title: The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations.
abstract: Free-energy calculations in multiple dimensions constitute a challenging problem, owing to the significant computational cost incurred to achieve ergodic sampling. The generalized adaptive biasing force (gABF) algorithm calculates n one-dimensional lists of biasing forces to approximate the n-dimensional matrix by ignoring the coupling terms ordinarily taken into account in classical ABF simulations, thereby greatly accelerating sampling in the multidimensional space. This approximation may however occasionally lead to poor, incomplete exploration of the conformational space compared to classical ABF, especially when the selected coarse variables are strongly coupled. It has been found that introducing extended potentials coupled to the coarse variables of interest can virtually eliminate this shortcoming, and, thus, improve the efficiency of gABF simulations. In the present contribution, we propose a new free-energy method, coined extended generalized ABF (egABF), combining gABF with an extended Lagrangian strategy. The results for three illustrative examples indicate that (i) egABF can explore the transition coordinate much more efficiently compared with classical ABF, eABF, and gABF, in both simple and complex cases and (ii) egABF can achieve a higher accuracy than gABF, with a root mean-squared deviation between egABF and eABF free-energy profiles on the order of kBT. Furthermore, the new egABF algorithm outruns the previous ABF-based algorithms in high-dimensional free-energy calculations and, hence, represents a powerful importance-sampling alternative for the investigation of complex chemical and biological processes.
authors.affiliation: Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.
authors.forename: Tanfeng
authors.initials: T
authors.lastname: Zhao
authors.affiliation: Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.
authors.forename: Haohao
authors.initials: H
authors.lastname: Fu
authors.affiliation: Université Paris-Est , CERMICS (ENPC), INRIA, 77455 Marne-la-Vallée, France.
authors.forename: Tony
authors.initials: T
authors.lastname: Lelièvre
authors.affiliation: Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.|Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071, China.|State Key Laboratory of Medicinal Chemical Biology, Nankai University , Tianjin 300071, China.
authors.forename: Xueguang
authors.initials: X
authors.lastname: Shao
authors.affiliation: Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign , Unité Mixte de Recherche No. 7565, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France.|Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.|Department of Physics, University of Illinois at Urbana-Champaign , 1110 West Green Street, Urbana, Illinois 61801, United States.
authors.forename: Christophe
authors.identifier: http://orcid.org/0000-0002-9122-1698
authors.initials: C
authors.lastname: Chipot
authors.affiliation: Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University , Tianjin 300071, China.|Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071, China.
authors.forename: Wensheng
authors.initials: W
authors.lastname: Cai