Steady-state solutions of cell volume in a cardiac myocyte model elaborated for membrane excitation, ion homeostasis and Ca2+ dynamics.

The cell volume continuously changes in response to varying physiological conditions, and mechanisms underlying volume regulation have been investigated in both experimental and theoretical studies. Here, general formulations concerning cell volume change are presented in the context of developing a comprehensive cell model which takes Ca(2+) dynamics into account. Explicit formulas for charge conservation and steady-state volumes of the cytosol and endoplasmic reticulum (ER) are derived in terms of membrane potential, amount of ions, Ca(2+)-bound buffer molecules, and initial cellular conditions. The formulations were applied to a ventricular myocyte model which has plasma-membrane Ca(2+) currents with dynamic gating mechanisms, Ca(2+)-buffering reactions with diffusive and non-diffusive buffer proteins, and Ca(2+) uptake into or release from the sarcoplasmic reticulum (SR) accompanied by compensatory cationic or anionic currents through the SR membrane. Time-dependent volume changes in cardiac myocytes induced by varying extracellular osmolarity or by action potential generation were successfully simulated by the novel formulations. Through application of bifurcation analysis, the existence and uniqueness of steady-state solutions of the cell volume were validated, and contributions of individual ion channels and transporters to the steady-state volume were systematically analyzed. The new formulas are consistent with previous fundamental theory derived from simple models of minimum compositions. The new formulations may be useful for examination of the relationship between cell function and volume change in other cell types.