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Dynamical Mechanisms of Pacemaker Generation in I_K1-Downregulated Human Ventricular Myocytes: Insights from Bifurcation Analyses of a Mathematical Model

Yasutaka Kurata ^*, Ichiro Hisatome , Hiroyuki Matsuda ^* and Toshishige Shibamoto ^*

^* Department of Physiology, Kanazawa Medical University, Ishikawa 920-0293, Japan; and Division of Regenerative Medicine and Therapeutics, Tottori University Graduate School of Medical Science, Yonago 683-0826, Japan

Correspondence: Address reprint requests to Yasutaka Kurata, Dept. of Physiology, Kanazawa Medical University, 1-1 Daigaku, Uchinada-machi, Kahoku-gun, Ishikawa 920-0293, Japan, E-mail: yasu{at}kanazawa-med.ac.jp.

Dynamical mechanisms of the biological pacemaker (BP) generation in human ventricular myocytes were investigated by bifurcation analyses of a mathematical model. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were determined as functions of bifurcation parameters, such as the maximum conductance of inward-rectifier K⁺ current (I_K1), for constructing bifurcation diagrams. Stable limit cycles (BP activity) abruptly appeared around an unstable EP via a saddle-node bifurcation when I_K1 was suppressed by 84.6%. After the bifurcation at which a stable EP disappears, the I_K1-reduced system has an unstable EP only, which is essentially important for stable pacemaking. To elucidate how individual sarcolemmal currents contribute to EP instability and BP generation, we further explored the bifurcation structures of the system during changes in L-type Ca²⁺ channel current (I_Ca,L), delayed-rectifier K⁺ currents (I_K), or Na⁺/Ca²⁺ exchanger current (I_NaCa). Our results suggest that 1), I_Ca,L is, but I_K or I_NaCa is not, responsible for EP instability as a requisite to stable BP generation; 2), I_K is indispensable for robust pacemaking with large amplitude, high upstroke velocity, and stable frequency; and 3), I_NaCa is the dominant pacemaker current but is not necessarily required for the generation of spontaneous oscillations.

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