Circulation Research, Vol 58, 706-720, Copyright © 1986 by American Heart Association

ARTICLES

Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model

DC Michaels, EP Matyas and J Jalife

Dynamic interactions and mutual entrainment of coupled sinoatrial pacemaker cells with different intrinsic frequencies were investigated using a computerized mathematical model. Transmembrane potentials were simulated using equations of individual membrane currents based on voltage clamp data for the sinoatrial node. The intrinsic frequency of a given cell was altered by applying bias hyperpolarizing current, or by changing the amount of slow inward current. Cells were coupled through simple ohmic resistances to form linear arrays of two or more cells. Simulations closely reproduced previous experimental work showing that the mutual interactions between pacemakers are mediated electrotonically and show phase dependence. Results from the present simulations provide an explanation for the ionic basis of these phase- dependent interactions. In addition, it is demonstrated that the mutual entrainment of coupled pacemakers can lead to their coordinated behavior (synchronization). Two pacemaker cells can synchronize at simple harmonic (i.e., 1:1, 2:1, etc.) or more complex ratios (3:2, 5:3, etc.), depending on the differences in intrinsic frequencies and the degree of electrical coupling between cells. Simulations using larger numbers of linearly connected cells yielded various patterns of pacemaker activity including 2:1 sinoatrial block and complex dysrhythmic activity. The overall results may be used to predict higher order interactions of thousands of cells comprising the sinus node. Under such a scheme, synchronization occurs not by the conducted influence of a dominant pacemaker cell, but by the mutual "democratic" interaction of individual pacemaker cells.

This article has been cited by other articles:

				J. P. Fahrenbach, R. Mejia-Alvarez, and K. Banach The relevance of non-excitable cells for cardiac pacemaker function J. Physiol., December 1, 2007; 585(2): 565 - 578. [Abstract] [Full Text] [PDF]

				H.-S. Chang, K. Staras, and M. P. Gilbey Multiple Oscillators Provide Metastability in Rhythm Generation J. Neurosci., July 1, 2000; 20(13): 5135 - 5143. [Abstract] [Full Text] [PDF]

				K. F. Kwong, R. B. Schuessler, K. G. Green, J. G. Laing, E. C. Beyer, J. P. Boineau, and J. E. Saffitz Differential Expression of Gap Junction Proteins in the Canine Sinus Node Circ. Res., March 23, 1998; 82(5): 604 - 612. [Abstract] [Full Text] [PDF]

				E. E. Verheijck, R. Wilders, R. W. Joyner, D. A. Golod, R. Kumar, H. J. Jongsma, L. N. Bouman, and A. C.G. v. Ginneken Pacemaker Synchronization of Electrically Coupled Rabbit Sinoatrial Node Cells J. Gen. Physiol., January 1, 1998; 111(1): 95 - 112. [Abstract] [Full Text] [PDF]

				Zeng Wanzhen, L. Glass, and A. Shrier The Topology of Phase Response Curves Induced by Single and Paired Stimuli in Spontaneously Oscillating Chick Heart Cell Aggregates J Biol Rhythms, July 1, 1992; 7(2): 89 - 104. [Abstract] [PDF]

				R. Traub, R Miles, and R. Wong Model of the origin of rhythmic population oscillations in the hippocampal slice Science, March 10, 1989; 243(4896): 1319 - 1325. [Abstract] [PDF]