A Computational Model for the Prediction of Aqueous Solubility That Includes Crystal Packing, Intrinsic Solubility, and Ionization Effects

Will we ever be able to accurately predict solubility?

Accurate prediction of thermodynamic solubility by machine learning remains a challenge. Recent models often display good performances, but their reliability may be deceiving when used prospectively. This study investigates the origins of these discrepancies, following three directions: a historical perspective, an analysis of the aqueous solubility dataverse and data quality. We investigated over 20 years of published solubility datasets and models, highlighting overlooked datasets and the overlaps between popular sets. We benchmarked recently published models on a novel curated solubility dataset and report poor performances. We also propose a workflow to cure aqueous solubility data aiming at producing useful models for bench chemist. Our results demonstrate that some state-of-the-art models are not ready for public usage because they lack a well-defined applicability domain and overlook historical data sources. We report the impact of factors influencing the utility of the models: interlaboratory standard deviation, ionic state of the solute and data sources. The herein obtained models, and quality-assessed datasets are publicly available.

Comparison of the Predictive Performance and Interpretability of Random Forest and Linear Models on Benchmark Data Sets

The ability to interpret the predictions made by quantitative structure-activity relationships (QSARs) offers a number of advantages. While QSARs built using nonlinear modeling approaches, such as the popular Random Forest algorithm, might sometimes be more predictive than those built using linear modeling approaches, their predictions have been perceived as difficult to interpret. However, a growing number of approaches have been proposed for interpreting nonlinear QSAR models in general and Random Forest in particular. In the current work, we compare the performance of Random Forest to those of two widely used linear modeling approaches: linear Support Vector Machines (SVMs) (or Support Vector Regression (SVR)) and partial least-squares (PLS). We compare their performance in terms of their predictivity as well as the chemical interpretability of the predictions using novel scoring schemes for assessing heat map images of substructural contributions. We critically assess different approaches for interpreting Random Forest models as well as for obtaining predictions from the forest. We assess the models on a large number of widely employed public-domain benchmark data sets corresponding to regression and binary classification problems of relevance to hit identification and toxicology. We conclude that Random Forest typically yields comparable or possibly better predictive performance than the linear modeling approaches and that its predictions may also be interpreted in a chemically and biologically meaningful way. In contrast to earlier work looking at interpretation of nonlinear QSAR models, we directly compare two methodologically distinct approaches for interpreting Random Forest models. The approaches for interpreting Random Forest assessed in our article were implemented using open-source programs that we have made available to the community. These programs are the rfFC package ( https://r-forge.r-project.org/R/?group_id=1725 ) for the R statistical programming language and the Python program HeatMapWrapper [ https://doi.org/10.5281/zenodo.495163 ] for heat map generation.

Equilibrium solubility measurement of compounds with low dissolution rate by Higuchi's Facilitated Dissolution Method. A validation study

Incubation time plays a critical role in the accurate measurement of equilibrium solubility of compounds. Substances which dissolve very slowly generally need long incubation times (days or weeks) to reach equilibrium. However, long times may pose several problems, such as decomposition of solute, molding of buffer, and drifting of pH. Higuchi in 1979 proposed the Facilitated Dissolution Method (FDM) to dramatically reduce incubation time. It employs a small volume of water-immiscible organic solvent to partly solubilize the sample and thereby increase the surface area available for dissolution. The method has been used only rarely. In this study we performed a systematic validation of FDM using progesterone as model compound. The reference solubility value, 7.95±0.21μg/mL (p<0.05, n=5), was determined in Britton-Robinson buffer solution (pH7.4) at 25.0°C by the standardized protocol of Saturation Shake-Flask (SSF) method. Also, the solubility was measured by the FDM approach under varied experimental conditions (e.g., type and volume of organic solvent, time of agitation, and amount of solid excess), and compared to the reference value. It was demonstrated that the small amount of organic solvent used in the FDM does not impact the measured solubility, compared to the reference value. Additionally, four compounds of low dissolution rate (dexamethasone, digoxin, haloperidol and cosalane) were used to demonstrate that FDM can reduce the long equilibration time to the standardized 24h (6h stirring and 18h sedimentation). The time dependence of solubility equilibrium was measured by SSF, and the results were compared with those obtained by FDM. Our study, based on >200 solubility experiments, supports the validity of Higuchi's method. In this study we propose a standardized protocol for the FDM, where 1% v/v of organic solvent is used. Octane (or isooctane) was found to be suitable for highly hydrophobic compounds. Alternatively, octanol or 1,2-dichloroethane can be used for less lipophilic compounds.

