking revealed that dynein-mediated transport of aggregates was highly episodic, with average velocity positively correlated with aggregate size. Our mechanistic model suggests that the recurrent formation of the dynein transport complex biases larger aggregates towards the active transport state, compensating for the slowdown due to viscosity. Both episodic transport and positive size selectivity are specifically associated with aggresome-dynein adaptors. Coupling conventional dynein-activating adaptors to the aggregates perturbs aggresome formation and reverses size selectivity.

Septin-coated microtubules promote maturation of multivesicular bodies by inhibiting their motility

The microtubule cytoskeleton consists of microtubule subsets with distinct compositions of microtubule-associated proteins, which instruct the position and traffic of subcellular organelles. In the endocytic pathway, these microtubule-associated cues are poorly understood. Here, we report that in MDCK cells, endosomes with multivesicular body (MVB) and late endosome (LE) markers localize preferentially to microtubules coated with septin GTPases. Compared with early endosomes, CD63-containing MVBs/LEs are largely immotile on septin-coated microtubules. In vitro reconstitution assays revealed that the motility of isolated GFP-CD63 endosomes is directly inhibited by microtubule-associated septins. Quantification of CD63-positive endosomes containing the early endosome antigen (EEA1), the Rab7 effector and dynein adaptor RILP or Rab27a, showed that intermediary EEA1- and RILP-positive GFP-CD63 preferentially associate with septin-coated microtubules. Septin knockdown enhanced GFP-CD63 motility and decreased the percentage of CD63-positive MVBs/LEs with lysobiphosphatidic acid without impacting the fraction of EEA1-positive CD63. These results suggest that MVB maturation involves immobilization on septin-coated microtubules, which may facilitate multivesiculation and/or organelle-organelle contacts.

Modelling intracellular transport in crowded environments: effects of motor association to cargos

In intracellular transports, motor proteins transport macromolecules as cargos to desired locations by moving on biopolymers such as microtubules. Recent experiments suggest that, while moving in crowded environments, cargos that can associate motor proteins during their translocation have larger run-length and association time compared to free motors. Here, we model the dynamics of a cargo that can associate at the most m free motors present on the microtubule track as obstacles to its motion. The proposed models display competing effects of association and crowding, leading to a peak in the run-length with the free-motor density. For m = 2 and 3, we show that this feature is governed by the largest eigenvalue of the transition matrix describing the cargo dynamics. In all the above cases, free motors are assumed to be present on the microtubule as stalled obstacles. We finally compare simulation results for the run-length for general scenarios where the free motors undergo processive motion in addition to binding and unbinding to or from the microtubule.

CKAP5 stabilizes CENP-E at kinetochores by regulating microtubule-chromosome attachments

Stabilization of microtubule plus end-directed kinesin CENP-E at the metaphase kinetochores is important for chromosome alignment, but its mechanism remains unclear. Here, we show that CKAP5, a conserved microtubule plus tip protein, regulates CENP-E at kinetochores in human cells. Depletion of CKAP5 impairs CENP-E localization at kinetochores at the metaphase plate and results in increased kinetochore-microtubule stability and attachment errors. Erroneous attachments are also supported by computational modeling. Analysis of CKAP5 knockout cancer cells of multiple tissue origins shows that CKAP5 is preferentially essential in aneuploid, chromosomally unstable cells, and the sensitivity to CKAP5 depletion is correlated to that of CENP-E depletion. CKAP5 depletion leads to reduction in CENP-E-BubR1 interaction and the interaction is rescued by TOG4-TOG5 domain of CKAP5. The same domain can rescue CKAP5 depletion-induced CENP-E removal from the kinetochores. Interestingly, CKAP5 depletion facilitates recruitment of PP1 to the kinetochores and furthermore, a PP1 target site-specific CENP-E phospho-mimicking mutant gets stabilized at kinetochores in the CKAP5-depleted cells. Together, the results support a model in which CKAP5 controls mitotic chromosome attachment errors by stabilizing CENP-E at kinetochores and by regulating stability of the kinetochore-attached microtubules.

Mechanochemical Coupling of Catalysis and Motion in a Cellulose-Degrading Multienzyme Nanomachine

The cellulosome is a megadalton-size protein complex that functions as a biological nanomachine of cellulosic fiber degradation. We show that the cellulosome behaves as a Brownian ratchet that rectifies protein motions on the cellulose surface into a propulsion mechanism by coupling to the hydrolysis of cellulose chains. Movement on cellulose fibrils is unidirectional and results from "macromolecular crawl" composed of dynamic switches between elongated and compact spatial arrangements of enzyme subunits. Deletion of the main exocellulase Cel48S eliminates conformational bias for aligning the subunits to the long fibril axis, which we reveal as crucial for optimum coupling between directional movement and substrate degradation. Implications of the cellulosome acting as a mechanochemical motor suggest a distinct mechanism of enzymatic machinery in the deconstruction of cellulose assemblies.

