Regularity and Synchrony in Motor Proteins

Deville, Robert; Vanden‐Eijnden, Eric

doi:10.1007/s11538-007-9266-1

Cited by 15 publications

(18 citation statements)

References 25 publications

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“…[9] we introduced a slightly modified version of Badoual's model, which to a large extent explains the experimentally observed independence of τ rev on N. We argued that the origin of this behavior can be attributed to the tension developed in the actin track due to the action of the attached myosin II motors. An increase in the number of attached motors leads to an increase in the mechanical load which, in turn, leads to an increase in the detachment rate of the motors, as already suggested in models of muscle contraction [29][30][31][32]. But unlike most previous studies where the myosin conformational energy was calculated, in ref.…”

Section: Introductionmentioning

confidence: 99%

Cooperative molecular motors moving back and forth

et al. 2009

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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., Proc. Natl. Acad. Sci. USA 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. † Authors with equal contributions 1

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Section: Introductionmentioning

confidence: 99%

Cooperative molecular motors moving back and forth

et al. 2009

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“…For cargoes carried by multiple motor proteins, transport occurs as each motor steps along the microtubule lattice, sequentially binding, translocating and releasing from the microtubule in a well defined mechanochemical cycle [16, 21, 30, 31]. Eventually, the condition where no motors are attached to the microtubule will be reached and the cargo will diffuse away from the microtubule.…”

Section: Resultsmentioning

confidence: 99%

Interrogating Emergent Transport Properties for Molecular Motor Ensembles: A Semi-analytical Approach

Bhaban

Materassi

et al. 2016

PLoS Comput Biol

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Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins—proteins converting chemical energy into kinetic energy. It is understood that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington’s disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in the expected run-length when the load on the cargo is in the vicinity of the mutant’s stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables a computation of biologically relevant quantities like average velocity and run-length without resorting to Monte Carlo simulations. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use.

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“…Indeed, some Monte Carlo simulations of escape time histograms (not shown) indicate that in the C v < 1 regime, the probability distribution for the escape time has a higher probability for a very fast escape relative to the mean than an exponential distribution. )>0.0055 we mention a very interesting self-induced stochastic resonance mechanism described recently [6,30,7] for how attaching a massive cargo to a motor can produce nearly deterministic jump times for the motor between potential minima [53]. The coefficient of variation of the jump times C v in these motor-cargo models is tied to a small parameter characterizing the mobility of the cargo relative to that of the motor [30].…”

Section: Comparison With Theoretical Criteriamentioning

confidence: 95%

Two coarse-graining studies of stochastic models in molecular biology

Kramer¹,

Latorre²,

Khan³

2010

Communications in Mathematical Sciences

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Abstract. We examine stochastic coarse-graining strategies for two biomolecular systems. First, we compute the large-scale transport properties of the basic flashing ratchet mathematical model for (Brownian) molecular motors and consider in this light whether the underlying continuous-space, continuous-time Markovian model can be coarse-grained as a discrete-state, continuous-time Markovian random walk model. Through careful computation of associated statistical signatures of Markovianity, we find that such a discrete coarse-graining is an excellent approximation over much but not all of the parameter regime. In particular, for the parameter values associated with the fastest transport by the flashing ratchet, the discretized model displays non-Markovian features such as waiting times between jumps which are not exponentially distributed. We provide a theoretical framework for understanding the conditions under which Markovianity is to be expected in the discretized model and two mechanisms by which the flashing ratchet model coarse-grains to a non-Markovian discretized model. Next we turn to a basic question of how the dynamics of water molecules near the surface of a solute can be represented by a simple drift-diffusion stochastic model. This question is of most interest for the purpose of accelerating molecular dynamics simulations of proteins, but for simplicity, here we examine the simple case where the solute is a C 60 buckyball, which has a homogenous, roughly isotropic form. We compare the mathematical drift-diffusion framework with a statistical quantification of water dynamics near a solute discussed in the biophysical literature. A key concern is the choice of time interval on which to sample the molecular dynamics data to generate estimators for the drift and diffusivity. We use a simple mathematical toy model to establish insight and a strategy, but find for the actual molecular dynamics data that the sampling times which produce the most faithful drift coefficient and the sampling times which produce the most faithful diffusion coefficient do not overlap, so that sacrifice of quality in one or the other parameter appears necessary.

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Regularity and Synchrony in Motor Proteins

Cited by 15 publications

References 25 publications

Cooperative molecular motors moving back and forth

Cooperative molecular motors moving back and forth

Interrogating Emergent Transport Properties for Molecular Motor Ensembles: A Semi-analytical Approach

Two coarse-graining studies of stochastic models in molecular biology

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