Conclusions about osmotically inactive volume and osmotic fragility from a detailed erythrocyte model

This paper develops a detailed model of human and bovine erythrocytes quantifying the dependence of total cell volume upon composition of an aqueous solution in which it is immersed. The cytoplasm is represented as an aqueous solution of hemoglobin and salt (KCl or NaCl). Model-based analysis of literature data on human erythrocytes, and of new experiments with bovine erythrocytes, leads to two findings. First, the Boyle-van't Hoff plot for human erythrocytes is found to be well described based on a solid volume fraction of ∼0.3 in complete agreement with desiccation experiments. The linear portion of the calculated curve turns out to be numerically indistinguishable from the commonly used ideal model parameterized with an apparent osmotically inactive volume fraction of ∼0.5. This mathematical outcome explains the longstanding perceived (but actually nonexistent) disconnect between the aforementioned fractions ∼0.3 and ∼0.5. A corollarial implication is that the actual volume fraction of osmotically nonparticipant (vicinal) water is very small (∼0.035). Second, an initial crenation of bovine erythrocytes (which occurs in classical techniques for measuring membrane permeability) is found to increase their fragility to an extent which correlates well with the crenated cell volume, and would affect the permeability determination.