Force and Stress along Simulated Dissociation Pathways of Cucurbituril–Guest Systems

The field of host–guest chemistry provides computationally tractable yet informative model systems for biomolecular recognition. We applied molecular dynamics simulations to study the forces and mechanical stresses associated with forced dissociation of aqueous cucurbituril–guest complexes with high binding affinities. First, the unbinding transitions were modeled with constant velocity pulling (steered dynamics) and a soft spring constant, to model atomic force microscopy experiments. The computed length–force profiles yield rupture forces in good agreement with available measurements. We also used steered dynamics with high spring constants to generate paths characterized by a tight control over the specified pulling distance; these paths were then equilibrated via umbrella sampling simulations and used to compute time-averaged mechanical stresses along the dissociation pathways. The stress calculations proved to be informative regarding the key interactions determining the length–force profiles and rupture forces. In particular, the unbinding transition of one complex is found to be a stepwise process, which is initially dominated by electrostatic interactions between the guest’s ammoniums and the host’s carbonyl groups and subsequently limited by the extraction of the guest’s bulky bicyclooctane moiety; the latter step requires some bond stretching at the cucurbituril’s extraction portal. Conversely, the dissociation of a second complex with a more slender guest is mainly driven by successive electrostatic interactions between the different guest’s ammoniums and the host’s carbonyl groups. The calculations also provide information on the origins of thermodynamic irreversibilities in these forced dissociation processes

Evaluating Force Field Performance in Thermodynamic Calculations of Cyclodextrin Host–Guest Binding: Water Models, Partial Charges, and Host Force Field Parameters

Computational prediction of noncovalent binding free energies with methods based on molecular mechanical force fields has become increasingly routine in drug discovery projects, where they promise to speed the discovery of small molecule ligands to bind targeted proteins with high affinity. Because the reliability of free energy methods still has significant room for improvement, new force fields, or modifications of existing ones, are regularly introduced with the aim of improving the accuracy of molecular simulations. However, comparatively little work has been done to systematically assess how well force fields perform, particularly in relation to the calculation of binding affinities. Hardware advances have made these calculations feasible, but comprehensive force field assessments for protein–ligand sized systems still remain costly. Here, we turn to cyclodextrin host–guest systems, which feature many hallmarks of protein–ligand binding interactions but are generally much more tractable due to their small size. We present absolute binding free energy and enthalpy calculations, using the attach-pull-release (APR) approach, on a set of 43 cyclodextrin-guest pairs for which experimental ITC data are available. The test set comprises both α- and β-cyclodextrin hosts binding a series of small organic guests, each with one of three functional groups: ammonium, alcohol, or carboxylate. Four water models are considered (TIP3P, TIP4Pew, SPC/E, and OPC), along with two partial charge assignment procedures (RESP and AM1-BCC) and two cyclodextrin host force fields. The results suggest a complex set of considerations when choosing a force field for biomolecular simulations. For example, some force field combinations clearly outperform others at the binding enthalpy calculations but not for the binding free energy. Additionally, a force field combination which we expected to be the worst performer gave the most accurate binding free energies – but the least accurate binding enthalpies. The results have implications for the development of improved force fields, and we propose this test set, and potential future elaborations of it, as a powerful validation suite to evaluate new force fields and help guide future force field development

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

Attach-Pull-Release Calculations of Ligand Binding and Conformational Changes on the First BRD4 Bromodomain

Bromodomains, protein domains involved in epigenetic regulation, are able to bind small molecules with high affinity. In the present study, we report free energy calculations for the binding of seven ligands to the first BRD4 bromodomain, using the attach-pull-release (APR) method to compute the reversible work of removing the ligands from the binding site and then allowing the protein to relax conformationally. We test three different water models, TIP3P, TIP4PEw, and SPC/E, as well as the GAFF and GAFF2 parameter sets for the ligands. Our simulations show that the apo crystal structure of BRD4 is only metastable, with a structural transition happening in the absence of the ligand typically after 20 ns of simulation. We compute the free energy change for this transition with a separate APR calculation on the free protein and include its contribution to the ligand binding free energies, which generally causes an underestimation of the affinities. By testing different water models and ligand parameters, we are also able to assess their influence in our results and determine which one produces the best agreement with the experimental data. Both free energies associated with the conformational change and ligand binding are affected by the choice of water model, with the two sets of ligand parameters affecting their binding free energies to a lesser degree. Across all six combinations of water model and ligand potential function, the Pearson correlation coefficients between calculated and experimental binding free energies range from 0.55 to 0.83, and the root-mean-square errors range from 1.4–3.2 kcal/mol. The current protocol also yields encouraging preliminary results when used to assess the relative stability of ligand poses generated by docking or other methods, as illustrated for two different ligands. Our method takes advantage of the high performance provided by graphics processing units and can readily be applied to other ligands as well as other protein systems

Mean square fluctuations of the residue-averaged stresses computed from the 1 ms BPTI trajectory.

<p>(Left) Cluster 2; values range from 1.50 to 5.08 Mbar. (Right) Difference between cluster 1 and 2 (cluster 1 minus cluster 2); values range from −90.3 to 63.6 kbar. Purple (negative) and orange (positive) indicate regions where cluster 1 has less or more stress fluctuations than cluster 2, respectively.</p

Formulae for mean principal stress (negative hydrostatic pressure) associated with potential terms in common classical force-fields.

<p>Formulae for mean principal stress (negative hydrostatic pressure) associated with potential terms in common classical force-fields.</p

Stress decomposition of a wave pulse traveling left to right through graphene nanotubes either in the armchair (upper) or zigzag (lower) configurations.

<p>Data are shown for the 450 fs time-point.</p

Computational Calorimetry: High-Precision Calculation of Host–Guest Binding Thermodynamics

We present a strategy for carrying out high-precision calculations of binding free energy and binding enthalpy values from molecular dynamics simulations with explicit solvent. The approach is used to calculate the thermodynamic profiles for binding of nine small molecule guests to either the cucurbit[7]­uril (CB7) or β-cyclodextrin (βCD) host. For these systems, calculations using commodity hardware can yield binding free energy and binding enthalpy values with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days. Crucially, the self-consistency of the approach is established by calculating the binding enthalpy directly, via end point potential energy calculations, and indirectly, via the temperature dependence of the binding free energy, i.e., by the van’t Hoff equation. Excellent agreement between the direct and van’t Hoff methods is demonstrated for both host–guest systems and an ion-pair model system for which particularly well-converged results are attainable. Additionally, we find that hydrogen mass repartitioning allows marked acceleration of the calculations with no discernible cost in precision or accuracy. Finally, we provide guidance for accurately assessing numerical uncertainty of the results in settings where complex correlations in the time series can pose challenges to statistical analysis. The routine nature and high precision of these binding calculations opens the possibility of including measured binding thermodynamics as target data in force field optimization so that simulations may be used to reliably interpret experimental data and guide molecular design

The delta in residue-averaged hydrostatic pressure between clusters 1 and 2 (solid, blue line) and the associated standard error of the mean (dashed, red line) for all 58 residues of BPTI.

<p>Residues with large (greater in magnitude than 500 bar) are labeled.</p

Residue-averaged differences in stress between clusters 1 and 2 (cluster 1 minus cluster 2).

<p>The left color spectrum applies to the total stress, and the right color spectrum applies to all of the stress components.</p