Multimotor transport in a system of active and inactive kinesin-1 motors

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.

Cooperation and competition in the collective drive by motor proteins: mean active force, fluctuations, and self-load

We consider the dynamics of a bio-filament under the collective drive of motor proteins. They are attached irreversibly to a substrate and undergo stochastic attachment-detachment with the filament to produce a directed force on it. We establish the dependence of the mean directed force and force correlations on the parameters describing the individual motor proteins using analytical theory and direct numerical simulations. The effective Langevin description for the filament motion gives mean-squared displacement, asymptotic diffusion constant, and mobility leading to an effective temperature. Finally, we show how competition between motor protein extensions generates a self-load, describable in terms of the effective temperature, affecting the filament motion.

Motility resilience of molecular shuttles against defective motors

Myosin and kinesin are biomolecular motors found in living cells. By propelling their associated cytoskeletal filaments, these biomolecular motors facilitate force generation and material transport in the cells. When extracted, the biomolecular motors are promising candidates for in vitro applications such as biosensor devices, on account of their high operating efficiency and nanoscale size. However, during integration into these devices, some of the motors become defective due to unfavorable adhesion to the substrate surface. These defective motors inhibit the motility of the cytoskeletal filaments which make up the molecular shuttles used in the devices. Difficulties in controlling the fraction of active and defective motors in experiments discourage systematic studies concerning the resilience of the molecular shuttle motility against the impedance of defective motors. Here, we used mathematical modelling to systematically examine the resilience of the propulsion by these molecular shuttles against the impedance of the defective motors. The model showed that the fraction of active motors on the substrate is the essential factor determining the resilience of the molecular shuttle motility. Approximately 40% of active kinesin or 80% of active myosin motors are required to constitute continuous gliding of molecular shuttles in their respective substrates. The simplicity of the mathematical model in describing motility behavior offers utility in elucidating the mechanisms of the motility resilience of molecular shuttles.

Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies

The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Cooperative motor action to regulate microtubule length dynamics

Motivated by the recent experimental observations on motor induced cooperative mechanism controlling the length dynamics of microtubules (MTs), we examine how plus-end-targeted proteins of the kinesin family regulate MT polymerization and depolymerization routines. Here, we study a stochastic mathematical model capturing the unusual form of collective motor interaction on MT dynamics originating due to the molecular traffic near the MT tip. We provide an extensive analysis of the joint effect of motor impelled MT polymerization and complete depolymerization. The effect of the cooperative action is included by modifying the intrinsic depolymerization rate. We analyze the model within the framework of continuum mean-field theory and the resultant steady-state analytic solution is expressed in terms of Lambert W functions. Four distinct steady-state phases including a shock phase have been reported. The significant features of the shock including its position and height have been analyzed. Theoretical outcomes are supported by extensive Monte Carlo simulations. To explore the system alterations between the regime of growth and shrinkage phase, we consider kymographs of the microtubule along with the length distributions. Finally, we investigated the dependence of MT length kinetics both on modifying factor of depolymerization rate and motor concentration. The overall extensive study reveals that the flux of molecular traffic at the microtubule plus end initiates a cooperative mechanism, resulting in significant change in MT growth and shrinkage regime as also observed experimentally.

Collective effects of yeast cytoplasmic dynein based microtubule transport

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

A fluid membrane enhances the velocity of cargo transport by small teams of kinesin-1

Kinesin-1 (hereafter referred to as kinesin) is a major microtubule-based motor protein for plus-end-directed intracellular transport in live cells. While the single-molecule functions of kinesin are well characterized, the physiologically relevant transport of membranous cargos by small teams of kinesins remains poorly understood. A key experimental challenge remains in the quantitative control of the number of motors driving transport. Here we utilized "motile fraction" to overcome this challenge and experimentally accessed transport by a single kinesin through the physiologically relevant transport by a small team of kinesins. We used a fluid lipid bilayer to model the cellular membrane in vitro and employed optical trapping to quantify the transport of membrane-enclosed cargos versus traditional membrane-free cargos under identical conditions. We found that coupling motors via a fluid membrane significantly enhances the velocity of cargo transport by small teams of kinesins. Importantly, enclosing a cargo in a fluid lipid membrane did not impact single-kinesin transport, indicating that membrane-dependent velocity enhancement for team-based transport arises from altered interactions between kinesins. Our study demonstrates that membrane-based coupling between motors is a key determinant of kinesin-based transport. Enhanced velocity may be critical for fast delivery of cargos in live cells.

