Entropy production of DNA-translocating molecular motors

: Helicases are molecular motors that convert the chemical energy of ATP hydrolysis into mechanical work to move along one strand of DNA and unzip the double helix. Using magnetic tweezers (MT) we follow the activity of a single helicase unzipping a DNA hairpin. From these experiments we can characterize the enzyme motion (e.g. velocity and diffusion) but the ATP hydrolysis reaction is not directly measured. Here we investigate whether we can infer information about the helicase chemical cycle from our helicase displacement data by using non-equilibrium relations such as the thermodynamic uncertainty relation (TUR) and the fluctuation theorem (FT) for entropy production. To address this question, we use the random walk formalism to model the helicase motion and we analytically derive expressions for the TUR and the FT. The derived theoretical results are verified with simulations of the model and compared with experiments. We find qualitatively agreement between experiments and theory. However, some important differences are observed. In particular, the distributions of the helicase displacement deviates from the Gaussian distribution predicted by the theory and the experimental test of the FT fails. We conclude that a refined model is needed to better describe the real experimental system.