Meta-analysis of the Boyle van 't Hoff relation: Turgor and leak models explain non-ideal volume equilibrium

There has been much recent attention paid to the interaction of cell volume, its regulation, and the molecular biology of the cell. Cells are generally assumed to behave as linear osmometers, with their water volume linearly proportionate to the inverse of osmotic pressure as described by the Boyle van 't Hoff (BvH) relation. This study evaluates the generality of this and other long-standing assumptions about cell responses to anisotonic conditions. We present alternative models that account for osmoregulation including mechanical resistance to volumetric expansion (the turgor model) and ion-osmolyte leakage (the leak model). To evaluate the generality of the BvH relation and determine the suitability of alternative models, we performed a comprehensive survey of the literature and a careful analysis of the resulting data, and then we used these data to compare among models. We identified 137 articles published from 1964 to 2019 spanning 14 animal species and 26 cell types and determined the BvH relation is not an appropriate general model but is adequate when restricted to the hypertonic region. In contrast, models that account for either mechanical resistance or ion-osmolyte leakage fit well to almost all collected data. The leak model has fitted parameters that are in the same range as the current literature estimate, while the turgor model typically requires an elastic modulus value of one or multiple orders of magnitude larger than literature values. However, confirmation of the underlying mechanism of osmotic regulation is required at the cell-specific level and cannot be assumed a priori.