A comparative study of the target search of end monomers of real and Rouse chains under spherical confinement

We study the dynamics of the end monomers of a real chain confined in a spherical cavity to search for a small target on the cavity surface using Langevin dynamics simulation. The results are compared and contrasted with those of a Rouse chain to understand the influence of excluded volume interactions on the search dynamics, as characterized by the first passage time (FPT). We analyze how the mean FPT depends on the cavity size R-b, the target size a, and the degree of confinement quantified by R-g/R-b, with R-g being the polymer radius of gyration in free space. As a basic finding, the equilibrium distribution of the end monomers of a real chain in a closed spherical cavity differs from that of a Rouse chain at a given R-g/R-b, which leads to the differences between the mean FPTs of real and Rouse chains. Fitting the survival probability S(t) by a multi-exponential form, we show that the S(t) of real chains exhibits multiple characteristic times at large R-g/R-b. Our simulation results indicate that the search dynamics of a real chain exhibit three characteristic regimes as a function of R-g/R-b, including the transition from the Markovian to non-Markovian process at R-g/R-b approximate to 0.39, along with two distinct regimes at 0.39 < R-g/R-b < 1.0 and R-g/R-b > 1.0, respectively, where S(t) exhibits a single characteristic time and multiple characteristic times.