Free-energy landscape of a polymer in the presence of two nanofluidic entropic traps

TL;DR

This study uses computer simulations to accurately calculate the free-energy landscape of a polymer in complex nanofluidic geometries, highlighting the limitations of simplified analytical models and emphasizing the importance of numerical methods.

Contribution

The paper introduces a simulation-based approach to compute polymer free-energy landscapes in complex geometries, testing and comparing with existing analytical models.

Findings

Simulation results align qualitatively with analytical predictions.

Quantitative discrepancies highlight limitations of simplified models.

Numerical methods provide more accurate free-energy estimates for complex geometries.

Abstract

Recently, nanofluidics experiments have been used to characterize the behavior of single DNA molecules confined to narrow slits etched with arrays of nanopits. Analysis of the experimental data relies on analytical estimates of the underlying free-energy landscape. In this study we use computer simulations to explicitly calculate the free energy and test the approximations employed in such analytical models. Specifically, Monte Carlo simulations were used to study a polymer confined to complex geometry consisting of a nanoslit with two square nanopits embedded in one of the surfaces. The two-dimensional Weighted Histogram Analysis Method (WHAM2D) is used to calculate the free energy, $F$, as a function of the sum ($\lambda_1$) and the difference ($\lambda_2$) of the length of the polymer contour contained in the two nanopits. We find the variation of the free-energy function with respect to confinement dimensions to be comparable to the analytical predictions that employ a simplistic theoretical model. However, there are some noteworthy quantitative discrepancies, particularly between the predicted and observed variation of $F$ with respect to $\lambda_1$. Our study provides a useful lesson on the limitations of using simplistic analytical expressions for polymer free-energy landscapes to interpret results for experiments of DNA confined to a complex geometry and points to the value of carrying out accurate numerical calculations of the free energy instead.