Separation of ionic timescales explains dynamics of cellular volume regulation

Living cells actively regulate their volume in response to changes in the extra-cellular environment, such as osmolarity and chemo-attractant concentration. While the basic physical mechanisms of volume regulation are understood from the classic "pump-leak" model, it does not provide an explicit expression for the volume during dynamic regulation and can benefit from further insight into the volume dynamics. Here, we propose a simple explanation of volume dynamics in terms of two phases: fast volume adjustment to membrane potential, largely determined by Cl$^-$ leakage, and slow potential adaptation after shock, constrained by Na$^+$ leakage. The volume change may predominantly occur in either of these two phases, as we demonstrate for the scenarios of regulatory volume decrease and increase. Our theoretical predictions are validated by two recent independent shock experiments: osmotic shocks in HeLa cells and neutrophil activation upon sudden exposure to chemoattractants. Our theory aims to elucidate cellular volume dynamics on the scale of tens of minutes in various biological contexts.