Work distribution for unzipping processes

Abstract

A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature $T$ and subject to an external force $f$, which couples to the free length $L$ of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force $f_c\left(T\right)$ in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature $T$ and force $f$, the full distribution $P\left(L\right)$ of free lengths in the thermodynamic limit and show that it is qualitatively very different for $f<f_c, f=f_c$, and $f>f_c$. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained $P\left(L\right)$ already allows us to derive an analytical expression for the work distribution $P\left(W\right)$ in the zipped phase $f<f_c$ for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as ${10}^{-200}$ with numerical simulations performed by applying sophisticated large-deviation algorithms.