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

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.

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.

Actin Architecture Steers Microtubules in Active Cytoskeletal Composite

Motility assays use surface-immobilized molecular motors to propel cytoskeletal filaments. They have been widely used to characterize motor properties and their impact on cytoskeletal self-organization. Moreover, the motility assays are a promising class of bioinspired active tools for nanotechnological applications. While these assays involve controlling the filament direction and speed, either as a sensory readout or a functional feature, designing a subtle control embedded in the assay is an ongoing challenge. Here, we investigate the interaction between gliding microtubules and networks of actin filaments. We demonstrate that the microtubule's behavior depends on the actin architecture. Both unbranched and branched actin decelerate microtubule gliding; however, an unbranched actin network provides additional guidance and effectively steers the microtubules. This effect, which resembles the recognition of cortical actin by microtubules, is a conceptually new means of controlling the filament gliding with potential application in the design of active materials and cytoskeletal nanodevices.

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.

Magnetic Measurement and Stimulation of Cellular and Intracellular Structures

From single-pole magnetic tweezers to robotic magnetic-field generation systems, the development of magnetic micromanipulation systems, using electromagnets or permanent magnets, has enabled a multitude of applications for cellular and intracellular measurement and stimulation. Controlled by different configurations of magnetic-field generation systems, magnetic particles have been actuated by an external magnetic field to exert forces/torques and perform mechanical measurements on the cell membrane, cytoplasm, cytoskeleton, nucleus, intracellular motors, etc. The particles have also been controlled to generate aggregations to trigger cell signaling pathways and produce heat to cause cancer cell apoptosis for hyperthermia treatment. Magnetic micromanipulation has become an important tool in the repertoire of toolsets for cell measurement and stimulation and will continue to be used widely for further explorations of cellular/intracellular structures and their functions. Existing review papers in the literature focus on fabrication and position control of magnetic particles/structures (often termed micronanorobots) and the synthesis and functionalization of magnetic particles. Differently, this paper reviews the principles and systems of magnetic micromanipulation specifically for cellular and intracellular measurement and stimulation. Discoveries enabled by magnetic measurement and stimulation of cellular and intracellular structures are also summarized. This paper ends with discussions on future opportunities and challenges of magnetic micromanipulation in the exploration of cellular biophysics, mechanotransduction, and disease therapeutics.

Kinesin and Dynein Mechanics: Measurement Methods and Research Applications

Motor proteins play critical roles in the normal function of cells and proper development of organisms. Among motor proteins, failings in the normal function of two types of proteins, kinesin and dynein, have been shown to lead many pathologies, including neurodegenerative diseases and cancers. As such, it is critical to researchers to understand the underlying mechanics and behaviors of these proteins, not only to shed light on how failures may lead to disease, but also to guide research toward novel treatment and nano-engineering solutions. To this end, many experimental techniques have been developed to measure the force and motility capabilities of these proteins. This review will (a) discuss such techniques, specifically microscopy, atomic force microscopy (AFM), optical trapping, and magnetic tweezers, and (b) the resulting nanomechanical properties of motor protein functions such as stalling force, velocity, and dependence on adenosine triphosophate (ATP) concentrations will be comparatively discussed. Additionally, this review will highlight the clinical importance of these proteins. Furthermore, as the understanding of the structure and function of motor proteins improves, novel applications are emerging in the field. Specifically, researchers have begun to modify the structure of existing proteins, thereby engineering novel elements to alter and improve native motor protein function, or even allow the motor proteins to perform entirely new tasks as parts of nanomachines. Kinesin and dynein are vital elements for the proper function of cells. While many exciting experiments have shed light on their function, mechanics, and applications, additional research is needed to completely understand their behavior.

Diffusive tail anchorage determines velocity and force produced by kinesin-14 between crosslinked microtubules

Form and function of the mitotic spindle depend on motor proteins that crosslink microtubules and move them relative to each other. Among these are kinesin-14s, such as Ncd, which interact with one microtubule via their non-processive motor domains and with another via their diffusive tail domains, the latter allowing the protein to slip along the microtubule surface. Little is known about the influence of the tail domains on the protein's performance. Here, we show that diffusive anchorage of Ncd's tail domains impacts velocity and force considerably. Tail domain slippage reduced velocities from 270 nm s^-1 to 60 nm s^-1 and forces from several piconewtons to the sub-piconewton range. These findings challenge the notion that kinesin-14 may act as an antagonizer of other crosslinking motors, such as kinesin-5, during mitosis. It rather suggests a role of kinesin-14 as a flexible element, pliantly sliding and crosslinking microtubules to facilitate remodeling of the mitotic spindle.