The Use of Anisotropic Potentials in Modeling Water and Free Energies of Hydration

We propose a novel, anisotropic rigid-body intermolecular potential model to predict the properties of water and the hydration free energies of neutral organic solutes. The electrostatic interactions of water and the solutes are modeled using atomic multipole moments up to hexadecapole; these are obtained from distributed multipole analysis of the quantum mechanically computed charge densities and include average polarization effects in solution. The repulsion-dispersion water-water interactions are modeled with a three-site, exp-6 model fitted to the experimental liquid water density and oxygen-oxygen radial distribution function at ambient conditions. The proposed water model reproduces well several water properties not used in its parametrization, including vapor-liquid coexistence densities, the maximum in liquid water density at atmospheric pressure, the structure of ordered ice polymorphs, and the liquid water heat capacity. The model is used to compute the hydration free energy of 10 neutral organic solutes using explicit-solvent free energy perturbation. The solute-solute repulsion-dispersion intermolecular potential is obtained from previous parametrizations on organic crystal structures. In order to calculate the free energies of hydration, water-solute repulsion-dispersion interactions are modeled using Lorenz-Berthelot combining rules. The root-mean-square error of the predicted hydration free energies is 1.5 kcal mol(-1), which is comparable to the error found using a continuum mean-field quantum mechanical approach parametrized using experimental free energy of hydration data. The results are also contrasted with explicit-solvent hydration free energies obtained with an atomic charge representation of the solute's charge density computed at the same level of theory used to compute the distributed multipoles. Replacing the multipole description of the solute's charge density with an atomic charge model changes the free energy of hydration by as much as 3 kcal mol(-1) and provides an estimate for the effect of the modeling quality of the intermolecular electrostatic forces in free energy of solvation calculations.

Upper critical solution temperature behavior of cinnamic acid and polyethyleneimine mixture and its effect on temperature-dependent release of liposome

The mixture of polyethyleneimine (PEI) and cinnamic acid (CA) in HEPES buffer (pH 7.0) exhibited an upper critical solution temperature in the temperature range of 20-50 °C. CA would be electrostatically conjugated with PEI and the PEI-CA conjugate is thought to act as a thermo-sensitive polymer. On the optical microscope image of PEI/CA mixture, microparticles were found at 25 °C, disappeared when heated to 50 °C, and formed again upon cooling to 25 °C. PEI-CA conjugate was immobilized on the surface of egg phosphatidylcholine (EPC) liposome by adding PEI to the suspension of liposome incorporating CA. The size and the zeta potential of the liposome markedly increased by cooling the liposomal suspension from 50 °C to 20 °C. This could be ascribed to the cooling-induced self-assembling property of PEI-CA conjugate. The release profile of Rhodamine B base from liposome incorporating CA with PEI was investigated while the liposome suspension of 50 °C was exposed to the release medium of 20 °C, 30 °C, 40 °C and 50 °C. The release degree was higher at a lower temperature. When exposed to a lower temperature (20 °C, 30 °C, 40 °C), PEI-CA could be self-assembled and change its configuration on the surface of liposome, promoting the release from the liposome.

Scaling predictive modeling in drug development with cloud computing

Growing data sets with increased time for analysis is hampering predictive modeling in drug discovery. Model building can be carried out on high-performance computer clusters, but these can be expensive to purchase and maintain. We have evaluated ligand-based modeling on cloud computing resources where computations are parallelized and run on the Amazon Elastic Cloud. We trained models on open data sets of varying sizes for the end points logP and Ames mutagenicity and compare with model building parallelized on a traditional high-performance computing cluster. We show that while high-performance computing results in faster model building, the use of cloud computing resources is feasible for large data sets and scales well within cloud instances. An additional advantage of cloud computing is that the costs of predictive models can be easily quantified, and a choice can be made between speed and economy. The easy access to computational resources with no up-front investments makes cloud computing an attractive alternative for scientists, especially for those without access to a supercomputer, and our study shows that it enables cost-efficient modeling of large data sets on demand within reasonable time.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Aqueous solubility: simple predictive methods (in silico, in vitro and bio-relevant approaches)

Aqueous solubility is a key physicochemical attribute required for the characterisation of an active pharmaceutical ingredient (API) during drug discovery and beyond. Furthermore, aqueous solubility is highly important for formulation selection and subsequent development processes. This review provides a summary of simple predictive methods used to assess aqueous solubility as well as an assessment of the more complex in silico methodologies and a review of the recent solubility challenge. In addition, a summary of experimental methods to determine solubility is included, with a discussion of some potential pitfalls.

