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

Tunable intracellular transport on converging microtubule morphologies

A common type of cytoskeletal morphology involves multiple microtubules converging with their minus ends at the microtubule organizing center (MTOC). The cargo-motor complex will experience ballistic transport when bound to microtubules or diffusive transport when unbound. This machinery allows for sequestering and subsequent dispersal of dynein-transported cargo. The general principles governing dynamics, efficiency, and tunability of such transport in the MTOC vicinity are not fully understood. To address this, we develop a one-dimensional model that includes advective transport toward an attractor (such as the MTOC) and diffusive transport that allows particles to reach absorbing boundaries (such as cellular membranes). We calculated the mean first passage time (MFPT) for cargo to reach the boundaries as a measure of the effectiveness of sequestering (large MFPT) and diffusive dispersal (low MFPT). We show that the MFPT experiences a dramatic growth, transitioning from a low to high MFPT regime (dispersal to sequestering) over a window of cargo on-/off-rates that is close to in vivo values. Furthermore, increasing either the on-rate (attachment) or off-rate (detachment) can result in optimal dispersal when the attractor is placed asymmetrically. Finally, we also describe a regime of rare events where the MFPT scales exponentially with motor velocity and the escape location becomes exponentially sensitive to the attractor positioning. Our results suggest that structures such as the MTOC allow for the sensitive control of the spatial and temporal features of transport and corresponding function under physiological conditions.

Kinesin-1-transported liposomes prefer to go straight in 3D microtubule intersections by a mechanism shared by other molecular motors

Kinesin-1 ensembles maneuver vesicular cargoes through the three-dimensional (3D) intracellular microtubule (MT) network. To define how such cargoes navigate MT intersections, we first determined how many kinesins from an ensemble on a lipid-based cargo simultaneously engage a MT, and then determined the directional outcomes (straight, turn, terminate) for liposome cargoes at perpendicular MT intersections. Run lengths of 350-nm diameter liposomes decorated with up to 20, constitutively active, truncated kinesin-1 KIF5B (K543) were longer than single motor transported cargo, suggesting multiple motor engagement. However, detachment forces of lipid-coated beads with ~20 kinesins, measured using an optical trap, showed no more than three simultaneously engaged motors, with a single engaged kinesin predominating, indicating anticooperative MT binding. At two-dimensional (2D) and 3D in vitro MT intersections, liposomes frequently paused (~2 s), suggesting kinesins simultaneously bind both MTs and engage in a tug-of-war. Liposomes showed no directional outcome bias in 2D (1.1 straight:turn ratio) but preferentially went straight (1.8 straight:turn ratio) in 3D intersections. To explain these data, we developed a mathematical model of liposome transport incorporating the known mechanochemistry of kinesins, which diffuse on the liposome surface, and have stiff tails in both compression and extension that impact how motors engage the intersecting MTs. Our model predicts the ~3 engaged motor limit observed in the optical trap and the bias toward going straight in 3D intersections. The striking similarity of these results to our previous study of liposome transport by myosin Va suggests a "universal" mechanism by which cargoes navigate 3D intersections.

A new method to experimentally quantify dynamics of initial protein-protein interactions

Cells run on initiation of protein-protein interactions, which are dynamically tuned spatially and temporally to modulate cellular events. This tuning can be physical, such as attaching the protein to a cargo or protein complex, thereby altering its diffusive properties, or modulating the distance between protein pairs, or chemical, by altering the proteins' conformations (e.g., nucleotide binding state of an enzyme, post-translational modification of a protein, etc.). Because a dynamic and changing subset of proteins in the cell could be in any specific state, ensemble measurements are not ideal-to untangle which of the factors are important, and how, we need single-molecule measurements. Experimentally, until now we have not had good tools to precisely measure initiation of such protein-protein interactions at the single-molecule level. Here, we develop a new method to measure dynamics of initial protein-protein interactions, allowing measurement of how properties such as the distance between proteins, and their tethered length can modulate the rate of interactions. In addition to precise measurement distance dependent motor-MT rebinding dynamics, we demonstrate the use of a dithered optical trap to measure dynamic motor-MT interactions and further discuss the possibilities of this technique being applicable to other systems.

