Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking:: insights from stability and bifurcation analyses of a mathematical model
Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking:: insights from stability and bifurcation analyses of a mathematical model
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DOI：
10.1152/ajpheart.01050.2002
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发表时间：
2003-12-01
影响因子：
4.8
通讯作者：
Shibamoto, T
中科院分区：
文献类型：
--
作者：
Kurata, Y;Hisatome, I;Shibamoto, T
为了阐明窦房结起搏活动的动力学机制，我们通过对家兔窦房结模型的稳定性和分叉分析，研究了L型Ca ~（2+）（I-Ca，I-L）和延迟整流K ~+（I-Kr）电流在起搏中的作用。Am J Physiol Heart Circ Physiol 283：H2074-H2101，2002）。平衡点（EPs），周期轨道，EPs的稳定性，和Hopf分岔点作为函数的电导或门控时间常数的电流构建分岔图计算。结构稳定性（鲁棒性）的系统也进行了评估，通过计算稳定性和动态过程中的应用程序的恒定偏置电流（I-偏置）。阻断I-Ca、I-L或I-Kr引起EP稳定，并通过Hopf分叉停止起搏。用Ibias确定的不稳定的零电流电位区出现自发振荡，随着I-Ca，I-L的减小，该区域缩小并最终消失，但当I-Kr被消除时，该区域几乎不缩小。还原系统除I-Ca、I-L外无时间依赖性电流，显示起搏活动。这些结果表明，I-Ca，I-L是EP不稳定和起搏产生的原因，而I-Kr不是构建起搏细胞系统所必需的。我们进一步探讨了具有不同动力学的各种K+电流对模型细胞的稳定性和动力学的影响。延迟激活和内向整流的原始I-Kr似乎最有利于产生具有稳定频率的大振幅振荡，这表明I-Kr充当振荡放大器和频率稳定器。I-Kr也可能在阻止系统分岔到静止中起重要作用。
To elucidate the dynamical mechanisms of the sinoatrial (SA) node pacemaker activity, we investigated the roles of L-type Ca2+ (I-Ca,I- L) and delayedrectifier K+ (I-Kr) currents in pacemaking by stability and bifurcation analyses of our rabbit SA node model (Kurata Y, Hisatome I, Imanishi S, and Shibamoto T. Am J Physiol Heart Circ Physiol 283: H2074-H2101, 2002). Equilibrium points (EPs), periodic orbits, stability of EPs, and Hopf bifurcation points were calculated as functions of conductance or gating time constants of the currents for constructing bifurcation diagrams. Structural stability ( robustness) of the system was also evaluated by computing stability and dynamics during applications of constant bias currents (I-bias). Blocking I-Ca,I- L or I-Kr caused stabilization of an EP and cessation of pacemaking via a Hopf bifurcation. The unstable zero-current potential region determined with Ibias applications, where spontaneous oscillations appear, shrunk and finally disappeared as I-Ca,I- L diminished, but shrunk little when I-Kr was eliminated. The reduced system, including no time-dependent current except I-Ca,I- L, exhibited pacemaker activity. These results suggest that I-Ca,I- L is responsible for EP instability and pacemaker generation, whereas I-Kr is not necessarily required for constructing a pacemaker cell system. We further explored the effects of various K+ currents with different kinetics on stability and dynamics of the model cell. The original I-Kr of delayed activation and inward rectification appeared to be most favorable for generating large-amplitude oscillations with stable frequency, suggesting that I-Kr acts as an oscillation amplifier and frequency stabilizer. I-Kr may also play an important role in preventing bifurcation to quiescence of the system.