Trapping of diffusing particles by small absorbers localized in a spherical region

Abstract

We study trapping of particles diffusing in a spherical cavity with an absorbing wall containing small static spherical absorbers localized in a spherical region in the center of the cavity. The focus is on the competition between the absorbers and the cavity wall for diffusing particles. Assuming that the absorbers and, initially, the particles are uniformly distributed in the central region, we derive an expression for the particle trapping probability by the cavity wall. The expression gives this probability as a function of two dimensionless parameters: the transparency parameter, characterizing the efficiency of the particle trapping by the absorbers, and the ratio of the absorber-containing region radius to that of the cavity. This work is a generalization of a recent study by Krapivsky and Redner [J. Chem. Phys. 147, 214903 (2017)] who considered the case where the absorber-containing region occupies the entire cavity. The expression for the particle trapping probability is derived in the framework of a steady-state approach which, in our opinion, is much simpler than the time-dependent approach used in the above-mentioned study.

Physical observables to determine the nature of membrane-less cellular sub-compartments

“…While in principle rebinding events complicate this picture, they can be renormalized into a lower effective unbinding rate [27]. Assuming that interactions between binding sites do not affect their binding to the particle of interest, the binding rate can be approximated in the presence of partially reflecting binding sites by the Smoluchowski rate [28,29] (Appendix A):…”

Physical observables to determine the nature of membrane-less cellular sub-compartments

“…While in principle rebinding events complicate this picture, it has been showed that the period where rebindings to the same binding site occurs can be included in the time they are bound, and thus can be renormalized into a lower effective unbinding rate (Kaizu et al, 2014). Assuming that interactions between binding sites do not affect their binding to the particle of interest, the binding rate can be approximated in the presence of partially reflecting binding sites by the Smoluchowski rate (Nadler and Stein, 1996;Berezhkovskii et al, 2019) (Appendix 1):…”