Deep learning models for the estimation of free energy of permeation of small molecules across lipid membranes

Abstract

Calculating the free energy of drug permeation across membranes carries great importance in pharmaceutical and related applications. Traditional methods, including experiments and molecular simulations, are expensive and time-consuming, and existing statistical methods suffer from low accuracy. In this work, we propose a hybrid approach that combines molecular dynamics simulations and deep learning techniques to predict the free energy of permeation of small drug-like molecules across lipid membranes with high accuracy and at a fraction of the computational cost of advanced sampling methods like umbrella sampling. We have performed several molecular dynamics simulations of molecules in water and lipid bilayers to obtain multidimensional time-series data of features. Deep learning architectures based on Long Short-Term Memory networks, attention mechanisms, and dense layers are built to estimate free energy from the time series data. The prediction errors for the test set and an external validation set are much lower than that of existing data-driven approaches, with R² of the best model around 0.99 and 0.82 for the two cases. Our approach estimates free energy with satisfactory accuracy using deep learning models within an order-of-magnitude less computational time than required by extensive simulations. This work presents an attractive option for high-throughput virtual screening of molecules based on their membrane permeabilities, demonstrates the applicability of language processing techniques in biochemical problems, and suggests a novel way of integrating physics with statistical learning to great success.