Anomalous lifetime statistics of ligand–receptor binding in a tethered polymer system

In this paper, motivated by observations of non-exponential decay times in the stochastic binding and release of ligand–receptor systems, exemplified by the work of Rogers et al on optically trapped DNA-coated colloids (Rogers et al 2013 Soft Matter 9 6412), we explore the general problem of polymer-mediated surface adhesion using a simplified model of the phenomenon in which a single polymer molecule, fixed at one end, binds through a ligand at its opposite end to a flat surface a fixed distance L away and uniformly covered with receptor sites. Working within the Wilemski–Fixman approximation to diffusion-controlled reactions, we show that for a flexible Gaussian chain, the predicted distribution of times $f\left(t\right)$ for which the ligand and receptor are bound is given, for times much shorter than the longest relaxation time of the polymer, by a power law of the form $t^{-1/4}$. We also show when the effects of chain stiffness are incorporated into this model (approximately), the structure of $f\left(t\right)$ is altered to $t^{-1/2}$. These results broadly mirror the experimental trends in the work cited above. (paper)