(M1030-05-28) Solubility Prediction Using Manifold Embedding of Molecular Surface

Purpose: The bioavailability of a drug compound is dependent on the extent of solubility. Predicting solubility of drug compounds remains a challenging task. Recent research into this area has increasingly focused on machine learning algorithms which may outperform solubility estimations using the popular General Solubility Equation from Yalkowsky et. al [1]. However, the first and second Solubility Challenges conducted by Avdeef et. al revealed that there are two significant shortcomings of current predictive models [2,3]. The first hurdle to overcome in solubility prediction is data quality. Assuring high quality data for predictive methods is challenging due to the difficulty of experimentally determining solubility values. The second hurdle is the specificity of molecular descriptors. Parameters which appropriately differentiate the factors which affect solubility between molecules have not yet been found but are critical in narrowing the gap between predicted and experimental solubility values. Many researchers use a combination of easily determinable molecular descriptors or ab initio methods to perform predictions [4,5]. The results from these simulations suggest that there is still significant room for improvement in selection of parameters which significantly impact solubility. The goal of this project is to develop a deep learning model to predict the solubility values of drug-like compounds.

Methods: The model we have developed is a Deep Sets-based Graph and Self-Attention Network with input from a computational chemistry approach to evaluating electron density and solubility values as labels. Our hypothesis is that intermolecular interactions are very important in determining the solubility of a molecule and are represented well by electron density. As a result, we hypothesize that the electron density of the drug molecules may be used to predict solubility. A good dataset is critical to the success of a solubility prediction algorithm. Our prediction algorithm uses molecules found in the first and second Solubility Challenge conducted by Avdeef et. al, a solubility prediction challenge which pitted human predictors against machine learning algorithms [2,3]. There are a total of 90 molecules with an inherently normal distribution of solubility values. We have created a method of generating unique descriptors of intermolecular interactions by: 1) using quantum mechanical conceptual density functional theory (CDFT) calculations to generate measures of electron density from crystal structures; 2) generating the molecular surface by determining the contribution of electron in the crystal structure from individual molecules; and 3) creating a method called Manifold Embedding of the Molecular Surface (MEMS). MEMS embeds the CDFT calculated values onto the three-dimensional (3D) molecular surface which is then projected into two dimensions (2D) using a stochastic neighborhood embedding approach. From each atom location in the 2D space, radially and angularly distributed electrostatic potential and Fukui function values are taken as input for the neural network.

Results: Using the current dataset, the neural network can correctly predict the solubility of a compound within 1 log unit at a rate of 100%. The total set of 90 molecules with a normal distribution shown in Figure 1 was split 1000 different times, each repeated 50 times through the neural network in order to find and confirm the best results of the prediction. The lowest mean absolute error (MAE) and root mean squared error (RMSE) obtained from the prediction was 0.20 and 0.24, respectively. The distribution of MAE is combined with plots of the average RMSE and R² values for each bin from the histogram in the middle and bottom frames of Figure 3. As expected, the low MAE values correspond with low RMSE and high R².

Conclusion: The results from our initial studies with this novel method of deriving molecule descriptors indicate that MEMS largely captures the information of both the strength and specificity of molecular interactions. MEMS achieves a much-improved prediction performance as compared to most of the reported literature studies. Further studies are currently under way to improve the quality of prediction through data curation and retention of the most accurate chemical information as possible.

References: 1. Ran Y, Yalkowsky SH. Prediction of drug solubility by the general solubility equation (GSE). Journal of Chemical Information and Computer Sciences. 2001;41:354–7.
2. Llinàs A, Glen RC, Goodman JM. Solubility challenge: Can you predict solubilities of 32 molecules using a database of 100 reliable measurements? Journal of Chemical Information and Modeling. 2008;48:1289–303.
3. Llinas A, Avdeef A. Solubility Challenge Revisited after Ten Years, with Multilab Shake-Flask Data, Using Tight (SD ∼0.17 log) and Loose (SD ∼0.62 log) Test Sets. Journal of Chemical Information and Modeling. American Chemical Society; 2019;59:3036–40.
4. Klamt A, Eckert F, Hornig M, Beck ME, Brger T. Prediction of aqueous solubility of drugs and pesticides with COSMO-RS. Journal of Computational Chemistry. 2002;23:275–81.
5. Tung HH, Tabora J, Variankaval N, Bakken D, Chen CC. Prediction of pharmaceutical solubility via NRTL-SAC and COSMO-SAC. Journal of Pharmaceutical Sciences [Internet]. Elsevier Masson SAS; 2008;97:1813–20.

Acknowledgments: The authors thank the Chao Endowment for funding our research.

Results from solubility prediction. (Top) Distribution of solubility values, (middle) distribution of MAE with corresponding average RMSE per bin and (bottom) distribution of MAE with corresponding average R2 values.