Ensembles of Bidirectional Kinesin Cin8 Produce Additive Forces in Both Directions of Movement

Most kinesin motors move in only one direction along microtubules. Members of the kinesin-5 subfamily were initially described as unidirectional plus-end-directed motors and shown to produce piconewton forces. However, some fungal kinesin-5 motors are bidirectional. The force production of a bidirectional kinesin-5 has not yet been measured. Therefore, it remains unknown whether the mechanism of the unconventional minus-end-directed motility differs fundamentally from that of plus-end-directed stepping. Using force spectroscopy, we have measured here the forces that ensembles of purified budding yeast kinesin-5 Cin8 produce in microtubule gliding assays in both plus- and minus-end direction. Correlation analysis of pause forces demonstrated that individual Cin8 molecules produce additive forces in both directions of movement. In ensembles, Cin8 motors were able to produce single-motor forces up to a magnitude of ∼1.5 pN. Hence, these properties appear to be conserved within the kinesin-5 subfamily. Force production was largely independent of the directionality of movement, indicating similarities between the motility mechanisms for both directions. These results provide constraints for the development of models for the bidirectional motility mechanism of fission yeast kinesin-5 and provide insight into the function of this mitotic motor.

Control of molecular shuttles by designing electrical and mechanical properties of microtubules

Kinesin-driven microtubules have been focused on to serve as molecular transporters, called "molecular shuttles," to replace micro/nanoscale molecular manipulations necessitated in micro total analysis systems. Although transport, concentration, and detection of target molecules have been demonstrated, controllability of the transport directions is still a major challenge. Toward broad applications of molecular shuttles by defining multiple moving directions for selective molecular transport, we integrated a bottom-up molecular design of microtubules and a top-down design of a microfluidic device. The surface charge density and stiffness of microtubules were controlled, allowing us to create three different types of microtubules, each with different gliding directions corresponding to their electrical and mechanical properties. The measured curvature of the gliding microtubules enabled us to optimize the size and design of the device for molecular sorting in a top-down approach. The integrated bottom-up and top-down design achieved separation of stiff microtubules from negatively charged, soft microtubules under an electric field. Our method guides multiple microtubules by integrating molecular control and microfluidic device design; it is not only limited to molecular sorters but is also applicable to various molecular shuttles with the high controllability in their movement directions.

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

Kinesin-1 Expressed in Insect Cells Improves Microtubule in Vitro Gliding Performance, Long-Term Stability and Guiding Efficiency in Nanostructures

The cytoskeletal motor protein kinesin-1 has been successfully used for many nanotechnological applications. Most commonly, these applications use a gliding assay geometry where substrate-attached motor proteins propel microtubules along the surface. So far, this assay has only been shown to run undisturbed for up to 8 h. Longer run times cause problems like microtubule shrinkage, microtubules getting stuck and slowing down. This is particularly problematic in nanofabricated structures where the total number of microtubules is limited and detachment at the structure walls causes additional microtubule loss. We found that many of the observed problems are caused by the bacterial expression system, which has so far been used for nanotechnological applications of kinesin-1. We strive to enable the use of this motor system for more challenging nanotechnological applications where long-term stability and/or reliable guiding in nanostructures is required. Therefore, we established the expression and purification of kinesin-1 in insect cells which results in improved purity and--more importantly--long-term stability > 24 h and guiding efficiencies of > 90% in lithographically defined nanostructures.

Understanding the role of transport velocity in biomotor-powered microtubule spool assembly

We examined the role of transport velocity in the active assembly of microtubule spools. We found that transport velocity influences the kinetics of spool assembly, but not the steady-state properties of assembled spools.

