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 (<i>1p</i>-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 (<i>pp</i>-LFER) approach. This study introduces a two-parameter (<i>2p</i>-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 <i>K</i>_ow) and air-water (log <i>K</i>_aw) partition coefficients. Our <i>2p</i>-LFER model, utilizing linear combinations of log <i>K</i>_ow and log <i>K</i>_aw, showed promising results. It accurately predicted structural protein-water (log <i>K</i>_pw) and bovine serum albumin-water (log <i>K</i>_BSA) partition coefficients, with <i>R</i>² values of 0.878 and 0.760 and root mean squared errors (RMSEs) of 0.334 and 0.422, respectively. Additionally, the <i>2p</i>-LFER model favorably compares with <i>pp</i>-LFER predictions for neutral per- and polyfluoroalkyl substances. In a multiphase partitioning model parametrized with <i>2p</i>-LFER-derived coefficients, we observed close alignment with experimental <i>in vivo</i> and <i>in vitro</i> distribution data for diverse mammalian tissues/organs (<i>n</i> = 137, RMSE = 0.44 log unit) and milk-water partitioning data (<i>n</i> = 108, RMSE = 0.29 log units). The performance of the <i>2p</i>-LFER is comparable to <i>pp</i>-LFER and significantly surpasses <i>1p</i>-LFER. Our findings highlight the utility of the <i>2p</i>-LFER model in estimating chemical partitioning to proteins based on hydrophobicity, volatility, and solubility, offering a viable alternative in scenarios where <i>pp</i>-LFER descriptors are unavailable.