Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains

Grebenkov, Denis S.; Metzler, Ralf; Oshanin, Gleb

doi:10.1088/1367-2630/aa8ed9

Cited by 36 publications

(63 citation statements)

References 52 publications

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“…which corresponds to the surface-averaged MFPT investigated in Ref. [38]. This result is expected for diffusion in a bounded domain.…”

Section: B the Right-tail Of The Fpt Distributionsupporting

confidence: 71%

“…We note that the effect of κ on the shape of the full distribution of the FPT is a novel feature here. The only available previous analysis concerned solely its effect on the MFPT, and showed that in related settings it can indeed be decisive [28,38]. This naturally raises the question of the effects of a finite reactivity beyond the MFPT.…”

Section: Resultsmentioning

confidence: 99%

“…In this regime the MFPT becomes dominated by chemical reactivity, T r ∼ 1/κ (see Refs. [28,38]). The most probable FPT exhibits a weak dependence on κ.…”

Section: Imperfect Reactionsmentioning

confidence: 99%

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Towards a full quantitative description of single-molecule reaction kinetics in biological cells

Grebenkov

Metzler

Oshanin

2018

Phys. Chem. Chem. Phys.

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114

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The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it is typically very broad in many biological situations, thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.

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“…which corresponds to the surface-averaged MFPT investigated in Ref. [38]. This result is expected for diffusion in a bounded domain.…”

Section: B the Right-tail Of The Fpt Distributionsupporting

confidence: 71%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Towards a full quantitative description of single-molecule reaction kinetics in biological cells

Grebenkov

Metzler

Oshanin

2018

Phys. Chem. Chem. Phys.

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114

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“…(ii) The concept of the search-controlled versus barrier-controlled NEP proposed in [4,30] holds indeed for the mean FRT, see equation (C.6). In contrast, we observe that two other important characteristic time-scales-t mp and t c -are unaffected by the reactivity and solely depend on the diffusion coefficient and the geometry.…”

mentioning

confidence: 93%

Full distribution of first exit times in the narrow escape problem

2019

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In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean firstreaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.

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“…On the other hand, homogenization techniques were used to substitute piecewise constant reactivity κ(s) by an effective homogeneous reactivity [31][32][33][51][52][53][54][55][56][57][58]. More recent works investigated how the mean reaction time is affected by a finite lifetime of diffusing particles [59][60][61], by partial reactivity and interactions [63,64], by target aspect ratio [65], by reversible target-binding kinetics [66,67] and surface-mediated diffusion [68][69][70][71], by heterogeneous diffusivity [72], and by rapid re-arrangments of the medium [73][74][75]. Some of the related effects onto the whole distribution of reaction times were analyzed [76][77][78][79][80].…”

Section: Introductionmentioning

confidence: 99%

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

Grebenkov

2019

The Journal of Chemical Physics

108

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We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially reactive surface is expressed in terms of a much simpler propagator toward a homogeneous perfectly reactive surface. In other words, the original problem with general Robin boundary condition that includes in particular mixed Robin-Neumann condition, is reduced to that with Dirichlet boundary condition. Chemical kinetics on the surface is incorporated as a matrix representation of the surface reactivity in the eigenbasis of the Dirichlet-to-Neumann operator. New spectral representations of important characteristics of diffusion-controlled reactions, such as the survival probability, the distribution of reaction times, and the reaction rate, are deduced. Theoretical and numerical advantages of this spectral approach are illustrated by solving interior and exterior problems for a spherical surface that may describe either an escape from a ball or hitting its surface from outside. The effect of continuously varying or piecewise constant surface reactivity (describing, e.g., many reactive patches) is analyzed.

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Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains

Cited by 36 publications

References 52 publications

Towards a full quantitative description of single-molecule reaction kinetics in biological cells

Towards a full quantitative description of single-molecule reaction kinetics in biological cells

Full distribution of first exit times in the narrow escape problem

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

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