The neuronal system is composed of a large number of neurons and astrocytes and it is confirmed that astrocytes can play important role in regulating the electric modes of activities1,2,3,4. Most of the neuronal models mainly emphasize the dynamical properties of electric activities and often bifurcation parameters are carefully adjusted to trigger possible mode transition in electrical activities. These models are helpful to understand the synchronization problems of neurons. Gu et al. proposed a neuronal model to detect the possible dynamical behavior of a sciatic nerve chronic constriction injury model5. Multiple modes can be observed in neuronal activities, Gu et al. investigated the dependence of model selection on bifurcation parameter and initials selection6. Furthermore, Ma et al. proposed an improved model to describe the emergence and transition of multiple modes in electric activities by introducing magnetic flux in the original Hindmarsh-Rose neuron according to electromagnetic induction effect7,8. Some intermediate neurons are connected with autapse, a specific autapse connected to the body of neuron, which counts the emergence of intrinsic time delay in neuron9. The previous works confirmed that autapse connection plays important biological function by regulating the electric activities of isolate neuron and collective behaviors of neuronal network as pacemakers10,11,12,13,14,15,16,17. Particularly, coupling between neurons and astrocytes could be more reliable to understand the complex behavior of neuronal systems.

Over the past decades, our understanding of astrocytes has fundamentally changed: they were first considered as passive cells before being subsequently recognized as biologically excitable cells1,2. One form of excitability is a change in intracellular Ca2+ concentration, which occurs both spontaneously and in response to the neuronal activity3,4. Consequently, an elevation of Ca2+ concentration can induce a release of gliotransmitters from astrocytes in a Ca2+ -dependent manner18,19. Here, astrocytic glutamate (AG) is one of the major gliotransmitters and exerts its signal transducing effect on neurons via N-methyl-D-aspartic acid (NMDA) receptors20,21. Finally, astrocytes can “listen” and respond to neurons in a “tripartite synapse” loop (i.e., an astrocyte-neuron feedback loop)22,23.

Recent studies showed that the normal function of astrocytes is to support some physiological functions, such as neuronal synaptic information processing24,25,26,27 or synaptic plasticity28.

In an experimental study by Tian et al. in 200529, the authors suggested that astrocytes may contribute to the neuronal depolarization underlying epilepsy. Also, Fellin et al. challenged the traditional concept that synchronous neuronal activity during seizures arises from an entirely neuronal origin, since they found that astrocytes can also induce synchronous neuronal activity30,31. Therefore, some scientists have proposed that astrocytes are likely to be potential targets for anti-epileptic therapeutic strategies32. Although astrocytes have been reported to play a potential role in epileptic seizure, the underlying causes are diverse and not completely understood33,34.

Computational modeling has been widely used for understanding the dynamics of neurons and neuronal networks35,36,37 and those dynamic characteristics of neurons predicted by modeling analysis were also proved in experimental results38,39, which verifies the significance of modeling analysis of neurons. These computational methods are also used to identify the impaired neurons underlying epilepsy40,41,42 and in recent years some models have been developed to study the astrocyte-induced epilepsy43,44,45,46,47. In the study of Nardkarni et al., a two-compartment neuron-astrocyte model was established to account for epilepsy in these experiments, when the astrocytic neurotransmitter receptors were over-expressed43,44. Some other neuron-astrocyte models have been developed to investigate the synchrony network epilepsy which is induced by an AG release45. However, few studies have paid attention to the relation between the different dynamic phases of the AG and epilepsy. Recent experiments have shown that a large amount of glutamate transporters are located in the astrocyte to uptake the AG48,49 and that a low-efficiency hydrolysis may trigger an epileptic seizure50. However, to the best of our knowledge, this effect has not been considered in previous modeling studies. Thus we investigated how the uptake-related AG decay process can affect the seizure dynamics.

In this paper, we incorporated the dynamics model of AG, which could well describe the decay process of AG, into a classical astrocyte-neuron feedback loop model44 in order to investigate how a low-efficiency AG decay affects the generation of seizure-like discharge.

With this model, we explored how an increase of AG equilibrium concentration and decay period changes the regular neuronal spiking into a seizure-like discharge. In addition, we also analyzed different phases of seizure-like discharge and the corresponding AG concentration states. Finally, we also adopted the energy cost theory of Hodgkin-Huxley model51 to distinguish seizure-like discharge from normal spiking.