Coordination, cooperation, competition, crowding and congestion of molecular motors: Theoretical models and computer simulations

Cytoskeletal motor proteins are biological nanomachines that convert chemical energy into mechanical work to carry out various functions such as cell division, cell motility, cargo transport, muscle contraction, beating of cilia and flagella, and ciliogenesis. Most of these processes are driven by the collective operation of several motors in the crowded viscous intracellular environment. Imaging and manipulation of the motors with powerful experimental probes have been complemented by mathematical analysis and computer simulations of the corresponding theoretical models. In this article, we illustrate some of the key theoretical approaches used to understand how coordination, cooperation and competition of multiple motors in the crowded intra-cellular environment drive the processes that are essential for biological function of a cell. In spite of the focus on theory, experimentalists will also find this article as an useful summary of the progress made so far in understanding multiple motor systems.

Theoretical analysis of cargo transport by catch bonded motors in optical trapping assays

Dynein motors exhibit catch bonding, where the unbinding rate of the motors from microtubule filaments decreases with increasing opposing load. The implications of this catch bond on the transport properties of dynein-driven cargo are yet to be fully understood. In this context, optical trapping assays constitute an important means of accurately measuring the forces generated by molecular motor proteins. We investigate, using theory and stochastic simulations, the transport properties of cargo transported by catch bonded dynein molecular motors - both singly and in teams - in a harmonic potential, which mimics the variable force experienced by cargo in an optical trap. We estimate the biologically relevant measures of first passage time - the time during which the cargo remains bound to the microtubule and detachment force - the force at which the cargo unbinds from the microtubule, using both two-dimensional and one-dimensional force balance frameworks. Our results suggest that even for cargo transported by a single motor, catch bonding may play a role depending on the force scale which marks the onset of the catch bond. By comparing with experimental measurements on single dynein-driven transport, we estimate realistic bounds of this catch bond force scale. Generically, catch bonding results in increased persistent motion, and can also generate non-monotonic behaviour of first passage times. For cargo transported by multiple motors, emergent collective effects due to catch bonding can result in non-trivial re-entrant phenomena wherein average first passage times and detachment forces exhibit non-monotonic behaviour as a function of the stall force and the motor velocity.

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.

ADP release can explain spatially-dependent kinesin binding times

The self-organization of cells relies on the profound complexity of protein-protein interactions. Challenges in directly observing these events have hindered progress toward understanding their diverse behaviors. One notable example is the interaction between molecular motors and cytoskeletal systems that combine to perform a variety of cellular functions. In this work, we leverage theory and experiments to identify and quantify the rate-limiting mechanism of the initial association between a cargo-bound kinesin motor and a microtubule track. Recent advances in optical tweezers provide binding times for several lengths of kinesin motors trapped at varying distances from a microtubule, empowering the investigation of competing models. We first explore a diffusion-limited model of binding. Through Brownian dynamics simulations and simulation-based inference, we find this simple diffusion model fails to explain the experimental binding times, but an extended model that accounts for the ADP state of the molecular motor agrees closely with the data, even under the scrutiny of penalizing for additional model complexity. We provide quantification of both kinetic rates and biophysical parameters underlying the proposed binding process. Our model suggests that most but not every motor binding event is limited by their ADP state. Lastly, we predict how these association rates can be modulated in distinct ways through variation of environmental concentrations and spatial distances.

A general model for the motion of multivalent cargo interacting with substrates

Multivalent interactions are common in biology at many different length scales, and can result in the directional motion of multivalent cargo along substrates. Here, a general analytical model has been developed that can describe the directional motion of multivalent cargo as a response to position dependence in the binding and unbinding rates exhibited by their interaction sites. Cargo exhibit both an effective velocity, which acts in the direction of increasing cargo-substrate binding rate and decreasing cargo-substrate unbinding rate, and an effective diffusivity. This model can reproduce previously published experimental findings using only the binding and unbinding rate distributions of cargo interaction sites, and without any further parameter fitting. Extension of the cargo binding model to two dimensions reveals an effective velocity with the same properties as that derived for the one-dimensional case.

