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 $\lambda$, the end-to-end distance of the polymer. In the case of a flexible linear polymer, $F(\lambda )$ is a linear function in the folded regime with a gradient that scales as $f\equiv |dF/d\lambda |\sim N^0{D}^{-1.20\pm 0.01}$ for a tube of diameter $D$ and a polymer of length $N$. This is close to the prediction $f\sim N^0{D}^{-1}$ 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 $f\sim N^0{D}^{-1.72\pm 0.02}{P}^{-0.35\pm 0.01}$, which is close to the prediction $f\sim N^0{D}^{-5/3}{P}^{-1/3}$ 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 $F(\lambda )$ 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 $f\sim D^{-1.91\pm 0.03}{P}^{-0.36\pm 0.01}$. Thus, the quantitative discrepancy between this measurement and the predicted scaling is somewhat greater for S-loops than for single hairpins.

arXiv comment17 papes, 12 figures

References in corpus (12)

• Scaling theory of DNA confined in nanochannels and nanoslits
• A review of Monte Carlo simulations of polymers with PERM
• DNA Confined in Nanochannels: Hairpin Tightening by Entropic Depletion
• Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects
• Time scale of entropic segregation of flexible polymers in confinement: Implications for chromosome segregation in filamentous bacteria
• Polymer Translocation Dynamics in the Quasi-Static Limit
• Nanoconfined circular and linear DNA - equilibrium conformations and unfolding kinetics
• Scaling regimes of a semi-flexible polymer in a rectangular channel
• Polymer translocation into and out of an ellipsoidal cavity
• Polymer segregation under confinement: Free energy calculations and segregation dynamics simulations
• Segregation of Polymers in Confined Spaces
• Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study

Cited by in corpus (5)

• Polymer translocation into cavities: Effects of confinement geometry, crowding and bending rigidity on the free energy
• Free energy of a folded semiflexible polymer confined to a nanochannel of various geometries
• Hairpins in the conformations of a confined polymer
• Entropic force of cone-tethered polymers interacting with a planar surface
• Free Energy of a Knotted Polymer Confined to Narrow Cylindrical and Conical Channels