Self-organization and cooperativity of weakly coupled molecular motors under unequal loading

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.

Intracellular cargo transport by single-headed kinesin motors

Kinesin motor proteins that drive intracellular transport share an overall architecture of two motor domain-containing subunits that dimerize through a coiled-coil stalk. Dimerization allows kinesins to be processive motors, taking many steps along the microtubule track before detaching. However, whether dimerization is required for intracellular transport remains unknown. Here, we address this issue using a combination of in vitro and cellular assays to directly compare dimeric motors across the kinesin-1, -2, and -3 families to their minimal monomeric forms. Surprisingly, we find that monomeric motors are able to work in teams to drive peroxisome dispersion in cells. However, peroxisome transport requires minimal force output, and we find that most monomeric motors are unable to disperse the Golgi complex, a high-load cargo. Strikingly, monomeric versions of the kinesin-2 family motors KIF3A and KIF3B are able to drive Golgi dispersion in cells, and teams of monomeric KIF3B motors can generate over 8 pN of force in an optical trap. We find that intracellular transport and force output by monomeric motors, but not dimeric motors, are significantly decreased by the addition of longer and more flexible motor-to-cargo linkers. Together, these results suggest that dimerization of kinesin motors is not required for intracellular transport; however, it enables motor-to-motor coordination and high force generation regardless of motor-to-cargo distance. Dimerization of kinesin motors is thus critical for cellular events that require an ability to generate or withstand high forces.

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.

Self-Propelled Nanomotors Autonomously Seek and Repair Cracks

Biological self-healing involves the autonomous localization of healing agents at the site of damage. Herein, we design and characterize a synthetic repair system where self-propelled nanomotors autonomously seek and localize at microscopic cracks and thus mimic salient features of biological wound healing. We demonstrate that these chemically powered catalytic nanomotors, composed of conductive Au/Pt spherical Janus particles, can autonomously detect and repair microscopic mechanical defects to restore the electrical conductivity of broken electronic pathways. This repair mechanism capitalizes on energetic wells and obstacles formed by surface cracks, which dramatically alter the nanomotor dynamics and trigger their localization at the defects. By developing models for self-propelled Janus nanomotors on a cracked surface, we simulate the systems' dynamics over a range of particle speeds and densities to verify the process by which the nanomotors autonomously localize and accumulate at the cracks. We take advantage of this localization to demonstrate that the nanomotors can form conductive "patches" to repair scratched electrodes and restore the conductive pathway. Such a nanomotor-based repair system represents an important step toward the realization of biomimetic nanosystems that can autonomously sense and respond to environmental changes, a development that potentially can be expanded to a wide range of applications, from self-healing electronics to targeted drug delivery.

Formation of helical membrane tubes around microtubules by single-headed kinesin KIF1A

The kinesin-3 motor KIF1A is in charge of vesicular transport in neuronal axons. Its single-headed form is known to be very inefficient due to the presence of a diffusive state in the mechanochemical cycle. However, recent theoretical studies have suggested that these motors could largely enhance force generation by working in teams. Here we test this prediction by challenging single-headed KIF1A to extract membrane tubes from giant vesicles along microtubule filaments in a minimal in vitro system. Remarkably, not only KIF1A motors are able to extract tubes but they feature a novel phenomenon: tubes are wound around microtubules forming tubular helices. This finding reveals an unforeseen combination of cooperative force generation and self-organized manoeuvreing capability, suggesting that the diffusive state may be a key ingredient for collective motor performance under demanding traffic conditions. Hence, we conclude that KIF1A is a genuinely cooperative motor, possibly explaining its specificity to axonal trafficking.

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

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

Catch-bond behaviour facilitates membrane tubulation by non-processive myosin 1b

Myosin 1b is a single-headed membrane-associated motor that binds to actin filaments with a catch-bond behaviour in response to load. In vivo, myosin 1b is required to form membrane tubules at both endosomes and the trans-Golgi network. To establish the link between these two fundamental properties, here we investigate the capacity of myosin 1b to extract membrane tubes along bundled actin filaments in a minimal reconstituted system. We show that single-headed non-processive myosin 1b can extract membrane tubes at a biologically relevant low density. In contrast to kinesins we do not observe motor accumulation at the tip, suggesting that the underlying mechanism for tube formation is different. In our theoretical model, myosin 1b catch-bond properties facilitate tube extraction under conditions of increasing membrane tension by reducing the density of myo1b required to pull tubes.

