Rigidity Theory-Based Approximation of Vibrational Entropy Changes upon Binding to Biomolecules.

We introduce a computationally efficient approximation of vibrational entropy changes (ΔSvib) upon binding to biomolecules based on rigidity theory. From constraint network representations of the binding partners, ΔSvib is estimated from changes in the number of low frequency ("spongy") modes with respect to changes in the networks' coordination number. Compared to ΔSvib computed by normal-mode analysis (NMA), our approach yields significant and good to fair correlations for data sets of protein-protein and protein-ligand complexes. Our approach could be a valuable alternative to NMA-based ΔSvib computation in end-point (free) energy methods.

Influence of the solvent representation on vibrational entropy calculations: generalized born versus distance-dependent dielectric model.

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.

Hot spots and transient pockets: predicting the determinants of small-molecule binding to a protein-protein interface.

Protein-protein interfaces are considered difficult targets for small-molecule protein-protein interaction modulators (PPIMs ). Here, we present for the first time a computational strategy that simultaneously considers aspects of energetics and plasticity in the context of PPIM binding to a protein interface. The strategy aims at identifying the determinants of small-molecule binding, hot spots, and transient pockets, in a protein-protein interface in order to make use of this knowledge for predicting binding modes of and ranking PPIMs with respect to their affinity. When applied to interleukin-2 (IL-2), the computationally inexpensive constrained geometric simulation method FRODA outperforms molecular dynamics simulations in sampling hydrophobic transient pockets. We introduce the PPIAnalyzer approach for identifying transient pockets on the basis of geometrical criteria only. A sequence of docking to identified transient pockets, starting structure selection based on hot spot information, RMSD clustering and intermolecular docking energies, and MM-PBSA calculations allows one to enrich IL-2 PPIMs from a set of decoys and to discriminate between subgroups of IL-2 PPIMs with low and high affinity. Our strategy will be applicable in a prospective manner where nothing else than a protein-protein complex structure is known; hence, it can well be the first step in a structure-based endeavor to identify PPIMs.