Free Energy of a Folded Polymer under Cylindrical Confinement

Abstract

Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy F is measured as a function of λ, the end-to-end distance of the polymer. In the case of a flexible linear polymer, F (λ) is a linear function in the folded regime with a gradient that scales as f ≡ |dF/dλ| ∼ N 0 D −1.20±0.01 for a tube of diameter D and a polymer of length N. This is close to the prediction f ∼ N 0 D −1 obtained from simple scaling arguments. The discrepancy is due in part to finite-size effects associated with the de-Gennes blob model. A similar discrepancy was observed for the folding of a single arm of a three-arm star polymer. We also examine backfolding of a semiflexible polymer of persistence length P in the classic Odijk regime. In the overlap regime, the derivative scales f ∼ N 0 D −1.72±0.02 P −0.35±0.01 , which is close to the prediction f ∼ N 0 D −5/3 P −1/3 obtained from a scaling argument that treats interactions between deflection segments at the second virial level. In addition, the measured free energy cost of forming a hairpin turn is quantitatively consistent with a recent theoretical calculation. Finally, we examine the scaling of F (λ) for a confined semiflexible chain in the presence of an S-loop composed of two hairpins. While the predicted scaling of the free energy gradient is the same as that for a single hairpin, we observe a scaling of f ∼ D −1.91±0.03 P −0.36±0.01 . Thus, the quantitative discrepancy between this measurement and the predicted scaling is somewhat greater for Sloops than for single hairpins.

Single molecule electrophoresis of star polymers through nanopores: Simulations

“…11,12 Understanding the behavior of star polymers under confinement has been the focus of various recent studies. [13][14][15][16][17][18][19][20][21][22][23][24] This is an interesting problem because the distribution of arms of the star polymer under confinement can lead to rich dynamics, and developing such an understanding is required in devising many applications. For asymmetric star polymers, arm length has been found to have a profound effect on the transport properties of the polymer in gel electrophoresis.…”

Free Energy of a Folded Semiflexible Polymer Confined to a Nanochannel of Various Geometries

“…1 are straightforward and were mostly explained in Ref. 27. The steep rise in F as λ decreases from λ min is associated with the formation of a hairpin turn in the polymer.…”

“…Most simulations employed a polymer of length N=200 monomers, which is sufficient to obtain reliable values of the free energy gradient in the overlap regime and the hairpin free energy. 27 The system was equilibrated for typically 10 7 MC cycles, following which a production run of 4 × 10 8 MC cycles was carried out. On average, during each MC cycle a displacement or rotation move for each monomer and a reptation move is attempted once.…”

Hairpins in the conformations of a confined polymer

“…While it is possible to provide a more accurate estimate of the entropic force, for example by using the methods of Ref. 28, we cannot directly apply the results of the latter reference to our analysis. The confinement free energy of a high aspect ratio rectangular channel, which arises in part due to excluded volume, is different than in a circular tube.…”