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.

"Spatial Relationships Matter: Kinesin-1 Molecular Motors Transport Liposome Cargo Through 3D Microtubule Intersections In Vitro"

Kinesin-1 ensembles maneuver vesicular cargoes through intersections in the 3-dimensional (3D) intracellular microtubule (MT) network. To characterize directional outcomes (straight, turn, terminate) at MT intersections, we challenge 350 nm fluid-like liposomes transported by ~10 constitutively active, truncated kinesin-1 KIF5B (K543) with perpendicular 2-dimensional (2D) and 3D intersections in vitro. Liposomes frequently pause at 2D and 3D intersections (~2s), suggesting that motor teams can simultaneously engage each MT and undergo a tug-of-war. Once resolved, the directional outcomes at 2D MT intersections have a straight to turn ratio of 1.1; whereas at 3D MT intersections, liposomes more frequently go straight (straight to turn ratio of 1.8), highlighting that spatial relationships at intersections bias directional outcomes. Using 3D super-resolution microscopy (STORM), we define the gap between intersecting MTs and the liposome azimuthal approach angle heading into the intersection. We develop an in silico model in which kinesin-1 motors diffuse on the liposome surface, simultaneously engage the intersecting MTs, generate forces and detach from MTs governed by the motors' mechanochemical cycle, and undergo a tug-of-war with the winning team determining the directional outcome in 3D. The model predicts that 1-3 motors typically engage the MT, consistent with optical trapping measurements. Modeled liposomes also predominantly go straight through 3D intersections over a range of intersection gaps and liposome approach angles, even when obstructed by the crossing MT. Our observations and modeling offer mechanistic insights into how cells might tune the MT cytoskeleton, cargo, and motors to modulate cargo transport.

Vesicles driven by dynein and kinesin exhibit directional reversals without regulators

Intracellular vesicular transport along cytoskeletal filaments ensures targeted cargo delivery. Such transport is rarely unidirectional but rather bidirectional, with frequent directional reversals owing to the simultaneous presence of opposite-polarity motors. So far, it has been unclear whether such complex motility pattern results from the sole mechanical interplay between opposite-polarity motors or requires regulators. Here, we demonstrate that a minimal system, comprising purified Dynein-Dynactin-BICD2 (DDB) and kinesin-3 (KIF16B) attached to large unilamellar vesicles, faithfully reproduces in vivo cargo motility, including runs, pauses, and reversals. Remarkably, opposing motors do not affect vesicle velocity during runs. Our computational model reveals that the engagement of a small number of motors is pivotal for transitioning between runs and pauses. Taken together, our results suggest that motors bound to vesicular cargo transiently engage in a tug-of-war during pauses. Subsequently, stochastic motor attachment and detachment events can lead to directional reversals without the need for regulators.

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.

On the use of thermal forces to probe kinesin's response to force

The stepping dynamics of cytoskeletal motor proteins determines the dynamics of cargo transport. In its native cellular environment, a molecular motor is subject to forces from several sources including thermal forces and forces ensuing from the interaction with other motors bound to the same cargo. Understanding how the individual motors respond to these forces can allow us to predict how they move their cargo when part of a team. Here, using simulation, we show that details of how the kinesin motor responds to small assisting forces-which, at the moment, are not experimentally constrained-can lead to significant changes in cargo dynamics. Using different models of the force-dependent detachment probability of the kinesin motor leads to different predictions on the run-length of the cargo they carry. These differences emerge from the thermal forces acting on the cargo and transmitted to the motor through the motor tail that tethers the motor head to the microtubule. We show that these differences appear for cargo carried by individual motors or motor teams, and use our findings to propose the use of thermal forces as a probe of kinesin's response to force in this otherwise inaccessible force regime.

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.

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.

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of conditional mean first passage times for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.