Free energy measurements by the generalized fluctuation theorems: Theory and numerical study of a model filament
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Free energy measurements by the generalized fluctuation theorems: Theory and numerical study of a model filament Min-Kyung Chae1 , Yunha Kim1 , Nam-Kyung Lee1,2,a , A. Johner2 , and Jeong-Man Park3,b 1 2 3
Department of Physics and Astronomy, Sejong University, Seoul 05006, South Korea Institute Charles Sadron, CNRS 23 Rue du Loess, 67034 Strasbourg cedex 2, France Department of Physics, The Catholic University of Korea, Bucheon 14662, South Korea Received 20 July 2020 / Accepted 25 August 2020 Published online: 29 September 2020 c EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 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.
1 Introduction Over the last decades, the notion of the second law of thermodynamics has been extended to small scale systems where thermal fluctuations are relevant for work, heat exchange, and internal energy. For mesoscopic systems embedded in a heat bath with well-defined temperature, stochastic energetics has been developed and entropy can be defined along the fluctuating trajectory [1,2]. Theoretical relations like the fluctuation theorems (FT) such as the Jarzynski equality (JE) [3–6] and the Crooks fluctuation theorem (CFT) [7,8] involve the probability distribution of external work and allow us to obtain the free energy from non-equilibrium measurements. These theorems have been put into experimental test, using biomolecules under mechanical control [9,10], as well as colloidal particles in time-dependent optical traps [11]. The case of an underdamped particle was examined in ref. [12]. In RNA folding/unfolding experiments, the free energy is successfully obtained from the JE and the CFT [9, 10]. In these experiments, the domain undergoing a folda b
e-mail: [email protected] e-mail: [email protected]
ing/unfolding transition ca
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