Estimating Translational and Orientational Entropies Using the k-Nearest Neighbors Algorithm.

Inhomogeneous fluid solvation theory (IFST) and free energy perturbation (FEP) calculations were performed for a set of 20 solutes to compute the hydration free energies. We identify the weakness of histogram methods in computing the IFST hydration entropy by showing that previously employed histogram methods overestimate the translational and orientational entropies and thus underestimate their contribution to the free energy by a significant amount. Conversely, we demonstrate the accuracy of the k-nearest neighbors (KNN) algorithm in computing these translational and orientational entropies. Implementing the KNN algorithm within the IFST framework produces a powerful method that can be used to calculate free-energy changes for large perturbations. We introduce a new KNN approach to compute the total solute-water entropy with six degrees of freedom, as well as the translational and orientational contributions. However, results suggest that both the solute-water and water-water entropy terms are significant and must be included. When they are combined, the IFST and FEP hydration free energies are highly correlated, with an R(2) of 0.999 and a mean unsigned difference of 0.9 kcal/mol. IFST predictions are also highly correlated with experimental hydration free energies, with an R(2) of 0.997 and a mean unsigned error of 1.2 kcal/mol. In summary, the KNN algorithm is shown to yield accurate estimates of the combined translational-orientational entropy and the novel approach of combining distance metrics that is developed here could be extended to provide a powerful method for entropy estimation in numerous contexts.This work was supported by the MRC under grant ML/L007266/1. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the EPSRC under grants EP/F032773/1 and EP/J017639/1.This is the final published version. It's also available from the journal website can be found at: http://pubs.acs.org/doi/abs/10.1021/ct500415

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet.

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P-2005 and TIP5P-Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water-water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application.Acknowledgements go to Mike Payne for careful reading of the manuscript, Stuart Rankin for technical help and the NVIDIA CUDA Centre of Excellence at the Cambridge HPCS for use of the CUDA-accelerated GPUs. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the EPSRC under grant EP/F032773/1. Thanks for financial support go to the MRC, Wellcome Trust and EPSRC.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/jcc.2297

Studying the role of cooperative hydration in stabilizing folded protein states.

Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.Work in DJH’s lab was supported by the Medical Research Council (MRC) under grant ML/L007266/1. We thank Arno Proeme for porting the Solvaware package to ARCHER as part of the EPSRC embedded computational science and engineering grant eCSE03-3.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.jsb.2016.09.00

Quantifying the entropy of binding for water molecules in protein cavities by computing correlations.

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.Acknowledgments go to the Cambridge High Performance Computing Service for technical assistance, Professor Mike Gilson for helpful discussions, and Professor Bruce Tidor for support. This work was supported by the MRC under grant ML/L007266/1. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell, Inc., using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the EPSRC under grants EP/F032773/1 and EP/J017639/1.This is the final published version. It first appeared in Biophysics Journal, Volume 108 February 2015, 928–936 DOI: http://dx.doi.org/10.1016/j.bpj.2014.12.035

Correlations in liquid water for the TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP models.

Water is one of the simplest molecules in existence, but also one of the most important in biological and engineered systems. However, understanding the structure and dynamics of liquid water remains a major scientific challenge. Molecular dynamics simulations of liquid water were performed using the water models TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP to calculate the radial distribution functions (RDFs), the relative angular distributions, and the excess enthalpies, entropies, and free energies. In addition, lower-order approximations to the entropy were considered, identifying the fourth-order approximation as an excellent estimate of the full entropy. The second-order and third-order approximations are ~20% larger and smaller than the true entropy, respectively. All four models perform very well in predicting the radial distribution functions, with the TIP5P-Ewald model providing the best match to the experimental data. The models also perform well in predicting the excess entropy, enthalpy, and free energy of liquid water. The TIP4P-2005 and SWM4-NDP models are more accurate than the TIP3P-Ewald and TIP5P-Ewald models in this respect. However, the relative angular distribution functions of the four water models reveal notable differences. The TIP5P-Ewald model demonstrates an increased preference for water molecules to act both as tetrahedral hydrogen bond donors and acceptors, whereas the SWM4-NDP model demonstrates an increased preference for water molecules to act as planar hydrogen bond acceptors. These differences are not uncovered by analysis of the RDFs or the commonly employed tetrahedral order parameter. However, they are expected to be very important when considering water molecules around solutes and are thus a key consideration in modelling solvent entropy.Acknowledgements go to Mike Payne for careful reading of the paper; Peter Freddolino, Chris Baker, David Payne, and Bracken King for helpful discussions; Stuart Rankin for technical help; and the NVIDIA CUDA Centre of Excellence at the Cambridge HPCS for use of the CUDA-accelerated GPUs. Thanks also go to the reviewers for their helpful comments. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the Engineering and Physical Sciences Research Consul (United Kingdom) (EPSRC) under Grant No. EP/F032773/1. Thanks for financial support go to the MRC, Wellcome Trust, and EPSRC.This is the author accepted manuscript. The final version is available from AIP Publishing via http://dx.doi.org/10.1063/1.368344

Quantitative metrics for drug-target ligandability.

Ligandability is a prerequisite for druggability and is a much easier concept to understand, model and predict because it does not depend on the complex pharmacodynamic and pharmacokinetic mechanisms in the human body. In this review, we consider a metric for quantifying ligandability from experimental data. We discuss ligandability in terms of the balance between effort and reward. The metric is evaluated for a standard set of well-studied drug targets - some traditionally considered to be ligandable and some regarded as difficult. We suggest that this metric should be used to systematically improve computational predictions of ligandability, which can then be applied to novel drug targets to predict their tractability

Optimization of Protein-Ligand Electrostatic Interactions Using an Alchemical Free-Energy Method.

