Spiking synchronization of ion channel clusters on an axon

Ion channels are distributed in clusters in squid giant axons, rat retinal nerve fiber layers, pyramidal cell dendrites of Apteronotus, etc. Ion channel clusters along the unmyelinated axon generate spontaneous spiking due to ion channel noise. Ion channel clusters are coupled by the axonal cable, and spontaneous spiking of each ion channel cluster can be synchronized. This paper considers the spiking synchronization of two ion channel clusters coupled by an axon. It is shown that axonal parameters affect the spiking synchronization exponentially and ion channel clusters have maximal spiking synchronization when they have the same size. It is further shown that there is an optimal length of the ion channel clusters with maximal spiking synchronization and the optimal length accords with the length of the node of Ranvier in the myelinated axon.