Spontaneous Oscillations of Collective Molecular Motors (original) (raw)
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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.
Coordination and collective properties of molecular motors: theory
Current Opinion in Cell Biology, 2010
Many cellular processes require molecular motors to produce motion and forces. Single molecule experiments have led to a precise description of how a motor works. Under most physiological conditions, however, molecular motors operate in groups. Interactions between motors yield collective behaviors that cannot be explained only from single molecule properties. The aim of this paper is to review the various theoretical descriptions that explain the emergence of collective effects in molecular motor assemblies. These include bidirectional motion, hysteretic behavior, spontaneous oscillations, and self-organization into dynamical structures. We discuss motors acting on the cytoskeleton both in a prescribed geometry such as in muscles or flagella and in the cytoplasm.
‘Life is motion’: multiscale motility of molecular motors
Physica A: Statistical Mechanics and its Applications, 2005
Life is intimately related to complex patterns of directed movement. It is quite remarkable that all of this movement is based on filaments and motor molecules which perform mechanical work on the nanometer scale. This article reviews recent theoretical work on the motility of molecular motors and motor particles that bind to cytoskeletal filaments and walk along these filaments in a directed fashion. It is emphasized that these systems exhibit several motility regimes which are well seperated in time. In their bound state, the motor particles move with a typical velocity of about 1 mm=s: The motor cycles underlying this bound motor movement can be understood in terms of driven Brownian ratchets and networks. On larger length and time scales, the motor particles unbind from the filaments and undergo peculiar motor walks consisting of many diffusional encounters with the filaments. If the mutual exclusion (or hardcore repulsion) of these motor particles is taken into account, one finds a variety of cooperative phenomena and self-organized processes: build-up of traffic jams; active structure formation leading to steady states with spatially nonuniform density and current patterns; and active phase transitions between different steady states far from equilibrium. A particularly simple active phase transition with spontaneous symmetry breaking is predicted to occur in systems with two species of motor particles which walk on the filaments in opposite directions.
COLLECTIVE OSCILLATIONS OF PROCESSIVE MOLECULAR MOTORS
Biophysical Reviews and Letters, 2009
We present both a theoretical and an experimental study of the long time behavior of membrane nanotubes pulled from giant unilamellar vesicles by molecular motors. Experimentally, two types of behaviors are observed, either tubes stall at a finite length or they undergo periodic oscillations. Theoretically we write the equations for the tube dynamics as a two-dimensional dynamical system where the variables are the tube length (or the force required to pull the tube at a given length) and the number of motors at the tip pulling the tube. We construct stability diagrams showing the stalling and oscillating states and present an example of oscillations in a non-linear regime. These results can explain the membrane tube retractions and oscillations observed in living cells.
Molecular Motors: From Individual to Collective Behavior
Progress of Theoretical Physics Supplement, 1998
We present a simple two state model for the force generation and motion of molecular motors. We discuss the behavior of individual motors and describe how the coupling of motors in large groups can lead to new collective effects like dynamical phase transitions and spontaneous oscillations.
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.
Self-Organized Beating and Swimming of Internally Driven Filaments
Physical Review Letters, 1999
We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wavelike propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments, could be able to show beating motion and self-propulsion. [S0031-9007(99)08456-2] PACS numbers: 87.10. + e, 02.30.Jr, 46.25.Cc, 47.15.Gf Cilia and flagella are hairlike appendages of many cells which generate motion and are used for self-propulsion and to stir the surrounding fluid. They all share the characteristic architecture of their core structure, the axoneme, a common structural motive that was developed early in evolution. It is characterized by nine parallel pairs of microtubules, which are long and rigid protein filaments, that are arranged in a circular fashion together with a large number of dynein molecular motors . In the presence of adenosine triphosphate (ATP) which is a fuel, the dynein motors attached to the microtubules generate relative forces while acting on neighboring microtubules; the resulting internal stresses induce relative sliding motion of filaments which leads to the propagation of bending waves [1,2].
Bidirectional cooperative motion of molecular motors
Proceedings of the National Academy of Sciences, 2002
Recently, in a beautiful set of experiments, it has been shown that a Ncd mutant, NK11, which lacks directionality in its individual motion, was able to exhibit a new kind of directed motion in motility assays (Endow, S. A. & Higuchi, H. (2000) Nature (London) 406, 913-916): the filaments keep a given velocity for a while and then suddenly move in the opposite direction with similar velocity. We show that these observations nicely illustrate the concept of dynamic transitions in motor collections introduced earlier in the case of an infinite number of motors. We investigate the experimentally relevant case of a finite number of motors both when directionality is present (kinesins, myosins, Ncd) and absent (NK11). Using a symmetric two-state model, we demonstrate that bidirectional motion is the signature of a dynamic transition that results from the collective behavior of many motors acting on the same filament. For motors exhibiting directional bias individually, an asymmetric two-state model is appropriate. In that case, dynamic transitions exist for motor collections in the presence of an external force. We give predictions for the dependence of motion on ATP concentration, external forces, and the number of motors involved. In particular, we show that the reversal time grows exponentially with the number of motors per filament.