A formalism of polymer translocation through a cylindrical channel of finite diameter and length between two spherical compartments is developed. Unlike previous simplified systems, the finite diameter of the channel allows the number of polymer segments inside the channel to be adjusted during translocation according to the free energy of possible conformations. The translocation process of a Gaussian chain without excluded volume and hydrodynamic interactions is studied using exact formulas of confinement free energy under this formalism. The free energy landscape for the translocation process, the distribution of the translocation time, and the average translocation time are presented. The complex dependencies of the average translocation time on the length and diameter of the channel, the sizes of the donor and receptor compartments, and the chain length are illustrated
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