Solutions of burnt-bridge models for molecular motor transport

Morozov, A. Yu.; Pronina, Ekaterina; Kolomeisky, Anatoly B.; Artyomov, Maxim N.

doi:10.1103/physreve.75.031910

Cited by 21 publications

(70 citation statements)

References 10 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the strong bonds remain unaffected if crossed by the walker in any direction, the weak ones (termed "bridges") might be broken (or "burnt") with a probability 0 < p 1 1 when crossed in the specific direction, and the walker cannot cross the burnt bridges again, unless they are restored, which can occur with probability 0 < p 2 1. In [6,7] an analytical approach was developed which permitted us to derive the explicit formulas for molecular motor velocity V (c, p 1 ) and diffusion constant D(c, p 1 ) for the entire ranges of burning probability 0 < p 1 1 and concentration of the bridges 0 < c 1 which were also confirmed by extensive Monte Carlo computer simulations. This theoretical method has been applied to several problems with periodic bridge distribution.…”

Section: Introductionmentioning

confidence: 94%

“…To find the walker's velocity, we generalize the method used in [6] (for irreversible bridge burning, i.e. p 2 = 0) to allow for non-zero probability p 2 .…”

Section: Velocitymentioning

confidence: 99%

“…This theoretical method has been applied to several problems with periodic bridge distribution. However, the results in [6,7] have been obtained only for irreversible bridge burning (bridge recovery probability was taken to be p 2 = 0), and also for unbiased random walker between bridges (equal forward and backward transition rates). In present work, we generalize The details of breaking weak bonds in BBM have a strong effect on the dynamic properties of motor proteins [6].…”

Section: Introductionmentioning

confidence: 99%

“…It was proposed that a good description of the collagenase dynamics could be provided by the so-called "burnt-bridge model" (BBM) [2][3][4][5][6][7][8][9]. In this model, the motor protein is depicted as a random walker that translocates along the one-dimensional lattice that consists of strong and weak bonds.…”

Section: Introductionmentioning

confidence: 99%

“…This description is more realistic for collagenases' dynamics [2,3]. The model below will be studied using continuous time analysis as it better describes chemical transitions in motor proteins [6].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Dynamics of molecular motors in reversible burnt-bridge models

Artyomov¹,

Morozov²,

Kolomeisky³

2010

Condens. Matter Phys.

View full text Add to dashboard Cite

Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random walkers that can destroy or rebuild periodically distributed weak connections ("bridges") when crossing them, with probabilities p 1 and p 2 correspondingly. Dynamic properties, such as velocities and dispersions, are obtained in exact and explicit form for arbitrary values of parameters p 1 and p 2 . For the unbiased random walker, reversible burning of the bridges results in a biased directed motion with a dynamic transition observed at very small concentrations of bridges. In the case of backward biased molecular motor its backward velocity is reduced and a reversal of the direction of motion is observed for some range of parameters. It is also found that the dispersion demonstrates a complex, non-monotonic behavior with large fluctuations for some set of parameters. Complex dynamics of the system is discussed by analyzing the behavior of the molecular motors near burned bridges.

show abstract

Section: Introductionmentioning

confidence: 94%

“…To find the walker's velocity, we generalize the method used in [6] (for irreversible bridge burning, i.e. p 2 = 0) to allow for non-zero probability p 2 .…”

Section: Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamics of molecular motors in reversible burnt-bridge models

Artyomov¹,

Morozov²,

Kolomeisky³

2010

Condens. Matter Phys.

View full text Add to dashboard Cite

show abstract

Force Transduction by the Microtubule-Bound Dam1 Ring

Armond

Turner

2010

Biophysical Journal

View full text Add to dashboard Cite

The coupling between the depolymerization of microtubules (MTs) and the motion of the Dam1 ring complex is now thought to play an important role in the generation of forces during mitosis. Our current understanding of this motion is based on a number of detailed computational models. Although these models realize possible mechanisms for force transduction, they can be extended by variation of any of a large number of poorly measured parameters and there is no clear strategy for determining how they might be distinguished experimentally. Here we seek to identify and analyze two distinct mechanisms present in the computational models. In the first, the splayed protofilaments at the end of the depolymerizing MT physically prevent the Dam1 ring from falling off the end, and in the other, an attractive binding secures the ring to the microtubule. Based on this analysis, we discuss how to distinguish between competing models that seek to explain how the Dam1 ring stays on the MT. We propose novel experimental approaches that could resolve these models for the first time, either by changing the diffusion constant of the Dam1 ring (e.g., by tethering a long polymer to it) or by using a time-varying load.

show abstract

Physical Modeling of Chromosome Segregation in Escherichia coli Reveals Impact of Force and DNA Relaxation

Lampo

Kuwada

Wiggins

et al. 2015

Biophysical Journal

View full text Add to dashboard Cite

The physical mechanism by which Escherichia coli segregates copies of its chromosome for partitioning into daughter cells is unknown, partly due to the difficulty in interpreting the complex dynamic behavior during segregation. Analysis of previous chromosome segregation measurements in E. coli demonstrates that the origin of replication exhibits processive motion with a mean displacement that scales as t(0.32). In this work, we develop a model for segregation of chromosomal DNA as a Rouse polymer in a viscoelastic medium with a force applied to a single monomer. Our model demonstrates that the observed power-law scaling of the mean displacement and the behavior of the velocity autocorrelation function is captured by accounting for the relaxation of the polymer chain and the viscoelastic environment. We show that the ratio of the mean displacement to the variance of the displacement during segregation events is a critical metric that eliminates the compounding effects of polymer and medium dynamics and provides the segregation force. We calculate the force of oriC segregation in E. coli to be ∼0.49 pN.

show abstract

Solutions of burnt-bridge models for molecular motor transport

Cited by 21 publications

References 10 publications

Dynamics of molecular motors in reversible burnt-bridge models

Dynamics of molecular motors in reversible burnt-bridge models

Force Transduction by the Microtubule-Bound Dam1 Ring

Physical Modeling of Chromosome Segregation in Escherichia coli Reveals Impact of Force and DNA Relaxation

Contact Info

Product

Resources

About