Narrow-escape times for diffusion in microdomains with a particle-surface affinity: Mean-field results

Abstract

We analyze the mean time t(app) that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, etc. Using a mean-field approximation, we define t(app) analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion.

Interfacial territory covered by surface-mediated diffusion

“…This is in strong contrast with the behavior of the mean first-passage time to the exit zone averaged over the initial distribution (sometimes referred to in the literature as the narrow escape time problem [13,16,22,23]), which can display a nonmonotonic behavior with the desorption rate λ [17,18]. We now turn to the case of a fixed entrance point, which leads to strikingly different behaviors.…”

“…The trajectories involved in such reactions, combining bulk and surface-mediated diffusion phases, can now be observed at the single molecule scale [14]. At the theoretical level, surface-mediated diffusion has generated a growing attention these last years [15][16][17][18][19][20][21]. Importantly, it has been recently shown to minimize reaction times by a proper tuning of the desorption rate from the surface and could thus constitute a general mechanism of enhancement and regulation of chemical and biological reactivity [17,18].…”

Enhanced diffusion through surface excursion: A master-equation approach to the narrow-escape-time problem

“…The NET problem is prominent in cellular biology, since it is related to the random time needed by a particle (released inside the cell) to activate a given mechanism on the cell membrane, for example, the particle may be a protein that looks for a specific site on a DNA string [3][4][5]. Since the seminal work of Berg and Purcell [13], the research in the area has experienced steady growth over time and has motivated a great deal of work [14][15][16][17][18][19][20][21][22][23][24][25].…”

“…For instance, in Ref. [23] a mean-field approximation to calculate the mean reaction (search) time is developed, and in Ref. [24] a backward equation-type formalism is presented.…”

Splitting probabilities and interfacial territory covered by two-dimensional and three-dimensional surface-mediated diffusion

“…At the experimental level, the corresponding trajectories, which combine bulk and surface-mediated diffusion phases, can now be observed at the single molecule scale [6,7]. At the theoretical level, surface-mediated diffusion has raised a growing interest over the past years [8][9][10][11][12][13][14][15][16][17]. Such interest is partly due to the possibility of minimizing reaction times by a proper tuning of the desorption rate from the surface, which could constitute a general mechanism of enhancement of reaction kinetics [11,12].…”