Vesicle-mediated transport of ALIX and ESCRT-III to the intercellular bridge during cytokinesis

Cellular abscission is the final step of cytokinesis that leads to the physical separation of the two daughter cells. The scaffold protein ALIX and the ESCRT-I protein TSG101 contribute to recruiting ESCRT-III to the midbody, which orchestrates the final membrane scission of the intercellular bridge. Here, we addressed the transport mechanisms of ALIX and ESCRT-III subunit CHMP4B to the midbody. Structured illumination microscopy revealed gradual accumulation of ALIX at the midbody, resulting in the formation of spiral-like structures extending from the midbody to the abscission site, which strongly co-localized with CHMP4B. Live-cell microscopy uncovered that ALIX appeared together with CHMP4B in vesicular structures, whose motility was microtubule-dependent. Depletion of ALIX led to structural alterations of the midbody and delayed recruitment of CHMP4B, resulting in delayed abscission. Likewise, depletion of the kinesin-1 motor KIF5B reduced the motility of ALIX-positive vesicles and delayed midbody recruitment of ALIX, TSG101 and CHMP4B, accompanied by impeded abscission. We propose that ALIX, TSG101 and CHMP4B are associated with endosomal vesicles transported on microtubules by kinesin-1 to the cytokinetic bridge and midbody, thereby contributing to their function in abscission.

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.

Cargo transport properties are enhanced by cylindrical microtubule geometry and elliptical contact zone on cargo surface

Molecular motors are responsible for carrying cellular transport of various membranous vesicles or organelles along cytoskeletal tracks. Transport of cellular cargos require high forces that are generated by motors working in groups. Hence, the properties of cargo transport can be modulated by varying various parameters such as cargo size and shape, microtubule geometry, motor number and their arrangement on cargo surface. Only those motors which are present in the contact zone on cargo surface have potential to bind to microtubule. Although earlier studies revealed the importance of cargo size, total motors attached to microtubule and their arrangement on cargo transport, yet how the contact zone influences binding of motors to microtubule largely remains unexplored. Here, it has been shown that contact zone is elliptical in shape for a spherical cargo and increases with cargo size for Kinesin-1 motors. To further understand the combined effect of elliptical contact zone and microtubule geometry on cargo transport, 3D mean-field model with uniform and clustered arrangement of motors for different cargo sizes and motor number has been used. Our findings indicate that cylindrical microtubule geometry maximizes the microtubule-bound motors which enhances the runlength and velocity of cargo transport. Our results show that microtubule-bound motors decrease with cargo size for uniform arrangement of motors on cargo thus decreasing its runlength and velocity, whereas in clustered arrangement, the number of microtubule-bound motors increase with cargo size which leads to increase in runlength and velocity.

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.

Poroviscoelasto-plasticity of agarose-based hydrogels

Agarose gels are excellent candidates for tissue engineering as they are tunable, viscoelastic, and show a pronounced strain-stiffening response. These characteristics make them ideal to create in vitro environments to grow cells and develop tissues. As in many other biopolymers, viscoelasticity and poroelasticity coexist as time-dependent behaviors in agarose gels. While the viscoelastic behavior of these hydrogels has been considered using both phenomenological and continuum models, there remains a lack of connection between the underlying physics and the macroscopic material response. Through a finite element analysis and complimentary experiments, we evaluated the complex time-dependent mechanical response of agarose gels in various conditions. We then conceptualized these gels as a dynamic network where the global dissociation/association rate of intermolecular bonds is described as a combination of a fast rate native to double helices forming between aligned agarose molecules and a slow rate of the agarose molecules present in the clusters. Using the foundation of the transient network theory, we developed a physics-based constitutive model that accurately describes agarose behavior. Integrating experimental results and model prediction, we demonstrated that the fast dissociation/association rate follows a nonlinear force-dependent response, whose exponential evolution agrees with Eyring's model based on the transition state theory. Overall, our results establish a more accurate understanding of the time-dependent mechanics of agarose gels and provide a model that can inform design of a variety of biopolymers with a similar network topology.

Cholesterol in the cargo membrane amplifies tau inhibition of kinesin-1-based transport

Intracellular cargos are often membrane-enclosed and transported by microtubule-based motors in the presence of microtubule-associated proteins (MAPs). Whereas increasing evidence reveals how MAPs impact the interactions between motors and microtubules, critical questions remain about the impact of the cargo membrane on transport. Here we combined in vitro optical trapping with theoretical approaches to determine the effect of a lipid cargo membrane on kinesin-based transport in the presence of MAP tau. Our results demonstrate that attaching kinesin to a fluid lipid membrane reduces the inhibitory effect of tau on kinesin. Moreover, adding cholesterol, which reduces kinesin diffusion in the cargo membrane, amplifies the inhibitory effect of tau on kinesin binding in a dosage-dependent manner. We propose that reduction of kinesin diffusion in the cargo membrane underlies the effect of cholesterol on kinesin binding in the presence of tau, and we provide a simple model for this proposed mechanism. Our study establishes a direct link between cargo membrane cholesterol and MAP-based regulation of kinesin-1. The cholesterol effects uncovered here may more broadly extend to other lipid alterations that impact motor diffusion in the cargo membrane, including those associated with aging and neurological diseases.

Tug-of-War and Coordination in Bidirectional Transport by Molecular Motors

Many cargoes in cells are transported in a bidirectional fashion by molecular motors pulling into opposite directions along a cytoskeletal filament, e.g., by kinesins and dyneins along microtubules. How opposite-polarity motors are coordinated has been under debate for a long time, with experimental evidence supporting both a tug-of-war between the motors as well as biochemical coordination mechanisms. Here we propose a model that extends a tug-of-war model by a mechanism of motor activation and inactivation and show that this model can explain some observations that are incompatible with a simple tug-of-war scenario, specifically long unidirectional runs and a directional memory after unbinding from the filament. Both features are present in two variants of the model in which motors are activated and inactivated individually and in opposite-direction pairs, respectively.

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.

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

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

Impact of noise on the regulation of intracellular transport of intermediate filaments

Noise affects all biological processes from molecules to cells, organisms and populations. Although the effect of noise on these processes is highly variable, evidence is accumulating which shows natural stochastic fluctuations (noise) can facilitate biological functions. Herein, we investigate the effect of noise on the transport of intermediate filaments in cells by comparing the stochastic and deterministic formalizations of the bidirectional transport of intermediate filaments, long elastic polymers transported along microtubules by antagonistic motor proteins Dallon et al., 2019; Portet et al., 2019. By numerically exploring discrepancies in timescales and attractors between both formalizations, we characterize the impact of stochastic fluctuations on the individual and ensemble transport. Biologically, we find that noise promotes the collective movement of intermediate filaments and increases the efficiency of its regulation by the biochemical properties of motor-cargo interactions. While stochastic fluctuations reduce the impact of the initial distributions of motor proteins in cells, the number of binding sites and the affinity of motor-cargo interactions are the key parameters controlling transport efficiency and efficacy.

The nanocaterpillar's random walk: diffusion with ligand-receptor contacts

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.

Transport of lysosomes decreases in the perinuclear region: Insights from changepoint analysis

Lysosomes are membrane-bound organelles that serve as the endpoint for endocytosis, phagocytosis, and autophagy, degrading the molecules, pathogens, and organelles localized within them. These cellular functions require intracellular transport. We use fluorescence microscopy to characterize the motion of lysosomes as a function of intracellular region, perinuclear or periphery, and lysosome diameter. Single particle tracking data is complemented by changepoint identification and analysis of a mathematical model for state-switching. We first classify lysosomal motion as motile or stationary. We then study how lysosome location and diameter affects the proportion of time spent in each state and quantify the speed during motile periods. We find that the proportion of time spent stationary is strongly region-dependent, with significantly decreased motility in the perinuclear region. Increased lysosome diameter only slightly decreases speed. Overall, these results demonstrate the importance of decomposing particle trajectories into qualitatively different behaviors before conducting population-wide statistical analysis. Our results suggest that intracellular region is an important factor to consider in studies of intracellular transport.

A change point analysis protocol for comparing intracellular transport by different molecular motor combinations

Intracellular transport by microtubule-based molecular motors is marked by qualitatively different behaviors. It is a long-standing and still-open challenge to accurately quantify the various individual-cargo behaviors and how they are affected by the presence or absence of particular motor families. In this work we introduce a protocol for analyzing change points in cargo trajectories that can be faithfully projected along the length of a (mostly) straight microtubule. Our protocol consists of automated identification of velocity change points, estimation of velocities during the behavior segments, and extrapolation to motor-specific velocity distributions. Using simulated data we show that our method compares favorably with existing methods. We then apply the technique to data sets in which quantum dots are transported by Kinesin-1, by Dynein-Dynactin-BicD2 (DDB), and by Kinesin-1/DDB pairs. In the end, we identify pausing behavior that is consistent with some tug-of-war model predictions, but also demonstrate that the simultaneous presence of antagonistic motors can lead to long processive runs that could contribute favorably to population-wide transport.

