On proper linearization, construction and analysis of the Boyle-van't Hoff plots and correct calculation of the osmotically inactive volume

The Boyle–van’t Hoff (BVH) law of physics has been widely used in cryobiology for calculation of the key osmotic parameters of cells and optimization of cryo-protocols. The proper use of linearization of the Boyle–vant’Hoff relationship for the osmotically inactive volume (v_b) has been discussed in a rigorous way in (Katkov, Cryobiology, 2008, 57:142–149). Nevertheless, scientists in the field have been continuing to use inappropriate methods of linearization (and curve fitting) of the BVH data, plotting the BVH line and calculation of v_b. Here, we discuss the sources of incorrect linearization of the BVH relationship using concrete examples of recent publications, analyze the properties of the correct BVH line (which is unique for a given v_b), provide appropriate statistical formulas for calculation of v_b from the experimental data, and propose simplistic instructions (standard operation procedure, SOP) for proper normalization of the data, appropriate linearization and construction of the BVH plots, and correct calculation of v_b. The possible sources of non-linear behavior or poor fit of the data to the proper BVH line such as active water and/or solute transports, which can result in large discrepancy between the hyperosmotic and hypoosmotic parts of the BVH plot, are also discussed.