Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies

We have estimated free energies for the binding of nine cyclic carboxylate guest molecules to the octa-acid host in the SAMPL4 blind-test challenge with four different approaches. First, we used standard free-energy perturbation calculations of relative binding affinities, performed at the molecular-mechanics (MM) level with TIP3P waters, the GAFF force field, and two different sets of charges for the host and the guest, obtained either with the restrained electrostatic potential or AM1-BCC methods. Both charge sets give good and nearly identical results, with a mean absolute deviation (MAD) of 4 kJ/mol and a correlation coefficient (R ²) of 0.8 compared to experimental results. Second, we tried to improve these predictions with 28,800 density-functional theory (DFT) calculations for selected snapshots and the non-Boltzmann Bennett acceptance-ratio method, but this led to much worse results, probably because of a too large difference between the MM and DFT potential-energy functions. Third, we tried to calculate absolute affinities using minimised DFT structures. This gave intermediate-quality results with MADs of 5–9 kJ/mol and R ² = 0.6–0.8, depending on how the structures were obtained. Finally, we tried to improve these results using local coupled-cluster calculations with single and double excitations, and non-iterative perturbative treatment of triple excitations (LCCSD(T0)), employing the polarisable multipole interactions with supermolecular pairs approach. Unfortunately, this only degraded the predictions, probably because of a mismatch between the solvation energies obtained at the DFT and LCCSD(T0) levels.     

Binding affinities in the SAMPL3 trypsin and host–guest blind tests estimated with the MM/PBSA and LIE methods

We have estimated affinities for the binding of 34 ligands to trypsin and nine guest molecules to three different hosts in the SAMPL3 blind challenge, using the MM/PBSA, MM/GBSA, LIE, continuum LIE, and Glide score methods. For the trypsin challenge, none of the methods were able to accurately predict the experimental results. For the MM/GB(PB)SA and LIE methods, the rankings were essentially random and the mean absolute deviations were much worse than a null hypothesis giving the same affinity to all ligand. Glide scoring gave a Kendall's τ index better than random, but the ranking is still only mediocre, τ = 0.2. However, the range of affinities is small and most of the pairs of ligands have an experimental affinity difference that is not statistically significant. Removing those pairs improves the ranking metric to 0.4-1.0 for all methods except CLIE. Half of the trypsin ligands were non-binders according to the binding assay. The LIE methods could not separate the inactive ligands from the active ones better than a random guess, whereas MM/GBSA and MM/PBSA were slightly better than random (area under the receiver-operating-characteristic curve, AUC = 0.65-0.68), and Glide scoring was even better (AUC = 0.79). For the first host, MM/GBSA and MM/PBSA reproduce the experimental ranking fairly good, with τ = 0.6 and 0.5, respectively, whereas the Glide scoring was considerably worse, with a τ = 0.4, highlighting that the success of the methods is system-dependent.     

Influence of the [2Fe]H Subcluster Environment on the Properties of Key Intermediates in the Catalytic Cycle of [FeFe] Hydrogenases: Hints for the Rational Design of Synthetic Catalysts

Nature's recipe : A theoretical study analyzes how the environment of the [FeFe] hydrogenase's catalytic cofactor affects its chemical properties, particularly the relative stability of complexes with bridging and terminal hydride ligands (see picture; Fe teal, S yellow, C green, N blue, O red, H gray). The results help to elucidate key rules for the design of bioinspired synthetic catalysts for H₂ production.

     

Conversion of homocysteine to methionine by methionine synthase: a density functional study

This communication reports a theoretical study of the conversion of homocysteine to methionine by methionine synthase. The reaction pathway is based on density functional calculations with large basis sets, including thermodynamic, relativistic, and solvent effects. We find that the suggested SN2 mechanism explains well the experimentally observed reaction rate. The results show that the reaction is highly polar, as reflected in the change of charge density along the reaction coordinate. It is enhanced in the protein by two effects: deprotonation of the bound substrate and desolvation of substrate and cofactor in the rate-determining step.     

Interaction strength and shape difference for the h9/2 and h11/2 configurations in163Tm

The strongly shape driving πh_9/2[541]l/2^? configuration with α=+1/2 exhibits some anomalous, and so far unexplained, features concerning the crossing frequency, ?ω_c, the aligned angular momentum, i_x, and interaction strength, at the alignment of the first pair of i_13/2 quasineutrons in several odd-Z rare earth-nuclei. The h_9/2[541]1/2^? and h_11/2[523]7/2^? bands have been studied in the stably deformed rare-earth nucleus¹⁶³Tm to investigate these features. A difference in band crossing frequency of ～ 80 keV between the two bands is found. Rotational bands built on these two configurations have been found to cross in the spin range I=25/2–29/2 ?. Theγ-decay pattern between the two bands is established in the crossing region and analysed in terms of a moderate shape difference between them. A theoretical estimate of the size of the interaction strength between the two bands is presented and compared to the experimental value. The observed band structure in¹⁶³Tm is very similar to that of¹⁶⁷Lu which has 2 protons and 2 neutrons in addition. This observation is discussed in relation to the similarity of the yrast bands of the two even-even “core” nuclei¹⁶²Er and¹⁶⁶Yb, for which theγ-transition energies are identical within ～0.2 keV below the vi_13/2 crossing.     

Binding affinities of the farnesoid X receptor in the D3R Grand Challenge 2 estimated by free-energy perturbation and docking

We have studied the binding of 102 ligands to the farnesoid X receptor within the D3R Grand Challenge 2016 blind-prediction competition. First, we employed docking with five different docking software and scoring functions. The selected docked poses gave an average root-mean-squared deviation of 4.2 Å. Consensus scoring gave decent results with a Kendall’s τ of 0.26?±?0.06 and a Spearman’s ρ of 0.41?±?0.08. For a subset of 33 ligands, we calculated relative binding free energies with free-energy perturbation. Five transformations between the ligands involved a change of the net charge and we implemented and benchmarked a semi-analytic correction (Rocklin et al., J Chem Phys 139:184103, 2013) for artifacts caused by the periodic boundary conditions and Ewald summation. The results gave a mean absolute deviation of 7.5 kJ/mol compared to the experimental estimates and a correlation coefficient of R ²?=?0.1. These results were among the four best in this competition out of 22 submissions. The charge corrections were significant (7–8 kJ/mol) and always improved the results. By employing 23 intermediate states in the free-energy perturbation, there was a proper overlap between all states and the precision was 0.1–0.7 kJ/mol. However, thermodynamic cycles indicate that the sampling was insufficient in some of the perturbations.     

Quantum chemistry can locally improve protein crystal structures

We have re-refined the X-ray structure of the heme site in cytochrome c553, supplementing the crystallographic data with quantum chemical geometry optimizations, instead of the molecular mechanics force field used in standard crystallographic refinement. By comparing the resulting structure, obtained using medium-resolution data (170 pm), with an atomic-resolution structure (95 pm) of the same protein, we show that the inclusion of quantum chemical information into the refinement procedure improves the structure significantly. Thus, errors in the Fe-ligand distances are reduced from 3 to 32 pm in the low-resolution structure to 0-5 pm in the re-refined structure, one side-chain atom changes its conformation (a movement by 214 pm toward its position in the high-resolution structure), and the R factors are improved by up to 0.018. Thus, quantum refinement may be a powerful method to obtain an accurate structure for interesting parts of a protein.