Bifurcation Analysis of Genetically Engineered Pacemaking in Mammalian Heart

Author： Tong Wing   Holden Arun  

Publisher： Springer Publishing Company

ISSN： 0092-0606

Source： Journal of Biological Physics, Vol.32, Iss.2, 2006-10, pp. : 169-172

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Abstract

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.

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