Collective dynamics of processive cytoskeletal motors

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

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.

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.

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.

Mechanisms of Regulation in Intraflagellar Transport

Cilia are eukaryotic organelles essential for movement, signaling or sensing. Primary cilia act as antennae to sense a cell's environment and are involved in a wide range of signaling pathways essential for development. Motile cilia drive cell locomotion or liquid flow around the cell. Proper functioning of both types of cilia requires a highly orchestrated bi-directional transport system, intraflagellar transport (IFT), which is driven by motor proteins, kinesin-2 and IFT dynein. In this review, we explore how IFT is regulated in cilia, focusing from three different perspectives on the issue. First, we reflect on how the motor track, the microtubule-based axoneme, affects IFT. Second, we focus on the motor proteins, considering the role motor action, cooperation and motor-train interaction plays in the regulation of IFT. Third, we discuss the role of kinases in the regulation of the motor proteins. Our goal is to provide mechanistic insights in IFT regulation in cilia and to suggest directions of future research.

Cooperation and Competition Coexist in Bidirectional Transport by Motor Proteins

In intracellular transport, the cargo is usually simultaneously carried by two types of motor proteins that move oppositely, widely described as a "tug-of-war". We show theoretically that apart from the apparent competition, there is also a unintuitive cooperation between motors with opposite directionality. The model reproduces the in vivo experimental data with high accuracy. Under certain conditions, the cooperation can significantly increase the transport distance, rationalizing the choice of bidirectional over unidirectional transport in evolution. We further derive the exact analytical solution for the transport distance. Our results pave the road to understanding the physical nature of intracellular transport by motor proteins.

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.

F1-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory

In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F1-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F1-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium "controlled rotation" experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5-6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

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.

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.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Association between aberrant dynein cytoplasmic 1 light intermediate chain 1 expression levels, mucins and chemosensitivity in colorectal cancer

Dynein transport along the cytoskeletal microtubules towards the minus end is essential for cell division, cell migration and other basic cellular functions. Dynein cytoplasmic 1 light intermediate chain 1 (DYNC1LI1) has been previously associated with pancreatic ductal adenocarcinoma, hepatocellular carcinoma and prostate cancer. Cytoskeletal structures are involved in the regulation of the mucosal barrier integrity. Thus, improving our understanding of the molecular mechanisms that regulate the mucosal barrier is critical for cancer management and treatment. The present study aimed to investigate DYNC1LI1 expression in colorectal cancer (CRC) tissues. The American Joint Committee on Cancer Stage II CRC cell line LS 174T was used to determine the association between the cellular expression levels of DYNC1LI1 and different types of mucin (MUC) by reverse transcription-quantitative PCR. The role of DYNC1LI1 in cell chemosensitivity and proliferation was also evaluated in the presence of the DNA analog 5-fluorouracil (5-FU) or the platinum-based drug, oxaliplatin by the MTT assay. LS 174T cells with decreased expression levels of DYNC1LI1 were discovered to be more sensitive to 5-FU compared with LS 174T cells with endogenous DYNC1LI1 expression levels. Moreover, LS 174T cells transfected with short hairpin RNA targeting DYNC1LI1 were associated with low MUC1 and high MUC2, MUC4 and MUC5AC expression levels. Notably, the CRC cells with low MUC1 expression levels and high expression levels of the other MUCs (MUC2, MU4 and MUC5AC) were shown to benefit from 5-FU treatment. In conclusion, the findings of the present study have suggested that DYNC1LI1 expression may be significantly associated with MUC expression levels and may be used to predict the chemotherapeutic efficiency. However, additional functional studies and clinical reports are required for an improved understanding of the significance of these molecular interactions in tumorigenesis.

Tuning molecular motor transport through cytoskeletal filament network organization

Within cells, crosslinking proteins organize cytoskeletal filaments both temporally and spatially to create dynamic and structurally diverse networks. Molecular motors move on these networks for both force generation and transport processes. How the transport statistics depend on the network architecture remains poorly characterized. Using cross-linking proteins (α-actinin, fimbrin, fascin, or filamin) and purified actin, we create cytoskeletal networks with diverse microscopic architectures. We track the motion of myosin II motor proteins moving on these networks and calculate transport statistics. We observe that motor dynamics change predictably based on the bundling of filaments within the underlying networks and discuss implications for network function.