We present an explicit solvent alchemical free-energy method for optimizing the partial charges of a ligand to maximize the binding affinity with a receptor. This methodology can be applied to known ligand-protein complexes to determine an optimized set of ligand partial atomic changes. Three protein-ligand complexes have been optimized in this work: FXa, P38, and the androgen receptor. The sets of optimized charges can be used to identify design principles for chemical changes to the ligands which improve the binding affinity for all three systems. In this work, beneficial chemical mutations are generated from these principles and the resulting molecules tested using free-energy perturbation calculations. We show that three quarters of our chemical changes are predicted to improve the binding affinity, with an average improvement for the beneficial mutations of approximately 1 kcal/mol. In the cases where experimental data are available, the agreement between prediction and experiment is also good. The results demonstrate that charge optimization in explicit solvent is a useful tool for predicting beneficial chemical changes such as pyridinations, fluorinations, and oxygen to sulfur mutations

Rational methods for the selection of diverse screening compounds.

Traditionally a pursuit of large pharmaceutical companies, high-throughput screening assays are becoming increasingly common within academic and government laboratories. This shift has been instrumental in enabling projects that have not been commercially viable, such as chemical probe discovery and screening against high-risk targets. Once an assay has been prepared and validated, it must be fed with screening compounds. Crafting a successful collection of small molecules for screening poses a significant challenge. An optimized collection will minimize false positives while maximizing hit rates of compounds that are amenable to lead generation and optimization. Without due consideration of the relevant protein targets and the downstream screening assays, compound filtering and selection can fail to explore the great extent of chemical diversity and eschew valuable novelty. Herein, we discuss the different factors to be considered and methods that may be employed when assembling a structurally diverse compound collection for screening. Rational methods for selecting diverse chemical libraries are essential for their effective use in high-throughput screens.We are grateful for financial support from the MRC, Wellcome Trust, CRUK, EPSRC, BBSRC and Newman Trust.This is the author accepted manuscript. The final version is available from American Chemical Society via http://dx.doi.org/10.1021/cb100420

Exploring the role of water in molecular recognition: predicting protein ligandability using a combinatorial search of surface hydration sites

The interaction between any two biological molecules must compete with their interaction with water molecules. This makes water the most important molecule in medicine, as it controls the interactions of every therapeutic with its target. A small molecule binding to a protein is able to recognize a unique binding site on a protein by displacing bound water molecules from specific hydration sites. Quantifying the interactions of these water molecules allows us to estimate the potential of the protein to bind a small molecule. This is referred to as ligandability. In the study, we describe a method to predict ligandability by performing a search of all possible combinations of hydration sites on protein surfaces. We predict ligandability as the summed binding free energy for each of the constituent hydration sites, computed using inhomogeneous fluid solvation theory. We compared the predicted ligandability with the maximum observed binding affinity for 20 proteins in the human bromodomain family. Based on this comparison, it was determined that effective inhibitors have been developed for the majority of bromodomains, in the range from 10 to 100 nM. However, we predict that more potent inhibitors can be developed for the bromodomains BPTF and BRD7 with relative ease, but that further efforts to develop inhibitors for ATAD2 will be extremely challenging. We have also made predictions for the 14 bromodomains with no reported small molecule K d values by isothermal titration calorimetry. The calculations predict that PBRM1(1) will be a challenging target, while others such as TAF1L(2), PBRM1(4) and TAF1(2), should be highly ligandable. As an outcome of this work, we assembled a database of experimental maximal K d that can serve as a community resource assisting medicinal chemistry efforts focused on BRDs. Effective prediction of ligandability would be a very useful tool in the drug discovery process.Work in the DJH laboratory is supported by the Medical Research Council under grant ML/L007266/1. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England, and were funded by the EPSRC under grants EP/F032773/1 and EP/J017639/1

Overcoming Chemical, Biological, and Computational Challenges in the Development of Inhibitors Targeting Protein-Protein Interactions.

Protein-protein interactions (PPIs) underlie the majority of biological processes, signaling, and disease. Approaches to modulate PPIs with small molecules have therefore attracted increasing interest over the past decade. However, there are a number of challenges inherent in developing small-molecule PPI inhibitors that have prevented these approaches from reaching their full potential. From target validation to small-molecule screening and lead optimization, identifying therapeutically relevant PPIs that can be successfully modulated by small molecules is not a simple task. Following the recent review by Arkin et al., which summarized the lessons learnt from prior successes, we focus in this article on the specific challenges of developing PPI inhibitors and detail the recent advances in chemistry, biology, and computation that facilitate overcoming them. We conclude by providing a perspective on the field and outlining four innovations that we see as key enabling steps for successful development of small-molecule inhibitors targeting PPIs.Work in DRS’s laboratory is supported by the the European Union, Engineering and Physical Sciences Research Council, Biotechnology and Biological Sciences Research Council, Medical Research Council and Wellcome Trust. Work in ARV’s laboratory is supported by the Medical Research Council and Wellcome Trust. Work in DJH's laboratory is supported by the Medical Research Council under grant ML/L007266/1. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the EPSRC under grants EP/F032773/1 and EP/J017639/1. GJM and ARV are affiliated with PhoreMost Ltd, Cambridge. We thank Alicia Higueruelo and John Skidmore for helpful discussions.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.chembiol.2015.04.01