Banff
International
Research Station
for Mathematical Innovation and Discovery 

Freeenergy calculations. A
mathematical perspective

Workshop held from
July 19 to 24, 2015 at the Casa Matemática Oaxaca, Mexico
Organized
by Chris Chipot (Université de Lorraine and University of Illinois),
Tony Lelièvre (École des Ponts, ParisTech) and Robert Skeel (Purdue
University)




Background Scope List of participants Organizers Venue Program 
Background To
understand fully the vast majority of physical, chemical and biological
processes, it is often necessary to examine their underlying
freeenergy behavior. Such is the case, for instance, of molecular
recognition and association (e.g. binding of a drug to a target
protein; partitioning of the same drug across the cell membrane). These
processes, which are of paramount importance in a variety of fields,
like rational drug design, cannot be predicted accurately without the
knowledge of the associated freeenergy changes. Reliable determination
of freeenergy changes using numerical simulations based on the
fundamental principles of statistical mechanics is now within reach.
Developments on the methodological fronts in conjunction with the
continuous increase in computational power have brought freeenergy
calculations to the level of robust and wellcharacterized modeling
tools, while widening their field of applications. In particular,
development of robust numerical methods for determination of
freeenergy differences is connected to fundamental questions in
various scientific fields, ranging from rareevent simulations,
coarsegraining and reduced models to the thermodynamics of
outofequilibrium systems. Much of these methodological developments
would not have been possible without the contribution of mathematics.
For the most part, the statisticalmechanical framework for calculating freeenergy differences has been developed several years ago [14]. How to apply this framework in computer simulations in an effective fashion remains, however, an effervescent research area, in which mathematics continues to be a prominent actor. In recent years, remarkable progress has been made in this field. Noteworthy examples include the development of methods for calculating freeenergy differences between two states based on nonequilibrium dynamics [5] and by sampling paths connecting these states [6], great improvements in quantummechanical approaches to estimating free energies, clarifications of how to perform correctly thermodynamic integration employing constrained [7] and unconstrained dynamics [8,9], the construction of techniques that markedly reduce nonergodicity problems in freeenergy calculations [10] and the development of quasichemical approach to calculating the free energy. Furthermore, our understanding of conceptual connections between these different methods has improved markedly, as well as our ability to estimate statistical and systematic errors in molecular numerical simulations. (1) L. D. Landau. Statistical physics. The Clarendon Press, 1938. (2) R. Zwanzig. J. Chem. Phys. 1954, 22, 14201426. (3) G. M. Torrie ; J. P. Valleau. J. Comp. Phys. 1977, 23, 187199. (4) C. H. Bennett. J. Comp. Phys. 1976, 22, 245268. (5) C. Jarzynski. Phys. Rev. Lett., 1997, 78, 26902693. (6) P. G. Bolhuis, D. Chandler, C. Dellago, P. L. Geissler. Ann. Rev. Phys. Chem. 2002, 53, 291318. (7) W. K. den Otter. J. Chem. Phys. 2000, 112, 72837292. (8) E. Darve, A. Pohorille. J. Chem. Phys. 2001, 115, 91699183. (9) J. Hénin, C. Chipot. J. Chem. Phys. 2004, 121, 29042914. (10) B. J. Berne, J. E. Straub. Curr. Opin. Struct. Biol., 1997, 7, 181189. 