Protein-Ligand Binding Enthalpies from Near-Millisecond Simulations: Analysis of a Preorganization Paradox

Calorimetric studies of protein-ligand binding often yield thermodynamic data that are difficult to explain in physical terms. Today, explicit solvent molecular dynamics simulations are fast enough that we can begin to use them to look for explanations of such thermodynamic puzzles. Additionally, when such simulations generate results that do not agree well with experiment, this may motivate further development of computational methods and force fields. Here, we apply near-millisecond duration simulations to compute and analyze the binding of four peptidic ligands with the Grb2 SH2 domain, focusing on relative binding enthalpies. The ligands fall into matched pairs, which differ only in the presence or absence of a conformationally constraining bond, which preorganizes two of the ligands for binding. Prior experimental work had revealed, unexpectedly, that binding of the constrained ligands is favored enthalpically, rather than entropically, relative to their flexible<br>analogs. However, the present calculations yield the opposite trend. On further analysis, the computed relative binding enthalpies are found to be small balances of much larger underlying differences in the mean energies of structural components, such as the ligand and the binding site residues. As a consequence, the deviations from experiment in the relative binding enthalpies represent small differences between these large numbers. We also computed first order estimates of changes in configurational entropy on binding. These suggest that the more rigid constrained ligands reduce the entropy of binding site residues more than their flexible analogs do. The implications of these calculations for the use of simulations to understand the thermodynamics of molecular recognition, and for the computational analysis of binding thermodynamics, are discussed

Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches

Quantum mechanical (QM) calculations of noncovalent interactions are uniquely useful as tools to test and improve molecular mechanics force fields and to model the forces involved in biomolecular binding and folding. Because the more computationally tractable QM methods necessarily include approximations, which risk degrading accuracy, it is essential to evaluate such methods by comparison with high-level reference calculations. Here, we use the extensive Benchmark Energy and Geometry Database (BEGDB) of CCSD­(T)/CBS reference results to evaluate the accuracy and speed of widely used QM methods for over 1200 chemically varied gas-phase dimers. In particular, we study the semiempirical PM6 and PM7 methods; density functional theory (DFT) approaches B3LYP, B97-D, M062X, and ωB97X-D; and symmetry-adapted perturbation theory (SAPT) approach. For the PM6 and DFT methods, we also examine the effects of post hoc corrections for hydrogen bonding (PM6-DH+, PM6-DH2), halogen atoms (PM6-DH2X), and dispersion (DFT-D3 with zero and Becke–Johnson damping). Several orders of the SAPT expansion are also compared, ranging from SAPT0 up to SAPT2+3, where computationally feasible. We find that all DFT methods with dispersion corrections, as well as SAPT at orders above SAPT2, consistently provide dimer interaction energies within 1.0 kcal/mol RMSE across all systems. We also show that a linear scaling of the perturbative energy terms provided by the fast SAPT0 method yields similar high accuracy, at particularly low computational cost. The energies of all the dimer systems from the various QM approaches are included in the Supporting Information, as are the full SAPT2+(3) energy decomposition for a subset of over 1000 systems. The latter can be used to guide the parametrization of molecular mechanics force fields on a term-by-term basis

Attractive Interactions between Heteroallenes and the Cucurbituril Portal

In this paper, we report on the noteworthy attractive interaction between organic azides and the portal carbonyls of cucurbiturils. Five homologous bis-α,ω-azido­ethyl­ammonium alkanes were prepared, where the number of methylene groups between the ammonium groups ranges from 4 to 8. Their interactions with cucurbit[6]­uril were studied by NMR spectroscopy, IR spectroscopy, X-ray crystallography, and computational methods. Remarkably, while the distance between the portal plane and most atoms at the guest end groups increases progressively with the molecular size, the β-nitrogen atoms maintain a constant distance from the portal plane in all homologues, pointing at a strong attractive interaction between the azide group and the portal. Both crystallography and NMR support a specific electrostatic interaction between the carbonyl and the azide β-nitrogen, which stabilizes the canonical resonance form with positive charge on the β-nitrogen and negative charge on the γ-nitrogen. Quantum computational analyses strongly support electrostatics, in the form of orthogonal dipole–dipole interaction, as the main driver for this attraction. The alternative mechanism of n → π* orbital delocalization does not seem to play a significant role in this interaction. The computational studies also indicate that the interaction is not limited to azides, but generalizes to other isoelectronic heteroallene functions, such as isocyanate and isothiocyanate. This essentially unexploited attractive interaction could be more broadly utilized as a tool not only in relation to cucurbituril chemistry, but also for the design of novel supramolecular architectures