Bifurcation Analysis of Genetically Engineered Pacemaking in Mammalian Heart

Wing Chiu Tong and Arun V. Holden


Genetically engineered pacemaking in ventricular cells has been achieved by down-regulation of the time independent inward rectifying current (IK1), or insertion of the hyperpolarisation-activated funny current (If). 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¯g¯ ) of IK1 and If as bifurcation parameters. Pacemaker activity can be induced either via Hopf or homoclinic bifurcations. As g¯g¯ 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 g¯g¯ f induced periodicity via a subcritical Hopf bifurcation at g¯g¯ f≈ 0.25 mSμF−1. Stable autorhythmic action potentials occurred at g¯g¯ f > 0.329 mSμF−1.

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