Determining the Free Energy and Kinetics of a Translocating Polymer Chain

Polymer threading or translocation through nanopores is widely studied due to its ubiquity in biology and its recent use as a characterization method. In this work, we explored translocation of a chain from one spherical cavity to another, motivated by viruses and vesicles. The primary theoretical tool for studying a translocating chain is its free energy, which includes the free energy associated with the donor/acceptor compartments, and the polymer-pore interaction energy. In the first stage of the project, we focused on calculating chain free energy under spherical confinement, relevant for donor/acceptor compartments. Due to conflicting theoretical pictures, we implemented Monte Carlo simulations and investigated how the free energy relates to the confinement strength and how it varies when the chain is tethered. With the simulation results and previous translocation theories, we built a center of mass (CM) theory for polymer translocation. This theory establishes a physical interpretation for the translocation coordinate in terms of the CM. Also, our approach allows for the incorporation of hydrodynamics through the CM friction. Both the simulations and theory can be generalized to study other confined environments.