TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
JF  - Communications Chemistry
N2  - Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants—the inverse of the mean-first-passage-time to the reaction-event. In contradiction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly solvable model we study the effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delineated by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.
Y1  - 2018
U6  - https://doi.org/10.1038/s42004-018-0096-x
SN  - 2399-3669
VL  - 1
PB  - Macmillan Publishers Limited
CY  - London
ER  - 
TY  - GEN
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
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. 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 391 
KW  - aspect ratio
KW  - cylindrical geometry
KW  - first passage time
KW  - protein search
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-403726
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  -