Bifurcation Analysis of Genetically Engineered Pacemaking in Mammalian Heart

Genetically engineered pacemaking in ventricular cells has been achieved by down-regulation of the time independent inward rectifying current (I _K1), or insertion of the hyperpolarisation-activated funny current (I _f). We analyse the membrane system (i.e. ionic concentrations clamped) of an epicardial Luo-Rudy dynamic cell model using continuation algorithms with the maximum conductance () of I _K1 and I _f as bifurcation parameters. Pacemaker activity can be induced either via Hopf or homoclinic bifurcations. As _K1 is decreased by ≈74%, autorhythmicity emerged via a homoclinic bifurcation, i.e., the periodicity first appear with infinitely large periods. In contrast, the insertion of _f induced periodicity via a subcritical Hopf bifurcation at _f≈ 0.25 mSμF⁻¹. Stable autorhythmic action potentials occurred at _f > 0.329 mSμF⁻¹.