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Cardamone S.,Manchester Institute of Biotechnology MIB | Cardamone S.,University of Manchester | Hughes T.J.,Manchester Institute of Biotechnology MIB | Hughes T.J.,University of Manchester | And 2 more authors.
Physical Chemistry Chemical Physics | Year: 2014

Atomistic simulation of chemical systems is currently limited by the elementary description of electrostatics that atomic point-charges offer. Unfortunately, a model of one point-charge for each atom fails to capture the anisotropic nature of electronic features such as lone pairs or π-systems. Higher order electrostatic terms, such as those offered by a multipole moment expansion, naturally recover these important electronic features. The question remains as to why such a description has not yet been widely adopted by popular molecular mechanics force fields. There are two widely-held misconceptions about the more rigorous formalism of multipolar electrostatics: (1) Accuracy: the implementation of multipole moments, compared to point-charges, offers little to no advantage in terms of an accurate representation of a system's energetics, structure and dynamics. (2) Efficiency: atomistic simulation using multipole moments is computationally prohibitive compared to simulation using point-charges. Whilst the second of these may have found some basis when computational power was a limiting factor, the first has no theoretical grounding. In the current work, we disprove the two statements above and systematically demonstrate that multipole moments are not discredited by either. We hope that this perspective will help in catalysing the transition to more realistic electrostatic modelling, to be adopted by popular molecular simulation software. This journal is © the Partner Organisations 2014.

Griffiths M.Z.,Manchester Institute of Biotechnology MIB | Griffiths M.Z.,University of Manchester | Alkorta I.,Institute Quimica Medica IQM CSIC | Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
Molecular Informatics | Year: 2013

Here we applied a novel method1a to predict pKa values of the guanidine functional group, which is a notoriously difficult. This method, which was developed in our lab, uses only one ab initio bond length obtained at a low level of theory. The method is shown to work for drug molecules, delivers prediction errors of less than 0.5 log units, successfully treats tautomerisation in close relation with experiment, and demonstrates strong correlations with only a few data points. The high structural content of the ab initio bond length makes a given data set essentially divide itself into high correlation subsets. One then observes that molecules within a subset possess a common substructure. Each high correlation subset exists in its own region of chemical space. The high correlation subset method is explored with respect to this position in chemical space, in particular tautomerisation. The proposed method is able to distinguish between different tautomeric forms and the preferred tautomeric form emerges naturally, in agreement with experiment. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Graton J.,University of Nantes | Le Questel J.-Y.,University of Nantes | Maxwell P.,Manchester Institute of Biotechnology MIB | Maxwell P.,University of Manchester | And 2 more authors.
Journal of Chemical Information and Modeling | Year: 2016

The prediction of hydrogen-bond (H-bond) acceptor ability is crucial in drug design. This important property is quantified in a large pKBHX database of consistently measured values. We aim to expand the chemical diversity of the studied H-bond acceptors and to increase the range of H-bond strength considered. Two quantum chemical descriptors are contrasted, called ΔE(H) (the change in the energy of a topological hydrogen atom upon complexation) and Vmin (the local minimum in the electrostatic potential on the H-bond accepting site). We performed a systematic analysis of the correlations between pKBHX and Vmin for an initial set of 106 compounds (including O- and N-containing subsets, as well as compounds including sulfur, chlorine, and π-bases). Correlations improve for family dependent subsets, and after outlier treatment, a set of 90 compounds was used to set up a linear equation to predict pKBHX from Vmin. This equation and a previously published equation [Green and Popelier J. Chem. Inf. Model. 2014, 54 (2), 553-561], to predict pKBHX from ΔE(H), were used to predict the pKBHX values for 22 potentially biologically active heteroaromatic ring compounds, [Pitt et al. J. Med. Chem. 2009, 52 (9), 2952-2963], among which several structures still remain experimentally unavailable. H-Bond basicity of sp2 nitrogen sites were consistently predicted with both descriptors. A worse agreement was found with carbonyl acceptor sites, with the stronger deviations observed for the lactam groups. It was shown that secondary interactions involving the neighboring NH group were influencing the results. Substitution of the NH group with an NMe group resulted in an improved consistency from both Vmin and ΔE(H) predictions, the latter being more prominently affected by the methyl substitution. Both approaches appear as efficient procedures for the H-bond ability prediction of novel heteroaromatic rings. Nevertheless, the ΔE(H) parameter presents slight chemical structure limitations and requires more detailed H-bond structure investigations. © 2016 American Chemical Society.