Nano-Particles Carried by Multiple Dynein Motors Self-Regulate Their Number of Actively Participating Motors

Intra-cellular active transport by native cargos is ubiquitous. We investigate the motion of spherical nano-particles (NPs) grafted with flexible polymers that end with a nuclear localization signal peptide. This peptide allows the recruitment of several mammalian dynein motors from cytoplasmic extracts. To determine how motor–motor interactions influenced motility on the single microtubule level, we conducted bead-motility assays incorporating surface adsorbed microtubules and combined them with model simulations that were based on the properties of a single dynein. The experimental and simulation results revealed long time trajectories: when the number of NP-ligated motors N_m increased, run-times and run-lengths were enhanced and mean velocities were somewhat decreased. Moreover, the dependence of the velocity on run-time followed a universal curve, regardless of the system composition. Model simulations also demonstrated left- and right-handed helical motion and revealed self-regulation of the number of microtubule-bound, actively transporting dynein motors. This number was stochastic along trajectories and was distributed mainly between one, two, and three motors, regardless of N_m. We propose that this self-regulation allows our synthetic NPs to achieve persistent motion that is associated with major helicity. Such a helical motion might affect obstacle bypassing, which can influence active transport efficiency when facing the crowded environment of the cell.

Novel mechanism for oscillations in catchbonded motor-filament complexes

Generation of mechanical oscillations is ubiquitous to a wide variety of intracellular processes ranging from activity of muscle fibres to oscillations of the mitotic spindle. The activity of motors plays a vital role in maintaining the integrity of the mitotic spindle structure and in generating spontaneous oscillations. While the structural features and properties of the individual motors are well characterized, their implications on the functional behaviour of motor-filament complexes is more involved. We show that force-induced allosteric deformations in dynein, which results in catchbonding behaviour, provide a generic mechanism to generate spontaneous oscillations in motor-cytoskeletal filament complexes. The resultant phase diagram of such motor-filament systems - characterized by force-induced allosteric deformations - exhibits bistability and sustained limit cycle oscillations in biologically relevant regimes, such as for catchbonded dynein. The results reported here elucidate the central role of this mechanism in fashioning a distinctive stability behaviour and oscillations in motor-filament complexes, such as mitotic spindles.

Effect of Kinesin-5 Tail Domain on Motor Dynamics for Antiparallel Microtubule Sliding

Kinesin-5 motor consists of two pairs of heads and tail domains, which are situated at the opposite ends of a common stalk. The two pairs of heads can bind to two antiparallel microtubules (MTs) and move on the two MTs independently towards the plus ends, sliding apart the two MTs, which is responsible for chromosome segregation during mitosis. Prior experimental data showed that the tails of kinesin-5 Eg5 can modulate the dynamics of single motors and are critical for multiple motors to generate high steady forces to slide apart two antiparallel MTs. To understand the molecular mechanism of the tails modulating the ability of Eg5 motors, based on our proposed model the dynamics of the single Eg5 with the tails and that without the tails moving on single MTs is studied analytically and compared. Furthermore, the dynamics of antiparallel MT sliding by multiple Eg5 motors with the tails and that without the tails is studied numerically and compared. Both the analytical results for single motors and the numerical results for multiple motors are consistent with the available experimental data.

Tuning ensemble-averaged cargo run length via fractional change in mean kinesin number

The number of motors carrying cargos in biological cells is not well-defined, instead varying from cargo to cargo about a statistical mean. Predictive understanding of motility in cells therefore requires quantitative insights into mixed ensembles of cargos. Toward this goal, here we employed Monte Carlo simulations to investigate statistical ensembles of cargos carried by a Poisson-distributed number of motors. Focusing on the key microtubule-based motor kinesin-1, our simulations utilized experimentally determined single-kinesin characteristics and alterations in kinesin's on- and off-rates caused by cellular factors and/or physical load. We found that a fractional increase in mean kinesin number enhances the ensemble-averaged cargo run length and amplifies run-length sensitivity to changes in single-kinesin on-rate and off-rate. These tuning effects can be further enhanced as solution viscosity increases over the range reported for cells. Together, our data indicate that the physiological range of kinesin number sensitively tunes the motility of mixed cargo populations. These effects have rich implications for quantitative and predictive understanding of cellular motility and its regulation.

Diffusion of kinesin motors on cargo can enhance binding and run lengths during intracellular transport

Cellular cargoes, including lipid droplets and mitochondria, are transported along microtubules using molecular motors such as kinesins. Many experimental and computational studies focused on cargoes with rigidly attached motors, in contrast to many biological cargoes that have lipid surfaces that may allow surface mobility of motors. We extend a mechanochemical three-dimensional computational model by adding coupled-viscosity effects to compare different motor arrangements and mobilities. We show that organizational changes can optimize for different objectives: Cargoes with clustered motors are transported efficiently but are slow to bind to microtubules, whereas those with motors dispersed rigidly on their surface bind microtubules quickly but are transported inefficiently. Finally, cargoes with freely diffusing motors have both fast binding and efficient transport, although less efficient than clustered motors. These results suggest that experimentally observed changes in motor organization may be a control point for transport.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Motor Protein Transport Along Inhomogeneous Microtubules

