Molecular motors: a traffic cop within?

Tug-of-war between two elastically coupled molecular motors: a case study on force generation and force balance

Intracellular transport is performed by molecular motors that pull cargos along cytoskeletal filaments. Many cellular cargos are observed to move bidirectionally, with fast transport in both directions. This behaviour can be understood as a stochastic tug-of-war between two teams of antagonistic motors. The first theoretical model for such a tug-of-war, the Müller-Klumpp-Lipowsky (MKL) model, was based on two simplifying assumptions: (i) both motor teams move with the same velocity in the direction of the stronger team, and (ii) this velocity matching and the associated force balance arise immediately after the rebinding of an unbound motor to the filament. In this study, we extend the MKL model by including an elastic coupling between the antagonistic motors, and by allowing the motors to perform discrete motor steps. Each motor step changes the elastic interaction forces experienced by the motors. In order to elucidate the basic concepts of force balance and force fluctuations, we focus on the simplest case of two antagonistic motors, one kinesin against one dynein. We calculate the probability distribution for the spatial separation of the motors and the dependence of this distribution on the motors' unbinding rate. We also compute the probability distribution for the elastic interaction forces experienced by the motors, which determines the average elastic force 〈F〉 and the standard deviation of the force fluctuations around this average value. The average force 〈F〉 is found to decrease monotonically with increasing unbinding rate ε₀. The behaviour of the MKL model is recovered in the limit of small ε₀. In the opposite limit of large ε₀, 〈F〉 is found to decay to zero as 1/ε₀. Finally, we study the limiting case with ε₀ = 0 for which we determine both the force statistics and the time needed to attain the steady state. Our theoretical predictions are accessible to experimental studies of in vitro systems consisting of two antagonistic motors attached to a synthetic scaffold or crosslinked via DNA hybridization.

KymoAnalyzer: a software tool for the quantitative analysis of intracellular transport in neurons

In axons, proper localization of proteins, vesicles, organelles, and other cargoes is accomplished by the highly regulated coordination of kinesins and dyneins, molecular motors that bind to cargoes and translocate them along microtubule (MT) tracks. Impairment of axonal transport is implicated in the pathogenesis of multiple neurodegenerative disorders including Alzheimer's and Huntington's diseases. To understand how MT-based cargo motility is regulated and to delineate its role in neurodegeneration, it is critical to analyze the detailed dynamics of moving cargoes inside axons. Here, we present KymoAnalyzer, a software tool that facilitates the robust analysis of axonal transport from time-lapse live-imaging sequences. KymoAnalyzer is an open-source software that automatically classifies particle trajectories and systematically calculates velocities, run lengths, pauses, and a wealth of other parameters that are characteristic of motor-based transport. We anticipate that laboratories will easily use this package to unveil previously uncovered intracellular transport details of individually-moving cargoes inside neurons.

As the fat flies: The dynamic lipid droplets of Drosophila embryos

Research into lipid droplets is rapidly expanding, and new cellular and organismal roles for these lipid-storage organelles are continually being discovered. The early Drosophila embryo is particularly well suited for addressing certain questions in lipid-droplet biology and combines technical advantages with unique biological phenomena. This review summarizes key features of this experimental system and the techniques available to study it, in order to make it accessible to researchers outside this field. It then describes the two topics most heavily studied in this system, lipid-droplet motility and protein sequestration on droplets, discusses what is known about the molecular players involved, points to open questions, and compares the results from Drosophila embryo studies to what it is known about lipid droplets in other systems.

