Interplay between Conformational Entropy and Solvation Entropy in Protein-Ligand Binding.

Understanding the driving forces underlying molecular recognition is of fundamental importance in chemistry and biology. The challenge is to unravel the binding thermodynamics into separate contributions and to interpret these in molecular terms. Entropic contributions to the free energy of binding are particularly difficult to assess in this regard. Here we pinpoint the molecular determinants underlying differences in ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and molecular dynamics simulations followed by conformational entropy and grid inhomogeneous solvation theory (GIST) analyses. Using a pair of diastereomeric ligands that have essentially identical chemical potential in the unbound state, we reduced the problem of dissecting the thermodynamics to a comparison of the two protein-ligand complexes. While the free energies of binding are nearly equal for the R and S diastereomers, greater differences are observed for the enthalpy and entropy, which consequently exhibit compensatory behavior, ΔΔ H°(R - S) = -5 ± 1 kJ/mol and - TΔΔ S°(R - S) = 3 ± 1 kJ/mol. NMR relaxation experiments and molecular dynamics simulations indicate that the protein in complex with the S-stereoisomer has greater conformational entropy than in the R-complex. GIST calculations reveal additional, but smaller, contributions from solvation entropy, again in favor of the S-complex. Thus, conformational entropy apparently dominates over solvation entropy in dictating the difference in the overall entropy of binding. This case highlights an interplay between conformational entropy and solvation entropy, pointing to both opportunities and challenges in drug design.

Assessing the stability of free-energy perturbation calculations by performing variations in the method.

We have calculated relative binding affinities for eight tetrafluorophenyl-triazole-thiogalactoside inhibitors of galectin-3 with the alchemical free-energy perturbation approach. We obtain a mean absolute deviation from experimental estimates of only 2-3 kJ/mol and a correlation coefficient (R2) of 0.5-0.8 for seven relative affinities spanning a range of up to 11 kJ/mol. We also studied the effect of using different methods to calculate the charges of the inhibitor and different sizes of the perturbed group (the atoms that are described by soft-core potentials and are allowed to have differing coordinates). However, the various approaches gave rather similar results and it is not possible to point out one approach as consistently and significantly better than the others. Instead, we suggest that such small and reasonable variations in the computational method can be used to check how stable the calculated results are and to obtain a more accurate estimate of the uncertainty than if performing only one calculation with a single computational setup.

Can System Truncation Speed up Ligand-Binding Calculations with Periodic Free-Energy Simulations?

We have investigated whether alchemical free-energy perturbation calculations of relative binding energies can be sped up by simulating a truncated protein. Previous studies with spherical nonperiodic systems showed that the number of simulated atoms could be reduced by a factor of 26 without affecting the calculated binding free energies by more than 0.5 kJ/mol on average ( Genheden, S.; Ryde, U. J. Chem. Theory Comput. 2012 , 8 , 1449 ), leading to a 63-fold decrease in the time consumption. However, such simulations are rather slow, owing to the need of a large cutoff radius for the nonbonded interactions. Periodic simulations with the electrostatics treated by Ewald summation are much faster. Therefore, we have investigated if a similar speed-up can be obtained also for periodic simulations. Unfortunately, our results show that it is harder to truncate periodic systems and that the truncation errors are larger for these systems. In particular, residues need to be removed from the calculations, which means that atoms have to be restrained to avoid that they move in an unrealistic manner. The results strongly depend on the strength on this restraint. For the binding of seven ligands to dihydrofolate reductase and ten inhibitors of blood-clotting factor Xa, the best results are obtained with a small restraining force constant. However, the truncation errors were still significant (e.g., 1.5-2.9 kJ/mol at a truncation radius of 10 Å). Moreover, the gain in computer time was only modest. On the other hand, if the snapshots are truncated after the MD simulations, the truncation errors are small (below 0.9 kJ/mol even for a truncation radius of 10 Å). This indicates that postprocessing with a more accurate energy function (e.g., with quantum chemistry) on truncated snapshots may be a viable approach.

Prediction of hydration free energies for the SAMPL4 data set with the AMOEBA polarizable force field.