An automated in vitro motility assay for high-throughput studies of molecular motors

Molecular motors, essential to force-generation and cargo transport within cells, are invaluable tools for powering nanobiotechnological lab-on-a-chip devices. These devices are based on in vitro motility assays that reconstitute molecular transport with purified motor proteins, requiring a deep understanding of the biophysical properties of motor proteins and thorough optimization to enable motility under varying environmental conditions. Until now, these assays have been prepared manually, severely limiting throughput. To overcome this limitation, we developed an in vitro motility assay where sample preparation, imaging and data evaluation are fully automated, enabling the processing of a 384-well plate within less than three hours. We demonstrate the automated assay for the analysis of peptide inhibitors for kinesin-1 at a wide range of concentrations, revealing that the IAK domain responsible for kinesin-1 auto-inhibition is both necessary and sufficient to decrease the affinity of the motor protein for microtubules, an aspect that was hidden in previous experiments due to scarcity of data.

Activation of mammalian cytoplasmic dynein in multi-motor motility assays

Long-range intracellular transport is facilitated by motor proteins like kinesin-1 and cyto-plasmic dynein walking along microtubules (MTs). These motors often work in teams for the transport of various intracellular cargos. While transport by multiple kinesin-1 motors has been studied extensively in the past, collective effects of cytoplasmic dynein are less well understood. On the level of single molecules, mammalian cytoplasmic dynein is not active in the absence of dynactin and adaptor proteins. However, when assembled into a team bound to the same cargo, processive motility has been observed. The underlying mechanism of this activation is not known. Here, we found that in MT gliding motility assays the gliding velocity increased with dynein surface density and MT length. Developing a mathematical model based on single-molecule parameters, we were able to simulate the observed behavior. Integral to our model is the usage of an activation term, which describes a mechanical activation of individual dynein motors when being stretched by the other motors. We hypothesize this activation to be similar to the activation of single dynein motors by dynactin and adaptor proteins.

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.

Neurofilaments and Neurofilament Proteins in Health and Disease

SUMMARYNeurofilaments (NFs) are unique among tissue-specific classes of intermediate filaments (IFs) in being heteropolymers composed of four subunits (NF-L [neurofilament light]; NF-M [neurofilament middle]; NF-H [neurofilament heavy]; and α-internexin or peripherin), each having different domain structures and functions. Here, we review how NFs provide structural support for the highly asymmetric geometries of neurons and, especially, for the marked radial expansion of myelinated axons crucial for effective nerve conduction velocity. NFs in axons extensively cross-bridge and interconnect with other non-IF components of the cytoskeleton, including microtubules, actin filaments, and other fibrous cytoskeletal elements, to establish a regionally specialized network that undergoes exceptionally slow local turnover and serves as a docking platform to organize other organelles and proteins. We also discuss how a small pool of oligomeric and short filamentous precursors in the slow phase of axonal transport maintains this network. A complex pattern of phosphorylation and dephosphorylation events on each subunit modulates filament assembly, turnover, and organization within the axonal cytoskeleton. Multiple factors, and especially turnover rate, determine the size of the network, which can vary substantially along the axon. NF gene mutations cause several neuroaxonal disorders characterized by disrupted subunit assembly and NF aggregation. Additional NF alterations are associated with varied neuropsychiatric disorders. New evidence that subunits of NFs exist within postsynaptic terminal boutons and influence neurotransmission suggests how NF proteins might contribute to normal synaptic function and neuropsychiatric disease states.

Velocity Fluctuations in Kinesin-1 Gliding Motility Assays Originate in Motor Attachment Geometry Variations

Motor proteins such as myosin and kinesin play a major role in cellular cargo transport, muscle contraction, cell division, and engineered nanodevices. Quantifying the collective behavior of coupled motors is critical to our understanding of these systems. An excellent model system is the gliding motility assay, where hundreds of surface-adhered motors propel one cytoskeletal filament such as an actin filament or a microtubule. The filament motion can be observed using fluorescence microscopy, revealing fluctuations in gliding velocity. These velocity fluctuations have been previously quantified by a motional diffusion coefficient, which Sekimoto and Tawada explained as arising from the addition and removal of motors from the linear array of motors propelling the filament as it advances, assuming that different motors are not equally efficient in their force generation. A computational model of kinesin head diffusion and binding to the microtubule allowed us to quantify the heterogeneity of motor efficiency arising from the combination of anharmonic tail stiffness and varying attachment geometries assuming random motor locations on the surface and an absence of coordination between motors. Knowledge of the heterogeneity allows the calculation of the proportionality constant between the motional diffusion coefficient and the motor density. The calculated value (0.3) is within a standard error of our measurements of the motional diffusion coefficient on surfaces with varying motor densities calibrated by landing rate experiments. This allowed us to quantify the loss in efficiency of coupled molecular motors arising from heterogeneity in the attachment geometry.

