Calculating protein–ligand binding affinities with MMPBSA: Method and error analysis

Abstract

MMPBSA methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here we investigated different computational alternatives on their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. We first studied the performance of nonpolar solvation models and found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the PoissonBoltzmann methods was analyzed next. Our data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Angstrom is already small enough to be negligible. We further analyzed the impact of different atomic radius sets and different molecular surface definitions and found weak influences on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. Our data also show that the converged simulations cause slight reduction in the agreement with experiment. Finally we briefly explored the direction of estimating absolute binding free energies. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities are also reduced dramatically when the modern nonpolar solvent model was used, though further developments are apparently necessary to further improve the MMPBSA methods. Graphical abstract HHS Public Access Author Manuscript Author ManuscriptAuthor Manuscript Author ManuscriptThe modern nonpolar solvent model that separately models solvation hydrophobic and dispersion interactions dramatically reduces RMSDs of computed relative binding affinities in Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods.

A Continuum Poisson–Boltzmann Model for Membrane Channel Proteins

“…Our previous studies have shown that a high protein dielectric constant best reproduces experimental results in MMPBSA calculations when charged ligands/active sites present in globular proteins 118, 124 . A similar conclusion can also be drawn in the tested membrane protein: when the “default” protein dielectric value of 4 is used, the correlation is reduced from 0.79 to 0.75 with INP=1.…”

“…The membrane dielectric constant was set to be 7.0 124 . And the protein dielectric constant was set to be 20.0 due to the presence of charged ligand molecules 118, 124 . The water phase ionic strength was set to be 150 mM.…”

“…Predicting protein-ligand binding affinities is one of the major applications for implicit solvent free energy calculations. In the Amber software package, MMPBSA is the module performing such calculations 113-118 . Implicit membrane modeling has also been applied and developed in binding free energy calculations.…”

“…The implicit membrane model can be readily interfaced with the existing MMPBSA program 113-118 to perform binding free energy calculations of several protein structures embedded in a membrane 87, 124 . However, a problem arises when those membrane proteins contain a pore or a gated channel, since the region of the channel is usually permeable and should be composed of water.…”

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

“…This classical surface area-dependent method is widely adopted for practical biomolecular applications to estimate the total nonpolar solvation contribution in the case of macromolecules, although its deficiencies were also reported due to overlooking solvation contributions of interior (buried) atoms. 24, 33–52 Newer models were proposed to overcome these deficiencies, though they are yet to be widely received by the community.…”