Free energy calculation methods: A theoretical and empirical comparison of numerical errors and a new method qualitative estimates of free energy changes

We present a comparison of four free energy calculation methods: thermodynamic integration (TI); traditional free energy perturbation (FEP); Bennett's acceptance ratio method (IPS); and a method that is related to an implementation of the WHAM method (CRS). The theoretical bases of the methods are first described, then calculations of the solvation free energies of methane and ethane are performed to determine the magnitude of the errors for the different methods. We find that the methods give similar errors when many intermediate states (windows) are used, but the IPS and CRS methods give smaller errors than the TI and FEP methods when no intermediate states are used. We also present a new procedure (based on the CRS method) that uses coordinates from simulations of a set of solutes to calculate the salvation free energies of additional solutes for which no simulations were performed. Solvation free energies for nine solutes (methanol, dimethylether, methylamine, methylammonium, dimethylamine, fluoromethane, difluoromethane, trifluoromethane, and tetrafluoromethane) are estimated based only on simulations of set of small hydrophobic solutes (including methane, ethane, and propane). These estimates can be surprisingly accurate and appear to be useful for making rapid estimates of solvation free energies. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 902–919, 1997     

Theoretical and experimental studies of biotin analogues that bind almost as tightly to streptavidin as biotin

We have used a newly developed qualitative computational approach, PROFEC (Pictorial Representation of Free Energy Changes), to visualize the areas of the ligand biotin where modifications of its structure might lead to tighter binding to the protein streptavidin. The PROFEC analysis, which includes protein flexibility and ligand solvation/desolvation, led to the suggestion that the pro-9R hydrogen atom of biotin, which is in alpha-position to the CO(2)(-) group, might be changed to a larger group and lead to better binding with streptavidin and avidin. Free energy calculations supported this suggestion and predicted that the methyl analogue should bind approximately 3 kcal/mol more tightly to streptavidin, with this difference coming exclusively from the relative desolvation free energy of the ligand. The PROFEC analysis further suggested little or no improvement for changing the pro-9S hydrogen atom to a methyl group, and great reduction in changing the ureido N-H groups to N-CH(3). Stimulated by these results, we synthesized 9R-methylbiotin and 9S-methylbiotin, and their binding free energies and enthalpies were measured for interaction with streptavidin and avidin, respectively. In contrast to the calculated results, experiments found both 9-methylbiotin isomers to bind more weakly to streptavidin than biotin. The calculated preference for the binding of the 9R- over the 9S-stereoisomer was observed. In addition, 9-methylbiotin is considerably less soluble in water than biotin, as predicted by the calculation, and the 9R isomer is, to our knowledge, thus far the tightest binding analogue of biotin to streptavidin. Subsequently, X-ray structures of the complexes between streptavidin and both 9R- and 9S-methylbiotin were determined, and the structures were consistent with those used in the free energy calculations. Thus, the reason for the discrepancy between the calculated and experimental binding free energy does not lie in unusual binding modes for the 9-methylbiotins.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.     

The application of three approximate free energy calculations methods to structure based ligand design: Trypsin and its complex with inhibitors

Three approximate free energy calculation methods are examined and applied to an example ligand design problem. The first of the methods uses a single simulation to estimate the relative binding free energies for related ligands that are not simulated. The second method is similar, except that it uses only first derivatives of free energy with respect to atomic parameters (most often charge, van der Waals equilibrium distance, and van der Waals well depth) to calculate free energy differences. The last method PROFEC (Pictorial Representation of Free Energy Components), generates contour maps that show how binding free energy changes when additional particles are added near the ligand. These three methods are applied to a benzamidine/trypsin complex. They each reproduce the general trends in the binding free energies, indicating that they might be useful for suggesting how ligands could be modified to improve binding and, consequently, useful in structure-based drug design.