Selecting, Acquiring, and Using Small Molecule Libraries for High-Throughput Screening

The selection, acquisition and use of high quality small molecule libraries for screening is an essential aspect of drug discovery and chemical biology programs. Screening libraries continue to evolve as researchers gain a greater appreciation of the suitability of small molecules for specific biological targets, processes and environments. The decisions surrounding the make-up of any given small molecule library is informed by a multitude of variables and opinions vary on best-practices. The fitness of any collection relies upon upfront filtering to avoiding problematic compounds, assess appropriate physicochemical properties, install the ideal level of structural uniqueness and determine the desired extent of molecular complexity. These criteria are under constant evaluation and revision as academic and industrial organizations seek out collections that yield ever improving results from their screening portfolios. Practical questions including cost, compound management, screening sophistication and assay objective also play a significant role in the choice of library composition. This overview attempts to offer advice to all organizations engaged in small molecule screening based upon current best practices and theoretical considerations in library selection and acquisition.

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.

Exploratory analysis of kinetic solubility measurements of a small molecule library

Kinetic solubility measurements using prototypical assay buffer conditions are presented for a ∼58,000 member library of small molecules. Analyses of the data based upon physical and calculated properties of each individual molecule were performed and resulting trends were considered in the context of commonly held opinions of how physicochemical properties influence aqueous solubility. We further analyze the data using a decision tree model for solubility prediction and via a multi-dimensional assessment of physicochemical relationships to solubility in the context of specific 'rule-breakers' relative to common dogma. The role of solubility as a determinant of assay outcome is also considered based upon each compound's cross-assay activity score for a collection of publicly available screening results. Further, the role of solubility as a governing factor for colloidal aggregation formation within a specified assay setting is examined and considered as a possible cause of a high cross-assay activity score. The results of this solubility profile should aid chemists during library design and optimization efforts and represent a useful training set for computational solubility prediction.

Informatics, machine learning and computational medicinal chemistry

This article reviews the use of informatics and computational chemistry methods in medicinal chemistry, with special consideration of how computational techniques can be adapted and extended to obtain more and higher-quality information. Special consideration is given to the computation of protein–ligand binding affinities, to the prediction of off-target bioactivities, bioactivity spectra and computational toxicology, and also to calculating absorption-, distribution-, metabolism- and excretion-relevant properties, such as solubility.

Towards interoperable and reproducible QSAR analyses: Exchange of datasets

BACKGROUND

QSAR is a widely used method to relate chemical structures to responses or properties based on experimental observations. Much effort has been made to evaluate and validate the statistical modeling in QSAR, but these analyses treat the dataset as fixed. An overlooked but highly important issue is the validation of the setup of the dataset, which comprises addition of chemical structures as well as selection of descriptors and software implementations prior to calculations. This process is hampered by the lack of standards and exchange formats in the field, making it virtually impossible to reproduce and validate analyses and drastically constrain collaborations and re-use of data.

RESULTS

We present a step towards standardizing QSAR analyses by defining interoperable and reproducible QSAR datasets, consisting of an open XML format (QSAR-ML) which builds on an open and extensible descriptor ontology. The ontology provides an extensible way of uniquely defining descriptors for use in QSAR experiments, and the exchange format supports multiple versioned implementations of these descriptors. Hence, a dataset described by QSAR-ML makes its setup completely reproducible. We also provide a reference implementation as a set of plugins for Bioclipse which simplifies setup of QSAR datasets, and allows for exporting in QSAR-ML as well as old-fashioned CSV formats. The implementation facilitates addition of new descriptor implementations from locally installed software and remote Web services; the latter is demonstrated with REST and XMPP Web services.

CONCLUSIONS

Standardized QSAR datasets open up new ways to store, query, and exchange data for subsequent analyses. QSAR-ML supports completely reproducible creation of datasets, solving the problems of defining which software components were used and their versions, and the descriptor ontology eliminates confusions regarding descriptors by defining them crisply. This makes is easy to join, extend, combine datasets and hence work collectively, but also allows for analyzing the effect descriptors have on the statistical model's performance. The presented Bioclipse plugins equip scientists with graphical tools that make QSAR-ML easily accessible for the community.

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.