Cooperativity of self-organized Brownian motors pulling on soft cargoes

Unraveling the hidden complexity of quasideterministic ratchets: Random walks, graphs, and circle maps

Brownian ratchets are shown to feature a nontrivial vanishing-noise limit where the dynamics is reduced to a stochastic alternation between two deterministic circle maps (quasideterministic ratchets). Motivated by cooperative dynamics of molecular motors, here we solve exactly the problem of two interacting quasideterministic ratchets. We show that the dynamics can be described as a random walk on a graph that is specific to each set of parameters. We compute point by point the exact velocity-force V(f) function as a summation over all paths in the specific graph for each f, revealing a complex structure that features self-similarity and nontrivial continuity properties. From a general perspective, we unveil that the alternation of two simple piecewise linear circle maps unfolds a very rich variety of dynamical complexity, in particular the phenomenon of piecewise chaos, where chaos emerges from the combination of nonchaotic maps. We show convergence of the finite-noise case to our exact solution.

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.

Quasi-steady-state analysis of coupled flashing ratchets

We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

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.

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.

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.

Metrics for characterizing collective transport by multiple dimeric kinesins

Kinesin is a processive molecular motor which transports various cellular cargos by converting chemical energy into mechanical movements. Although the motion of a single molecule has been characterized in several studies, the dynamics of collective transport remains controversial. Since the chemical reactions fueling molecular motors are stochastic processes, the movements of coupled motors are not perfectly synchronized. The goal of this study is to develop metrics to analyze the level of synchronization of coupled (stochastic) motors. The correlation among movements of coupled motors, the slackness, the cooperativity, and the power loss of kinesins are explored using the developed metrics. These metrics can be extended to characterize collective work done by other molecular motors also.

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

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