Geometry-controlled kinetics

Bénichou, Olivier; Chevalier, Claire; Klafter, J.; Meyer, Béatrice; Voituriez, Raphaël

doi:10.1038/nchem.622

Cited by 357 publications

(456 citation statements)

References 46 publications

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“…In particular, the role of compact versus noncompact explorations has been revealed in generality [16]. Much less is known about MFPT properties in potential landscapes.…”

Section: Discussionmentioning

confidence: 99%

How a finite potential barrier decreases the mean first-passage time

Palyulin¹,

Metzler²

2012

J. Stat. Mech.

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Abstract. We consider the mean first passage time of a random walker moving in a potential landscape on a finite interval, starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first passage time for a piecewise linear curve between these two points is minimised by introduction of a potential barrier. Due to thermal fluctuations this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first passage time is shorter than for a linear potential drop between the two points.

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“…In particular, the role of compact versus noncompact explorations has been revealed in generality [16]. Much less is known about MFPT properties in potential landscapes.…”

Section: Discussionmentioning

confidence: 99%

How a finite potential barrier decreases the mean first-passage time

Palyulin¹,

Metzler²

2012

J. Stat. Mech.

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“…Recently, emphasis has been given to geometry controlled reaction kinetics (39). In particular, the role of the first passage time and its moments in determining reaction kinetics on fractal geometries has been elucidated.…”

Section: Discussionmentioning

confidence: 99%

Anomalies in the vibrational dynamics of proteins are a consequence of fractal-like structure

Reuveni

Granek

Klafter

2010

Proc. Natl. Acad. Sci. U.S.A.

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Proteins have been shown to exhibit strange/anomalous dynamics displaying non-Debye density of vibrational states, anomalous spread of vibrational energy, large conformational changes, nonexponential decay of correlations, and nonexponential unfolding times. The anomalous behavior may, in principle, stem from various factors affecting the energy landscape under which a protein vibrates. Investigating the origins of such unconventional dynamics, we focus on the structure-dynamics interplay and introduce a stochastic approach to the vibrational dynamics of proteins. We use diffusion, a method sensitive to the structural features of the protein fold and them alone, in order to probe protein structure. Conducting a large-scale study of diffusion on over 500 Protein Data Bank structures we find it to be anomalous, an indication of a fractal-like structure. Taking advantage of known and newly derived relations between vibrational dynamics and diffusion, we demonstrate the equivalence of our findings to the existence of structurally originated anomalies in the vibrational dynamics of proteins. We conclude that these anomalies are a direct result of the fractal-like structure of proteins. The duality between diffusion and vibrational dynamics allows us to make, on a single-molecule level, experimentally testable predictions. The time dependent vibrational mean square displacement of an amino acid is predicted to be subdiffusive. The thermal variance in the instantaneous distance between amino acids is shown to grow as a power law of the equilibrium distance. Mean first passage time analysis is offered as a practical tool that may aid in the identification of amino acid pairs involved in large conformational changes.protein dynamics | Gaussian network model | anomalous diffusion | intramolecular distance distributions | mean first passage time IntroductionProteins are commonly envisioned vibrating under the influence of a complicated energy landscape (1) held responsible for their intricate dynamics (1-9). Despite its overall complexity the energy landscape is approximately harmonic near its minima, a fact that does not seem to coincide with the rich dynamics mentioned above. Attacking the validity of the harmonic approximation is one way out of this puzzle. One might have suggested that the harmonic approximation is unable to capture the anomalous dynamics displayed by proteins since the latter is dominated by large excursions from the native state structure. The failure of the harmonic approximation then follows from the fact that it does not describe the energy of conformations which considerably deviate from the native state structure. In this paper we argue differently showing that the native state structure of proteins is fractal-like and hence anomalous in its basis. As a result one needs not go beyond the harmonic approximation in order to observe anomalous dynamics since anomalous structure leads to it even in the presence of the simplest interactions. Interestingly, when the structure is fractal-like, large con...

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“…This interest in the concept of FPTs is motivated by the crucial role played by FPTs in various contexts, including diffusion limited chemical reactions [3][4][5], the spreading of diseases [6], or target search processes [7][8][9][10]. A general formalism for the calculation of the mean first-passage time (MFPT) of a scale-invariant random process r t in a confined domain of volume V has recently been derived in the large V limit in [11,12], and the full distribution of the FPT has been obtained [13]. These results highlight the asymptotic dependence of the MFPT T and its higher order moments on both the source-to-target distance r and on the confinement volume in the case of scale-invariant processes, which can be characterized by the walk dimension d w (defined by r 2 t ∝ t 2/dw ) and the fractal dimension d f of the support of the random process [14].…”

Section: Introductionmentioning

confidence: 99%

Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

Tejedor¹,

Bénichou²,

Metzler³

et al. 2011

J. Phys. A: Math. Theor.

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We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of Lévy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behaviour. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.

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Geometry-controlled kinetics

Cited by 357 publications

References 46 publications

How a finite potential barrier decreases the mean first-passage time

How a finite potential barrier decreases the mean first-passage time

Anomalies in the vibrational dynamics of proteins are a consequence of fractal-like structure

Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

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