TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Kumar, Aanjaneya
T1  - First-passage times of multiple diffusing particles with reversible target-binding kinetics
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number K among N particles independently diffusing in a solvent are simultaneously bound to a target region. 
In the irreversible target-binding setting, the particles that bind to the target stay there forever, and the reaction time is the Kth fastest first-passage time to the target, whose distribution is well-known. In turn, reversible binding, which is common for most applications, renders theoretical analysis much more challenging and drastically changes the distribution of reaction times. 
We develop a renewal-based approach to derive an approximate solution for the probability density of the reaction time. 
This approximation turns out to be remarkably accurate for a broad range of parameters. 
We also analyze the dependence of the mean reaction time or, equivalently, the inverse reaction rate, on the main parameters such as K, N, and binding/unbinding constants. Some biophysical applications and further perspectives are briefly discussed.
KW  - first-passage time
KW  - diffusion-controlled reactions
KW  - reversible binding
KW  - extreme statistics
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac7e91
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 32
PB  - IOP Publ.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
T1  - An encounter-based approach for restricted diffusion with a gradient drift
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We develop an encounter-based approach for describing restricted diffusion with a gradient drift toward a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive a spectral decomposition for the full propagator, i.e. the joint probability density function for the particle position and its boundary local time. This is the central quantity that determines various characteristics of diffusion-influenced reactions such as conventional propagators, survival probability, first-passage time distribution, boundary local time distribution, and reaction rate. As an illustration, we investigate the impact of a constant drift onto the boundary local time for restricted diffusion on an interval. More generally, this approach accesses how external forces may influence the statistics of encounters of a diffusing particle with the reactive boundary.
KW  - boundary local time
KW  - reflected Brownian motion
KW  - diffusion-influenced
KW  - reactions
KW  - surface reactivity
KW  - Robin boundary condition
KW  - Heterogeneous
KW  - catalysis
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac411a
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -