Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell

Model Status

This model was created from Version 01 by Penny Noble of Oxford University. Version 02 is known to run in COR and PCEnv. A PCEnv session is also associated with this model.

Model Structure

The pacemaker activity of the sinoatrial (SA) node initiates the spontaneous beating of the heart. Over the past decade a large body of data on the ionic currents underlying this pacemaker activity has been elucidated in patch-clamp experiments. On the basis of this data, several mathematical models describing the pace maker activity of a single rabbit SA node cell have been developed. These include:

• Demir et al. Sinoatrial Node Model, 1994;

• Modelling the Ion Currents Underlying Sinoatrial Node Pacemaker Activity, Dokos et al., 1996;

• A Model of Sinoatrial Node Vagal Control, Dokos et al., 1996;

• Demir et al. Sinoatrial Node Model, 1999;

• Zhang et al. Sinoatrial Node Model, 2000; and

• Boyett et al. Sinoatrial Node Model, 2001.

With the elucidation of more experimental data, these models have become increasingly complex, with equations that describe calcium buffering, intracellular compartmentation, and additional ionic currents through channels, pumps and exchangers. In the study by Kurata et al. described here, the aim is to develop an improved mathematical model of a single primary pacemaker cell of the rabbit SA node, in order to investigate the mechanisms underlying pacemaker generation. On the basis of the most recent experimental data, Kurata et al. updated the previously published models (see list above) in several ways:

• A sustained inward current has been added (I_st ).

• The voltage- and Ca²⁺-dependent activation kinetics of the L-type calcium channel current (I_Ca,L ) have been reformulated.

• Expressions for the activation kinetics of the rapidly activating delayed rectifier potassium current (I_Kr ) have been updated.

• Revised kinetic equations for two 4-AP sensitive currents (I_to and I_sus ) have been incorporated.

• Voltage- and concentration-dependent kinetics of the Na⁺-K⁺ pump current (I_NaK ) have been reformulated.

• The subsarcolemmal space (see the figure below) as a diffusion barrier for intracellular Ca²⁺ has been added.

The model was validated by comparing simulation results with experimental data, and also by comparing them with those of previous mathematical models. The authors concluded that their model represented a significant improvement over previous models because it can:

• Simulate whole cell voltage-clamp data for I_Ca,L , I_Kr , and I_st ;

• Reproduce the wave shapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and

• Mimic the effects of channel blockers or Ca ²⁺ buffers on pacemaker activity more accurately than the previous models.

The complete original paper reference is cited below:

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell, Yasutaka Kurata, Ichiro Hisatome, Sunao Imanishi, and Toshishige Shibamoto, 2002, American Journal of Physiology , 283, H2074-H2101. (Full text (HTML) and PDF versions of the article are available on the American Journal of Physiology website.) PubMed ID: 12384487

Schematic diagram depicting the intracellular compartments for Ca2+.