Hydration free energy calculations are often used to validate molecular simulation methodologies and molecular mechanics force fields. We use the free-energy perturbation method together with the AMOEBA polarizable force field and the Poltype parametrization protocol to predict the hydration free energies of 52 molecules as part of the SAMPL4 blind challenge. For comparison, similar calculations are performed using the non-polarizable General Amber force field. Against our expectations, the latter force field gives the better results compared to experiment. One possible explanation is the sensitivity of the AMOEBA results to the conformation used for parametrization.

Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data. Corrigendum.

Corrections are published for the article by Caldararu et al. [(2019), Acta Cryst. D75, 368-380].

Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data.

Neutron crystallography is a powerful method to determine the positions of H atoms in macromolecular structures. However, it is sometimes hard to judge what would constitute a chemically reasonable model, and the geometry of H atoms depends more on the surroundings (for example the formation of hydrogen bonds) than heavy atoms, so that the empirical geometry information for the H atoms used to supplement the experimental data is often less accurate. These problems may be reduced by using quantum-mechanical calculations. A method has therefore been developed to combine quantum-mechanical calculations with joint crystallographic refinement against X-ray and neutron data. A first validation of this method is provided by re-refining the structure of the galectin-3 carbohydrate-recognition domain in complex with lactose. The geometry is improved, in particular for water molecules, for which the method leads to better-resolved hydrogen-bonding interactions. The method has also been applied to the active copper site of lytic polysaccharide monooxygenase and shows that the protonation state of the amino-terminal histidine residue can be determined.

Elucidation of Hydrogen Bonding Patterns in Ligand-Free, Lactose- and Glycerol-Bound Galectin-3C by Neutron Crystallography to Guide Drug Design.

The medically important drug target galectin-3 binds galactose-containing moieties on glycoproteins through an intricate pattern of hydrogen bonds to a largely polar surface-exposed binding site. All successful inhibitors of galectin-3 to date have been based on mono- or disaccharide cores closely resembling natural ligands. A detailed understanding of the H-bonding networks in these natural ligands will provide an improved foundation for the design of novel inhibitors. Neutron crystallography is an ideal technique to reveal the geometry of hydrogen bonds because the positions of hydrogen atoms are directly detected rather than being inferred from the positions of heavier atoms as in X-ray crystallography. We present three neutron crystal structures of the C-terminal carbohydrate recognition domain of galectin-3: the ligand-free form and the complexes with the natural substrate lactose and with glycerol, which mimics important interactions made by lactose. The neutron crystal structures reveal unambiguously the exquisite fine-tuning of the hydrogen bonding pattern in the binding site to the natural disaccharide ligand. The ligand-free structure shows that most of these hydrogen bonds are preserved even when the polar groups of the ligand are replaced by water molecules. The protonation states of all histidine residues in the protein are also revealed and correlate well with NMR observations. The structures give a solid starting point for molecular dynamics simulations and computational estimates of ligand binding affinity that will inform future drug design.

Perdeuteration, crystallization, data collection and comparison of five neutron diffraction data sets of complexes of human galectin-3C.

Galectin-3 is an important protein in molecular signalling events involving carbohydrate recognition, and an understanding of the hydrogen-bonding patterns in the carbohydrate-binding site of its C-terminal domain (galectin-3C) is important for the development of new potent inhibitors. The authors are studying these patterns using neutron crystallography. Here, the production of perdeuterated human galectin-3C and successive improvement in crystal size by the development of a crystal-growth protocol involving feeding of the crystallization drops are described. The larger crystals resulted in improved data quality and reduced data-collection times. Furthermore, protocols for complete removal of the lactose that is necessary for the production of large crystals of apo galectin-3C suitable for neutron diffraction are described. Five data sets have been collected at three different neutron sources from galectin-3C crystals of various volumes. It was possible to merge two of these to generate an almost complete neutron data set for the galectin-3C-lactose complex. These data sets provide insights into the crystal volumes and data-collection times necessary for the same system at sources with different technologies and data-collection strategies, and these insights are applicable to other systems.