Influence of the solvent representation on vibrational entropy calculations: Generalized born versus distance‐dependent dielectric model

Abstract

The harmonic model is the most popular approximation for estimating the "configurational" entropy of a solute in molecular mechanics/Poisson-Boltzmann solvent accessible surface area (MM/PBSA)-type binding free energy calculations. Here, we investigate the influence of the solvent representation in the harmonic model by comparing estimates of changes in the vibrational entropies for 30 trypsin/ligand complexes on ligand binding. Second derivatives of Amber generalized Born (GB) solvation models are available in the nucleic acid builder code. They allow one to use these models for the calculation of vibrational entropies instead of using a simpler solvation model based on a distance-dependent dielectric (DDD) constant. Estimates of changes in the vibrational entropies obtained with a DDD model are systematically and significantly larger, by on average, 6 kcal mol(-1) (at T = 300 K), than estimates obtained with a GB model and so are more favorable for complex formation. The difference becomes larger the more the vibrational entropy contribution disfavors complex formation, that is, the larger the ligand is (for the complexes considered here). A structural decomposition of the estimates into per-residue contributions reveals polar interactions between the ligand and the surrounding protein, in particular involving charged nitrogens, as a main source of the differences. Snapshots minimized with the DDD model showed a structural deviation from snapshots minimized in explicit water that is larger by, on average, 0.5 Å RMSD compared to snapshots that were minimized with GB(HCT) . As experimental vibrational entropies of biomacromolecules are elusive, there is no direct way to establish a solvent model's superiority. Thus, we can only recommend using the GB harmonic model for vibrational entropy calculations based on the reasoning that smaller structural deviations should point to the implicit solvent model that closer approximates the energy landscape of the solute in explicit solvent.

The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

“…8,9,10,11,12 The latter two estimates seem to be very hard to converge to any useful precision, whereas NMA estimates of entropies converge much better. 10,11,12 In practice, the NMA calculations are performed by first stripping off all water molecules. Typically, the protein is also truncated by removing all residues more than ~8 Å from the ligand, 2 because the frequency calculations are very demanding in terms of computer time and memory.…”

“…counting the number of rotable bonds in the ligand, dihedral-distribution histogramming, or quasi-harmonic analysis. 8,9,10,11,12 The latter two estimates seem to be very hard to converge to any useful precision, whereas NMA estimates of entropies converge much better. 10,11,12 In practice, the NMA calculations are performed by first stripping off all water molecules.…”

Potential Targets of Actein Identified by Systems Chemical Biology Methods

“…Second, the energy minimization was performed on the whole system for 2,000 cycles of steepest descent and 1,000 cycles of conjugated gradient minimization. After energy minimization, the binding energy of the complex was calculated by using MM/PBSA and MM/GBSA (molecular mechanics energies combined with Poisson‐Boltzmann or generalized Born and surface area continuum solvation) approaches . The two approaches aim at estimating ligand‐binding affinities and have been applied to a large number of systems with varying success .…”

Exploring the flap dynamics of the South African HIV subtype C protease in presence of FDA‐approved inhibitors: MD study

“…[42] The solvent accessible surface area (SASA), the surface tension proportionality constant (γ) and the free energy of non-polar solvation of a point solute (β), were set to 0.00542 kcal mol −1 Å −2 and 0 kcal mol −1 , respectively. [43] The entropy contribution to the binding free energies were calculated using normal mode analysis [44][45][46][47] for the complexes from changes in the translational, rotational and vibrational entropy components (Table 1).…”

“…To understand the major determinants for the binding affinity of the FDA-approved second-generation drugs, MM-GBSA binding free energy analyses were carried out for all four drug-PR complexes. The calculated binding free energies [∆G bind(T) ] and their components (∆E vdw , ∆E elec , ∆G gas , ∆G polar , ∆G nonpolar , ∆G solvation , TΔS) were calculated by MM-GBSA [40] binding free energy method and normal mode analysis (NMA) [44][45][46][47] and are presented in Table 1.…”