Optimal Target Search on a Fast-Folding Polymer Chain with Volume Exchange

We study the search process of a target on a rapidly folding polymer (“DNA”) by an ensemble of particles (“proteins”), whose search combines 1D diffusion along the chain, Lévy type diffusion mediated by chain looping, and volume exchange. A rich behavior of the search process is obtained with respect to the physical parameters, in particular, for the optimal search.

Figure 1

Search mechanisms in Eq. (1).

Figure 2

Number of proteins arrived at the target up to $t$. Numerical solutions of Eq. (3) and limiting regimes.

Figure 3

Optimal choice of off rate $k_{\mathrm{off}}$ as a function of the LF diffusion constant, from numerical evaluation of Eq. (14). The circle on the abscissa marks where $k_{\mathrm{off}}^{\mathrm{opt}}$ becomes 0 [Eq. (17)].