Subdiffusion-limited reactions

Yuste, S. B.; Lindenberg, Katja

doi:10.1016/s0301-0104(02)00546-3

Cited by 135 publications

(79 citation statements)

References 31 publications

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“…The first-passage time (FPT), which is the time needed for a particle starting from site S to reach a target T for the first time. This quantity is fundamental in the study of transportlimited reactions (31)(32)(33), because it gives the reaction time in the limit of perfect reaction. This quantity is also useful in target search problems (34)(35)(36)(37)(38)(39) and other physical systems (40)(41)(42).…”

mentioning

confidence: 99%

Probing microscopic origins of confined subdiffusion by first-passage observables

Condamin

Tejedor

Voituriez

et al. 2008

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

197

165

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Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widespread. This deviation from Brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios that cannot be identified solely by the MSD data. In this article we present a theoretical framework that permits the analytical calculation of first-passage observables (mean first-passage times, splitting probabilities, and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover, we suggest experiments based on first-passage observables that could help in determining the origin of subdiffusion in complex media, such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.anomalous diffusion ͉ cellular transport ͉ reaction kinetics ͉ random motion I n the past few years, subdiffusion has been observed in an increasing number of systems (1, 2), ranging from physics (3, 4) or geophysics (5) to biology (6, 7). In particular, living cells provide striking examples for systems where subdiffusion has been repeatedly observed experimentally, either in the cytoplasm (6-9), the nucleus (10, 11), or the plasmic membrane (12-14). However, the microscopic origin of subdiffusion in cells is still debated, even if believed to be caused by crowding effects in a wide sense, as indicated by in vitro experiments (15-18).The subdiffusive behavior significantly deviates from the usual Gaussian solution of the simple diffusion equation, and is usually characterized by a mean square displacement (MSD) (1) that scales as ͗⌬r 2 ͘ ϳ t ␤ with ␤ Ͻ 1. Such a scaling law can be obtained from a few models based on different underlying microscopic mechanisms. Here, we focus on two possibilities (a third classical model of subdiffusion is given by the fractional Brownian motion that concerns processes with long-range correlations): (i) The first class of models that we consider stems from continuous time random walks (CTRWs) (1, 19) and their continuous limit described by fractional diffusion equations (1, 20). The anomalous behavior in these models originates from a heavy-tailed distribution of waiting times (21): at each step the walker lands on a trap, where it can be trapped for extended periods of time. When dealing with a tracer particle, traps can be out-of-equilibrium chemical binding configurations (22, 23), and the waiting times are then the dissociation times; traps can also be realized by the free cages around the tracer in a hard sphere-like crowded environment, and the waiting times are the life times of the ...

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mentioning

confidence: 99%

Probing microscopic origins of confined subdiffusion by first-passage observables

Condamin

Tejedor

Voituriez

et al. 2008

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

197

165

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“…In the last few decades, the theory of fractional derivatives has attracted significant attention in various areas, such as viscoelasticity 8 , signal processing 9 , biology 10,11 . In biology, one of its most prominent uses is in modelling diffusion processes 8,12 , and the fractional model has been used to describe anomalous diffusion in complex environments 10,11 .…”

Section: Fractional Reaction Diffusion Equationsmentioning

confidence: 99%

Untitled

Abdullah¹

2011

ScienceAsia

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Features inside living cells are complex and crowded, and in such complex environments diffusion processes exhibit three different behaviours; Fickian diffusion, subdiffusion, and superdiffusion. This study aims to investigate the phenomenon of subdiffusion, which occurs when there is molecular crowding, by proposing a new continuous spatial model involving fractional differential equations. The anomalous diffusion parameter is introduced to represent the spatial crowdedness in the media. The equations are solved numerically using an implicit fractional trapezoidal method. Simulations applied to the particular case of the Michaelis-Menten reaction demonstrate that, as a result of anomalous diffusion or a crowded situation in low dimensional biological media, kinetics are of the fractal type. The model also predicts that increasing obstacle density results in reactant segregation, which is similar to that observed in in vivo conditions in cells.

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“…Anomalous diffusion processes differ from classical diffusion in that the dispersion of particles proceeds faster (superdiffusion) or slower (subdiffusion) than for the regular case. These anomalous diffusion processes do, for instance, occur in biological tissues [15,16] or in chemical systems [17]. They can also be observed in porous media [18,19] or turbulent diffusion [20,21].…”

Section: Introductionmentioning

confidence: 96%

Time Evolution of Relative Entropies for Anomalous Diffusion

Prehl

Boldt

Essex

et al. 2013

Entropy

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The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is "nearer" to pure diffusion than another, placing pure wave propagation, desirably, "furthest" from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives.

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Subdiffusion-limited reactions

Cited by 135 publications

References 31 publications

Probing microscopic origins of confined subdiffusion by first-passage observables

Probing microscopic origins of confined subdiffusion by first-passage observables

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Time Evolution of Relative Entropies for Anomalous Diffusion

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