Collective Force Generation by Molecular Motors Is Determined by Strain-Induced Unbinding

In the living cell, we encounter a large variety of motile processes such as organelle transport and cytoskeleton remodeling. These processes are driven by motor proteins that generate force by transducing chemical free energy into mechanical work. In many cases, the molecular motors work in teams to collectively generate larger forces. Recent optical trapping experiments on small teams of cytoskeletal motors indicated that the collectively generated force increases with the size of the motor team but that this increase depends on the motor type and on whether the motors are studied in vitro or in vivo. Here, we use the theory of stochastic processes to describe the motion of N motors in a stationary optical trap and to compute the N-dependence of the collectively generated forces. We consider six distinct motor types, two kinesins, two dyneins, and two myosins. We show that the force increases always linearly with N but with a prefactor that depends on the performance of the single motor. Surprisingly, this prefactor increases for weaker motors with a lower stall force. This counter-intuitive behavior reflects the increased probability with which stronger motors detach from the filament during strain generation. Our theoretical results are in quantitative agreement with experimental data on small teams of kinesin-1 motors.

Multiple kinesins induce tension for smooth cargo transport

How cargoes move within a crowded cell—over long distances and at speeds nearly the same as when moving on unimpeded pathway—has long been mysterious. Through an in vitro force-gliding assay, which involves measuring nanometer displacement and piconewtons of force, we show that multiple mammalian kinesin-1 (from 2 to 8) communicate in a team by inducing tension (up to 4 pN) on the cargo. Kinesins adopt two distinct states, with one-third slowing down the microtubule and two-thirds speeding it up. Resisting kinesins tend to come off more rapidly than, and speed up when pulled by driving kinesins, implying an asymmetric tug-of-war. Furthermore, kinesins dynamically interact to overcome roadblocks, occasionally combining their forces. Consequently, multiple kinesins acting as a team may play a significant role in facilitating smooth cargo motion in a dense environment. This is one of few cases in which single molecule behavior can be connected to ensemble behavior of multiple motors.

The inside of a cell is a crowded space, full of proteins and other molecules. Yet, the molecular motors that transport some of those molecules within the cell move at the same speed as they would in pure water – about one micrometer per second. How the molecular motors could achieve such speeds in crowded cells was unclear. Nevertheless, Tjioe et al. suspected that the answer might be related to how multiple motors work together.

Molecular motors move by walking along filaments inside the cell and pulling their cargo from one location to another. Other molecules that bind to the filaments should, in theory, act like “roadblocks” and impede the movement of the cargo. Tjioe et al. studied a motor protein called kinesin, which walks on filaments called microtubules. But instead of looking at these motors moving along microtubules inside a cell, Tjioe et al. used a simpler system where the cell was eliminated, and all parts were purified. Specifically, Tjioe et al. tethered purified motors to a piece of glass and then observed them under an extremely accurate microscope as they moved free-floating, fluorescently labelled microtubules. The microtubules, in this scenario, were acting like cargoes, where many kinesins could bind. Each kinesin motor also had a small chemical tag that could emit light. By following the movement of the lights, it was possible to calculate what each kinesin was doing and how the cargo moved.

When more than one kinesin molecule was acting, the tension and speed of one kinesin affected the movement of the others. In any group of kinesins, about two-thirds of kinesin pulled the cargo, and unexpectedly, about one-third tended to resist and slow the cargo. These latter kinesins were moved along with the group without actually driving the cargo. These resisting kinesins did come off more rapidly than the driving kinesins, meaning the cargo should be able to quickly bypass roadblocks. This would help to keep the whole group travelling in the right direction at a steady pace.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

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.

Dynamics of cooperative cargo transport by two elastically coupled kinesin motors

Intracellular transport is performed often by multiple motor proteins bound to the same cargo. Here, we study theoretically collective transport of the cargo by two kinesin motors. We propose that the motor has only the elastic interaction with the cargo via the linker connecting them and has no interaction with another motor. With parameters values for single motors from the available single-molecule data, we show that at linker's elastic strength [Formula: see text] pN/nm the theoretical data of both velocity and run length of the two-motor assembly under no load are identical to the available experimental data. The run length distribution is single exponential. The single-motor-bound state of the assembly dominates the transport. Both the force dependence of the velocity of the cargo driven by single load-bearing motor and that by two load-bearing motors in the assembly are consistent with the experimental data. The stall force of the assembly is larger than the sum of stall forces of two uncoupled motors. Moreover, we predict that the stall force increases with the increase of K and becomes saturated at large K, with the saturated value being 1.5-fold larger than the sum of stall forces of the two uncoupled motors.