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.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Label-free imaging of lipid-droplet intracellular motion in early Drosophila embryos using femtosecond-stimulated Raman loss microscopy

Lipid droplets are complex organelles that exhibit highly dynamic behavior in early Drosophila embryo development. Imaging lipid droplet motion provides a robust platform for the investigation of shuttling by kinesin and dynein motors, but methods for imaging are either destructive or deficient in resolution and penetration to study large populations of droplets in an individual embryo. Here we report real-time imaging and quantification of droplet motion in live embryos using a recently developed technique termed "femtosecond-stimulated Raman loss" microscopy. We captured long-duration time-lapse images of the developing embryo, tracked single droplet motion within large populations of droplets, and measured the velocity and turning frequency of each particle at different apical-to-basal depths and stages of development. To determine whether the quantities for speed and turning rate measured for individual droplets are sufficient to predict the population distributions of droplet density, we simulated droplet motion using a velocity-jump model. This model yielded droplet density distributions that agreed well with experimental observations without any model optimization or unknown parameter estimation, demonstrating the sufficiency of a velocity-jump process for droplet trafficking dynamics in blastoderm embryos.

ACTIVE BIO-SYSTEMS: FROM SINGLE MOTOR MOLECULES TO COOPERATIVE CARGO TRANSPORT

Living cells contain a large number of molecular motors that convert the chemical energy released from nucleotide hydrolysis into mechanical work. This review focusses on stepping motors that move along cytoskeletal filaments. The behavior of these motors involves three distinct nonequilibrium processes that cover a wide range of length and time scales: (i) Directed stepping of single motors bound to a filament; (ii) Composite motor walks of single motors consisting of directed stepping interrupted by diffusive motion; and (iii) Cooperative transport by teams of several motors. On the molecular scale, the energy conversion of these motors leads to single steps along the filaments with a step size of about 10 nm. The corresponding chemomechanical coupling is governed by several distinct motor cycles, which represent the dominant pathways for different values of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses the direction of its motion. Because of thermal noise, the stepping motors unbind from the filaments after a certain run time and run length. For kinesin, the run time is about 1 s and the run length is about 1 μm for high ATP concentration and low load force. On length scales that are large compared to the run length, a single motor undergoes composite walks consisting of directed stepping interrupted by diffusive motion. The relative importance of bound and unbound motor states depends on the binding and unbinding rates of the motors. The effective transport velocity and diffusion coefficient of the motors are determined by the geometry of the compartments, in which the motors move. The effective diffusion coefficient can be enhanced by several orders of magnitude if the motors undergo active diffusion by interacting with certain filament patterns. In vivo, stepping motors are responsible for the transport of vesicles and other types of intracellular cargo particles that shuttle between the different cell compartments. This cargo transport is usually performed by teams of motors. If all motors belong to the same molecular species, the cooperative action of the motors leads to uni-directional transport with a strongly increased run length and to a characteristic force dependence of the velocity distributions. If two antagonistic species of motors pull on the cargo, they perform a stochastic tug-of-war, which is characterized by a subtle force balance between the two motor teams and leads to seven distinct patterns of uni- and bi-directional transport. So far, all experimental observations on bi-directional transport are consistent with such a tug-of-war. Finally, the traffic of interacting motors is also briefly discussed. Depending on their mutual interactions and the compartment geometry, the motors form various spatio-temporal patterns such as traffic jams, and undergo nonequilibrium phase transitions between such transport patterns.

Molecular motors: directing traffic during RNA localization

RNA localization, the enrichment of RNA in a specific subcellular region, is a mechanism for the establishment and maintenance of cellular polarity in a variety of systems. Ultimately, this results in a universal method for spatially restricting gene expression. Although the consequences of RNA localization are well-appreciated, many of the mechanisms that are responsible for carrying out polarized transport remain elusive. Several recent studies have illuminated the roles that molecular motor proteins play in the process of RNA localization. These studies have revealed complex mechanisms in which the coordinated action of one or more motor proteins can act at different points in the localization process to direct RNAs to their final destination. In this review, we discuss recent findings from several different systems in an effort to clarify pathways and mechanisms that control the directed movement of RNA.

Transport of germ plasm on astral microtubules directs germ cell development in Drosophila

BACKGROUND

In many organisms, germ cells are segregated from the soma through the inheritance of the specialized germ plasm, which contains mRNAs and proteins that specify germ cell fate and promote germline development. Whereas germ plasm assembly has been well characterized, mechanisms mediating germ plasm inheritance are poorly understood. In the Drosophila embryo, germ plasm is anchored to the posterior cortex, and nuclei that migrate into this region give rise to the germ cell progenitors, or pole cells. How the germ plasm interacts with these nuclei for pole cell induction and is selectively incorporated into the forming pole cells is not known.

