Eur. Phys. J. E (2020) 43: 62
https://doi.org/10.1140/epje/i2020-11984-5

Regular Article

Free energy measurements by the generalized fluctuation theorems: Theory and numerical study of a model filament

¹ Department of Physics and Astronomy, Sejong University, 05006, Seoul, South Korea
² Institute Charles Sadron, CNRS 23 Rue du Loess, 67034, Strasbourg cedex 2, France
³ Department of Physics, The Catholic University of Korea, 14662, Bucheon, South Korea

^* e-mail: lee@sejong.ac.kr
^** e-mail: jmanpark@catholic.ac.kr

Received: 20 July 2020
Accepted: 25 August 2020
Published online: 29 September 2020

Abstract

We measure the free energy of a model filament, which undergoes deformations and structural transitions, as a function of its extension, in silico. We perform Brownian Dynamics (BD) simulations of pulling experiments at various speeds, following a protocol close to experimental ones. The results from the fluctuation theorems are compared with the estimates from Monte Carlo (MC) simulation, where the rugged free energy landscape is produced by the density of states method. The fluctuation theorems (FT) give accurate estimates of the free energy up to moderate pulling speeds. At higher pulling speeds, the work distributions do not efficiently sample the domain of small work and FT slightly overestimates free energy. In order to comprehend the differences, we analyze the work distributions from the BD simulations in the framework of trajectory thermodynamics and propose the generalized fluctuation theorems that take into account the information (relative entropy) evaluated in the expanded phase space. The measured work - free energy relation is consistent with the results obtained from the generalized fluctuation theorems. We discuss operational methods to improve the estimates at high pulling speed.