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 v_b, and Arrhenius plot (AP) for the activation energy E_a are discussed. It is shown that the commonly used determination of the slope and the intercept (v_b), which are presumed to be independent from each other, is invalid if the initial intracellular molality m₀ is known. Instead, the linear regression with only one independent parameter (v_b) or the Least Square Method (LSM) with v_b as the only fitting LSM parameter must be applied. The slope can then be calculated from the BVH relationship as the function of v_b. In case of unknown m₀ (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 v_b and m₀. AP can be linearized only for water hydraulic conductivity (L_p) and solute mobility (ω_s) while water and solute permeabilities P_w ≡ L_pRT and P_s ≡ ω_sRT cannot be linearized because they have pre-exponential factor (RT) that depends on the temperature T.