Gong Pulin, Loi S T C, Robinson P A, Yang C Y J
School of Physics, University of Sydney, Sydney, NSW 2006, Australia.
Biol Cybern. 2013 Feb;107(1):1-13. doi: 10.1007/s00422-012-0518-2. Epub 2012 Sep 18.
Refractoriness is one of the most fundamental states of neural firing activity, in which neurons that have just fired are unable to produce another spike, regardless of the strength of afferent stimuli. Another essential and unavoidable feature of neural systems is the existence of noise. To study the role of these essential factors in spatiotemporal pattern formation in neural systems, a spatially expended neural network model is constructed, with the dynamics of its individual neurons capturing the three most essential states of the neural firing behavior: firing, refractory and resting, and the network topology consistent with the widely observed center-surround coupling manner in the real brain. By changing the refractory period with and without noise in a systematic way in the network, it is shown numerically and analytically that without refractoriness, or when the refractory period is smaller than a certain value, the collective activity pattern of the system consists of localized, oscillating patterns. However, when the refractory period is greater than a certain value, crescent-shaped, localized propagating patterns emerge in the presence of noise. It is further illustrated that the formation of the dynamical spiking patterns is due to a symmetry breaking mechanism, refractoriness-induced symmetry breaking; that is generated by the interplay of noise and refractoriness in the network model. This refractoriness-induced symmetry breaking provides a novel perspective on the emergence of localized, spiking wave patterns or spike timing sequences as ubiquitously observed in real neural systems; it therefore suggests that refractoriness may benefit neural systems in their temporal information processing, rather than limiting the performance of neurons, as has been conventionally thought. Our results also highlight the importance of considering noise in studying spatially extended neural systems, where it may facilitate the formation of spatiotemporal order.
不应期是神经放电活动最基本的状态之一，在此状态下，刚放电的神经元无法产生另一个动作电位，无论传入刺激的强度如何。神经系统另一个基本且不可避免的特征是噪声的存在。为了研究这些基本因素在神经系统时空模式形成中的作用，构建了一个空间扩展神经网络模型，其单个神经元的动力学捕捉神经放电行为的三个最基本状态：放电、不应期和静息期，并且网络拓扑结构与真实大脑中广泛观察到的中心 - 周边耦合方式一致。通过在网络中有系统地改变有无噪声情况下的不应期，数值和分析结果表明，没有不应期，或者当不应期小于某个值时，系统的集体活动模式由局部振荡模式组成。然而，当不应期大于某个值时，在有噪声的情况下会出现新月形的局部传播模式。进一步说明动态尖峰模式的形成是由于一种对称性破缺机制，即不应期诱导的对称性破缺；这是由网络模型中噪声和不应期的相互作用产生的。这种不应期诱导的对称性破缺为在真实神经系统中普遍观察到的局部尖峰波模式或尖峰时间序列的出现提供了一个新的视角；因此表明不应期可能有利于神经系统进行时间信息处理，而不是像传统认为的那样限制神经元的性能。我们的结果还强调了在研究空间扩展神经系统时考虑噪声的重要性，在这种情况下噪声可能有助于时空秩序的形成。
