Molecular Descriptors and Crystalline Data Predict Amorphous Drug Solubility in Computational Models

Computational models combining specific molecular descriptors with experimental crystalline solubility can predict the amorphous solubility of poorly soluble pharmaceutical compounds without requiring extensive solid-state trial formulations, according to a study published in AAPS Open. Researchers developed and validated in-silico regression frameworks using an experimental dataset of thirty-three structurally diverse, poorly water-soluble marketed drugs. In early pharmaceutical development, poor aqueous solubility represents a pervasive barrier that restricts oral bioavailability and diminishes the therapeutic efficacy of promising new chemical entities. While formulating active pharmaceutical ingredients into disordered amorphous solid dispersions offers a proven pathway to achieve supersaturation and substantially enhance molecular release at the solid-liquid interface, characterizing the true amorphous solubility of these candidates presents substantial experimental hurdles. The new investigation demonstrates that combining calculated chemical descriptors with measured crystalline baseline solubility yields robust predictive frameworks, while pure descriptor-based consensus models achieve dependable predictive accuracy using only three structural features representing lipophilicity, molecular topology, and internal hydrogen bonding.

The physical distinction between crystalline and amorphous states dictates their respective dissolution behavior in aqueous environments. In crystalline solids, molecules reside in ordered, tightly packed lattices where the thermodynamic barrier to dissolution is governed by lattice dissociation energy in tandem with the hydration barrier of the solute. In contrast, amorphous phases lack long-range three-dimensional molecular order, drastically lowering the energetic barrier required for molecules to detach across the solid-liquid boundary into solvent. Consequently, amorphous materials generate transient supersaturation levels that exceed thermodynamic equilibrium solubility. However, quantifying the exact saturation threshold of an amorphous drug is technically challenging because supersaturated solutions are thermodynamically unstable and prone to rapid, spontaneous crystallization. To overcome this limitation, pharmaceutical scientists monitor the point of liquid-liquid phase separation, an equilibrium condition where a drug-poor aqueous phase coexists with a drug-rich non-crystalline phase. This liquid-liquid phase separation concentration represents the practical ceiling of attainable supersaturation, serving as a reliable surrogate for intrinsic amorphous solubility.

To build an experimental database under stringent thermodynamic controls, the research team assembled solubility values for thirty-three commercially available drugs, acquiring data from curated literature and executing targeted microplate measurements for atazanavir, lopinavir, and darunavir. The buffer was supplemented with ten micrograms per milliliter of hydroxypropyl methylcellulose acetate succinate, a stabilizing polymer widely established for inhibiting crystallization while exerting negligible influence on the liquid-liquid phase separation transition at such dilute concentrations. Using ultraviolet extinction spectroscopy at an analytical non-absorbing wavelength of 450 nanometers on a microplate reader, the researchers tracked light scattering intensity as a function of titrated drug concentration, recording the sudden surge in scattering as the precise liquid-liquid phase separation transition point.

Computational feature generation was carried out using PaDEL-Descriptor software, translating the simplified molecular-input-line-entry system structures of all thirty-three compounds into 1,446 distinct one-dimensional and two-dimensional molecular descriptors. Prior to developing predictive algorithms, the dataset underwent systematic preprocessing to eliminate non-numeric values and uninformative near-constant descriptors exhibiting negligible variance across the chemical series. Principal component analysis paired with Hotelling’s T-squared statistics at a ninety-five percent confidence interval evaluated the spatial distribution of the compounds in chemical descriptor space. This multivariate diagnostic identified two compounds, paclitaxel and grazoprevir, as severe structural outliers whose elevated molecular weights, expansive architectures, and extreme leverage would disproportionately distort parametric regression models. Excluding these two high-leverage outliers produced a refined core dataset of thirty-one compounds. Pairwise correlation filtering subsequently pruned redundant variables exhibiting Pearson coefficients above 0.9, contracting the feature space to 733 descriptors that were standardized via z-score normalization to ensure balanced comparisons across differing physical scales.

Initial univariate correlation assessments revealed that several individual molecular descriptors correlated significantly with logarithmic amorphous solubility at a significance threshold of p less than 0.05. Every identified descriptor exhibited a negative correlation coefficient, indicating that larger molecular dimensions, greater lipophilicity, and enhanced structural complexity systematically depress intrinsic amorphous solubility. Among all evaluated descriptors, the calculated partition coefficient XLogP demonstrated the strongest individual linear correlation, generating a correlation coefficient of -0.62 and explaining approximately forty percent of the variance in logarithmic amorphous solubility. Other lipophilicity metrics, including CrippenLogP and ALogP, exhibited comparable negative associations, corroborating the principle that the aqueous solubility of modern pharmaceutical compounds is heavily governed by solvation dynamics. Secondary correlations emerged for topological and electronic descriptors such as C3SP2, AATSC1c, and nwHBa, demonstrating that extensive intermolecular bonding networks and structural rigidity hinder molecular release from amorphous drug-rich droplets into water.

