Free-energy perturbation method

1 Free energy perturbation methods Let us start by considering two systems 1 and 2, with Hamiltonians H and H2, respectively. The Helmholtz free energy difference is 

If the two systems in question have the same number of particles of the same mass, the kinetic energy terms cancel out and 

The free energy perturbation method (FEP), as prescribed by Eq. 17.15, was first introduced by Robert Zwanzig in 1954. Although in principle accurate, FEP methods do not converge in practice to a correct result, unless the two end points are sufficiently close. 

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Bash, P.A., Field, M.J.,Karplus, M. Free energy perturbation method for chemical reactions in the condensed phase A dynamical approach baaed on a combined quantum and molecular dynamics potential. J. Am. Chem. Soc. 109 (1987) 8092-8094. 

This principle has been applied in a contribution by Mark, Schafer, Liu and van Gunsteren to this volume, and in section 6 of this article. For a review of free energy perturbation methods see [8]. 

T.P. Lybrand, Computer simulations of biomolecular systems using molecular dynamics and free energy perturbation methods, in Reviews in Computational Chemistry, Vol. 1, K.B. Lipkowitz, D.B. Boyd (Eds.), VCH, New York, 1990, pp. 295-320. 

An early application of the free energy perturbation method was the determination of t] tree energy required to create a cavity in a solvent. Postma, Berendsen and Haak determin the free energy to create a cavity (A = 1) in pure water (A = 0) using isothermal-isobai... 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

CALCULATION OF SOLVATION ENERGIES BY FREE-ENERGY PERTURBATION METHODS... 

Free energy functions, 89, 90, 94 Free energy perturbation method (FEP), 81-82,146, 186-187 computer program for, 97-98 Free energy relationships, linear, 92-96, 148-149... 

Umbrella sampling method, see Free energy perturbation method... 

In our simulations of histone modifying enzymes, the computational approaches centered on the pseudobond ab initio quantum mechanical/molecular mechanical (QM/MM) approach. This approach consists of three major components [20,26-29] a pseudobond method for the treatment of the QM/MM boundary across covalent bonds, an efficient iterative optimization procedure which allows for the use of the ab initio QM/MM method to determine the reaction paths with a realistic enzyme environment, and a free energy perturbation method to take account... 

Kofke, D.A., Cummings, P.T., Precision and accuracy of staged free-energy perturbation methods for computing the chemical potential by molecular simulation, Fluid Phase... 

In spite of these potential concerns, the MEHMC method is expected to be a useful tool for many applications. One task for which it might be particularly well suited is to generate a canonical ensemble of representative configurations of a bio-molecular system quickly. Such an ensemble is needed, for example, to represent the initial conditions for the ensemble of trajectories used in fast-growth free energy perturbation methods such as the one suggested by Jarzynski s identity [104] (see also Chap. 5). 

Sakane, S. Yezdimer, E. M. Liu, W. B. Barriocanal, J. A. Doren, D. J. Wood, R. H., Exploring the ab initio/classical free energy perturbation method the hydration free energy of water, 7. Chem. Phys. 2000,113, 2583-93... 

G. A. Worth and W. G. Richards, Calculation of the tautomer ratio of histamine in aqueous solution using free energy perturbation methods An in depth study, J. Am. Chem. Soc. 116 239 (1994). 

B. G. Rao, and U. C. Singh, Studies on the binding of pepstatin and its derivatives to Rhizopus pepsin by quantum methanics, molecular mechanics, and free energy perturbation methods, J. Am. Chem. Soc. 113 6735 (1991). 

Terry P. Lybrand, Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods. 

To evaluate solvent effeets, statistieal meehanical Monte Carlo simulations have been carried out. An important quantity to be computed is the potential of mean force, or free energy profile, as a funetion of the reaction coordinate, X, for a chemical reaction in solution using free energy perturbation method. (44) A straightforward approaeh is to determine free energy differences for incremental changes of certain geometrieal variables that characteristically reflect the... 

The Free Energy Perturbation method provides the most accurate values of energy differences by simulations [37]. However, to our knowledge this method was only once applied to CD complexes [38], but too little information about the procedure applied, provided in this paper, precludes the assessment of its reliability. 

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