Fletcher T.L.,Manchester Institute of Biotechnology MIB | Fletcher T.L.,University of Manchester | Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
Journal of Chemical Theory and Computation | Year: 2016

A machine learning method called kriging is applied to the set of all 20 naturally occurring amino acids. Kriging models are built that predict electrostatic multipole moments for all topological atoms in any amino acid based on molecular geometry only. These models then predict molecular electrostatic interaction energies. On the basis of 200 unseen test geometries for each amino acid, no amino acid shows a mean prediction error above 5.3 kJ mol-1, while the lowest error observed is 2.8 kJ mol-1. The mean error across the entire set is only 4.2 kJ mol-1 (or 1 kcal mol-1). Charged systems are created by protonating or deprotonating selected amino acids, and these show no significant deviation in prediction error over their neutral counterparts. Similarly, the proposed methodology can also handle amino acids with aromatic side chains, without the need for modification. Thus, we present a generic method capable of accurately capturing multipolar polarizable electrostatics in amino acids. © 2016 American Chemical Society.

Alkorta I.,Institute Quimica Medica IQM CSIC | Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
ChemPhysChem | Year: 2015

Remarkably simple yet effective linear free energy relationships were discovered between a single ab initio computed bond length in the gas phase and experimental pKa values in aqueous solution. The formation of these relationships is driven by chemical features such as functional groups, meta/para substitution and tautomerism. The high structural content of the ab initio bond length makes a given data set essentially divide itself into high correlation subsets (HCSs). Surprisingly, all molecules in a given high correlation subset share the same conformation in the gas phase. Here we show that accurate pKa values can be predicted from such HCSs. This is achieved within an accuracy of 0.2 pKa units for 5 drug molecules. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

Hughes T.J.,University of Manchester | Kandathil S.M.,University of Manchester | Popelier P.L.A.,Manchester Institute of Biotechnology MIB
Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy | Year: 2014

As intermolecular interactions such as the hydrogen bond are electrostatic in origin, rigorous treatment of this term within force field methodologies should be mandatory. We present a method able of accurately reproducing such interactions for seven van der Waals complexes. It uses atomic multipole moments up to hexadecupole moment mapped to the positions of the nuclear coordinates by the machine learning method kriging. Models were built at three levels of theory: HF/6-31G∗∗, B3LYP/aug-cc-pVDZ and M06-2X/aug-cc-pVDZ. The quality of the kriging models was measured by their ability to predict the electrostatic interaction energy between atoms in external test examples for which the true energies are known. At all levels of theory, >90% of test cases for small van der Waals complexes were predicted within 1 kJ mol-1, decreasing to 60-70% of test cases for larger base pair complexes. Models built on moments obtained at B3LYP and M06-2X level generally outperformed those at HF level. For all systems the individual interactions were predicted with a mean unsigned error of less than 1 kJ mol-1. © 2014 Elsevier B.V. All rights reserved.

Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
Physica Scripta | Year: 2016

We are at the dawn of molecular simulations being carried out, literally, by atoms endowed by knowledge of how to behave quantum mechanically in the vicinity of other atoms. The 'next-next-generation' force field that aims to achieve this is called QCTFF, for now, although a more pronounceable name will be suggested in the conclusion. Classical force fields such as AMBER mimic the interatomic energy experienced by atoms during a molecular simulation, with simple expressions capturing a relationship between energy and nuclear position. Such force fields neither see the electron density nor exchange-delocalization itself, or exact electrostatic interaction; they only contain simple equations and elementary parameters such as point charges to imitate the energies between atoms. Next-generation force fields, such as AMOEBA, go further and make the electrostatics more accurate by introducing multipole moments and dipolar polarization. However, QCTFF goes even further and abolishes all traditional force field expressions (e.g. Hooke's law and extensions, Lennard-Jones) in favor of atomistic kriging models. These machine learning models learn how fundamental energy quantities, as well as high-rank multipole moments, all associated with an atom of interest, vary with the precise positions of atomic neighbors. As a result, all structural phenomena can be rapidly calculated as an interplay of intra-atomic energy, exchange-delocalization energy, electrostatic energy and dynamic correlation energy. The final QCTFF force field will generate a wealth of localized quantum information while being faster than a Car-Parrinello simulation (which does not generate local information). Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too? (Douglas Adams). © 2016 The Royal Swedish Academy of Sciences.

