David S. Palmer

Random forest models to predict aqueous solubility

Random Forest regression (RF), Partial-Least-Squares (PLS) regression, Support Vector Machines (SVM), and Artificial Neural Networks (ANN) were used to develop QSPR models for the prediction of aqueous solubility, based on experimental data for 988 organic molecules. The Random Forest regression model predicted aqueous solubility more accurately than those created by PLS, SVM, and ANN and offered methods for automatic descriptor selection, an assessment of descriptor importance, and an in-parallel measure of predictive ability, all of which serve to recommend its use. The prediction of log molar solubility for an external test set of 330 molecules that are solid at 25 degrees C gave an r2 = 0.89 and RMSE = 0.69 log S units. For a standard data set selected from the literature, the model performed well with respect to other documented methods. Finally, the diversity of the training and test sets are compared to the chemical space occupied by molecules in the MDL drug data report, on the basis of molecular descriptors selected by the regression analysis.

Why are some properties more difficult to predict than others? A study of QSPR models of solubility, melting point, and Log P

This paper attempts to elucidate differences in QSPR models of aqueous solubility (Log S), melting point (Tm), and octanol-water partition coefficient (Log P), three properties of pharmaceutical interest. For all three properties, Support Vector Machine models using 2D and 3D descriptors calculated in the Molecular Operating Environment were the best models. Octanol-water partition coefficient was the easiest property to predict, as indicated by the RMSE of the external test set and the coefficient of determination (RMSE = 0.73, r2 = 0.87). Melting point prediction, on the other hand, was the most difficult (RMSE = 52.8 degrees C, r2 = 0.46), and Log S statistics were intermediate between melting point and Log P prediction (RMSE = 0.900, r2 = 0.79). The data imply that for all three properties the lack of measured values at the extremes is a significant source of error. This source, however, does not entirely explain the poor melting point prediction, and we suggest that deficiencies in descriptors used in melting point prediction contribute significantly to the prediction errors.

Predicting Intrinsic Aqueous Solubility by a Thermodynamic Cycle

We report methods to predict the intrinsic aqueous solubility of crystalline organic molecules from two different thermodynamic cycles. We find that direct computation of solubility, via ab initio calculation of thermodynamic quantities at an affordable level of theory, cannot deliver the required accuracy. Therefore, we have turned to a mixture of direct computation and informatics, using the calculated thermodynamic properties, along with a few other key descriptors, in regression models. The prediction of log intrinsic solubility (referred to mol/L) by a three-variable linear regression equation gave r(2)=0.77 and RMSE=0.71 for an external test set comprising drug molecules. The model includes a calculated crystal lattice energy which provides a computational method to account for the interactions in the solid state. We suggest that it is not necessary to know the polymorphic form prior to prediction. Furthermore, the method developed here may be applicable to other solid-state systems such as salts or cocrystals.

Solvation thermodynamics of organic molecules by the molecular integral equation theory : approaching chemical accuracy

The integral equation theory (IET) of molecular liquids has been an active area of academic research in theoretical and computational physical chemistry for over 40 years because it provides a consistent theoretical framework to describe the structural and thermodynamic properties of liquid-phase solutions. The theory can describe pure and mixed solvent systems (including anisotropic and nonequilibrium systems) and has already been used for theoretical studies of a vast range of problems in chemical physics / physical chemistry, molecular biology, colloids, soft matter, and electrochemistry. A consider- able advantage of IET is that it can be used to study speci fi c solute − solvent interactions, unlike continuum solvent models, but yet it requires considerably less computational expense than explicit solvent simulations.

Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model.

We report on the results of testing the reference interaction site model (RISM) for the estimation of the hydration free energy of druglike molecules. The optimum model was selected after testing of different RISM free energy expressions combined with different quantum mechanics and empirical force-field methods of structure optimization and atomic partial charge calculation. The final model gave a systematic error with a standard deviation of 2.6 kcal/mol for a test set of 31 molecules selected from the SAMPL1 blind challenge set [J. P. Guthrie, J. Phys. Chem. B 113, 4501 (2009)]. After parametrization of this model to include terms for the excluded volume and the number of atoms of different types in the molecule, the root mean squared error for a test set of 19 molecules was less than 1.2 kcal/mol.

Hydration Thermodynamics Using the Reference Interaction Site Model: Speed or Accuracy?