Force sharing and force generation by two teams of elastically coupled molecular motors

Many active cellular processes such as long-distance cargo transport, spindle organization, as well as flagellar and ciliary beating are driven by molecular motors. These motor proteins act collectively and typically work in small teams. One particularly interesting example is two teams of antagonistic motors that pull a common cargo into opposite directions, thereby generating mutual interaction forces. Important issues regarding such multiple motor systems are whether or not motors from the same team share their load equally, and how the collectively generated forces depend on the single motor properties. Here we address these questions by introducing a stochastic model for cargo transport by an arbitrary number of elastically coupled molecular motors. We determine the state space of this motor system and show that this space has a rather complex and nested structure, consisting of multiple activity states and a large number of elastic substates, even for the relatively small system of two identical motors working against one antagonistic motor. We focus on this latter case because it represents the simplest tug-of-war that involves force sharing between motors from the same team. We show that the most likely motor configuration is characterized by equal force sharing between identical motors and that the most likely separation of these motors corresponds to a single motor step. These likelihoods apply to different types of motors and to different elastic force potentials acting between the motors. Furthermore, these features are observed both in the steady state and during the initial build-up of elastic strains. The latter build-up is non-monotonic and exhibits a maximum at intermediate times, a striking consequence of mutual unbinding of the elastically coupled motors. Mutual strain-induced unbinding also reduces the magnitude of the collectively generated forces. Our computational approach is quite general and can be extended to other motor systems such as motor teams working against an optical trap or mixed teams of motors with different single motor properties.

Engineering Heterodimeric Kinesins through Genetic Incorporation of Noncanonical Amino Acids

Kinesins are commonly homodimers with two identical heavy chains (protomers) and play indispensable roles in many intracellular processes. Engineered heterodimeric kinesins with two distinct protomers are important tools for dissecting coordination and regulation of naturally occurring kinesin homodimers. Here, we report a chemical-biology-based approach that generates kinesin heterodimers by combining genetic incorporation of reactive noncanonical amino acids and small-molecule-based cross-linking. We verified using yeast kinesin-8/Kip3 as a model system that our method yields kinesin heterodimers of desired properties without introducing unintended motility disruption. To demonstrate the utility of our method, we engineered a crippled Kip3 heterodimer that contains both a wild-type-like protomer and a catalytically inactive one, and our results revealed that the resulting heterodimer moves on the microtubule with a significant reduction in velocity but not processivity. Due to its versatility, we expect that our method can be broadly adopted to create novel heterodimers for other kinesins and will thus greatly expand the studies on kinesin mechanisms.

Retraction of rod-like mitochondria during microtubule-dependent transport

Molecular motors play relevant roles on the regulation of mitochondria size and shape, essential properties for the cell homeostasis. In this work, we tracked single rod-shaped mitochondria with nanometer precision to explore the performance of microtubule motor teams during processive anterograde and retrograde transport. We analyzed simultaneously the organelle size and verified that mitochondria retracted during retrograde transport with their leading tip moving slower in comparison with the rear tip. In contrast, mitochondria preserved their size during anterograde runs indicating a different performance of plus-end directed teams. These results were interpreted considering the different performance of dynein and kinesin teams and provide valuable information on the collective action of motors during mitochondria transport.

Coin Tossing Explains the Activity of Opposing Microtubule Motors on Phagosomes

How the opposing activity of kinesin and dynein motors generates polarized distribution of organelles inside cells is poorly understood and hotly debated [1, 2]. Possible explanations include stochastic mechanical competition [3, 4], coordinated regulation by motor-associated proteins [5-7], mechanical activation of motors [8], and lipid-induced organization [9]. Here, we address this question by using phagocytosed latex beads to generate early phagosomes (EPs) that move bidirectionally along microtubules (MTs) in an in vitro assay [9]. Dynein/kinesin activity on individual EPs is recorded as real-time force generation of the motors against an optical trap. Activity of one class of motors frequently coincides with, or is rapidly followed by opposite motors. This leads to frequent and rapid reversals of EPs in the trap. Remarkably, the choice between dynein and kinesin can be explained by the tossing of a coin. Opposing motors therefore appear to function stochastically and independently of each other, as also confirmed by observing no effect on kinesin function when dynein is inhibited on the EPs. A simple binomial probability calculation based on the geometry of EP-microtubule contact explains the observed activity of dynein and kinesin on phagosomes. This understanding of intracellular transport in terms of a hypothetical coin, if it holds true for other cargoes, provides a conceptual framework to explain the polarized localization of organelles inside cells.

