Predicting the transport of chemicals across the skin: Stochastic calculus and machine learning

Objectives: While quantitative structure–permeability relationships (QSPR) models have enhanced the understanding of structure–permeability relationships, their deterministic characteristics frequently underestimate the variability observed in experimental datasets, stemming from variations in skin shape, experimental circumstances, and measurement noise. Stochastic differential equations (SDEs) can be employed to model data that includes random noise from various sources. In this research project, the Euler–Maruyama (EM) algorithm, the Milstein scheme, and the Heston stochastic model were utilized to predict permeability coefficients. Materials and Methods: A curated dataset containing molecular weight, log Kow, Balaban Index, Harary Index, Ramification Index, and Forgotten Index served as inputs. Results: The Milstein method produced an MSE of 0.634 and an R 2 of 0.74. The Heston model resulted in a mean squared error (MSE) of 0.66 and an R 2 of 0.72. In a second set of studies, three machine learning models – gradient boost regression, support vector regression, and the LevenbergMarquardt algorithm – were applied to predict skin permeability coefficients from the same dataset. The models were trained on a dataset of eighty-seven chemicals. The LevenbergMarquardt method yielded a mean squared error (MSE) of 0.94 and a coefficient of determination (R 2 ) of 0.58. Gradient boost regression (GBR) achieved R 2 and MSE values of 0.84 and 0.45, respectively. Support vector regression (SVR) produced an R 2 of 0.78 and an MSE of 0.62. Conclusion: In this research project, we utilized the Euler–Maruyama (EM) algorithm, the Milstein scheme and the Heston stochastic model to predict permeability coefficient . Optimization of machine learning algorithms augments predictive accuracy and diminishes the time, resources, and labor expended on skin transport studies.