论文标题
确切的平均场理论解释了电突触在集体同步中的双重作用
Exact mean-field theory explains the dual role of electrical synapses in collective synchronization
论文作者
论文摘要
电突触在设置神经元同步方面起着重要作用，但是这些突触有助于同步的精确机制是微妙的，并且仍然难以捉摸。最近提出了这些机制的二次整合神经元的平均场理论。尽管如此，这些理论的有效性还是有争议的，因为它们假设神经元会产生不现实的对称尖峰，从而忽略了峰值形状对同步的众所周知的影响。在这里，我们表明，在这种理论中可以放松对称尖峰的假设。由此产生的平均场方程揭示了电突触的双重作用：首先，它们均衡膜电位有利于同步的出现。其次，电突触充当“虚拟化学突触”，根据尖峰形状，可以是兴奋性的或抑制性的。我们的结果提供了电气突触在集体同步中的复杂作用的精确数学解释。这与以前的理论和数字作品进行了核对，并确认了最近低维均值场理论来研究电耦合神经元网络的适合性。
Electrical synapses play a major role in setting up neuronal synchronization, but the precise mechanisms whereby these synapses contribute to synchrony are subtle and remain elusive. To investigate these mechanisms mean-field theories for quadratic integrate-and-fire neurons with electrical synapses have been recently put forward. Still, the validity of these theories is controversial since they assume that the neurons produce unrealistic, symmetric spikes, ignoring the well-known impact of spike shape on synchronization. Here we show that the assumption of symmetric spikes can be relaxed in such theories. The resulting mean-field equations reveal a dual role of electrical synapses: First, they equalize membrane potentials favoring the emergence of synchrony. Second, electrical synapses act as "virtual chemical synapses", which can be either excitatory or inhibitory depending upon the spike shape. Our results offer a precise mathematical explanation of the intricate effect of electrical synapses in collective synchronization. This reconciles previous theoretical and numerical works, and confirms the suitability of recent low-dimensional mean-field theories to investigate electrically coupled neuronal networks.
