What determines the van der Waals coefficient β in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?
Wei Wang, Jian Wang, Peter A. Kollman · Proteins Structure Function and Bioinformatics · 1999
Recently a semiempirical method has been proposed by Åqvist et al.1, 2, 3to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as ΔGbind = α〈V − V〉 + β〈V − V, where V and V are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and V and V are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, α = 0.5 and β = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of β were found in studies of compounds binding to P450cam4and avidin.5The present work investigates how the optimal value of β depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of β and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of β for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of β found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-β value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies. Proteins 1999;34:395–402. © 1999 Wiley-Liss, Inc.