School of Mathematics, Queen Mary University of London, London, United Kingdom.
Laboratory of Cardiovascular Science, Biomedical Research Center, Intramural Research Program, National Institute on Aging, NIH, Baltimore, Maryland.
Biophys J. 2019 Jun 4;116(11):2212-2223. doi: 10.1016/j.bpj.2019.04.031. Epub 2019 May 3.
Heart muscle contraction is normally activated by a synchronized Ca release from sarcoplasmic reticulum (SR), a major intracellular Ca store. However, under abnormal conditions, Ca leaks from the SR, decreasing heart contraction amplitude and increasing risk of life-threatening arrhythmia. The mechanisms and regimes of SR operation generating the abnormal Ca leak remain unclear. Here, we employed both numerical and analytical modeling to get mechanistic insights into the emergent Ca leak phenomenon. Our numerical simulations using a detailed realistic model of the Ca release unit reveal sharp transitions resulting in Ca leak. The emergence of leak is closely mapped mathematically to the Ising model from statistical mechanics. The system steady-state behavior is determined by two aggregate parameters: the analogs of magnetic field (h) and the inverse temperature (β) in the Ising model, for which we have explicit formulas in terms of SR [Ca] and release channel opening and closing rates. The classification of leak regimes takes the shape of a phase β-h diagram, with the regime boundaries occurring at h = 0 and a critical value of β (β) that we estimate using a classical Ising model and mean field theory. Our theory predicts that a synchronized Ca leak will occur when h > 0 and β >β, and a disordered leak occurs when β <β and h is not too negative. The disorder leak is distinguished from synchronized leak (in long-lasting sparks) by larger Peierls contour lengths, an output parameter reflecting degree of disorder. Thus, in addition to our detailed numerical model approach, we also offer an instantaneous computational tool using analytical formulas of the Ising model for respective ryanodine receptor parameters and SR Ca load that describe and classify phase transitions and leak emergence.
心肌收缩通常是通过肌浆网（SR）的同步 Ca 释放激活的，肌浆网是主要的细胞内 Ca 储存库。然而，在异常情况下，Ca 从 SR 泄漏，导致心脏收缩幅度减小，并增加发生危及生命的心律失常的风险。导致异常 Ca 泄漏的 SR 操作机制和方案仍不清楚。在这里，我们采用数值和分析建模来深入了解新兴的 Ca 泄漏现象的机制。我们使用 Ca 释放单元的详细现实模型进行的数值模拟揭示了导致 Ca 泄漏的急剧转变。泄漏的出现与统计力学中的伊辛模型在数学上紧密相关。系统稳态行为由两个聚合参数决定：伊辛模型中的磁场（h）和逆温度（β）的类似物，对于这两个参数，我们有 SR [Ca]和释放通道打开和关闭速率的显式公式。泄漏区的分类采用β-h 相图的形状，泄漏区的边界出现在 h = 0 和β的临界值（β）处，我们使用经典伊辛模型和平均场理论来估计β。我们的理论预测，当 h > 0 且β>β时，将发生同步 Ca 泄漏，当β<β且 h 不太负时，将发生无序泄漏。无序泄漏与同步泄漏（在长时间火花中）的区别在于较大的佩尔尔斯轮廓长度，该输出参数反映了无序程度。因此，除了我们详细的数值模型方法外，我们还提供了一种使用伊辛模型的解析公式的即时计算工具，用于描述和分类相应的肌浆网钙负荷和 Ryanodine 受体参数的相转变和泄漏出现。
