Molecular Motors: From Individual to Collective Behavior (original) (raw)
Related papers
Spontaneous Oscillations of Collective Molecular Motors
Physical Review Letters, 1997
We present a physical mechanism which can lead to oscillatory motion of molecular motors cooperating in large groups when the system is elastically coupled to its environment. Analytical and numerical calculations reveal a characteristic type of oscillatory behavior with cusplike extrema. Typical oscillation frequencies are determined by the internal time scales of the motors. The physical mechanism we describe generates in a natural way many of the characteristic properties of spontaneous oscillations observed in some muscles and myofibrils. [S0031-9007(97)03323-1] PACS numbers: 87.10. + e, 05.40. + j Motor proteins are highly specialized macromolecules which can consume mechanical energy to induce motion and to generate forces. These molecules are involved in active transport processes, cell locomotion, and muscle contraction . A typical motor molecule specifically attaches to a certain protein filament which serves as a track for its motion. In the presence of fuel, which in the cell is the molecule adenosine triphosphate (ATP), the motor starts moving in a direction defined by the polarity of the track. Experimental methods allow one to measure forces and velocities of individual motors or small groups of motors .
Collective Dynamics of Interacting Molecular Motors
Physical Review Letters, 2006
The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N * 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.
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.
Physical Review Letters, 1995
We present a simple stochastical model for motor molecules that cooperate in large groups. This model could apply for actin-myosin motors in muscles and for motility assays with a high concentration of motor molecules. We calculate the dependence of the velocity on the applied force as a function of ATP concentration and show the existence of a dynamical phase transition allowing for spontaneous directed motion even if the system is spatially symmetric. In the symmetric case, the problem is isomorphous to a paramagnet-ferromagnet transition, in the asymmetric case to a liquid-vapor transition.
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.
Self-Organization and Cooperativity of Weakly Coupled Molecular Motors under Unequal Loading
Physical Review Letters, 2009
We study the collective dynamics of Brownian motors moving on a one-dimensional track when an external load is applied to the leading motor. Motors are driven by a two-state ratchet mechanism, which is appropriate to single-headed kinesins, and their relative motion is only constrained by their mutual interaction potential (weak coupling). We show that unequal loading enhances cooperativity, leading to the formation of clusters with velocities and efficiencies higher than those predicted by simple superposition. When a weak attraction between motors is present, we find nonmonotonic collective velocity-force curves, hysteretic phenomena, and a dynamic self-regulation mechanism that selects the cluster size for optimal performance.
Reviews of Modern Physics, 1997
The authors present general considerations and simple models for the operation of isothermal motors at small scales, in asymmetric environments. Their work is inspired by recent observations on the behavior of molecular motors in the biological realm, where chemical energy is converted into mechanical energy. A generic Onsager-like description of the linear (close to equilibrium) regime is presented, which exhibits structural differences from the usual Carnot engines. Turning to more explicit models for a single motor, the authors show the importance of the time scales involved and of the spatial dependence of the motor's chemical activity. Considering the situation in which a large collection of such motors operates together. The authors exhibit new features among which are dynamical phase transitions formally similar to paramagnetic-ferromagnetic and liquid-vapor transitions. [S0034-6861 CONTENTS
An approach which has been recently introduced to construct microscopic engines is investigated. The main characteristic of the approach is the possibility to determine dynamically the direction of motion of the engines. The engines, which are moving objects on a substrate, are able to move translationally or rotationally and simultaneously perform useful functions such as pulling of a cargo. We discuss an example in which the energy is fed into the engine by changing locally the intrinsic lengths of the moving object. The local changes might be obtained by externally exciting the system. The transformation of the supplied energy into directed motion is through dynamical competition between the intrinsic lengths given by the moving object and the characteristic lengths of the substrate. r
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.
Correlations and symmetry of interactions influence collective dynamics of molecular motors
Journal of Statistical Mechanics: Theory and Experiment, 2015
Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and they frequently work together in large groups. To understand the mechanisms of collective behavior of motor proteins we study the effect of interactions in the transport of molecular motors along linear filaments. It is done by analyzing a recently introduced class of totally asymmetric exclusion processes that takes into account the intermolecular interactions via thermodynamically consistent approach. We develop a new theoretical method that allows us to compute analytically all dynamic properties of the system. Our analysis shows that correlations play important role in dynamics of interacting molecular motors. Surprisingly, we find that the correlations for repulsive interactions are weaker and more short-range than the correlations for the attractive interactions. In addition, it is shown that symmetry of interactions affect dynamic properties of molecular motors. The implications of these findings for motor proteins transport are discussed. Our theoretical predictions are tested by extensive Monte Carlo computer simulations.