Theoretical Investigation of Distributions of Run Lengths for Biological Molecular Motors

Motor proteins, also known as biological molecular motors, are active enzymatic molecules that support a variety of fundamental biological processes, including cellular transport, cell division, and cell motility. They usually function by transforming chemical energy into mechanical motion, which propels them along linear structures such as protein filaments and nucleic acids. Recent single-molecule experiments measured with high-precision distributions of various dynamic properties of molecular motors. However, it is difficult to utilize these observations to obtain a better description of molecular mechanisms in motor proteins because of the lack of corresponding theoretical methods. To fill this gap, we developed a new theoretical framework to describe the distributions of dynamic properties of biological molecular motors. It is based on the method of first-passage processes. To illustrate our approach, the distributions of run lengths of motor proteins are analyzed. It is found that these distributions depend on the finite length of linear tracks along which the motors move, on the initial position of the motor proteins along the filaments, and on the intermediate chemical transitions during the enzymatic cycle. The physical mechanisms of the observed phenomena are discussed.

Bidirectional motion of filaments: the role of motor proteins and passive cross linkers

In eukaryotic cells, motor proteins (MPs) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules forms whose stability and dynamics under the influence of MPs have been studied extensively. Although passive cross linkers (PCLs) are known to provide structural stability to a filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on filamentous overlap remain largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In the presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the filaments of an overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.

Mechanical coupling of microtubule-dependent motor teams during peroxisome transport in Drosophila S2 cells

BACKGROUND

Intracellular transport requires molecular motors that step along cytoskeletal filaments actively dragging cargoes through the crowded cytoplasm. Here, we explore the interplay of the opposed polarity motors kinesin-1 and cytoplasmic dynein during peroxisome transport along microtubules in Drosophila S2 cells.

METHODS

We used single particle tracking with nanometer accuracy and millisecond time resolution to extract quantitative information on the bidirectional motion of organelles. The transport performance was studied in cells expressing a slow chimeric plus-end directed motor or the kinesin heavy chain. We also analyzed the influence of peroxisomes membrane fluidity in methyl-β-ciclodextrin treated cells. The experimental data was also confronted with numerical simulations of two well-established tug of war scenarios.

RESULTS AND CONCLUSIONS

The velocity distributions of retrograde and anterograde peroxisomes showed a multimodal pattern suggesting that multiple motor teams drive transport in either direction. The chimeric motors interfered with the performance of anterograde transport and also reduced the speed of the slowest retrograde team. In addition, increasing the fluidity of peroxisomes membrane decreased the speed of the slowest anterograde and retrograde teams.

GENERAL SIGNIFICANCE

Our results support the existence of a crosstalk between opposed-polarity motor teams. Moreover, the slowest teams seem to mechanically communicate with each other through the membrane to trigger transport.

Intraflagellar transport: mechanisms of motor action, cooperation, and cargo delivery

Intraflagellar transport (IFT) is a form of motor-dependent cargo transport that is essential for the assembly, maintenance, and length control of cilia, which play critical roles in motility, sensory reception, and signal transduction in virtually all eukaryotic cells. During IFT, anterograde kinesin-2 and retrograde IFT dynein motors drive the bidirectional transport of IFT trains that deliver cargo, for example, axoneme precursors such as tubulins as well as molecules of the signal transduction machinery, to their site of assembly within the cilium. Following its discovery in Chlamydomonas, IFT has emerged as a powerful model system for studying general principles of motor-dependent cargo transport and we now appreciate the diversity that exists in the mechanism of IFT within cilia of different cell types. The absence of heterotrimeric kinesin-2 function, for example, causes a complete loss of both IFT and cilia in Chlamydomonas, but following its loss in Caenorhabditis elegans, where its primary function is loading the IFT machinery into cilia, homodimeric kinesin-2-driven IFT persists and assembles a full-length cilium. Generally, heterotrimeric kinesin-2 and IFT dynein motors are thought to play widespread roles as core IFT motors, whereas homodimeric kinesin-2 motors are accessory motors that mediate different functions in a broad range of cilia, in some cases contributing to axoneme assembly or the delivery of signaling molecules but in many other cases their ciliary functions, if any, remain unknown. In this review, we focus on mechanisms of motor action, motor cooperation, and motor-dependent cargo delivery during IFT.

Ensemble and single-molecule dynamics of IFT dynein in Caenorhabditis elegans cilia

Cytoplasmic dyneins drive microtubule-based, minus-end directed transport in eukaryotic cells. Whereas cytoplasmic dynein 1 has been widely studied, IFT dynein has received far less attention. Here, we use fluorescence microscopy of labelled motors in living Caenorhabditis elegans to investigate IFT-dynein motility at the ensemble and single-molecule level. We find that while the kinesin composition of motor ensembles varies along the track, the amount of dynein remains relatively constant. Remarkably, this does not result in directionality changes of cargo along the track, as has been reported for other opposite-polarity, tug-of-war motility systems. At the single-molecule level, IFT-dynein trajectories reveal unexpected dynamics, including diffusion at the base, and pausing and directional switches along the cilium. Stochastic simulations show that the ensemble IFT-dynein distribution depends upon the probability of single-motor directional switches. Our results provide quantitative insight into IFT-dynein dynamics in vivo, shedding light on the complex functioning of dynein motors in general.

