Mathematical Study of the Dynamical Cell Assembly Hypothesis as the Encoding Principle of the Brain

缝隙连接偶联抑制网络的时空动力学研究新皮层中的抑制神经元（FS/LTS细胞）是通过大量缝隙连接偶联的。这种间隙连接耦合系统在大脑中的编码和信息表征的动力学以及功能意义在很大程度上是未知的。我们从数学的角度研究了这种系统的动力学。主要结果是，具有A通道的I类神经元的间隙连接连接系统可能表现出广泛的时空混沌，这与Hodgkin-Huxley或FitzHugh-Nagumo神经元等II类神经元形成鲜明对比。这一结果的结果可以扩展到大脑的编码理论。此外，本研究结果与实验观察到的新皮层局部场电位的波动和同步性的关系可能是一个有趣的研究课题。目前正在编写关于本成果的报告。

Spatio-temporal dynamics of the inhibitory networks coupled by gap junctionsInhibitory neurons as FS/LTS cells in the neocortex are recently reported to be coupled by a vast amount of gap junctions. The dynamics as well as functional significance in the coding and information representation in the brain of such gap junction-coupled systems are largely unknown. We investigated the dynamics of such systems from a mathematical point of view. The main result is that gap junction-connected systems of Class I neurons with A-channels may exhibit an extensive spatio-temporal chaos, which shows a sharp contrast with Class II neurons like Hodgkin-Huxley or FitzHugh-Nagumo neurons. The consequence of this result could extend to the encoding theory of the brain. Also the relation of the present result with the experimentally observed fluctuation and synchrony in the local field potentials in the neocortex may be an interesting research subject. Reports of the present result are now under preparation.