Gao Juan, Holmes Philip
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.
J Comput Neurosci. 2007 Feb;22(1):39-61. doi: 10.1007/s10827-006-9676-3. Epub 2006 Sep 19.
We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators.
我们研究了通过缝隙连接和抑制性突触耦合的无噪声神经元的动力学和分岔，使用延迟δ函数和α函数对后者进行建模。如同Chow和Kopell（2000年）以及Lewis和Rinzel（2003年）的研究那样，我们重点关注两个细胞的情况，但同时也表明，对于由亚阈值电耦合主导的N个细胞的全局耦合网络，稳定的异步展开状态是存在的。在弱耦合范围内，我们的结果与Lewis和Rinzel（2003年）的结果一致，但我们的庞加莱映射分析产生了更多关于全局行为和吸引域的信息，并且我们表明，使用延迟δ函数导出的显式不连续映射与从α函数导出的连续历史依赖的隐式定义映射相比效果良好。我们发现，增加偏置电流、超阈值电耦合和突触延迟会促进同步，而亚阈值电耦合和快速突触会促进异步。我们将我们的分析结果与尖峰细胞离子电流模型的模拟进行了比较，并简要讨论了对蓝斑刺激反应模式和中枢模式发生器的影响。