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.

Exploiting molecular motors as nanomachines: the mechanisms of de novo and re-engineered cytoskeletal motors

Cytoskeletal molecular motors provide exciting proof that nanoscale transporters can be highly efficient, moving for microns along filamentous tracks by hydrolyzing ATP to fuel nanometer-size steps. For nanotechnology, such conversion of chemical energy into productive work serves as an enticing platform for re-purposing and re-engineering. It also provides a roadmap for successful molecular mechanisms that can be mimicked to create de novo molecular motors for nanotechnology applications. Here we focus specifically on how the mechanisms of molecular motors are being re-engineered for greater control over their transport parameters. We then discuss mechanistic work to create fully synthetic motors de novo and conclude with future directions in creating novel motor systems.

Cargo rigidity affects the sensitivity of dynein ensembles to individual motor pausing

Cytoplasmic dynein is a minus-end directed microtubule-based motor protein that drives intracellular cargo transport in eukaryotic cells. Although many intracellular cargos are propelled by small groups of dynein motors, the biophysical mechanisms governing ensemble motility remain largely unknown. To investigate the emergent motility of motor ensembles, we have designed a programmable DNA origami synthetic cargo "chassis" enabling us to control the number of dynein motors in the ensemble and vary the rigidity of the cargo chassis itself. Using total internal reflection fluorescence microscopy, we have observed dynein ensembles transporting these cargo chassis along microtubules in vitro. We find that ensemble motility depends on cargo rigidity: as the number of motors increases, ensembles transporting flexible cargos move comparatively faster than a single motor, whereas ensembles transporting rigid cargos move slower than a single motor. To explain this, we show that ensembles connected through flexible cargos are less sensitive to the pauses of individual motors within the ensemble. We conclude that cargo rigidity plays an important role in communicating and coordinating the states of motors, and consequently in the subsequent mechanisms of collective motility. The insensitivity of ensemble-driven cargos to the pausing of individual motors may contribute to the robustness and versatility of intracellular cargo transport. © 2016 Wiley Periodicals, Inc.

Simultaneous nano-tracking of multiple motor proteins via spectral discrimination of quantum dots

Simultaneous nanometric tracking of multiple motor proteins was achieved by combining multicolor fluorescent labeling of target proteins and imaging spectroscopy, revealing dynamic behaviors of multiple motor proteins at the sub-diffraction-limit scale. Using quantum dot probes of distinct colors, we experimentally verified the localization precision to be a few nanometers at temporal resolution of 30 ms or faster. One-dimensional processive movement of two heads of a single myosin molecule and multiple myosin molecules was successfully traced. Furthermore, the system was modified for two-dimensional measurement and applied to tracking of multiple myosin molecules. Our approach is useful for investigating cooperative movement of proteins in supramolecular nanomachinery.

Multimotor Driven Cargos: From Single Motor under Load to the Role of Motor-Motor Coupling

Motor proteins constitute an essential part of the cellular machinery. They have been the subject of intensive studies in the past two decades. Yet, when several motors simultaneously carry a single cargo, the effect of motor-motor coupling, such as mutual stalling and jamming, remains unclear. We commence by constructing a general model for single motor motion, which is a product of a derived load-dependent expression and a phenomenological motor specific function. Forming the latter according to recent single molecule measurements for a given load, the model correctly predicts the motor full step-size distribution for all other measured loads. We then use our proposed model to predict transport properties of multimotor complexes, with particular attention to 1-dimensional constructs with variable flexibility, motor density, and number of motors: (i) a chain of motors connected by springs, a recently studied construction of a pair, and (ii) an array of motors all connected by identical springs to a stiff rod, which is essentially a mirror image of standard gliding motility assays. In both systems, and for any number of carrying motors, we find that, while low flexibility results in a strongly damped velocity, increased flexibility renders an almost single motor velocity. Comparing our model based simulations to recent gliding assays we find remarkable qualitative agreement. We also demonstrate consistency with other multimotor motility assays. In all cases, the characteristic spring constant, that controls the crossover behavior between high and low velocity regimes, is found to be the stalling force divided by the mean step size. We conjecture that this characteristic spring constant can serve as a tool for engineering multimotor complexes.