Extreme synchronization events in a model neuron-astrocyte network
Authors: Tsybina Yu. A. , Kastalskiy I. A. , Andreev A. V. , Frolov N. S. , Hramov A. E. , Gordleeva S. Yu. 
Published: May 2024

The examination of synchronization in neural networks is essential to comprehend how the brain functions in normal and pathological states. The synchronization of signals between groups of neurons is paramount for brain activity and associated with various brain functions, including memory, movement, sleep, and attention. However, a balance between synchronization and desynchronization must be maintained for proper brain function. During epilepsy, spontaneous transitions occur between two states of brain activity: synchronous and asynchronous. These transitions can be induced by various factors, including imbalances in chemical signals, changes in network activity, and other mechanisms that are not yet fully understood. Understanding these spontaneous transitions and the underlying mechanisms is a crucial aspect of epilepsy research. It will lead to the development of novel treatment approaches and strategies for inhibiting synchronized activity and averting seizure episodes.
A neuron-astrocyte network model was constructed in this study, which displayed spontaneous and induced transitions between asynchronous and synchronous states triggered by external stimuli. The network model utilized 1000 Izhikevich neurons [1] interconnected with excitatory synapses and organized according to a scale-free graph. Each neuron had a bidirectional interaction with a single astrocyte, resulting in a total of 1000 astrocytes in the network. The Ullah model [2] simulated intracellular calcium ion concentration dynamics in a single astrocyte. The action potential generated by a neuron causes the release of neurotransmitters into the synaptic cleft, which triggers the corresponding astrocyte to release calcium ions from its endoplasmic reticulum into the cytoplasm, generating a calcium impulse. The calcium pulse within the astrocyte led to the release of a gliotransmitter. This gliotransmitter has the potential to regulate the synaptic transmission efficiency of both presynaptic and postsynaptic terminals associated with the respective astrocyte. The study simulated the effect of astrocytic suppression on neurotransmitter release. The strength of the synaptic input connection to the neuron that interacts with the astrocyte decreased in proportion to the amplitude of the calcium pulse in the astrocyte.
Within the context of the implemented model study, we analyzed the global order parameter’s dependence on the maximum synaptic weight. Our bifurcation analysis showed the presence of hysteresis within a specific range of parameter values for connection weight maximums. In this range, the system under consideration is capable of displaying both synchronous and asynchronous regimes. However, an asynchronous regime was the only observed outcome below the lower boundary of the range, and only a synchronous regime was observed above the upper boundary. A statistical analysis was carried out on the duration of the model’s asynchronous states, specifically for the parameter value of the maximum synaptic weight near the upper boundary of the hysteresis region. The network dynamics were simulated for a prolonged period, and a histogram of the asynchronous state durations was plotted on a double logarithmic scale. The resulting data points were approximated using linear regression, which yielded a power-law exponent of –3/2.
Based on the obtained results, the neuron-astrocyte network can exhibit spontaneous transitions between two states: synchronous and asynchronous, similar to pathological processes in the brain. More precisely, the power-law exponent of –3/2 aligns with values discovered in experimental recordings of epileptic activity in rodent brains [3–5]. Detailed modeling of biophysical processes revealed the spontaneous emergence of global order in the network induced by noise. Astrocytic effects mediated the disruption of synchronization in the neural network by reducing the efficiency of synaptic transmission.