Interplay of halogen bonding and solvation in protein-ligand binding.

Halogen bonding is increasingly utilized in efforts to achieve high affinity and selectivity of molecules designed to bind proteins, making it paramount to understand the relationship between structure, dynamics, and thermodynamic driving forces. We present a detailed analysis addressing this problem using a series of protein-ligand complexes involving single halogen substitutions - F, Cl, Br, and I - and nearly identical structures. Isothermal titration calorimetry reveals an increasingly favorable binding enthalpy from F to I that correlates with the halogen size and σ-hole electropositive character, but is partially counteracted by unfavorable entropy, which is constant from F to Cl and Br, but worse for I. Consequently, the binding free energy is roughly equal for Cl, Br, and I. QM and solvation-free-energy calculations reflect an intricate balance between halogen bonding, hydrogen bonds, and solvation. These advances have the potential to aid future drug design initiatives involving halogenated compounds.

Comparison of Grand Canonical and Conventional Molecular Dynamics Simulation Methods for Protein-Bound Water Networks.

Water molecules play important roles in all biochemical processes. Therefore, it is of key importance to obtain information of the structure, dynamics, and thermodynamics of water molecules around proteins. Numerous computational methods have been suggested with this aim. In this study, we compare the performance of conventional and grand-canonical Monte Carlo (GCMC) molecular dynamics (MD) simulations to sample the water structure, as well GCMC and grid-based inhomogeneous solvation theory (GIST) to describe the energetics of the water network. They are evaluated on two proteins: the buried ligand-binding site of a ferritin dimer and the solvent-exposed binding site of galectin-3. We show that GCMC/MD simulations significantly speed up the sampling and equilibration of water molecules in the buried binding site, thereby making the results more similar for simulations started from different states. Both GCMC/MD and conventional MD reproduce crystal-water molecules reasonably for the buried binding site. GIST analyses are normally based on restrained MD simulations. This improves the precision of the calculated energies, but the restraints also significantly affect both absolute and relative energies. Solvation free energies for individual water molecules calculated with and without restraints show a good correlation, but with large quantitative differences. Finally, we note that the solvation free energies calculated with GIST are ∼5 times larger than those estimated by GCMC owing to differences in the reference state.

Entropy-Entropy Compensation between the Protein, Ligand, and Solvent Degrees of Freedom Fine-Tunes Affinity in Ligand Binding to Galectin-3C.

Molecular recognition is fundamental to biological signaling. A central question is how individual interactions between molecular moieties affect the thermodynamics of ligand binding to proteins and how these effects might propagate beyond the immediate neighborhood of the binding site. Here, we investigate this question by introducing minor changes in ligand structure and characterizing the effects of these on ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and computational approaches including molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). We studied a congeneric series of ligands with a fluorophenyl-triazole moiety, where the fluorine substituent varies between the ortho, meta, and para positions (denoted O, M, and P). The M and P ligands have similar affinities, whereas the O ligand has 3-fold lower affinity, reflecting differences in binding enthalpy and entropy. The results reveal surprising differences in conformational and solvation entropy among the three complexes. NMR backbone order parameters show that the O-bound protein has reduced conformational entropy compared to the M and P complexes. By contrast, the bound ligand is more flexible in the O complex, as determined by 19F NMR relaxation, ensemble-refined X-ray diffraction data, and MD simulations. Furthermore, GIST calculations indicate that the O-bound complex has less unfavorable solvation entropy compared to the other two complexes. Thus, the results indicate compensatory effects from ligand conformational entropy and water entropy, on the one hand, and protein conformational entropy, on the other hand. Taken together, these different contributions amount to entropy-entropy compensation among the system components involved in ligand binding to a target protein.

Exploring ligand dynamics in protein crystal structures with ensemble refinement.

Understanding the dynamics of ligands bound to proteins is an important task in medicinal chemistry and drug design. However, the dominant technique for determining protein-ligand structures, X-ray crystallography, does not fully account for dynamics and cannot accurately describe the movements of ligands in protein binding sites. In this article, an alternative method, ensemble refinement, is used on six protein-ligand complexes with the aim of understanding the conformational diversity of ligands in protein crystal structures. The results show that ensemble refinement sometimes indicates that the flexibility of parts of the ligand and some protein side chains is larger than that which can be described by a single conformation and atomic displacement parameters. However, since the electron-density maps are comparable and Rfree values are slightly increased, the original crystal structure is still a better model from a statistical point of view. On the other hand, it is shown that molecular-dynamics simulations and automatic generation of alternative conformations in crystallographic refinement confirm that the flexibility of these groups is larger than is observed in standard refinement. Moreover, the flexible groups in ensemble refinement coincide with groups that give high atomic displacement parameters or non-unity occupancy if optimized in standard refinement. Therefore, the conformational diversity indicated by ensemble refinement seems to be qualitatively correct, indicating that ensemble refinement can be an important complement to standard crystallographic refinement as a tool to discover which parts of crystal structures may show extensive flexibility and therefore are poorly described by a single conformation. However, the diversity of the ensembles is often exaggerated (probably partly owing to the rather poor force field employed) and the ensembles should not be trusted in detail.

On the Use of Interaction Entropy and Related Methods to Estimate Binding Entropies.

Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is extremely poorly conditioned. Using stochastic simulations, assuming that the interaction energies follow a Gaussian distribution, we show that if the standard deviation of the interaction energies (σIE) is larger than 15 kJ/mol, it becomes practically impossible to converge the interaction entropies (more than 10 million energies are needed, and the number increases exponentially). A cumulant approximation to the second order of the exponential average shows a better convergence, but for σIE > 25 kJ/mol, it gives entropies that are unrealistically large. Moreover, in practical applications, both methods show a steady increase in the entropy with the number of energies considered.