TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
JF  - New journal of physics : the open-access journal for physics
N2  - We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry-characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
KW  - first passage time
KW  - cylindrical geometry
KW  - aspect ratio
KW  - protein search
Y1  - 2017
U6  - https://doi.org/10.1088/1367-2630/aa8ed9
SN  - 1367-2630
VL  - 19
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
JF  - New journal of physics
N2  - Westudy the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
KW  - first passage time
KW  - cylindrical geometry
KW  - aspect ratio
KW  - protein search
Y1  - 2017
U6  - https://doi.org/10.1088/1367-2630/aa8ed9
SN  - 1367-2630
VL  - 19
SP  - 1
EP  - 11
PB  - IOP
CY  - London
ER  - 
TY  - JOUR
A1  - Godec, Aljaž
A1  - Metzler, Ralf
T1  - First passage time statistics for two-channel diffusion
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling.
KW  - first passage time
KW  - Markov additive processes
KW  - Fokker-Planck equation
KW  - random search processes
KW  - coupled initial boundary value problem
KW  - cellular signalling
KW  - asymptotic analysis
Y1  - 2017
U6  - https://doi.org/10.1088/1751-8121/aa5204
SN  - 1751-8113
SN  - 1751-8121
VL  - 50
IS  - 8
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -