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 (-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 (-LFER) approach. This study introduces a two-parameter (-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 ) and air-water (log ) partition coefficients. Our -LFER model, utilizing linear combinations of log and log , showed promising results. It accurately predicted structural protein-water (log ) and bovine serum albumin-water (log ) partition coefficients, with values of 0.878 and 0.760 and root mean squared errors (RMSEs) of 0.334 and 0.422, respectively. Additionally, the -LFER model favorably compares with -LFER predictions for neutral per- and polyfluoroalkyl substances. In a multiphase partitioning model parametrized with -LFER-derived coefficients, we observed close alignment with experimental and distribution data for diverse mammalian tissues/organs ( = 137, RMSE = 0.44 log unit) and milk-water partitioning data ( = 108, RMSE = 0.29 log units). The performance of the -LFER is comparable to -LFER and significantly surpasses -LFER. Our findings highlight the utility of the -LFER model in estimating chemical partitioning to proteins based on hydrophobicity, volatility, and solubility, offering a viable alternative in scenarios where -LFER descriptors are unavailable.