Many cellular processes rely on the cell's ability to transport material to and from the nucleus. Networks consisting of many microtubules and actin filaments are key to this transport. Recently, the inhibition of intracellular transport has been implicated in neurodegenerative diseases such as Alzheimer's disease and Amyotrophic Lateral Sclerosis. Furthermore, microtubules may contain so-called defective regions where motor protein velocity is reduced due to accumulation of other motors and microtubule-associated proteins. In this work, we propose a new mathematical model describing the motion of motor proteins on microtubules which incorporate a defective region. We take a mean-field approach derived from a first principle lattice model to study motor protein dynamics and density profiles. In particular, given a set of model parameters we obtain a closed-form expression for the equilibrium density profile along a given microtubule. We then verify the analytic results using mathematical analysis on the discrete model and Monte Carlo simulations. This work will contribute to the fundamental understanding of inhomogeneous microtubules providing insight into microscopic interactions that may result in the onset of neurodegenerative diseases. Our results for inhomogeneous microtubules are consistent with prior work studying the homogeneous case.

Dynamic multimerization of Dab2-Myosin VI complexes regulates cargo processivity while minimizing cortical actin reorganization

Myosin VI ensembles on endocytic cargo facilitate directed transport through a dense cortical actin network. Myosin VI is recruited to clathrin-coated endosomes via the cargo adaptor Dab2. Canonically, it has been assumed that the interactions between a motor and its cargo adaptor are stable. However, it has been demonstrated that the force generated by multiple stably attached motors disrupts local cytoskeletal architecture, potentially compromising transport. In this study, we demonstrate that dynamic multimerization of myosin VI-Dab2 complexes facilitates cargo processivity without significant reorganization of cortical actin networks. Specifically, we find that Dab2 myosin interacting region (MIR) binds myosin VI with a moderate affinity (184 nM) and single-molecule kinetic measurements demonstrate a high rate of turnover (1 s⁻¹) of the Dab2 MIR–myosin VI interaction. Single-molecule motility shows that saturating Dab2-MIR concentration (2 μM) promotes myosin VI homodimerization and processivity with run lengths comparable with constitutive myosin VI dimers. Cargo-mimetic DNA origami scaffolds patterned with Dab2 MIR-myosin VI complexes are weakly processive, displaying sparse motility on single actin filaments and “stop-and-go” motion on a cellular actin network. On a minimal actin cortex assembled on lipid bilayers, unregulated processive movement by either constitutive myosin V or VI dimers results in actin remodeling and foci formation. In contrast, Dab2 MIR–myosin VI interactions preserve the integrity of a minimal cortical actin network. Taken together, our study demonstrates the importance of dynamic motor–cargo association in enabling cargo transportation without disrupting cytoskeletal organization.

Effective behavior of cooperative and nonidentical molecular motors

Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.

Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport

In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion dynamics is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed renewal reward framework are illustrated for several case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of molecular motor proteins.

Modelling cytoskeletal transport by clusters of non-processive molecular motors with limited binding sites

Molecular motors are responsible for intracellular transport of a variety of biological cargo. We consider the collective behaviour of a finite number of motors attached on a cargo. We extend previous analytical work on processive motors to the case of non-processive motors, which stochastically bind on and off cytoskeletal filaments with a limited number of binding sites available. Physically, motors attached to a cargo cannot bind anywhere along the filaments, so the number of accessible binding sites on the filament should be limited. Thus, we analytically study the distribution and the velocity of a cluster of non-processive motors with limited number of binding sites. To validate our analytical results and to go beyond the level of detail possible analytically, we perform Monte Carlo latticed based stochastic simulations. In particular, in our simulations, we include sequence preservation of motors performing stepping and binding obeying a simple exclusion process. We find that limiting the number of binding sites reduces the probability of non-processive motors binding but has a relatively small effect on force-velocity relations. Our analytical and stochastic simulation results compare well to published data from in vitro and in vivo experiments.

Microtubule Detachment in Gliding Motility Assays Limits the Performance of Kinesin-Driven Molecular Shuttles

The creation of complex active nanosystems integrating cytoskeletal filaments propelled by surface-adhered motor proteins often relies on the filaments' ability to glide over up to meter-long distances. While theoretical considerations support this ability, we show that microtubule detachment (either spontaneous or triggered by a microtubule crossing event) is a non-negligible phenomenon that has been overlooked until now. The average gliding distance before spontaneous detachment was measured to be 30 ± 10 mm for a functional kinesin-1 density of 500 μm^-2 and 9 ± 4 mm for a functional kinesin-1 density of 100 μm^-2 at 1 mM ATP. Even microtubules longer than 3 μm detached, suggesting that spontaneous detachment is not caused by the stochastic absence of motors or their stochastic release due to a limited run length.

