Streamlining Linear Free Energy Relationships of Proteins through Dimensionality Analysis and Linear Modeling

Linear free energy relationships (LFERs) are pivotal in predicting protein-water partition coefficients, with traditional one-parameter (1p-LFER) models often based on octanol. However, their limited scope has prompted a shift toward the more comprehensive but parameter-intensive Abraham solvation-based poly-parameter (pp-LFER) approach. This study introduces a two-parameter (2p-LFER) model, aiming to balance simplicity and predictive accuracy. We showed that the complex six-dimensional intermolecular interaction space, defined by the six Abraham solute descriptors, can be efficiently simplified into two key dimensions. These dimensions are effectively represented by the octanol-water (log K_ow) and air-water (log K_aw) partition coefficients. Our 2p-LFER model, utilizing linear combinations of log K_ow and log K_aw, showed promising results. It accurately predicted structural protein-water (log K_pw) and bovine serum albumin-water (log K_BSA) partition coefficients, with R² values of 0.878 and 0.760 and root mean squared errors (RMSEs) of 0.334 and 0.422, respectively. Additionally, the 2p-LFER model favorably compares with pp-LFER predictions for neutral per- and polyfluoroalkyl substances. In a multiphase partitioning model parametrized with 2p-LFER-derived coefficients, we observed close alignment with experimental in vivo and in vitro distribution data for diverse mammalian tissues/organs (n = 137, RMSE = 0.44 log unit) and milk-water partitioning data (n = 108, RMSE = 0.29 log units). The performance of the 2p-LFER is comparable to pp-LFER and significantly surpasses 1p-LFER. Our findings highlight the utility of the 2p-LFER model in estimating chemical partitioning to proteins based on hydrophobicity, volatility, and solubility, offering a viable alternative in scenarios where pp-LFER descriptors are unavailable.