Free energy from simulations

We assume that the unbinding reaction takes place on a time scale long ( ompared to the relaxation times of all other degrees of freedom of the system, so that the friction coefficient can be considered independent of time. This condition is difficult to satisfy on the time scales achievable in MD simulations. It is, however, the most favorable case for the reconstruction of energy landscapes without the assumption of thermodynamic reversibility, which is central in the majority of established methods for calculating free energies from simulations (McCammon and Harvey, 1987 Elber, 1996) (for applications and discussion of free energy calculation methods see also the chapters by Helms and McCammon, Hermans et al., and Mark et al. in this volume). 

A review is given of the application of Molecular Dynamics (MD) computer simulation to complex molecular systems. Three topics are treated in particular the computation of free energy from simulations, applied to the prediction of the binding constant of an inhibitor to the enzyme dihydrofolate reductase the use of MD simulations in structural refinements based on two-dimensional high-resolution nuclear magnetic resonance data, applied to the lac repressor headpiece the simulation of a hydrated lipid bilayer in atomic detail. The latter shows a rather diffuse structure of the hydrophilic head group layer with considerable local compensation of charge density. 

J. A. McCammon. Free energy from simulations. Curr, Opin, Struct. BioL 7 196-200... 

Estimating Relative Free Energies from a Single Simulation of the Initial State... 

Jayaram, B., Beveridge, D. L. A simple method to estimate free energy from molecular simulation Renormalization on the unit interval. J. Phys. Chem. 94 (1990) 7288-7293... 

Other attempts to predict free energies from a single simulation have explored the relati ship between the coupling parameter. A, and the free energy. Specifically, the free energ ... 

Ding YB, Bernardo DN, Kroghjespersen K, Levy RM (1995) Solvation free-energies of small amides and amines from molecular-dynamics free-energy perturbation simulations using pairwise additive and many-body polarizable potentials. J Phys Chem 99(29) 11575—11583... 

Free Energies from Transition Path Sampling Simulations... 

Lechner, W. Oberhofer, H. Dellago, C. Geissler, P. L., Equilibrium free energies from fast-switching simulations with larg time steps, J. Chem. Phys 2006,124, 04113/1-12... 

Woo, H.J. Roux, B., Calculation of absolute protein ligand binding free energy from computer simulations, Proc. Natl Acad. Sci. USA 2005,102, 6825-6830... 

Figure 4. The free energy calculation results for all mutations. The numbers in italics are the relative binding free energies calculated from experimental Kj values. Other numbers are the relative binding free energies from the simulations. Units are kcal/mol.

This relation is called the Jarzynski equality (hereafter referred to as JE) and can be used to recover free energies from nonequilibrium simulations or experiments (see Section IV.B.2). The FT in Eq. (27) becomes the Crooks fluctuation theorem (hereafter referred to as GET) [45, 46] ... 

Aqvist, J. (1990), Ion-Water Interaction Potentials Derived from Free Energy Perturbation Simulations,... 

Solvation Free Energies of Small Amides and Amines from Molecular Dynamics/Free Energy Perturbation Simulations Using Pairwise Additive and Many-Body Polarizable Potentials. 

Marelius J, Hansson T, Aqvist J. Calculation of ligand binding free energies from molecular dynamics simulations. Intemat. J. Quantum Chem. 1998 69 77-88. 

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