BPCPPDYSOE21 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Posters DY - Statistical Physics, Brownian Motion and Nonlinear Dynamics

DY 32.14: Poster

Dienstag, 23. März 2021, 16:30–19:00, DYp

The narrow escape problem in two-shell circular domains — •Matthieu Mangeat and Heiko Rieger — Saarland University, Saarbrücken, Germany

The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments [1,2]. As a first step to understand the consequence of the existence of two compartments for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusivities and potentials in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary (cell membrane). We find that the MFPT can be minimized for a specific value of the width of the outer shell only if the particle is sufficiently attracted in the outer shell whereas the MFPT depends monotonously on all model parameters without attraction. A criterion on the difference of potential between the two shells can be calculated analytically with respect to the escape region size and the ratio of diffusivities. Moreover we show that the limit of small width of the outer shell is equivalent to the surface-mediated diffusion problem [3].

[1] K. Schwarz et al., Phys. Rev. Lett. 117, 068101 (2016).

[2] A. E. Hafner and H. Rieger, Phys. Biol. 13, 066003 (2016); Biophys. J 114, 1420-1432 (2018).

[3] J.-F. Rupprecht et al., Phys. Rev. E 86, 041135 (2012).