Free Energy Calculations: Use and Limitations in Predicting Ligand Binding Affinities. In: Lipkowitz KB, Boyd DB, editors. Reviews in Computational Chemistry. Hoboken: John Wiley & Sons, Inc.; 2000. pp. 217-304. [DOI: 10.1002/9780470125939.ch4]

Uncertainty Quantification in Alchemical Free Energy Methods

Alchemical free energy methods have gained much importance recently from several reports of improved ligand–protein binding affinity predictions based on their implementation using molecular dynamics simulations. A large number of variants of such methods implementing different accelerated sampling techniques and free energy estimators are available, each claimed to be better than the others in its own way. However, the key features of reproducibility and quantification of associated uncertainties in such methods have barely been discussed. Here, we apply a systematic protocol for uncertainty quantification to a number of popular alchemical free energy methods, covering both absolute and relative free energy predictions. We show that a reliable measure of error estimation is provided by ensemble simulation—an ensemble of independent MD simulations—which applies irrespective of the free energy method. The need to use ensemble methods is fundamental and holds regardless of the duration of time of the molecular dynamics simulations performed.

Soft-core potentials in thermodynamic integration: comparing one- and two-step transformations

Molecular dynamics-based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This "singularity" problem can be addressed with "soft-core" potential functions which keep pairwise interaction energies finite for all configurations and provide smooth free energy curves. "One-step" transformations, in which electrostatic and van der Waals forces are simultaneously modified, can be simpler and less expensive than "two-step" transformations in which these properties are changed in separate calculations. Here, we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters α(LJ) and β(C) controlling the behavior of the soft-core Lennard-Jones and Coulomb potentials and compare one- and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates.

Tools for building a comprehensive modeling system for virtual screening under real biological conditions: The Computational Titration algorithm

Computational tools utilizing a unique empirical modeling system based on the hydrophobic effect and the measurement of logP(o/w) (the partition coefficient for solvent transfer between 1-octanol and water) are described. The associated force field, Hydropathic INTeractions (HINT), contains much rich information about non-covalent interactions in the biological environment because of its basis in an experiment that measures interactions in solution. HINT is shown to be the core of an evolving virtual screening system that is capable of taking into account a number of factors often ignored such as entropy, effects of solvent molecules at the active site, and the ionization states of acidic and basic residues and ligand functional groups. The outline of a comprehensive modeling system for virtual screening that incorporates these features is described. In addition, a detailed description of the Computational Titration algorithm is provided. As an example, three complexes of dihydrofolate reductase (DHFR) are analyzed with our system and these results are compared with the experimental free energies of binding.

Getting it right: modeling of pH, solvent and “nearly” everything else in virtual screening of biological targets

"Getting it right" refers to the careful modeling of all elements in the living system, i.e. biological macromolecules, ligands and water molecules. In addition, careful attention should be paid to the protonation state of ionizable functional groups on the ligands and residues at the active site. Computational technology based on the empirical HINT program is described to: (1) calculate free energy scores for ligand binding; (2) include the implicit and explicit effects of water in and around the ligand binding site; and (3) incorporate the effects of global and local pH in molecular models. This last point argues for the simultaneous consideration of a number of molecular models, each with different protonation profiles. Data from recent studies of protein-ligand systems (trypsin, thrombin, neuraminidase, HIV-1 protease and others) are used to illustrate the concepts in the paper. Also discussed are experimental factors related to accurate free energy predictions with this and other computational technologies.