We report a method to dramatically improve the accuracy of hydration free energies (HFE) calculated by the 1D and 3D reference interaction site models (RISM) of molecular integral equation theory. It is shown that the errors in HFEs calculated by RISM approaches using the Gaussian fluctuations (GF) free energy functional are not random, but can be decomposed into linear combination of contributions from different structural elements of molecules (number of double bonds, number of OH groups, etc.). Therefore, by combining RISM/GF with cheminformatics, one can develop an accurate method for HFE prediction. We call this approach the structural description correction model (SDC) ( Ratkova et al. J. Phys. Chem. B 2010 , 114 , 12068 ). In this work, we investigated the prediction quality of the SDC model combined with 1D and 3D RISM approaches. In parallel, we analyzed the computational performance of these two methods. The SDC model parameters were obtained by fitting against a training set of 53 simple organic molecules. To demonstrate that the values of these parameters were transferable between different classes of molecules, the models were tested against 98 more complex molecules (including 38 polyfragment compounds). The results show that the 3D RISM/SDC model predicts the HFEs with very good accuracy (RMSE of 0.47 kcal/mol), while the 1D RISM approach provides only moderate accuracy (RMSE of 1.96 kcal/mol). However, a single 1D RISM/SDC calculation takes only a few seconds on a PC, whereas a single 3D RISM/SDC HFE calculation is approximately 100 times more computationally expensive. Therefore, we suggest that one should use the 1D RISM/SDC model for large-scale high-throughput screening of molecular hydration properties, while further refinement of these properties for selected compounds should be carried out with the more computationally expensive but more accurate 3D RISM/SDC model.

First-Principles Calculation of the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules.

We demonstrate that the intrinsic aqueous solubility of crystalline druglike molecules can be estimated with reasonable accuracy from sublimation free energies calculated using crystal lattice simulations and hydration free energies calculated using the 3D Reference Interaction Site Model (3D-RISM) of the Integral Equation Theory of Molecular Liquids (IET). The solubilities of 25 crystalline druglike molecules taken from different chemical classes are predicted by the model with a correlation coefficient of R = 0.85 and a root mean square error (RMSE) equal to 1.45 log10S units, which is significantly more accurate than results obtained using implicit continuum solvent models. The method is not directly parametrized against experimental solubility data, and it offers a full computational characterization of the thermodynamics of transfer of the drug molecule from crystal phase to gas phase to dilute aqueous solution.

Toward a Universal Model To Calculate the Solvation Thermodynamics of Druglike Molecules: The Importance of New Experimental Databases

We demonstrate that a new free energy functional in the integral equation theory of molecular liquids gives accurate calculations of hydration thermodynamics for druglike molecules. The functional provides an improved description of excluded volume effects by incorporating two free coefficients. When the values of these coefficients are obtained from experimental data for simple organic molecules, the hydration free energies of an external test set of druglike molecules can be calculated with an accuracy of about 1 kcal/mol. The 3D RISM/UC method proposed here is easily implemented using existing computational software and allows in silico screening of the solvation thermodynamics of potential pharmaceutical molecules at significantly lower computational expense than explicit solvent simulations.

Chemoinformatics-based classification of prohibited substances employed for doping in sport.

Representative molecules from 10 classes of prohibited substances were taken from the World Anti-Doping Agency (WADA) list, augmented by molecules from corresponding activity classes found in the MDDR database. Together with some explicitly allowed compounds, these formed a set of 5245 molecules. Five types of fingerprints were calculated for these substances. The random forest classification method was used to predict membership of each prohibited class on the basis of each type of fingerprint, using 5-fold cross-validation. We also used a k-nearest neighbors (kNN) approach, which worked well for the smallest values of k. The most successful classifiers are based on Unity 2D fingerprints and give very similar Matthews correlation coefficients of 0.836 (kNN) and 0.829 (random forest). The kNN classifiers tend to give a higher recall of positives at the expense of lower precision. A naïve Bayesian classifier, however, lies much further toward the extreme of high recall and low precision. Our results suggest that it will be possible to produce a reliable and quantitative assignment of membership or otherwise of each class of prohibited substances. This should aid the fight against the use of bioactive novel compounds as doping agents, while also protecting athletes against unjust disqualification.

Communication: Accurate hydration free energies at a wide range of temperatures from 3D-RISM

We present a new model for computing hydration free energies by 3D reference interaction site model (3D-RISM) that uses an appropriate initial state of the system (as suggested by Sergiievskyi et al.). The new adjustment to 3D-RISM theory significantly improves hydration free energy predictions for various classes of organic molecules at both ambient and non-ambient temperatures. An extensive benchmarking against experimental data shows that the accuracy of the model is comparable to (much more computationally expensive) molecular dynamics simulations. The calculations can be readily performed with a standard 3D-RISM algorithm. In our work, we used an open source package AmberTools; a script to automate the whole procedure is available on the web (https://github.com/MTS-Strathclyde/ISc).