Despite the prominent role of lipophilicity, residual analysis of the univariate XLogP regression model revealed marked prediction errors for several specific compounds, producing a mean absolute residual of 0.38 log units. A ranked residual analysis revealed an apparent threshold near 0.3 log units, beyond which prediction discrepancies diverged substantially from the primary trend. An exploratory subset assessment excluding compounds exceeding this threshold improved the regression coefficient of determination from 0.40 to 0.55 and compressed the mean squared error from 0.23 to 0.03 log units across seventeen highly uniform molecules. However, the researchers emphasized that such post-hoc filtering merely served an illustrative purpose to highlight how idiosyncratic molecular mobility and specific hydrogen-bonding geometries elude simple lipophilicity models. The widespread residual scatter observed across the complete thirty-one-compound dataset proved that univariate models relying exclusively on octanol-water partitioning cannot adequately capture the intricate thermodynamic and molecular interactions governing amorphous dissolution across structurally diverse drug classes.

To establish more grounded thermodynamic models, the researchers evaluated linear regressions integrating experimental crystalline solubility as a primary predictive factor. By itself, logarithmic crystalline solubility accounted for a substantial portion of the variability in amorphous solubility, achieving a leave-one-out cross-validated coefficient of determination of 0.64 and a mean squared error of 0.13. Because crystalline solubility reflects the chemical potential difference between solid and liquid phases, incorporating it captures the baseline thermodynamic energy needed to break crystal lattices. The team subsequently constructed a bivariate model combining logarithmic crystalline solubility and standardized XLogP. This bivariate equation produced a cross-validated coefficient of determination of 0.70 and lowered the cross-validated mean squared error to 0.11. Standardized regression coefficients demonstrated that crystalline solubility exerted a stronger relative influence than lipophilicity, aligning conceptually with classical thermodynamic frameworks like the General Solubility Equation while bypassing the need to measure melting points.

Each descriptor was evaluated by adding it independently to the bivariate model under leave-one-out cross-validation to prevent artificial parameter inflation and minimize overfitting risks. The addition of the hydrogen-bond donor count delivered the most measurable predictive enhancement, raising the cross-validated predictive coefficient of determination to 0.72 and dropping the cross-validated mean squared error to 0.10. By contrast, metrics like rotatable bond counts and McGowan volume provided negligible predictive gains, confirming that while polar interaction parameters offer modest refining capacity, the combination of baseline crystalline solubility and lipophilic partitioning remains the dominant physical driver of amorphous solubility within this curated pharmaceutical library.

To formulate fully autonomous in-silico models that do not depend on experimentally measured crystalline solubility, the researchers implemented a consensus feature selection strategy designed for high-dimensional, low-sample-size data environments. Six heterogeneous selection algorithms—LASSO regression, Ridge regression, Random Forest importance rankings, Pearson correlation screening, standard linear regression, and Mutual Information—were executed concurrently across the 733 candidate descriptors. Tracking the selection frequency across these diverse computational methods identified the five most consistently selected variables, effectively mitigating the algorithmic bias inherent to any individual feature selector. Subsequent combinatorial testing proved that a concise three-descriptor subset consisting of XLogP, SpMax3_Bhv, and nHBint6 yielded the most resilient predictive architecture across multiple linear modeling techniques, including Ordinary Least Squares, Ridge regression, Bayesian Ridge, and Huber regression, all of which achieved cross-validated coefficients of determination near 0.55 with mean squared errors around 0.17.

The biological and physical significance of these three consensus descriptors provides clear mechanistic insight into the factors that modulate amorphous solubility. The researchers noted that while these multivariate in-silico equations successfully demonstrate that amorphous solubility can be estimated directly from two-dimensional chemical structures, broader validation across larger external datasets will be essential to establish formal applicability domains. Nevertheless, by capturing the specific thermodynamic advantage of non-crystalline phases through accessible molecular features, this modeling framework offers pharmaceutical scientists an efficient material-sparing methodology for prioritizing pipeline candidates during early preformulation screening.

Subject of Research: In-silico prediction of amorphous drug solubility using molecular descriptors and crystalline solubility data

Article Title: Predicting amorphous drug solubility using molecular descriptors: an in-silico approach

Article References: Alsaafin, F., Alzghoul, A., Bergström, C. A. S., & Alhalaweh, A. (2026). Predicting amorphous drug solubility using molecular descriptors: an in-silico approach. AAPS Open, 12(1), Article 38. https://doi.org/10.1186/s41120-026-00166-2

Image Credits: AI Generated

DOI: 10.1186/s41120-026-00166-2

Keywords: amorphous solubility, crystalline solubility, molecular descriptors, in-silico modeling, liquid-liquid phase separation, XLogP, SpMax3_Bhv, nHBint6, PaDEL-Descriptor, leave-one-out cross-validation, consensus feature selection, supersaturation, poorly soluble drugs, pharmaceutical formulation, quantitative structure-property relationship, ultraviolet spectroscopy, hydroxypropyl methylcellulose acetate succinate