Green A.J.,Manchester Institute of Biotechnology MIB | Green A.J.,University of Manchester | Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
Journal of Chemical Information and Modeling | Year: 2014

Hydrogen bonding plays an important role in the interaction of biological molecules and their local environment. Hydrogen-bond strengths have been described in terms of basicities by several different scales. The pK BHX scale has been developed with the interests of medicinal chemists in mind. The scale uses equilibrium constants of acid··· base complexes to describe basicity and is therefore linked to Gibbs free energy. Site specific data for polyfunctional bases are also available. The pKBHX scale applies to all hydrogen-bond donors (HBDs) where the HBD functional group is either OH, NH, or NH+. It has been found that pKBHX can be described in terms of a descriptor defined by quantum chemical topology, ΔE(H), which is the change in atomic energy of the hydrogen atom upon complexation. Essentially the computed energy of the HBD hydrogen atom correlates with a set of 41 HBAs for five common HBDs, water (r2 = 0.96), methanol (r2 = 0.95), 4-fluorophenol (r 2 = 0.91), serine (r2 = 0.93), and methylamine (r 2 = 0.97). The connection between experiment and computation was strengthened with the finding that there is no relationship between ΔE(H) and pKBHX when hydrogen fluoride was used as the HBD. Using the methanol model, pKBHX predictions were made for an external set of bases yielding r2 = 0.90. Furthermore, the basicities of polyfunctional bases correlate with ΔE(H), giving r2 = 0.93. This model is promising for the future of computation in fragment-based drug design. Not only has a model been established that links computation to experiment, but the model may also be extrapolated to predict external experimental pKBHX values. © 2014 American Chemical Society.

Fletcher T.L.,University of Manchester | Davie S.J.,University of Manchester | Popelier P.L.A.,Manchester Institute of Biotechnology MIB
Journal of Chemical Theory and Computation | Year: 2014

Present computing power enables novel ways of modeling polarization. Here we show that the machine learning method kriging accurately captures the way the electron density of a topological atom responds to a change in the positions of the surrounding atoms. The success of this method is demonstrated on the four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine. A new technique of varying training set sizes to vastly reduce training times while maintaining accuracy is described and applied to each amino acid. Each amino acid has its geometry distorted via normal modes of vibration over all local energy minima in the Ramachandran map. These geometries are then used to train the kriging models. Total electrostatic energies predicted by the kriging models for previously unseen geometries are compared to the true energies, yielding mean absolute errors of 2.9, 5.1, 4.2, and 2.8 kJ mol-1for histidine, phenylalanine, tryptophan, and tyrosine, respectively. © 2014 American Chemical Society.

Griffiths M.Z.,Manchester Institute of Biotechnology MIB | Griffiths M.Z.,University of Manchester | Popelier P.L.A.,Manchester Institute of Biotechnology MIB | Popelier P.L.A.,University of Manchester
Journal of Chemical Information and Modeling | Year: 2013

Five-membered rings are found in a myriad of molecules important in a wide range of areas such as catalysis, nutrition, and drug and agrochemical design. Systematic insight into their largely unexplored chemical space benefits from first principle calculations presented here. This study comprehensively investigates a grand total of 764 different rings, all geometry optimized at the B3LYP/6-311+G(2d,p) level, from the perspective of Quantum Chemical Topology (QCT). For the first time, a 3D space of local topological properties was introduced, in order to characterize rings compactly. This space is called RCP space, after the so-called ring critical point. This space is analogous to BCP space, named after the bond critical point, which compactly and successfully characterizes a chemical bond. The relative positions of the rings in RCP space are determined by the nature of the ring scaffold, such as the heteroatoms within the ring or the number of π-bonds. The summed atomic QCT charges of the five ring atoms revealed five features (number and type of heteroatom, number of π-bonds, substituent and substitution site) that dictate a ring's net charge. Each feature independently contributes toward a ring's net charge. Each substituent has its own distinct and systematic effect on the ring's net charge, irrespective of the ring scaffold. Therefore, this work proves the possibility of designing a ring with specific properties by fine-tuning it through manipulation of these five features. © 2013 American Chemical Society.

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