Nonequilibrium thermodynamics of single DNA hairpins in a dual-trap optical tweezers setup

Abstract

We use two counter propagating laser beams to create a dual trap optical tweezers setup which is free from cross interference between the beams and provides great instrumental stability. This setup works by direct measurement of light momentum, separately for each trap, and is based on the Minitweezers design [1]. The dual trap setup has many applications: it can be used to study the force‐dependent unfolding kinetics of single molecules and to address fundamental problems in nonequilibrium thermodynamics of small systems [2]. Recent progress in statistical physics has shown the importance of considering large energy deviations in the beahvior of systems that are driven out‐of‐equilibrium by time‐dependent forces. Prominent examples are nonequilibrium work relations (e.g. the Jarzynski equality [3]) and fluctuation theorems. By repeated measurement of the irreversible work the Jarzynski equality allows us to recover the free energy difference between two thermodynamic states, AF, by taking exponential averages of the work W done by the external agent on the system, e−βΔF = 〈e−βW〈, where the average in the rhs is taken over an infinite number of experiments. A crucial aspect of nonequilibrium work relations and fluctuation theorems in general is their non‐invariance under Galilean transformations. This implies that mechanical work must be measured in the proper reference that is solidary with the thermal bath for these relations to hold. We have carried out repeated mechanical unfolding/folding cycles on short (20 bp) DNA hairpins and measured work distributions in the dual‐trap setup along this process. Our aim is to check under which experimental conditions we can discern the non‐invariance property of fluctuation relations thereby establishing the correct operative definition of the work in our setting. This study may help to identify and quantify potential violations of the fluctuation relations.