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 (g) of I(K1) and I(f) as bifurcation parameters. Pacemaker activity can be induced either via Hopf or homoclinic bifurcations. As g(K1) is decreased by approximately 74%, autorhythmicity emerged via a homoclinic bifurcation, i.e., the periodicity first appear with infinitely large periods. In contrast, the insertion of g(f) induced periodicity via a subcritical Hopf bifurcation at g(f) approximately 0.25 mSmicroF(-1). Stable autorhythmic action potentials occurred at g(f) > 0.329 mSmicroF(-1).