Mostly Biomathematics Lunchtime Seminar
A Mathematical Model of Cell Volume Control with Realistic Na⁺/K⁺ Pump Dynamics
Speaker: Evan Rowbotham, Courant Institute of Mathematical Sciences
Location: Warren Weaver Hall 1314
Date: Tuesday, March 31, 2026, 12:45 p.m.
Synopsis:
In mammalian cells, cell volume regulation is crucial because it maintains cell structure, enables essential biological processes such as cell division, and prevents damage from osmotic stress. Cell volume regulation depends critically on active ionic transport, imposing a major energetic cost due to the continual maintenance of ionic gradients. Among active ionic transport mechanisms, the Na⁺/K⁺ pump plays a central role in establishing ionic gradients, maintaining osmotic balance, and supporting core physiological functions: cardiac contraction, action potential generation, and renal salt and water reabsorption.
The present work builds upon the mathematical model of cell volume control developed by Peskin, in which cell volume and membrane voltage are determined by the balance between passive ionic leaks and an active Na⁺/K⁺ pump. In that model, Na⁺/K⁺ pump activity is treated as a given parameter, corresponding to the transport of a fixed number of ions per unit time, and steady states are obtained under this assumption. Here, we improve this model by allowing the pump rate to depend explicitly on intracellular and extracellular Na⁺ and K⁺ concentrations, as well as on membrane potential. For this purpose, we employ the mathematical model of the Na⁺/K⁺-ATPase introduced by Pan et al., which describes pump cycling as an energy-dependent process. Coupling pump activity to cellular energetics produces distinct steady states for membrane voltage and cell volume compared to fixed-rate pump models.