TY - JOUR
T1 - Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks
T2 - A Mechanism for Multiscale Variability
AU - Liang, Junhao
AU - Zhou, Tianshou
AU - Zhou, Changsong
N1 - Funding Information:
This work was supported by the Hong Kong Baptist University (HKBU) Strategic Development Fund, the Hong Kong Research Grant Council (GRF12200217), the HKBU Research Committee and Interdisciplinary Research Clusters Matching Scheme 2018/19 (RC-IRCMs/18-19/SCI01), the National Natural Science Foundation of China (Grants Nos. 11775314, 91530320, and 11975194), and Key-Area Research and Development Program of Guangzhou (Grants No. 202007030004). This research was conducted using the resources of the High-Performance Computing Cluster Centre at HKBU, which receives funding from the RGC and the HKBU.
PY - 2020/11/26
Y1 - 2020/11/26
N2 - Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.
AB - Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.
KW - cortical dynamics
KW - criticality
KW - excitation-inhibition balance
KW - mean-field theory
KW - neuronal avalanches
UR - http://www.scopus.com/inward/record.url?scp=85097385425&partnerID=8YFLogxK
U2 - 10.3389/fnsys.2020.580011
DO - 10.3389/fnsys.2020.580011
M3 - Journal article
AN - SCOPUS:85097385425
SN - 1662-5137
VL - 14
JO - Frontiers in Systems Neuroscience
JF - Frontiers in Systems Neuroscience
M1 - 580011
ER -