Streamlining Linear\nFree Energy Relationships of Proteins\nthrough Dimensionality Analysis and Linear Modeling

Linear free energy relationships (LFERs) are pivotal\nin predicting\nprotein–water partition coefficients, with traditional one-parameter\n(<i>1p</i>-LFER) models often based on octanol. However,\ntheir limited scope has prompted a shift toward the more comprehensive\nbut parameter-intensive Abraham solvation-based poly-parameter (<i>pp</i>-LFER) approach. This study introduces a two-parameter\n(<i>2p</i>-LFER) model, aiming to balance simplicity and\npredictive accuracy. We showed that the complex six-dimensional intermolecular\ninteraction space, defined by the six Abraham solute descriptors,\ncan be efficiently simplified into two key dimensions. These dimensions\nare effectively represented by the octanol–water (log <i>K</i><sub>ow</sub>) and air–water (log <i>K</i><sub>aw</sub>) partition coefficients. Our <i>2p</i>-LFER\nmodel, utilizing linear combinations of log <i>K</i><sub>ow</sub> and log <i>K</i><sub>aw</sub>, showed promising\nresults. It accurately predicted structural protein–water (log <i>K</i><sub>pw</sub>) and bovine serum albumin–water (log <i>K</i><sub>BSA</sub>) partition coefficients, with <i>R</i><sup>2</sup> values of 0.878 and 0.760 and root mean squared errors\n(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.\nIn 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\nfor diverse mammalian tissues/organs (<i>n</i> = 137, RMSE\n= 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\nsurpasses <i>1p</i>-LFER. Our findings highlight the utility\nof the <i>2p</i>-LFER model in estimating chemical partitioning\nto proteins based on hydrophobicity, volatility, and solubility, offering\na viable alternative in scenarios where <i>pp</i>-LFER descriptors\nare unavailable.