RESULTS

Live imaging of two conserved germ plasm components, nanos mRNA and Vasa protein, revealed that germ plasm segregation is a dynamic process involving active transport of germ plasm RNA-protein complexes coordinated with nuclear migration. We show that centrosomes accompanying posterior nuclei induce release of germ plasm from the cortex and recruit these components by dynein-dependent transport on centrosome-nucleated microtubules. As nuclei divide, continued transport on astral microtubules partitions germ plasm to daughter nuclei, leading to its segregation into pole cells. Disruption of these transport events prevents incorporation of germ plasm into pole cells and impairs germ cell development.

CONCLUSIONS

Our results indicate that active transport of germ plasm is essential for its inheritance and ensures the production of a discrete population of germ cell progenitors endowed with requisite factors for germline development. Transport on astral microtubules may provide a general mechanism for the segregation of cell fate determinants.

Controlled and stochastic retention concentrates dynein at microtubule ends to keep endosomes on track

Bidirectional transport of early endosomes (EEs) involves microtubules (MTs) and associated motors. In fungi, the dynein/dynactin motor complex concentrates in a comet-like accumulation at MT plus-ends to receive kinesin-3-delivered EEs for retrograde transport. Here, we analyse the loading of endosomes onto dynein by combining live imaging of photoactivated endosomes and fluorescent dynein with mathematical modelling. Using nuclear pores as an internal calibration standard, we show that the dynein comet consists of ∼55 dynein motors. About half of the motors are slowly turned over (T(1/2): ∼98 s) and they are kept at the plus-ends by an active retention mechanism involving an interaction between dynactin and EB1. The other half is more dynamic (T(1/2): ∼10 s) and mathematical modelling suggests that they concentrate at MT ends because of stochastic motor behaviour. When the active retention is impaired by inhibitory peptides, dynein numbers in the comet are reduced to half and ∼10% of the EEs fall off the MT plus-ends. Thus, a combination of stochastic accumulation and active retention forms the dynein comet to ensure capturing of arriving organelles by retrograde motors.

Stochastic analysis of the motion of DNA nanomechanical bipeds

In this paper, we formulate and analyze a Markov process modeling the motion of DNA nanomechanical walking devices.We consider a molecular biped restricted to a well-defined one-dimensional track and study its asymptotic behavior.Our analysis allows for the biped legs to be of different molecular composition, and thus to contribute differently to the dynamics. Our main result is a functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model. A law of large numbers, a recurrence/transience characterization and large deviations estimates are also obtained.Our approach is applicable to a variety of other biological motors such as myosin and motor proteins on polymer filaments.

Queueing induced by bidirectional motor motion near the end of a microtubule

Recent live observations of motors in long-range microtubule (MT) dependent transport in the fungus Ustilago maydis have reported bidirectional motion of dynein and an accumulation of the motors at the polymerization-active (the plus-end) of the microtubule. Quantitative data derived from in vivo observation of dynein has enabled us to develop an accurate, quantitatively-valid asymmetric simple exclusion process (ASEP) model that describes the coordinated motion of anterograde and retrograde motors sharing a single oriented microtubule. We give approximate expressions for the size and distribution of the accumulation, and discuss queueing properties for motors entering this accumulation. We show for this ASEP model, that the mean accumulation can be modeled as an M/M/∞ queue that is Poisson distributed with mean F(arr)/p(d), where F(arr) is the flux of motors that arrives at the tip and p(d) is the rate at which individual motors change direction from anterograde to retrograde motion. Deviations from this can in principle be used to gain information about other processes at work in the accumulation. Furthermore, our work is a significant step toward a mathematical description of the complex interactions of motors in cellular long-range transport of organelles.

