Neural dynamic transitions caused by changes of synaptic strength in heterogeneous networks

Sleep-dependent memory consolidation (SDMC) is an unaddressed and challenging functional issue regarding neural dynamics. Based on experimental findings, the synaptic homeostasis hypothesis for understanding SDMC implies a link between changes of synaptic strength and transitions of neural dynamics (including tonic and bursting activities). However, the causality of the link has been unclear. Recently, it has been found that, the synaptic changes can cause the dynamical transitions and so can produce the slow-wave activity (SWA) similar to that observed during sleep in a homogeneous network (Zhou et al., 2021). Since many real neural networks are heterogeneous in topology, we herein further investigated the transitions and the SWA driven by the synaptic changes in heterogeneous networks. It was found that synaptic changes can also cause the dynamical transitions and the SWA. Differently, the transitions in heterogeneous networks are hierarchical for neurons with different degrees, whether in electrically or chemically coupled networks. The critical synaptic strengths related to the transitions for neurons depend strongly on their degrees. The larger the degree, the smaller the critical synaptic strength. We showed that, they obey power-law relations, both in electrically coupled networks and in chemically coupled networks in the presence of inhibitory synapses. Particularly, it was found that the networked critical synaptic strength depends only on the networked maximum degree in electrically coupled networks. We showed, both numerically and analytically, that they also satisfy a power-law function. In general, our study revealed a possible causal relationship between changes of synaptic strength and transitions of neural dynamics in heterogeneous networks. Further interesting and challenging investigations are briefly discussed as well.