Free-energy cost of localizing a single monomer of a confined polymer

Abstract

We describe a simple Monte Carlo simulation method to calculate the free-energy cost of localizing a single monomer of a polymer confined to a cavity. The localization position is chosen to be on the inside surface of the confining cavity. The method is applied to a freely-jointed hard-sphere polymer chain confined to cavities of spherical and cubic geometries. In the latter case we consider localization at a corner and at the center of a face of the confining cube. We consider cases of end-monomer localization both with and without tethering of the other end monomer to a point on the surface. We also examine localization of monomers at arbitrary position along the contour of the polymer. We characterize the dependence of the free energy on the cavity size and shape, the localization position, and the polymer length. The quantitative trends can be understood using standard scaling arguments and use of a simple theoretical model. The results are relevant to those theories of polymer translocation that focus on the importance of the free-energy barrier as the translocation process requires an initial localization of a monomer to the position of a nanopore.

Entropic force of cone-tethered polymers interacting with a planar surface

“…( 6), which is a closer match to the simulation data than was the case for the freely-jointed chains. The scaling exponent of the fit to the N = 5000 curve in the range h ∈ [4,30] is −0.95 ± 0.03, which is close to the predicted value of −1.…”

“…Presumably, this condition is of lesser importance than h R g . To estimate the scaling exponent for N = 5000 a finitedifference method was used to estimate the force in the range h ∈ [4,30], and a subsequent fit to a power-law function yields scaling exponent of −0.88 ± 0.08. The fitted curve is qualitatively consistent with the theoretical curve calculated using the value of ∆γ obtained from Fig.…”

“…the α = 90 • "cone") is only expected to have a tiny effect on F (h) and so does not explain the discrepancy. 30 Evidently, there is a regime scale crossover as α increases that is not accounted for in the derivation of Eq. ( 6).…”

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

“…As noted in Ref. 69 for the case of flexible chains the free-energy cost of such tethering is only 1-2 k B T for polymers of comparable length and packing fraction as that considered here. Thus, the effect on on the free energy is expected to be negligible.…”

“…In a recent study, we described a method to calculate the free-energy cost of localizing an end monomer of a confined polymer. 69 Using the same model for flexible chains as that employed here we find that for polymer lengths and packing fractions comparable to those used here that the end-monomer localization free energy was 1-2 k B T . Thus, the effect is very small and unlikely to be the principal cause of the discrepancy.…”