Multiple kinesins induce tension for smooth cargo transport

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.

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.

Kinesin-1 transports morphologically distinct intracellular virions during vaccinia infection

Intracellular mature virus (IMV) are the first and most abundant infectious form of vaccinia virus to assemble during its replication cycle. IMV can undergo microtubule-based motility, but their directionality and the motor involved in their transport remain unknown. Here, we demonstrate that IMV, like intracellular enveloped virus (IEV), the second form of vaccinia that is wrapped in Golgi-derived membrane, recruit kinesin-1 and undergo anterograde transport. In vitro reconstitution of virion transport in infected cell extracts reveals that IMV and IEV move toward microtubule plus-ends with respective velocities of 0.66 and 0.56 µm/s. Quantitative imaging establishes that IMV and IEV recruit an average of 139 and 320 kinesin-1 motor complexes respectively. In the absence of kinesin-1 there is a near-complete loss of in vitro motility and reduction in the intracellular spread of both types of virion. Our observations demonstrate that kinesin-1 transports two morphologically distinct forms of vaccinia. Reconstitution of vaccinia-based microtubule motility in vitro provides a new model to elucidate how motor number and regulation impacts transport of a bona fide kinesin-1 cargo.

High-throughput force measurement of individual kinesin-1 motors during multi-motor transport

Molecular motors often work in teams to move a cellular cargo. Yet measuring the forces exerted by each motor is challenging. Using a sensor made with denatured ssDNA and multi-color fluorescence, we measured picoNewtons of forces and nanometer distances exerted by individual constrained kinesin-1 motors acting together while driving a common microtubule in vitro. We find that kinesins primarily exerted less than 1 pN force, even while the microtubule is bypassing artificial obstacles of 20-100 nanometer size. Occasionally, individual forces increase upon encountering obstacles, although at other times they do not, with the cargo continuing in a directional manner. Our high-throughput technique, which can measure forces by many motors simultaneously, is expected to be useful for many different types of molecular motors.

Mechanical testing of particle streaming and intact extracellular mucilage nanofibers reveal a role of elastic force in diatom motility

Diatoms are unicellular microalgae with a rigid cell wall, able to glide on surfaces by releasing nanopolymeric fibers through central slits known as raphes. Here we consider the modelNitszchia communisto perform quantitative studies on two complementary aspects involved in diatom gliding. Using video microscopy and automated image analysis, we measure the motion of test beads as they are pulled by extracellular polymeric substances (EPS) fibers at the diatom raphe (particle streaming). A multimodal distribution of particle speed is found, evidencing the appearance of short-time events of high speed and acceleration (known as jerky motion) and suggesting that different mechanisms contribute to set diatom velocity during gliding. Furthermore, we use optical tweezers to obtain force-extension records for extracellular diatom nanofibers; records are well described by the worm-like chain model of polymer elasticity. In contrast to previous studies based on application of denaturing force (in the nN regime), application of low force (up to 6 pN) and using enable us to obtain the persistence length of intact fibers. From these measurements, mechanical parameters of EPS fibers such as radius and elastic constant are estimated. Furthermore, by modeling particle streaming as a spring in parallel with a dashpot, we show that the time involved in the release of mechanical energy after fiber detachment from beads (elastic snapping) agrees with our observations of jerky motion. We conclude that the smooth and jerky motions displayed by gliding diatoms correspond to molecular motors and elastic snapping, respectively, thus providing quantitative elements that incorporate to current models of the mechanics behind diatom locomotion.

Intracellular motor-driven transport of rodlike smooth organelles along microtubules

Molecular motors are fascinating proteins that use the energy of ATP hydrolysis to drive vesicles and organelles along cytoskeleton filaments toward their final destination within the cell. Several copies of these proteins bind to the cargo and take turns transporting the cargo attaching to and detaching from the track stochastically. Despite the relevance of molecular motors to cell physiology, key aspects of their collective functioning are still unknown. In this work we propose a one-dimensional model for the transport of extensive and smooth organelles driven by molecular motors. We ran numerical simulations to study the behavior of the cargo for different motor configurations, focusing on the transport properties observable in the experiments, e.g., average speed of the organelle and variations in length. We found that active motors drive the cargo using two different mechanisms: Either they locate in front of the cargo and pull the organelle or they situate at the cargo lagging edge and push. Variations in the organelle length is in close relation with the fraction of motors in each configuration, which depends on the resisting load. The results of this model were contrasted with experimental data obtained from the tracking of rodlike mitochondria during active transport in Xenopus laevis melanophores.

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.