Computational researchers from the National Center for Toxicological Research at the United States Food and Drug Administration and the University of Maryland have constructed a multi-architecture consensus modeling framework capable of predicting whether diverse chemical compounds bind to human sex hormone-binding globulin. Sex hormone-binding globulin is a circulating plasma glycoprotein that plays a fundamental regulatory role in human endocrine physiology by binding circulating androgens and estrogens with high affinity. This biological sequestration distributes circulating steroids across free, albumin-bound, and globulin-bound fractions, establishing a physiological equilibrium where only the unbound steroid molecules remain readily available for cellular membrane diffusion and intracellular receptor engagement. Consequently, external chemicals that bind to the protein can displace natural hormones, altering bioavailable concentrations even when total systemic hormone quantities remain unchanged. Because conventional laboratory testing through competitive binding assays requires extensive resources, calibrated radioisotopes, and multi-concentration protocols that restrict testing throughput, computational approaches offer a practical pathway for prioritizing large chemical inventories for safety assessments.

To establish a statistically robust computational foundation, the investigators utilized a benchmark training dataset comprising 125 structurally diverse chemical substances previously tested in human pregnancy plasma competitive displacement assays using radiolabeled dihydrotestosterone. In this primary dataset, 87 compounds demonstrated measurable competitive binding against the reference steroid, while 38 exhibited no observed competitive displacement under defined equilibrium conditions. The chemical space represented across these 125 substances spanned endogenous steroid hormones, synthetic pharmaceuticals, industrial chemical formulations, agricultural pesticides, and pervasive environmental contaminants. To process these heterogeneous structures across distinct analytical algorithms, chemical representations were converted from isomeric SMILES notations into two independent computational formats: high-dimensional traditional molecular descriptors calculated via the Mold2 software package and complete molecular graph topologies. The initial descriptor calculation generated 777 structural attributes per molecule, which were systematically reduced to a filtered set of 478 informative descriptors by eliminating constants and invariant metrics that shared identical values across more than 90 percent of the training cohort.

The modeling strategy deliberately paired conventional descriptor-based machine learning algorithms with graph-based deep learning architectures to capture complementary structural information. Three descriptor-driven classifiers—random forest, support vector machine with a radial basis function kernel, and a multilayer perceptron neural network—were trained directly on the autoscaled 478 Mold2 features. Simultaneously, a deep graph neural network architecture known as a graph isomorphism network with edge features was trained on topological molecular graphs. In this graph representation, individual atoms served as graph nodes encoded with elemental identity, formal charge, hybridization, aromaticity, and stereochemical chirality, while covalent bonds served as graph edges holding attributes for bond type, conjugation, ring membership, and spatial stereoisomerism. A comprehensive consensus model was subsequently generated by applying an equal-weight probability averaging rule that combined the continuous binder probability scores produced by the four independent base models, assigning a positive binder classification whenever the ensemble probability reached or exceeded the 0.5 decision threshold.

Rather than relying on a single arbitrary train-test split that can distort performance metrics on small datasets, the research team evaluated internal model performance through 100 repeated iterations of stratified five-fold cross-validation. Hyperparameters for each algorithmic architecture were systematically optimized during internal folds by maximizing the Matthews correlation coefficient, a performance metric that accounts for unbalanced class distributions. Across all 100 internal cross-validation repetitions, all five predictive systems demonstrated strong classification efficacy, with overall accuracy ranges spanning 0.811 to 0.855, sensitivities ranging from 0.865 to 0.920, and specificities ranging from 0.651 to 0.781. The graph isomorphism network achieved the highest individual sensitivity at 0.920, effectively detecting true binding molecules while incurring a higher false-positive rate. In contrast, the consensus model exhibited the superior overall performance across internal evaluations, securing the highest mean accuracy of 0.855 and the highest mean Matthews correlation coefficient of 0.671, demonstrating that combining distinct mathematical perspectives substantially dampens individual algorithmic errors.

Rigorous external validation was conducted using an independent chemical repository curated from the public ChEMBL bioactivity database, providing an objective benchmark for generalization across unseen chemical structures. After removing all chemical entities that overlapped with the original 125 training substances, the external validation library comprised 164 unique chemical structures annotated with experimental binding determinations, consisting of 155 confirmed binders and nine nonbinders. Within this external cohort, 157 substances held human binding records, while seven represented rodent or rabbit globulin targets. Evaluated against all 164 external chemicals, the consensus architecture achieved an accuracy of 0.884, a sensitivity of 0.890, a specificity of 0.778, and a Matthews correlation coefficient of 0.430. When the evaluation was restricted exclusively to the 157 verified human-specific assay targets, model performance climbed further, yielding an accuracy of 0.9236, a sensitivity of 0.9324, and a Matthews correlation coefficient of 0.5313, while maintaining a specificity of 0.7778 because all seven excluded non-human chemicals were confirmed binders.

