Cantalapiedra Inma R, Alvarez-Lacalle Enrique, Peñaranda Angelina, Echebarria Blas
Departament de Física. Universitat Politècnica de Catalunya, Av Dr. Marañon 50 (EPSEB), Barcelona, Spain.
Chaos. 2017 Sep;27(9):093928. doi: 10.1063/1.5000709.
In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.
在心脏中，快速的起搏频率可能会诱发心脏收缩强度的交替变化，称为交替脉。通常，这是由于细胞内钙浓度动态变化的不稳定性所致，其瞬变在连续的心跳中变得越来越大或越来越小。这种交替变化在实验和理论上与两种不同的机制有关：一种不稳定性是由于（1）钙释放对肌浆网（SR）负荷的强烈依赖性，以及钙重新摄取到SR中的速度较慢，或者（2）由于兰尼碱受体（RyR2）从失活状态缓慢恢复而导致的SR释放不应期。钙交替变化与RyR2不应期之间的关系比相应的SR钙负荷机制更难以捉摸。为了研究前者，我们将一个模拟钙释放单元确定性演化的通用钙模型简化为其最基本的要素。我们表明，可以使用一个关于二元空间中钙浓度的简单非线性方程，结合一个关于恢复的RyR2数量的弛豫方程来理解钙交替变化。根据刺激开始时恢复的RyR2数量，钙浓度的增加可能会超过或未超过一个限制大钙瞬变发生的兴奋性阈值。当RyR2的恢复缓慢时，这自然会产生倍周期分岔，导致钙交替变化。然后，我们研究失活、钙扩散和释放电导对交替变化起始的影响。我们发现，交替变化的发展需要一个明确的扩散值，而它对失活或释放电导的值不太敏感。
