Xu Kesheng, Maidana Jean P, Caviedes Mauricio, Quero Daniel, Aguirre Pablo, Orio Patricio
Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso Valparaíso, Chile.
Departamento de Matemática, Universidad Técnica Federico Santa María Valparaíso, Chile.
Front Comput Neurosci. 2017 Mar 10;11:12. doi: 10.3389/fncom.2017.00012. eCollection 2017.
In this article, we describe and analyze the chaotic behavior of a conductance-based neuronal bursting model. This is a model with a reduced number of variables, yet it retains biophysical plausibility. Inspired by the activity of cold thermoreceptors, the model contains a persistent Sodium current, a Calcium-activated Potassium current and a hyperpolarization-activated current (I) that drive a slow subthreshold oscillation. Driven by this oscillation, a fast subsystem (fast Sodium and Potassium currents) fires action potentials in a periodic fashion. Depending on the parameters, this model can generate a variety of firing patterns that includes bursting, regular tonic and polymodal firing. Here we show that the transitions between different firing patterns are often accompanied by a range of chaotic firing, as suggested by an irregular, non-periodic firing pattern. To confirm this, we measure the maximum Lyapunov exponent of the voltage trajectories, and the Lyapunov exponent and Lempel-Ziv's complexity of the ISI time series. The four-variable slow system (without spiking) also generates chaotic behavior, and bifurcation analysis shows that this is often originated by period doubling cascades. Either with or without spikes, chaos is no longer generated when the I is removed from the system. As the model is biologically plausible with biophysically meaningful parameters, we propose it as a useful tool to understand chaotic dynamics in neurons.
在本文中，我们描述并分析了一个基于电导的神经元爆发模型的混沌行为。这是一个变量数量减少的模型，但仍保留了生物物理合理性。受冷觉感受器活动的启发，该模型包含一个持续性钠电流、一个钙激活钾电流和一个超极化激活电流（I），它们驱动一个缓慢的阈下振荡。在这个振荡的驱动下，一个快速子系统（快速钠电流和钾电流）以周期性方式发放动作电位。根据参数的不同，该模型可以产生多种发放模式，包括爆发式、规则紧张性和多模式发放。我们在此表明，不同发放模式之间的转变通常伴随着一系列混沌发放，这由不规则的非周期性发放模式所暗示。为了证实这一点，我们测量了电压轨迹的最大李雅普诺夫指数，以及ISI时间序列的李雅普诺夫指数和莱姆尔 - 齐夫复杂度。四变量慢系统（无动作电位发放）也会产生混沌行为，分岔分析表明这通常源于倍周期级联。无论有无动作电位发放，当从系统中移除电流I时，混沌不再产生。由于该模型在生物学上具有合理性且参数具有生物物理意义，我们将其作为理解神经元混沌动力学的一个有用工具提出。