To confirm that external predictive accuracy was not merely an artifact of chemical redundancy, the investigators quantified pairwise structural similarities between all chemical combinations in the training and validation sets using autoscaled descriptor correlation coefficients. The resulting mean r-squared values revealed pronounced structural divergence, averaging 0.120 within the training library, 0.330 within the external ChEMBL collection, and 0.125 between the training and external datasets. These consistently low correlation coefficients verified that the vast majority of external compounds possessed descriptor profiles substantially distinct from the training examples, indicating that the consensus framework maintained legitimate predictive capability when confronted with unfamiliar chemical domains. Furthermore, comparison of the ensemble aggregation method demonstrated that equal-weight probability averaging slightly outperformed majority voting schemes during internal validation, while remaining comparable during external testing, verifying that simple arithmetic averaging provides a stable mathematical mechanism without introducing superfluous parameter fitting.

Model interpretation via feature importance analysis revealed the core structural characteristics governing chemical interactions with the transport globulin. Examining the mean decrease in Gini impurity across 500 random forest models generated during the internal cross-validation iterations identified seven primary molecular descriptors exceeding the threshold of two standard deviations above the log-transformed mean. Three of these informative attributes corresponded to average valence vertex connectivity indices, which reflect molecular branching, atomic connectivity, and spatial molecular topology. Two descriptors represented Burden matrix eigenvalues weighted by Sanderson electronegativity distributions, while two others quantified Burden matrix eigenvalues and topological autocorrelations weighted by atomic polarizability. To contextualize these numerical findings physically, the researchers examined the X-ray crystallographic structure of human sex hormone-binding globulin bound to dihydrotestosterone from Protein Data Bank entry 1KDM. Electrostatic surface mapping of the binding cavity confirmed a heterogeneous electrostatic landscape with distinct positive, negative, and neutral patches, demonstrating qualitative physical alignment with the identified topological, electronegative, and polarizability descriptors.

The study also established a functional relationship between mathematical prediction confidence and real-world classification accuracy. Prediction confidence scores were calculated as the normalized distance between the predicted binding probability and the 0.5 classification threshold, scaling from zero at maximal uncertainty to one at extreme certainty. When the 12,500 individual internal validation predictions were segmented into ten consecutive confidence intervals, empirical classification accuracy scaled upward in direct correspondence with increasing confidence scores. A corresponding phenomenon was demonstrated in the external validation dataset, where predictions divided into low-confidence and high-confidence bins exhibited dramatic performance differences. For instance, the random forest model reached perfect classification accuracy among high-confidence external predictions while suffering significantly higher error rates in low-confidence regions. This monotonic relationship indicates that computational confidence metrics provide a practical screening filter, enabling toxicologists and pharmacologists to flag ambiguous chemical classifications and prioritize high-certainty candidates for downstream decision-making.

Despite these encouraging validation results, the authors explicitly outlined critical technical constraints and limitations that temper broad extrapolations. First, the foundational development dataset was restricted to 125 experimental chemicals, meaning each outer training split contained only 100 compounds evaluated against 478 descriptors, a condition that necessitates strict regularization to guard against subtle mathematical overfitting. Second, severe class imbalance characterized the external validation set, which contained 155 active binders and only nine verified nonbinders. Because nonbinders were so scarce, misclassifying a single negative compound lowered calculated specificity by more than eleven percent, underscoring that specificity and Matthews correlation coefficients remain statistically sensitive to minor fluctuations. Additionally, external bioactivity annotations originated from heterogeneous assay formats, variable species backgrounds, diverse reporting endpoints, and differing concentration limits across ChEMBL, introducing potential experimental noise that cannot be fully corrected through standardized computational curation.

In their final synthesis, the researchers emphasized that computational prediction of plasma globulin affinity represents an essential component of comprehensive endocrine safety profiling rather than an isolated hazard determinant. Transport globulin interactions alter free hormone equilibria and influence systemic drug disposition, complementing traditional nuclear receptor binding assays, cellular steroidogenesis screenings, and toxicokinetic modeling. The developed open-source framework demonstrates that integrating descriptor-based machine learning with graph-based deep learning produces robust, balanced classifications that exceed the performance of isolated single-algorithm models. While the authors caution that structural dissimilarity does not necessarily prove complete chemical scaffold novelty, this consensus approach expands the scarce computational repertoire currently available for serum transport proteins. By facilitating high-throughput screening of massive commercial and environmental chemical inventories, these validated models offer regulatory scientists, toxicologists, and pharmaceutical developers a rapid, cost-effective methodology for prioritizing potential endocrine-active substances for targeted laboratory testing.

Subject of Research: Machine learning and deep learning consensus modeling for predicting chemical binding to sex hormone-binding globulin

Article Title: Consensus modeling of sex hormone-binding globulin binding using machine learning and deep learning approaches

Article References: Guo, W., Varghese, A., Yu, C., Liu, J., Patterson, T. A., & Hong, H. (2026). Consensus modeling of sex hormone-binding globulin binding using machine learning and deep learning approaches. Frontiers in Chemistry, 14, Article 1984441. https://doi.org/10.3389/fchem.2026.1984441

Image Credits: AI Generated

DOI: 10.3389/fchem.2026.1984441

Keywords: computational toxicology, sex hormone-binding globulin, machine learning, deep learning, consensus modeling, endocrine disruption, cheminformatics, toxicological screening, Consensus, modeling, hormone-binding, globulin