Effects of Intracellular Ca²⁺ Dynamics on Bifurcation Structures of Sinoatrial Node Pacemaker Cells: a theoretical study

Abstract

To elucidate the roles of intracellular Ca²⁺ dynamics in sinoatrial (SA) node pacemaking, we investigated the effects of SR Ca²⁺ cycling dynamics on bifurcation structures of mathematical models for the rabbit SA node cells. Modified versions of our model (Kurata et al. Am J Physiol, 2002) with various SR Ca²⁺ uptake and release rates were used. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were calculated for the model cells during changes in bifurcation parameters. Structural stability to applications of constant bias currents (I_bias) or hyperpolarizing loads was also evaluated. In all the model cells, blocking L-type Ca²⁺ current (I_Ca,L) caused EP stabilization and cessation of pacemaking via a Hopf bifurcation, and the unstable EP region determined with I_bias applications shrunk and finally disappeared as I_Ca,L diminished. All the model cells exhibited essentially the same bifurcation structures, regardless of whether or not intracellular Ca²⁺ dynamics significantly affects the action potential dynamics. Changing SR Ca²⁺ uptake and release rates only slightly altered the bifurcation structures of the model cells. These results suggest that the effect of intracellular Ca²⁺ dynamics on dynamical properties of SA node pacemaking is relatively small, and that the membrane clock plays a pivotal role in SA node pacemaking. [J Physiol Sci. 2008;58 Suppl:S177]