A single-cell model of phase-driven control of ventricular fibrillation frequency

The mechanisms controlling the rotation frequency of functional reentry in ventricular fibrillation (VF) are poorly understood. It has been previously shown that Ba2+ at concentrations up to 50 mumol/L slows the rotation frequency in the intact guinea pig (GP) heart, suggesting a role of the inward rectifier current (I(K1)) in the mechanism governing the VF response to Ba2+. Given that other biological (e.g., sinoatrial node) and artificial systems display phase-locking behavior, we hypothesized that the mechanism for controlling the rotation frequency of a rotor by I(K1) blockade is phase-driven, i.e., the phase shift between transmembrane current and voltage remains constant at varying levels of I(K1) blockade. We measured whole-cell admittance in isolated GP myocytes and in transfected human embryonic kidney (HEK) cells stably expressing Kir 2.1 and 2.3 channels. The admittance phase, i.e., the phase difference between current and voltage, was plotted versus the frequency in control conditions and at 10 or 50 micromol/L Ba2+ (in GP heart cells) or 1 mM Ba2+ (in HEK cells). The horizontal distance between plots was called the "frequency shift in a single cell" and analyzed. The frequency shift in a single cell was -14.14 +/- 5.71 Hz (n = 14) at 10 microM Ba2+ and -18.51 +/- 4.00 Hz (n = 10) at 50 microM Ba2+, p < 0.05. The values perfectly matched the Ba2+-induced reduction of VF frequency observed previously in GP heart. A similar relationship was found in the computer simulations. The phase of Ba2+-sensitive admittance in GP cells was -2.65 +/- 0.32 rad at 10 Hz and -2.79 +/- 0.26 rad at 30 Hz. In HEK cells, the phase of Ba2+-sensitive admittance was 3.09 +/- 0.03 rad at 10 Hz and 3.00 +/- 0.17 rad at 30 Hz. We have developed a biological single-cell model of rotation-frequency control. The results show that although rotation frequency changes as a result of I(K1) blockade, the phase difference between transmembrane current and transmembrane voltage remains constant, enabling us to quantitatively predict the change of VF frequency resulting from I(K1) blockade, based on single-cell measurement.