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

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.