Kinesin-1 motors can circumvent permanent roadblocks by side-shifting to neighboring protofilaments

Obstacles on the surface of microtubules can lead to defective cargo transport, proposed to play a role in neurological diseases such as Alzheimer's. However, little is known about how motor proteins, which follow individual microtubule protofilaments (such as kinesin-1), deal with obstacles on the molecular level. Here, we used rigor-binding mutants of kinesin-1 as roadblocks to permanently obstruct individual microtubule binding sites and studied the movement of individual kinesin-1 motors by single-molecule fluorescence and dark-field scattering microscopy in vitro. In the presence of roadblocks, kinesin-1 often stopped for ∼ 0.4 s before either detaching or continuing to move, whereby the latter circumvention events occurred in >30% after a stopping event. Consequently, and in agreement with numerical simulations, the mean velocity, mean run length, and mean dwell time of the kinesin-1 motors decreased upon increasing the roadblock density. Tracking individual kinesin-1 motors labeled by 40 nm gold particles with 6 nm spatial and 1 ms temporal precision revealed that ∼ 70% of the circumvention events were associated with significant transverse shifts perpendicular to the axis of the microtubule. These side-shifts, which occurred with equal likelihood to the left and right, were accompanied by a range of longitudinal shifts suggesting that roadblock circumvention involves the unbinding and rebinding of the motors. Thus, processive motors, which commonly follow individual protofilaments in the absence of obstacles, appear to possess intrinsic circumvention mechanisms. These mechanisms were potentially optimized by evolution for the motor's specific intracellular tasks and environments.

Forced desorption of semiflexible polymers, adsorbed and driven by molecular motors

We formulate and characterize a model to describe the dynamics of semiflexible polymers in the presence of activity due to motor proteins attached irreversibly to a substrate, and a transverse pulling force acting on one end of the filament. The stochastic binding-unbinding of the motor proteins and their ability to move along the polymer generate active forces. As the pulling force reaches a threshold value, the polymer eventually desorbs from the substrate. Performing underdamped Langevin dynamics simulation of the polymer, and with stochastic motor activity, we obtain desorption phase diagrams. The correlation time for fluctuations in the desorbed fraction increases as one approaches complete desorption, captured quantitatively by a power law spectral density. We present theoretical analysis of the phase diagram using mean field approximations in the weakly bending limit of the polymer and performing linear stability analysis. This predicts an increase in the desorption force with the polymer bending rigidity, active velocity and processivity of the motor proteins to capture the main features of the simulation results.

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.

Collective dynamics of processive cytoskeletal motors

Major cellular processes are supported by various biomolecular motors that usually operate together as teams. We present an overview of the collective dynamics of processive cytokeletal motor proteins based on recent experimental and theoretical investigations. Experimental studies show that multiple motors function with different degrees of cooperativity, ranging from negative to positive. This effect depends on the mechanical properties of individual motors, the geometry of their connections, and the surrounding cellular environment. Theoretical models based on stochastic approaches underline the importance of intermolecular interactions, the properties of single motors, and couplings with cellular medium in predicting the collective dynamics. We discuss several features that specify the cooperativity in motor proteins. Based on this approach a general picture of collective dynamics of motor proteins is formulated, and the future directions and challenges are discussed.

Building cells for quantitative, live-cell analyses of collective motor protein functions

Examining the collective mechanical behaviors of interacting cytoskeletal motors has become increasingly important to dissecting the complex and multifaceted mechanisms that regulate the transport and trafficking of materials in cells. Although studying these processes in living cells has been challenging, the development of new Synthetic Biology techniques has opened unique opportunities to both manipulate and probe how these motors function in groups as they navigate the native cytoskeleton. Here, we describe an approach to engineer mammalian cells for a new class of inducible cargo motility assays that utilize drug-dependent protein dimerization switches to regulate motor-cargo coupling and transport. Our adaptations provide genetic-level control over the densities of motor proteins coupled to, as well as the sizes of endogenous vesicular cargos in these assays. By allowing the examination of transport responses to changes in motor density and cargo size-dependent viscous drag force, such control can enable quantitative comparisons of mechanistic distinctions between the collective behaviors of different types of processive cytoskeletal motors.

Life at the mesoscale: the self-organised cytoplasm and nucleoplasm

The cell contains highly dynamic structures exploiting physical principles of self-organisation at the mesoscale (100 nm to 10 μm). Examples include non-membrane bound cytoplasmic bodies, cytoskeleton-based motor networks and multi-scale chromatin organisation. The challenges of mesoscale self-organisation were discussed at a CECAM workshop in July 2014. Biologists need approaches to observe highly dynamic, low affinity, low specificity associations and to perturb single structures, while biological physicists and biomathematicians need to work closely with biologists to build and validate quantitative models. A table of terminology is included to facilitate multidisciplinary efforts to reveal the richness and diversity of mesoscale cell biology.