Nonlinear mechanism of excitatory autapse-induced reduction or enhancement of firing frequency of neuronal bursting

Abstract

Excitatory and inhibitory effect always induces the enhancement and inhibitory effect of neural electronic activities, which is the common viewpoint of the modulations to the neural firing and plays important roles in the information processing of the nervous system. In the present paper, the Homoclinic/Homoclinic bursting pattern with alternation behavior between burst containing multiple spikes and subthreshold oscillations and the tough value of the burst lower than that of the subthreshold oscillations is chosen as representative, and the excitatory effect on the complex nonlinear dynamics of the representative bursting pattern is studied. For the excitatory autapse with suitable autaptic time delay and strength, the autaptic current pulse applied to the trough of the burst can induce the number of spikes within a burst to decrease and then the average firing frequency to decline, which presents a novel example different from the common viewpoint of the excitatory effect. The excitatory autapse induces the average firing frequency to increase in the remained parameter region of two-parameter plane of the autaptic time delay and strength. With bifurcations acquired by the fast/slow variable dissection method and phase trajectory, the subthreshold oscillations of the bursting correspond to a subthreshold limit cycle of the fast subsystem and the spike within burst corresponds to a suprathreshold limit cycle, and excitatory autaptic current can induce the transition from suprathreshold limit cycle to subthreshold limit cycle, which leads the spike to terminate in advance and is the cause for reducing the average firing frequency. The results is the present paper are compared with the phenomenon and bifurcation mechanism that the excitatory autapse can induce the spike number to decrease within a burst but the average firing frequency to increase as indicated in a recent study on the Fold/Homoclinic bursting. These results enrich the uncommon phenomenon of the neuronal electrical activities, reveal the underlying nonlinear mechanism, provide a new way to regulate the bursting pattern, and disclose the potential functions of the excitatory autapse.

Fast autaptic feedback induced-paradoxical changes of mixed-mode bursting and bifurcation mechanism

“…自突触引起簇的结束相位-Homoclinic分岔点-右 移导致簇的参数区间变宽, 这就给出了反常现象的 动力学机制 [18] ; 而快兴奋性自突触则不能引起反 常现象、只能引起正常现象: 簇内放电个数增加、 平均放电频率增强 [51] . 实验和理论模型研究都已 经发现簇放电是具有多类模式的 [2,5] , 因此, 探寻不…”

“…(u, V ) The blue, pink, cyan-blue, and brown curves correspond to g = 0, g = 0.02, g = 0.03, and g = 0.04, respectively. 化的机制, 丰富了神经动力学的内涵 [17][18][19]21,24,27,28] .…”

“…以前研究较多关注了"Fold/Homoclinic"型簇放电 以及"Homoclinic/Homoclinic"型簇放电, 簇结束 于同宿分岔 [18,19,21,49,51] . 本文关注的混合簇放电属 于"Circle/Fold cycle"型簇放电, 复杂之处在于簇 结束后会进入去极化阻滞.…”

“…其次, 给出了快自突触诱发反常现象的新示例 和分岔机制. 对于Chay模型的"Fold/Homoclinic" 型簇放电, 只有抑制性快自突触能诱发簇放电的反 常现象: 放电增强, 兴奋性快自突触则诱发正常现 象, 也是放电增多 [18,51] . 而本文揭示了抑制性和兴 奋性作用都能诱发反常现象, 这就给出了反常现象 的新示例.…”

“…本文的反常现象不仅与以前的快自突触诱发的反 常现象不同 [18,51] , 与具有时滞的自突触(对应慢突 触)诱发的簇放电 [19,49,50] 和峰放电 [45,48] 的反常现 象也不同. 以前发现抑制性自突触在合适的时滞下 可以增强簇放电或时滞合适的兴奋性自突触可以 引起簇放电变弱 [19,49,45] .…”