Lemieux D R, Roberge F A, Joly D
Institute of Biomedical Engineering, Ecole Polytechnique, Montréal, Québec, Canada.
J Theor Biol. 1992 Feb 7;154(3):335-58. doi: 10.1016/s0022-5193(05)80175-4.
The purpose of this paper is to examine the dynamic features of the electrogenic Na,K pump of cardiac cells, based on a comparative analysis of a mechanistic model and an ad hoc mathematical description of the Na,K pump. Both representations are incorporated into a modified version of the Beeler-Reuter model for the ventricular membrane, and the resulting action potential models are studied under conditions of repetitive stimulation at steady rates between 0 and 3 Hz. The two Na,K pump representations have nearly identical steady-state characteristics of sensitivity to internal Na+ concentration, external K+ concentration, and membrane potential. Rapid voltage-dependent transient pump currents are present in the mechanistic model, while they are absent in the ad hoc mathematical description we used. The stimulation results show that a sizable peak of pump current caused by the action potential upstroke in the mechanistic model affects phase 1 repolarization, and that this effect is relatively independent of the stimulation rate. The pump current generated by our ad hoc mathematical description is constant during the action potential and does not affect directly the repolarization time course. While the two Na,K pump models show similar pumping efficiency at low stimulation rates, the mechanistic pump is more efficient at high rates of activity. In essence, the distinctive features of the mechanistic model are due to an energy barrier expressing the voltage dependence of the translocation step of the mechanism, and to the redistribution of the intermediates of the biochemical reactions during activity. In comparison, the ad hoc mathematical description exhibits a fixed dependence of the pump current on voltage and ionic concentrations.
本文的目的是基于对钠钾泵的机制模型和特设数学描述的比较分析，研究心脏细胞电生钠钾泵的动态特征。这两种表述都被纳入了心室膜的Beeler-Reuter模型的修改版本中，并在0至3Hz的稳定速率重复刺激条件下研究由此产生的动作电位模型。这两种钠钾泵表述对细胞内钠离子浓度、细胞外钾离子浓度和膜电位的敏感性具有几乎相同的稳态特征。机制模型中存在快速电压依赖性瞬态泵电流，而在我们使用的特设数学描述中则不存在。刺激结果表明，机制模型中动作电位上升引起的泵电流的相当大的峰值影响1期复极化，并且这种影响相对独立于刺激速率。我们的特设数学描述产生的泵电流在动作电位期间是恒定的，并且不直接影响复极化时间进程。虽然这两种钠钾泵模型在低刺激速率下显示出相似的泵浦效率，但机制泵在高活动速率下更有效。本质上，机制模型的独特特征归因于一个能量屏障，它表达了该机制转运步骤对电压的依赖性，以及活动期间生化反应中间体的重新分布。相比之下，特设数学描述表现出泵电流对电压和离子浓度的固定依赖性。