Synchronization of elastically coupled processive molecular motors and regulation of cargo transport

The collective work of motor proteins plays an important role in cellular transport processes. Since measuring intermotor coupling and hence a comparison to theoretical predictions is difficult, we introduce the synchronization as an alternative observable for motor cooperativity. This synchronization can be determined from the ratio of the mean times of motor resting and stepping. Results from a multistate Markov chain model and Brownian dynamics simulations, describing the elastically coupled motors, coincide well. Our model can explain the experimentally observed effect of strongly increased transport velocities and powers by the synchronization and coupling of myosin V and kinesin I.

Biophysical challenges to axonal transport: motor-cargo deficiencies and neurodegeneration

Axonal transport is indispensable for the distribution of vesicles, organelles, messenger RNAs (mRNAs), and signaling molecules along the axon. This process is mediated by kinesins and dyneins, molecular motors that bind to cargoes and translocate on microtubule tracks. Tight modulation of motor protein activity is necessary, but little is known about the molecules and mechanisms that regulate transport. Moreover, evidence suggests that transport impairments contribute to the initiation or progression of neurodegenerative diseases, or both, but the mechanisms by which motor activity is affected in disease are unclear. In this review, we discuss some of the physical and biophysical properties that influence motor regulation in healthy neurons. We further discuss the evidence for the role of transport in neurodegeneration, highlighting two pathways that may contribute to transport impairment-dependent disease: genetic mutations or variation, and protein aggregation. Understanding how and when transport parameters change in disease will help delineate molecular mechanisms of neurodegeneration.

Tug-of-war of microtubule filaments at the boundary of a kinesin- and dynein-patterned surface

Intracellular cargo is transported by multiple motor proteins. Because of the force balance of motors with mixed polarities, cargo moves bidirectionally to achieve biological functions. Here, we propose a microtubule gliding assay for a tug-of-war study of kinesin and dynein. A boundary of the two motor groups is created by photolithographically patterning gold to selectively attach kinesin to the glass and dynein to the gold surface using a self-assembled monolayer. The relationship between the ratio of two antagonistic motor numbers and the velocity is derived from a force-velocity relationship for each motor to calculate the detachment force and motor backward velocity. Although the tug-of-war involves >100 motors, values are calculated for a single molecule and reflect the collective dynein and non-collective kinesin functions when they work as a team. This assay would be useful for detailed in vitro analysis of intracellular motility, e.g., mitosis, where a large number of motors with mixed polarities are involved.

Molecular adaptations allow dynein to generate large collective forces inside cells

Many cellular processes require large forces that are generated collectively by multiple cytoskeletal motor proteins. Understanding how motors generate force as a team is therefore fundamentally important but is poorly understood. Here, we demonstrate optical trapping at single-molecule resolution inside cells to quantify force generation by motor teams driving single phagosomes. In remarkable paradox, strong kinesins fail to work collectively, whereas weak and detachment-prone dyneins team up to generate large forces that tune linearly in strength and persistence with dynein number. Based on experimental evidence, we propose that leading dyneins in a load-carrying team take short steps, whereas trailing dyneins take larger steps. Dyneins in such a team bunch close together and therefore share load better to overcome low/intermediate loads. Up against higher load, dyneins "catch bond" tenaciously to the microtubule, but kinesins detach rapidly. Dynein therefore appears uniquely adapted to work in large teams, which may explain how this motor executes bewilderingly diverse cellular processes.

Novel systems for dynamically assessing insulin action in live cells reveals heterogeneity in the insulin response

Regulated GLUT4 trafficking is a key action of insulin. Quantitative stepwise analysis of this process provides a powerful tool for pinpointing regulatory nodes that contribute to insulin regulation and insulin resistance. We describe a novel GLUT4 construct and workflow for the streamlined dissection of GLUT4 trafficking; from simple high throughput screens to high resolution analyses of individual vesicles. We reveal single cell heterogeneity in insulin action highlighting the utility of this approach - each cell displayed a unique and highly reproducible insulin response, implying that each cell is hard-wired to produce a specific output in response to a given stimulus. These data highlight that the response of a cell population to insulin is underpinned by extensive heterogeneity at the single cell level. This heterogeneity is pre-programmed within each cell and is not the result of intracellular stochastic events.

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

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

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

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