Cooperative action of KIF1A Brownian motors with finite dwell time

We study in detail the cooperative action of small groups of KIF1A motors in its monomeric (single-headed) form within an arrangement relevant to vesicle traffic or membrane tube extraction. It has been recently shown that under these circumstances, the presence of a finite dwell time in the motor cycle contributes to remarkably enhance collective force generation [D. Oriola and J. Casademunt, Phys. Rev. Lett. 111, 048103 (2013)]. We analyze this mechanism in detail by means of a two-state noise-driven ratchet model with hard-core repulsive interactions. We obtain staircase-shaped velocity-force curves and show that motors self-organize in clusters with a nontrivial force distribution that conveys a large part of the load to the central motors. Under heavy loads, large clusters adopt a synchronic mode of totally asymmetric steps. We also find a dramatic increase of the collective efficiency with the number of motors. Finally, we complete the study by addressing different interactions that impose spatial constraints such as rigid coupling and raft-induced confinement. Our results reinforce the hypothesis that the specificity of KIF1A to axonal vesicular transport may be deeply related to its high cooperativity.

Cooperative force generation of KIF1A Brownian motors

KIF1A is a kinesin motor protein that can work processively in a monomeric (single-headed) form by using a noise-driven ratchet mechanism. Here, we show that the combination of a passive diffusive state and finite-time kinetics of adenosine triphosphate hydrolysis provides a powerful mechanism of cooperative force generation, implying for instance that ∼10 monomeric KIF1As can team up to become ∼100 times stronger than a single one. Consequently, we propose that KIF1A could outperform conventional (double-headed) kinesin collectively and thus explain its specificity in axonal trafficking. We elucidate the cooperativity mechanism with a lattice model that includes multiparticle transitions.

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the noninteracting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.

Asymmetry between pushing and pulling for crawling cells

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.

Efficiency at maximum power of interacting molecular machines

We investigate the efficiency of systems of molecular motors operating at maximum power. We consider two models of kinesin motors on a microtubule: for both the simplified and the detailed model, we find that the many-body exclusion effect enhances the efficiency at maximum power of the many-motor system, with respect to the single motor case. Remarkably, we find that this effect occurs in a limited region of the system parameters, compatible with the biologically relevant range.

Running faster together: huge speed up of thermal ratchets due to hydrodynamic coupling

We present simulations that reveal a surprisingly large effect of hydrodynamic coupling on the speed of thermal ratchet motors. The model that we use considers particles performing thermal ratchet motion in a hydrodynamic solvent. Using particle-based, mesoscopic simulations that maintain local momentum conservation, we analyze quantitatively how the coupling to the surrounding fluid affects ratchet motion. We find that coupling can increase the mean velocity of the moving particles by almost 2 orders of magnitude, precisely because ratchet motion has both a diffusive and a deterministic component. The resulting coupling also leads to the formation of aggregates at longer times. The correlated motion that we describe increases the efficiency of motor-delivered cargo transport and we speculate that the mechanism that we have uncovered may play a key role in speeding up molecular motor-driven intracellular transport.

Effects of phase disorder on transport of globally coupled Brownian motors

The transport of N globally coupled Brownian motors driven by a periodic force with phase disorder is investigated. An approximate theoretical analysis of the model is presented. The effects of the phase disorder and the driving strength of the periodic force on the transport of the coupled Brownian motors are discussed both theoretically and numerically. It is found that the increase of the periodical driving force decreases the average velocity, while the coupled particles may benefit from the phase disorder to enhance collective transport.

Tug of war of molecular motors: the effects of uneven load sharing

We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature: a quite widespread model which assumes equal force sharing, here referred to as the mean field model (MFM), and a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations, the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be the consequences of the load sharing assumptions and can be interpreted in terms of the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness, while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin-1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins.

Cooperativity of self-organized Brownian motors pulling on soft cargoes

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

Force-velocity relations for multiple-molecular-motor transport

A transition rate model of cargo transport by N molecular motors is proposed. Under the assumption of steady state, the force-velocity curve of multimotor system can be derived from the force-velocity curve of a single motor. Our work shows, in the case of low load, that the velocity of multimotor system can decrease or increase with increasing motor number, which is dependent on the single motor force-velocity curve; and most commonly, the velocity decreases. This gives a possible explanation to some recent experimental observations.