Free-energy-perturbation

In cases where substrates bind selectively to enzymes or catalysts, and in the area of selective host-guest interactions, changes in the free energy are of importance. These are usually not available computationally, except by ab-initio quantum me- 

The exponential in Eq. 2.14 represents the average over the system described by the hamiltonian Hx, and the corresponding series of conformers and configurational isomers is usually created by molecular dynamics or Monte Carlo methods. When the two systems X and Y are very similar, the exponential term vanishes, leading to a very slow convergence of the average in Eq. 2.14. A number of techniques have been described to overcome this problem 43 441. One of the few applications of this method to coordination compounds is the investigation of O2 and CO affinities to iron porphyrins[45]. 

If the ensembles in Eq. (12.2), over which tlie property averages for systems A and B are taken, were somehow to be the same, one would be able to take advantage of the properties of exponentials to write 

In order to avoid this problem, the switching between the two molecules may be broken up into smaller steps using a coupling parameter X that may take on values from 0 to 1. We then write the energy of the system as a general function of X 

By creating new ensembles with each increase in X, potentially offending water molecules in the region of tlie nitrogen atom like the one mentioned above are eased out of the way, since in each new ensemble die presence of Hp becomes more manifest. The cost, however, is that now 20 simulations need to be undertaken instead of one (assuming an interval width of 0.05 as in tlie example). 

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Free energy perturbation (FEP) theory is now widely used as a tool in computational chemistry and biochemistry [91]. It has been applied to detennine differences in the free energies of solvation of two solutes, free energy differences in confonnational or tautomeric fonns of the same solute by mutating one molecule or fonn into the other. Figure A2.3.20 illustrates this for the mutation of CFt OFl CFt CFt [92]. 

Wesolowski T A and Warshel A 1994 Ab initio free energy perturbation calculations of solvation free energy using the frozen density functional approach J. Phys. Chem. 98 5183... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

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. 

S. Miyamoto and P. A. Kollman. Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches. Proteins, 16 226-245, 1993. 

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]. 

Mark, A.E. Free energy perturbation calculations. Encyclopaedia of Computational Chemistry, Wiley, New York, (1998) (in press). 

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... 

Miyamoto S and P A Kollman 1993a. Absolute and Relative Binding Tree Energy Calculations of the Interaction of Biotin and its Analogues with Streptavidin Using Molecular Dynamics/Free Energy Perturbation Approaches. Proteins Structure, Function and Genetics 16 226-245. 

Pearlman D A and P A Kollman 1989. A New Method for Carrying Out Free-Energy Perturbation Calculations - Dynamically Modified Wmdows. Journal Of Chemical Physics 90 2460-2470. 

S Hirono, PA Kollman. Calculation of the relative binding free energy of 2 -GMP and 2 -AMP to ribonuclease T1 using molecular dynamics/free energy perturbation approaches. J Mol Biol 212 197-209, 1990. 

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

FIGURE 3.2. A free-energy perturbation calculation of the free energy associated with an adiabatic charging of an Na+ ion in water (Ref. 10). The parameter A transforms the solute from it uncharged (A = 0) to its charged form (A = 1). 

FIGURE 6.4. Examining the strain hypothesis by a free-energy perturbation study. The results are plotted as a function of rather than A, for simplicity. The AG is given relative to the reference potential [-Kcos( Ci 0s)]. The figure demonstrates that the strain effect is not significant. 

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