Dynamical systems analysis of spike-adding mechanisms in transient bursts.
Dynamical systems analysis of spike-adding mechanisms in transient bursts.
复制标题
瞬态突发中尖峰添加机制的动力学系统分析。
DOI：
10.1186/2190-8567-2-7
复制
发表时间：
2012-04-24
影响因子：
2.3
通讯作者：
Tsaneva-Atanasova K
中科院分区：
文献类型：
--
作者：
Nowacki J;Osinga HM;Tsaneva-Atanasova K
神经元等可兴奋细胞的瞬间爆发行为是实验观察到的一个共同特征，但从理论上讲，人们对此还不太了解。我们分析了一个五维简化的后去极化模型，当受到短电流注入的扰动时，该模型表现出瞬时猝发行为。利用扰动轨道段的单参数延拓表示为适定边值问题，我们证明了尖峰添加机制是一种鸭式转变，它具有不同于已知的周期猝发解机制的特征。该模型的生物物理基础给出了自然的时间-尺度分离，这使得我们可以用几何奇异微扰理论来解释尖峰增加的机制，但它不像周期爆发那样涉及实际的分叉。我们证明，临界流形的不稳定薄片是由系统的鞍形平衡点形成的，这些鞍形平衡点只存在于奇异极限中，这是尖峰相加转变的原因；转变是由这个流形折叠附近的临界流形上的慢流组织的。我们的分析表明，尖峰相变期间的轨道段包括两个鞍型慢流形的不稳定薄片之间的快速过渡。我们还讨论了一种不同的参数机制，其中完整系统的附加鞍点平衡的存在改变了尖峰添加机制。
Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.