Challenge from the simple: Some caveats in linearization of the Boyle–van’t Hoff and Arrhenius plots

Some aspects of proper linearization of the Boyle–van’t Hoff (BVH) relationship for calculation of the osmotically inactive volume vbvb, and Arrhenius plot (AP) for the activation energy EaEa are discussed. It is shown that the commonly used determination of the slope and the intercept (vbvb), which are presumed to be independent from each other, is invalid if the initial intracellular molality m0m0 is known. Instead, the linear regression with only one independent parameter (vbvb) or the Least Square Method (LSM) with vbvb as the only fitting LSM parameter must be applied. The slope can then be calculated from the BVH relationship as the function of vbvb. In case of unknown m0m0 (for example, if cells are preloaded with trehalose, or electroporation caused ion leakage, etc.), it is considered as the second independent statistical parameter to be found. In this (and only) scenario, all three methods give the same results for vbvb and m0m0. AP can be linearized only for water hydraulic conductivity (LpLp) and solute mobility (ωsωs) while water and solute permeabilities PwPw ≡ LpRT   and PsPs ≡ ωsRTωsRT cannot be linearized because they have pre-exponential factor (RT) that depends on the temperature T.