Extracting Equilibrium From Nonequilibrium: Free Energy Calculation From Steered Molecular Dynamics Simulations

The machinery of life is composed of molecules such as DNA and proteins. Technology has brought us today to the stage where one can investigate biomolecules at the single-molecule level. Atomistic simulations and experimental techniques such as atomic force microscopy and optical tweezer have already proved to be effective and are constantly being improved. Fluctuations play such an important role at the nanometer scale where biomolecules live that the theory of fluctuations (commonly known as nonequilibrium statistical mechanics) is indispensable for understanding the results of these experiments and simulations. This thesis explores the issue of calculating potentials of mean force (an equilibrium property) from steered molecular dynamics simulations (a nonequilibrium process). Recently discovered Jarzynski’s equality provides the theoretical basis. Derivations of Jarzynski’s equality are reviewed and related theoretical issues are discussed. A method of potential-of-mean-force calculation is developed; the method is based on the cumulant expansion of Jarzynski’s equality and the scheme of using stiff springs for the purpose of steering. The possibility that the resulting work distribution might be Gaussian regardless of the speed of the process is discussed. A benchmark study using deca-alanine as an exemplary system examines the accuracy of the method and demonstrates the Gaussian nature of the work distribution. The method is then applied to a process involving an actual protein, glycerol conduction through the membrane channel protein GlpF. From the potential of mean force thus obtained, important observables such as the binding constant and conductivity are estimated. And finally, the problem of finding reaction paths is discussed: a new method based on mean first-passage times is proposed and is applied to the excitation migration in photosynthesis.U of I OnlyPost 1923. No authorization form