‘Life is motion’: multiscale motility of molecular motors (original) (raw)
Related papers
Random walks of molecular motors arising from diffusional encounters with immobilized filaments
Physical Review E, 2004
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation in two and three dimensions. Results are obtained for the fraction of bound motors, their average velocity and displacement. The diffusion coefficient parallel to the filament becomes anomalously large since detachment and subsequent reattachment, in the presence of directed motion of the bound motors, leads to a broadening of the density distribution. The occurrence of protofilaments on a microtubule is modeled by internal states of the binding sites. After a transient time all protofilaments become equally populated.
2005
Molecular motors perform active movements along cytoskeletal filaments and drive the traffic of organelles and other cargo particles in cells. In contrast to the macroscopic traffic of cars, however, the traffic of molecular motors is characterized by a finite walking distance (or run length) after which a motor unbinds from the filament along which it moves. Unbound motors perform Brownian motion in the surrounding aqueous solution until they rebind to a filament. We use variants of driven lattice gas models to describe the interplay of their active movements, the unbound diffusion, and the binding/unbinding dynamics. If the motor concentration is large, motor-motor interactions become important and lead to a variety of cooperative traffic phenomena such as traffic jams on the filaments, boundary-induced phase transitions, and spontaneous symmetry breaking in systems with two species of motors. If the filament is surrounded by a large reservoir of motors, the jam length, i.e., the extension of the traffic jams, is of the order of the walking distance. Much longer jams can be found in confined geometries such as tube-like compartments.
Enhanced ordering of interacting filaments by molecular motors
Phys. Rev. Lett., 2006
We theoretically study the cooperative behavior of cytoskeletal filaments in motility assays in which immobilized motor proteins bind the filaments to substrate surfaces and actively pull them along these surfaces. Because of the mutual exclusion of the filaments, the coupled dynamics of filaments, motor heads, and motor tails leads to a nonequilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations show that the motor activity enhances the tendency for nematic ordering. We develop a quantitative theory for the location of the phase boundary as a function of motor density. At high detachment forces of motors, we also observe filament clusters arising from blocking effects.
Walks of molecular motors interacting with immobilized filaments
Physica A: Statistical Mechanics and its Applications, 2005
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation. Results are obtained for the fraction of bound motors, their average velocity and displacement. Enclosing the system in a finite geometry (tube, slab) leads to an experimentally realizable problem, that is studied in a continuum description and also numerically in a lattice simulation.
Cooperative molecular motors moving back and forth
Physical Review E, 2009
We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc. Natl. Acad. Sci. USA} {\bf 99}, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) a-polar tracks, while on even slightly polar tracks the motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion.
Intra-cellular traffic: bio-molecular motors on filamentary tracks
European Physical Journal B, 2008
Molecular motors are macromolecular complexes which use some form of input energy to perform mechanical work. The filamentary tracks, on which these motors move, are made of either proteins (e.g., microtubules) or nucleic acids (DNA or RNA). Often, many such motors move simultaneously on the same track and their collective properties have superficial similarities with vehicular traffic on highways. The models we have developed provide "unified" description: in the low-density limit, a model captures the transport properties of a single motor while, at higher densities the same model accounts for the collective spatio-temporal organization of interacting motors. By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks. We show how the traffic-like intracellular collective phenomena depend on the mechano-chemistry of the corresponding individual motors.
Biological Physics 2000, 2001
The movements of cytoskeletal motors such as kinesin or myosin V cover many length and time scales. When such a motor is bound to a filament, the consumption of a single fuel molecule leads to a certain motor displacement or step which is of the order of several nanometers. The motor typically makes about a hundred such steps in its bound state and, in this way, covers a walking distance which is of the order of micrometers. On even larger length scales, the motor undergoes random walks which consist of alternating sequences of bound and unbound motor states, i.e., of directed walks along the filaments and nondirected diffusion in the aqueous solution.
Walks of molecular motors in two and three dimensions
Europhysics Letters (EPL), 2002
Molecular motors interacting with cytoskeletal filaments undergo peculiar random walks consisting of alternating sequences of directed movements along the filaments and diffusive motion in the surrounding solution. An ensemble of motors is studied which interacts with a single filament in two and three dimensions. The time evolution of the probability distribution for the bound and unbound motors is determined analytically. The diffusion of the motors is strongly enhanced parallel to the filament. The analytical expressions are in excellent agreement with the results of Monte Carlo simulations.
Cooperative behavior of molecular motors: Cargo transport and traffic phenomena
Physica E-low-dimensional Systems & Nanostructures, 2010
All eukaryotic cells including those of our own body contain complex transport systems based on molecular motors which walk along cytoskeletal filaments. These motors are rather small and make discrete mechanical steps with a step size of the order of 10 nm but are able to pull cargo particles over much larger distances, from micrometers up to meters. In vivo, the intracellular cargos include large membrane-bounded organelles, smaller vesicles, a subset of mRNAs, cytoskeletal filaments, and various protein building blocks, which are transported between different cell compartments. This cargo transport is usually performed by teams of motors. If all motors belong to the same molecular species, the cooperative action of the motors leads to uni-directional transport with a strongly increased run length and with a characteristic force dependence of the velocity distributions. If two antagonistic teams of motors pull on the same cargo particle, they perform a stochastic tug-of-war, which is characterized by a subtle force balance between the two motor teams and leads to several distinct patterns of bi-directional transport. So far, all experimental observations on bi-directional transport are consistent with such a tug-of-war. If many motors and/or cargo particles are transported along the filaments, one encounters various traffic phenomena. Depending on their mutual interactions and the compartment geometry, the motors form various spatio-temporal patterns such as traffic jams, and undergo nonequilibrium phase transitions between different patterns of transport.