Berlin 2012 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 9: Statistical Physics of Biological Systems II (with BP, talks from BP)
DY 9.5: Vortrag
Montag, 26. März 2012, 16:00–16:15, H 1058
Mean Exit Time of a Brownian Particle from a Spherical Domain with Multiple Exit Sites on the Boundary — •Ronny Straube1, Michael J. Ward2, and Alexei F. Cheviakov3 — 1Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg — 2University of British Columbia, Vancouver, Canada — 3University of Saskatchewan, Saskatoon, Canada
In biological signal transduction a target molecule often has to find a small exit site on an otherwise impermeable boundary. Important examples of such narrow escape processes include diffusion through ion channels and trafficking through pores of the nuclear membrane. We have recently extended the calculation of the mean exit time (MET) from the case of a Brownian particle exiting from a spherical domain with a single exit site [1] to the case of multiple exit sites [2]. Using the method of matched asymptotic expansions we provide a three-term approximation of the MET which explicitly depends on the spatial configuration of the exit sites. We show that for a fixed surface fraction of exit sites the MET reaches a value close to its minimum already for 30-40 exit sites which suggests, for example, that cell nuclei have many more pores than would be needed if nuclear export was a purely diffusion-limited process.
[1] Singer A, Schuss Z, Holcman D, Eisenberg RS. Narrow escape, part I. J. Stat. Phys. 122, 437-463 (2006).
[2] Cheviakov AF, Ward MJ, Straube R. An asymptotic analysis of the mean first passage time for narrow escape problems: part II: The sphere. SIAM Multiscale Model. Simul. 8, 836–870 (2010).