The configurational dependence of binding free energies: A Poisson–Boltzmann study of Neuraminidase inhibitors

The linear finite difference Poisson-Boltzmann (FDPB) equation is applied to the calculation of the electrostatic binding free energies of a group of inhibitors to the Neuraminidase enzyme. An ensemble of enzyme-inhibitor complex conformations was generated using Monte Carlo simulations and the electrostatic binding free energies of subtly different configurations of the enzyme-inhibitor complexes were calculated. It was seen that the binding free energies calculated using FDPB depend strongly on the configuration of the complex taken from the ensemble. This configurational dependence was investigated in detail in the electrostatic hydration free energies of the inhibitors. Differences in hydration energies of up to 7 kcal mol^–1 were obtained for root mean square (RMS) structural deviations of only 0.5 Å. To verify the result, the grid size and parameter dependence of the calculated hydration free energies were systematically investigated. This showed that the absolute hydration free energies calculated using the FDPB equation were very sensitive to the values of key parameters, but that the configurational dependence of the free energies was independent of the parameters chosen. Thus just as molecular mechanics energies are very sensitive to configuration, and single-structure values are not typically used to score binding free energies, single FDPB energies should be treated with the same caution.     

Characterization of uranium isotopic abundances in depleted uranium metal assay standard 115

Certified reference material (CRM) 115, Uranium (Depleted) Metal (Uranium Assay Standard), was analyzed using a TRITON Thermal Ionization Mass Spectrometer to characterize the uranium isotope-amount ratios. The certified ²³⁵U/²³⁸U “major” isotope-amount ratio of 0.0020337 (12) in CRM 115 was determined using the total evaporation (TE) and the modified total evaporation (MTE) analytical techniques. In the MTE method, the total evaporation process is interrupted on a regular basis to allow correction of background from peak tailing, internal calibration of the secondary electron multiplier detector versus the Faraday cups, peak-centering, and ion source re-focusing. For the “minor” ²³⁴U/²³⁸U and ²³⁶U/²³⁸U isotope-amount ratio measurements using MTE, precision and accuracy comparable to conventional analyses are achieved, without compromising the quality of the ²³⁵U/²³⁸U isotope-amount ratios. Characterized values of the ²³⁴U/²³⁸U and ²³⁶U/²³⁸U isotope-amount ratios in CRM 115 are 0.000007545 (10) and 0.000032213 (84), respectively. The ²³³U/²³⁸U isotope-amount ratio in CRM 115 is estimated to be <5 × 10^?9. The homogeneity of the CRM 115 materials is established through the absence of any statistically significant unit-to-unit variation in the uranium isotope-amount ratios. The measurements leading to the certification of uranium isotope-amount ratios are discussed.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Molecular dynamics calculation of activation volumes

We propose a novel approach toward calculating activation and reaction volumes based on MD simulations of reaction systems. The accuracy of the calculated volumes, verified by the comparison to the experimental data, is suitable for quantitative analysis of the experimental volumes of activations in terms of structural parameters of the corresponding transition states.     

A cellular ligand-field model for l-l spectral intensities

The intensity distributions in the ‘d-d’ spectra of three planar CuCl^2- ₄ chromophores are reproduced quantitatively within the theoretical model described in the preceding paper. Intensity for these species, namely bis(1-methyl-4-oxo-3,3-diphenylhexyldimethylammonium)tetrachlorocopper(II), bis(2-iminol-1-methy-4-imidazolidinium)tetrachlorocopper(II) and bis(N-methylphenylethylammonium)-tetrachlorocopper(II), is deemed to arise dynamically via the bending vibrations. Fair reproduction of experimental absorbances is achieved using the b _2u mode alone, this being known to be the softest vibration in these systems. The roles of spin-orbit coupling and small departures from D _4h symmetry are discussed. Nearly perfect reproduction of experiment is obtained with addition of small contributions from the e_u bend. The intensity distribution in the ‘d-d’ spectrum of the pseudo-tetrahedral chromophore, bis(N-benzylpiper-azinium)tetrachlorocopper(II), is reproduced quantitatively within the ‘static’ model described in part I of this series. Comparisons between the parameter values obtained from the ‘static’ analysis with those from the ‘dynamic’ analysis for the planar chromophores suggest that dynamic modelling with both b _2u and e_u modes is the more physically persuasive. The efficacy of the model in part IV is critically reviewed in this first application.     

A Computational Study of Vicinal Fluorination in 2,3‐Difluorobutane: Implications for Conformational Control in Alkane Chains

A comprehensive conformational analysis of both 2,3‐difluorobutane diastereomers is presented based on density functional theory calculations in vacuum and in solution, as well as NMR experiments in solution. While for 1,2‐difluoroethane the fluorine gauche effect is clearly the dominant effect determining its conformation, it was found that for 2,3‐difluorobutane there is a complex interplay of several effects, which are of similar magnitude but often of opposite sign. As a result, unexpected deviations in dihedral angles, relative conformational energies and populations are observed which cannot be rationalised only by chemical intuition. Furthermore, it was found that it is important to consider the free energies of the various conformers, as these lead to qualitatively different results both in vacuum and in solvent, when compared to calculations based only on the electronic energies. In contrast to expectations, it was found that vicinal syn‐difluoride introduction in the butane and by extension, longer hydrocarbon chains, is not expected to lead to an effective stabilisation of the linear conformation. Our findings have implications for the use of the vicinal difluoride motif for conformational control.     

Classification of water molecules in protein binding sites

Water molecules play a crucial role in mediating the interaction between a ligand and a macromolecular receptor. An understanding of the nature and role of each water molecule in the active site of a protein could greatly increase the efficiency of rational drug design approaches: if the propensity of a water molecule for displacement can be determined, then synthetic effort may be most profitably applied to the design of specific ligands with the displacement of this water molecule in mind. In this paper, a thermodynamic analysis of water molecules in the binding sites of six proteins, each complexed with a number of inhibitors, is presented. Two classes of water molecules were identified: those conserved and not displaced by any of the ligands, and those that are displaced by some ligands. The absolute binding free energies of 54 water molecules were calculated using the double decoupling method, with replica exchange thermodynamic integration in Monte Carlo simulations. It was found that conserved water molecules are on average more tightly bound than displaced water molecules. In addition, Bayesian statistics is used to calculate the probability that a particular water molecule may be displaced by an appropriately designed ligand, given the calculated binding free energy of the water molecule. This approach therefore allows the numerical assessment of whether or not a given water molecule should be targeted for displacement as part of a rational drug design strategy.