Dynamic properties of molecular motors in burnt-bridge models

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

doi:10.1088/1742-5468/2007/08/p08002

Cited by 4 publications

(35 citation statements)

References 14 publications

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“…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: 86%

“…The diffusion coefficient is found by generalizing the method developed in [7] (where we found dynamic properties of the random walker in BBM with u = w = 1, p 2 = 0 and periodic bridge distribution), allowing for 0 < p 2 1 and u = w. We define P kN +i,m (t) as the probability that at time t the random walker is located at point x = kN + i (i = 0, 1, · · · , N − 1), the right end of the last burnt bridge being at the point mN . Parameters m and k 0 assume integer values.…”

Section: Diffusion Coefficientmentioning

confidence: 99%

“…Now we are able to obtain the expression for the random walker's velocity [7]. The mean position of the particle is given by…”

Section: -5mentioning

confidence: 99%

“…In (62), the function f (k + 1) is expressed according to equation (7). Plugging (59), (55) (with appropriate k, i) into (62) permits us to express θ k in terms of T kN in this way,…”

Section: -7mentioning

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%

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Dynamics of molecular motors in reversible burnt-bridge models

Artyomov¹,

Morozov²,

Kolomeisky³

2010

Condens. Matter Phys.

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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.

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Section: Introductionmentioning

confidence: 86%

Section: Diffusion Coefficientmentioning

confidence: 99%

“…Now we are able to obtain the expression for the random walker's velocity [7]. The mean position of the particle is given by…”

Section: -5mentioning

confidence: 99%

“…In (62), the function f (k + 1) is expressed according to equation (7). Plugging (59), (55) (with appropriate k, i) into (62) permits us to express θ k in terms of T kN in this way,…”

Section: -7mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of molecular motors in reversible burnt-bridge models

Artyomov¹,

Morozov²,

Kolomeisky³

2010

Condens. Matter Phys.

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Transport of molecular motor dimers in burnt-bridge models

Morozov¹,

Kolomeisky²

2007

J. Stat. Mech.

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Dynamics of molecular motor dimers, consisting of rigidly bound particles that move along two parallel lattices and interact with underlying molecular tracks, is investigated theoretically by analyzing discrete-state stochastic continuous-time burntbridge models. In these models the motion of molecular motors is viewed as a random walk along the lattices with periodically distributed weak links (bridges). When the particle crosses the weak link it can be destroyed with a probability p, driving the molecular motor motion in one direction. Dynamic properties and effective generated forces of dimer molecular motors are calculated exactly as a function of a concentration of bridges c and burning probability p and compared with properties of the monomer motors. It is found that the ratio of the velocities of the dimer and the monomer can never exceed 2, while the dispersions of the dimer and the monomer are not very different. The relative effective generated force of the dimer (as compared to the monomer) also cannot be larger than 2 for most sets of parameters. However, a very large force can be produced by the dimer in the special case of c = 1/2 for non-zero shift between the lattices. Our calculations do not show the significant increase in the force generated by collagenase motor proteins in real biological systems as predicted by previous computational studies. The observed behavior of dimer molecular motors is discussed by considering in detail the particle dynamics near burnt bridges.

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Molecular motors interacting with their own tracks

2008

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Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state "burnt-bridge" models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences nonmonotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes.

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Dynamic properties of molecular motors in burnt-bridge models

Cited by 4 publications

References 14 publications

Dynamics of molecular motors in reversible burnt-bridge models

Dynamics of molecular motors in reversible burnt-bridge models

Transport of molecular motor dimers in burnt-bridge models

Molecular motors interacting with their own tracks

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