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We study the first passage time for a polymer, that we call the narrowencounter time (NETP), to reach a small target located on the surface of amicrodomain. The polymer is modeled as a Freely Joint Chain (beads connected bysprings with a resting non zero length) and we use Brownian simulations tostudy two cases: when (i) any of the monomer or (ii) only one can be absorbedat the target window. Interestingly, we find that {in the first case} the NETPis an increasing function of the polymer length until a critical length, afterwhich it decreases. Moreover, in the long polymer regime, we identified anexponential scaling law for the NETP as a function of the polymer length. {Inthe second case, the position of the absorbed monomer along the polymer chainstrongly influences the NETP}. Our analysis can be applied to estimate the meanfirst time of a DNA fragment to a small target in the chromatin structure orfor mRNA to find a small target.

Encounter dynamics of a small target by a polymer diffusing in a confined domain