Bidirectional transport by molecular motors: enhanced processivity and response to external forces

Intracellular transport along cytoskeletal filaments is often mediated by two teams of molecular motors that pull on the same cargo and move in opposite directions along the filaments. We have recently shown theoretically that this bidirectional transport can be understood as a stochastic tug-of-war between the two motor teams. Here, we further develop our theory to investigate the experimentally accessible dynamic behavior of cargos transported by strong motors such as kinesin-1 or cytoplasmic dynein. By studying the run and binding times of such a cargo, we show that the properties of biological motors, such as the large ratio of stall/detachment force and the small ratio of superstall backward/forward velocity, are favorable for bidirectional cargo transport, leading to fast motion and enhanced diffusion. In addition, cargo processivity is shown to be strongly enhanced by transport via several molecular motors even if these motors are engaged in a tug-of-war. Finally, we study the motility of a bidirectional cargo under force. Frictional forces arising, e.g., from the viscous cytoplasm, lead to peaks in the velocity distribution, while external forces as exerted, e.g., by an optical trap, lead to hysteresis effects. Our results, in particular our explicit expressions for the cargo binding time and the distance of the peaks in the velocity relation under friction, are directly accessible to in vitro as well as in vivo experiments.

Bidirectional transport: matchmaking for motors

In bidirectional transport, opposing motors frequently require each other for full activity. A new study suggests that mechanical coupling between motors is the key to this reciprocal activation.

Lattice-gas model for active vesicle transport by molecular motors with opposite polarities

We introduce a multispecies lattice-gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargos being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process to characterize the motion of the interacting cargos, we allow for mass exchange with the environment, input, and output at filament boundaries and focus on the role of interconversion rates and how they affect the directionality of the net cargo transport. We quantify the effect of the various different competing processes in terms of nonequilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation-deposition processes, introduces qualitatively unique features in the phase diagrams. We observe regimes of three-phase coexistence, the possibility of phase re-entrance, and a significant flexibility in how the different phase boundaries shift in response to changes in control parameters. The moving steady-state solutions of this model allows for different possibilities for the spatial distribution of cargo vesicles, ranging from homogeneous distribution of vesicles to polarized distributions, characterized by inhomogeneities or shocks. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe that this minimal model will clarify the understanding of many features of collective vesicle transport, apart from serving as the basis for building more exact quantitative models for vesicle transport relevant to various in vivo situations.

Regulation of ER-Golgi intermediate compartment tubulation and mobility by COPI coats, motor proteins and microtubules

Little is known about the formation and regulation of endoplasmic reticulum (ER)-Golgi transport intermediates, although previous studies suggest that cargo is the main regulator of their morphology. In this study, we analyze the role of coat protein I (COPI) and cytoskeleton in the formation of tubular ER-Golgi intermediate compartment (ERGIC) and also show that partial COPI detachment by means of low temperature (15 degrees C) or brefeldin A induces the formation of transient tubular ERGIC elements. Most of them moved from the cell periphery to the perinuclear area and were 2.5x slower than vesicles. Time-lapse analysis of living cells demonstrates that the ERGIC elements are able to shift very fast from tubular to vesicular forms and vice versa, suggesting that the amount of cargo is not the determining factor for ERGIC morphology. Both the partial microtubule depolymerization and the inhibition of uncoating of the membranes result in the formation of long tubules that grow from round ERGICs and form at complex network. Interestingly, both COPI detachment and microtubule depolymerization induce a redistribution of kinesin from peripheral ERGIC elements to the Golgi area, while dynein distribution is not affected. However, both kinesin and dynein downregulation by RNA interference induced ERGIC tubulation. The tubules induced by kinesin depletion were static, whereas those resulting from dynein depletion were highly mobile. Our results strongly suggest that the interaction of motor proteins with COPI-coated membranes and microtubules is a key regulator of ERGIC morphology and mobility.

Fat on the move: intracellular motion of lipid droplets

Lipid droplets are intracellular organelles that play central roles in lipid metabolism. In many cells, lipid droplets undergo active motion, typically along microtubules. This motion has been proposed to aid growth and breakdown of droplets, to allow net transfer of nutrients from sites of synthesis to sites of need and to deliver proteins and lipophilic signals. This review summarizes the current understanding of where, why and how lipid droplets move.