Standard Free Energy of Releasing a Localized Water Molecule from the Binding Pockets of Proteins:  Double-Decoupling Method

Abstract

Localized water molecules in the binding pockets of proteins play an important role in noncovalent association of proteins and small drug compounds. At times, the dominant contribution to the binding free energy comes from the release of localized water molecules in the binding pockets of biomolecules. Therefore, to quantify the energetic importance of these water molecules for drug design purposes, we have used the double-decoupling approach to calculate the standard free energy of tying up a water molecule in the binding pockets of two protein complexes. The double-decoupling approach is based on the underlying principle of statistical thermodynamics. We have calculated the standard free energies of tying up the water molecule in the binding pockets of these complexes to be favorable. These water molecules stabilize the protein-drug complexes by interacting with the ligands and binding pockets. Our results offer ideas that could be used in optimizing protein-drug interactions, by designing ligands that are capable of targeting localized water molecules in protein binding sites. The resulting free energy of ligand binding could benefit from the potential free energy gain accompanying the release of these water molecules. Furthermore, we have examined the theoretical background of the double-decoupling method and its connection to the molecular dynamics thermodynamic integration techniques.

On the Application of Accelerated Molecular Dynamics to Liquid Water Simulations

“…Assuming ideal gas behavior, the term RT, where R is the gas constant and T is the absolute temperature, equals the work of expansion PΔV in a constantpressure process. Thus, equation 9 can be rewritten as, 10 The potential energy of the system was recorded every 100 steps for the calculation of heat of vaporization. 〈E l 〉 was obtained from the last 2 ns of the normal and accelerated MD simulations by re-weighting each configuration by its respective Boltzmann factor of the bias potential, e βΔV(r) .…”

“…9 In addition, some proteins show highly structured and localized water molecules in their binding sites, which play important roles in the protein-ligand interactions. 10,11 In this case, a description in which all atomic and structural details of the solvent molecules are ignored may result in deleterious effects in simulations of protein function. Therefore, there is a need for the development of methods that make feasible the atomistic computer simulation of biological systems over long time scales.…”

Rapid estimation of hydration thermodynamics of macromolecular regions

“…(13). 22 The value of k is nearly 10 times lower than 3RT δr 2 for all water molecules in the pockets and therefore does not significantly perturb the natural dynamics expected in absence of the restraint: 22…”

“…Following the method formulated by Gilson et al 21 and used by Hamelberg and McCammon, 22 the standard free energy of a stable water molecule binding to a site on the protein is decomposed into the negative of the decoupling free energy, the translational contribution, and the hydration free energy of water, as shown in the following equation. A contribution (=RT ln(2)) arising due to the symmetry number of water was not included: 23 …”

“…Instead of using a standard concentration C o of 1 M as done by Hamelberg and McCammon, 22 we used a value of 55 M so as to make comparison with our GCMC approach where excess free energy is calculated with respect to bulk water under standard conditions. The water molecules in the decoupling FEP simulations were harmonically restrained with a force-constant k of 0.5 kcal mol −1 Å −2 and the effective volume V 1 , which the water molecule is restrained to occupy was calculated as shown in Eq.…”