Temperature-dependent activity of kinesins is regulable

Cytoskeletal transport in cells is driven by enzymes whose activity shows sensitive, typically Arrhenius, dependence on temperature. Often, the duration and outcome of cargo transport is determined by the relative success of kinesin vs. dynein motors, which can simultaneously bind to individual cargos and move in opposite direction on microtubules. The question of how kinesin and dynein activity remain coupled over the large temperature ranges experienced by some cells is one of clear biological relevance. We report a break in the Arrhenius behavior of both kinesin-1 and kinesin-3 enzymatic activity at 4.7 °C and 10.5 °C, respectively. Further, we report that this transition temperature significantly changes as a function of chemical background: addition of 200 mM TMAO increases transition temperatures by ∼6 °C in all cases. Our results show that Arrhenius trend breaks are common to all cytoskeletal motors and open a broad question of how such activity transitions are regulated in vivo. STATEMENT OF SIGNIFICANCE: Many cytoskeletal motors studied to date follow Arrhenius kinetics, at least from room temperature up to mammalian body temperature. However the thermal dynamic range is typically finite, and breaks in Arrhenius trends are commonly observed at biologically relevant temperatures. Here we report that the thermal dynamic range of kinesins is also limited and moreover that the location of the Arrhenius break for kinesins can shift significantly based on chemical backgrounds. This implies that the balance of multiple motor cargo transport along the cytoskeleton is far more tunable as a function of temperature than previously appreciated.

Collective intracellular cargo transport by multiple kinesins on multiple microtubules

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Anomalous intracellular transport phases depend on cytoskeletal network features

Intracellular transport in eukaryotic cells consists of phases of passive, diffusion-based transport and active, motor-driven transport along filaments that make up the cell's cytoskeleton. The interplay between superdiffusive transport along cytoskeletal filaments and the anomalous nature of subdiffusion in the bulk can lead to novel effects in transport behavior at the cellular scale. Here we develop a computational model of the process with cargo being ballistically transported along explicitly modeled cytoskeletal filament networks and passively transported in the cytoplasm by a subdiffusive continuous-time random walk (CTRW). We show that, over a physiologically relevant range of filament lengths and numbers, the network introduces a filament-length sensitive superdiffusive phase at early times which crosses over to a phase where the CTRW is dominant and produces subdiffusion at late times. We apply our approach to the problem of insulin secretion from cells and show that the superdiffusive phase introduced by the filament network manifests as a peak in the secretion at early times followed by an extended sustained release phase that is dominated by the CTRW process at late times. Our results are consistent with in vivo observations of insulin transport in healthy cells and shed light on the potential for the cell to tune functionally important transport phases by altering its cytoskeletal network.

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.

Limited processivity of single motors improves overall transport flux of self-assembled motor-cargo complexes

Single kinesin molecular motors can processively move along a microtubule (MT) a few micrometers on average before dissociating. However, cellular length scales over which transport occurs are several hundred microns and more. Why seemingly unreliable motors are used to transport cellular cargo remains poorly understood. We propose a theory for how low processivity, the average length of a single bout of directed motion, can enhance cellular transport when motors and cargos must first diffusively self-assemble into complexes. We employ stochastic modeling to determine the effect of processivity on overall cargo transport flux. We show that, under a wide range of physiologically relevant conditions, possessing "infinite" processivity does not maximize flux along MTs. Rather, we find that lowering processivity, i.e., weaker binding of motors to MTs, can improve transport flux. These results shed light on the relationship between processivity and transport efficiency and offer a theory for the physiological benefits of low motor processivity.

Active cargo positioning in antiparallel transport networks

Cytoskeletal filaments assemble into dense parallel, antiparallel, or disordered networks, providing a complex environment for active cargo transport and positioning by molecular motors. The interplay between the network architecture and intrinsic motor properties clearly affects transport properties but remains poorly understood. Here, by using surface micropatterns of actin polymerization, we investigate stochastic transport properties of colloidal beads in antiparallel networks of overlapping actin filaments. We found that 200-nm beads coated with myosin Va motors displayed directed movements toward positions where the net polarity of the actin network vanished, accumulating there. The bead distribution was dictated by the spatial profiles of local bead velocity and diffusion coefficient, indicating that a diffusion-drift process was at work. Remarkably, beads coated with heavy-mero-myosin II motors showed a similar behavior. However, although velocity gradients were steeper with myosin II, the much larger bead diffusion observed with this motor resulted in less precise positioning. Our observations are well described by a 3-state model, in which active beads locally sense the net polarity of the network by frequently detaching from and reattaching to the filaments. A stochastic sequence of processive runs and diffusive searches results in a biased random walk. The precision of bead positioning is set by the gradient of net actin polarity in the network and by the run length of the cargo in an attached state. Our results unveiled physical rules for cargo transport and positioning in networks of mixed polarity.

