Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy

Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to N = 601 monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area A for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-A and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio >= 1.