Calculation of absolute protein–ligand binding free energy from computer simulations

Abstract

A general methodology for calculating the equilibrium binding constant of a flexible ligand to a protein receptor is formulated on the basis of potentials of mean force. The overall process is decomposed into several stages that can be computed separately: the free ligand in the bulk is first restrained into the conformation it adopts in the bound state, position, and orientation by applying biasing potentials, then it is translated into the binding site, where it is released completely. The conformational restraining potential is based on the root-mean-square deviation of the peptide coordinates relative to its average conformation in the bound complex. Free energy contributions from each stage are calculated by means of free energy perturbation potential of mean force techniques by using appropriate order parameters. The present approach avoids the need to decouple the ligand from its surrounding (bulk solvent and receptor protein) as is traditionally performed in the doubledecoupling scheme. It is believed that the present formulation will be particularly useful when the solvation free energy of the ligand is very large. As an application, the equilibrium binding constant of the phosphotyrosine peptide pYEEI to the Src homology 2 domain of human Lck has been calculated. The results are in good agreement with experimental values. Approaches at different levels of complexity and sophistication have been used to calculate binding free energies in complex biomolecular systems. Screening of large molecular databases of compounds to identify potential lead drug molecules typically relies on very simplified scoring schemes to achieve the needed efficiency (6). The binding free energy may be estimated on the basis of a continuum solvent approximation assuming quadratic fluctuations around a unique configuration (7,8). The Molecular Mechanics͞ Poisson-Boltzmann (PB) and Surface Area (MM͞PB-SA) method is a popular approach that relies on a mixed scheme combining configurations sampled from molecular dynamics (MD) simulations with explicit solvent, together with free energy estimators based on an implicit continuum solvent model (9). MM͞PB-SA shares some similarities with the linear interaction energy method, which also uses averages calculated from explicit solvent simulations within a linear response framework (10). Despite their usefulness, such approximate schemes can be limited, and how to improve the results is unclear because they do not offer a rigorous route to compute the equilibrium binding constant.In principle, treatments based on MD free energy perturbation (FEP) simulations with explicit solvent molecules offer the most powerful and promising approach to estimate the binding free energies of ligands to macromolecules (11). Nonetheless, although previous studies have provided many of the fundamental elements necessary for the calculation of binding free energy by means of MD (12-17), the computations so far have been limited mostly to fairly small and rigid ligands [e.g., rare gas atom (12, 15), water (14)...

Confinement effects on the kinetics and thermodynamics of protein dimerization

“…For the various cavity sizes, the ranges with weak interactions and the values of ⌬d* are different, indicating that the slopes of the free-energy profiles are different. The presence of a free-energy funnel allows the dimerization to be stabilized by confinement, which is very similar to the free energy of protein-ligand binding obtained theoretically and to the force measured for the ligandreceptor association and dissociation (30,31).…”

Solvent reaction field potential inside an uncharged globular protein: A bridge between implicit and explicit solvent models?

“…For other applications, such as simulation of protein enzymatic mechanisms [50] or analysis of biomolecular interactions [51,52], explicit solvent models will become increasingly preferred. At the same time, increases in computing power and MD/GRAvity-PipE [53] hardware-accelerated systems will enable investigators to calculate average explicit-solvent characteristics for particular conformations of molecular systems of all scales.…”

Energy landscape of the reactions governing the Na + deeply occluded state of the Na + /K + -ATPase in the giant axon of the Humboldt squid

“…36), and ΔH u and ΔS u are the total enthalpy and entropy, respectively, of the adjacent binding reaction (binding of the third Na þ and unbinding of the first Na þ released).…”