Theoretical Analysis of Run Length Distributions for Coupled Motor Proteins

Motor proteins, also known as biological molecular motors, play important roles in various biological processes. In recent years, properties of single-motor proteins have been intensively investigated using multiple experimental and theoretical tools. However, in real cellular systems biological motors typically function in groups, but the mechanisms of their collective dynamics remain not well understood. Here we investigate theoretically distributions of run lengths for coupled motor proteins that move along linear tracks. Our approach utilizes a method of first-passage processes, which is supplemented by Monte Carlo computer simulations. Theoretical analysis allowed us to clarify several aspects of the cooperativity mechanisms for coupled biological molecular motors. It is found that the run length distribution for two motors, in contrast to single motors, is nonmonotonic. In addition, the transport efficiency of two-motor complexes might be strongly increased. We also argue that the degree of cooperativity is influenced by several characteristics of motor proteins such as the strength of intermolecular interactions, stall forces, dissociations constants, and the detachment forces. The application of our theoretical analysis for several motor proteins is also discussed.

Bidirectional sliding of two parallel microtubules generated by multiple identical motors

It is often assumed in biophysical studies that when multiple identical molecular motors interact with two parallel microtubules, the microtubules will be crosslinked and locked together. The aim of this study is to examine this assumption mathematically. We model the forces and movements generated by motors with a time-continuous Markov process and find that, counter-intuitively, a tug-of-war results from opposing actions of identical motors bound to different microtubules. The model shows that many motors bound to the same microtubule generate a great force applied to a smaller number of motors bound to another microtubule, which increases detachment rate for the motors in minority, stabilizing the directional sliding. However, stochastic effects cause occasional changes of the sliding direction, which has a profound effect on the character of the long-term microtubule motility, making it effectively diffusion-like. Here, we estimate the time between the rare events of switching direction and use them to estimate the effective diffusion coefficient for the microtubule pair. Our main result is that parallel microtubules interacting with multiple identical motors are not locked together, but rather slide bidirectionally. We find explicit formulae for the time between directional switching for various motor numbers.

MAP7 regulates organelle transport by recruiting kinesin-1 to microtubules

Microtubule-associated proteins (MAPs) regulate microtubule polymerization, dynamics, and organization. In addition, MAPs alter the motility of kinesin and dynein to control trafficking along microtubules. MAP7 (ensconsin, E-MAP-115) is a ubiquitous MAP that organizes the microtubule cytoskeleton in mitosis and neuronal branching. MAP7 also recruits kinesin-1 to microtubules. To understand how the activation of kinesin-1 by MAP7 regulates the motility of organelles transported by ensembles of kinesin and dynein, we isolated organelles and reconstituted their motility in vitro In the absence of MAP7, isolated phagosomes exhibit approximately equal fractions of plus- and minus-end-directed motility along microtubules. MAP7 causes a pronounced shift in motility; phagosomes move toward the plus-end ∼80% of the time, and kinesin teams generate more force. To dissect MAP7-mediated regulation of kinesin-driven transport, we examined its effects on the motility and force generation of single and teams of full-length kinesin-1 motors. We find that MAP7 does not alter the force exerted by a single kinesin-1 motor, but instead increases its binding rate to the microtubule. For ensembles of kinesin, a greater number of kinesin motors are simultaneously engaged and generating force to preferentially target organelles toward the microtubule plus-end.

Force Generated by Two Kinesin Motors Depends on the Load Direction and Intermolecular Coupling

Kinesins are molecular motors that carry cellular cargoes. While the mechanics of single kinesins are well characterized experimentally, the behavior of multiple kinesins varies considerably among experiments. The basis for this variability is unknown. Here, we resolve single-motor force measurements into a vertical component, which accelerates kinesin detachment, and a horizontal component, which decelerates the detachment when resisting the motor. This directionality, when the different experimental geometries are considered, can account for much of the variation in multiple motor dynamics.

Subdiffusive continuous-time random walks with stochastic resetting

We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk scheme and independent resetting events generated uniformly in time according to the Poisson point process. In the first model the whole process is reset to the initial state, whereas in the second model only the position is subject to resets. The distinction between these two models arises from the non-Markovian character of the subdiffusive process. We derive exact expressions for the two lowest moments of the full propagator, stationary distributions, and first hitting time statistics. We also show, with an example of a constant drift, how these models can be generalized to include external forces. Possible applications to data analysis and modeling of biological systems are also discussed.

Force-Dependent Unbinding Rate of Molecular Motors from Stationary Optical Trap Data

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show how this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1.