Elsevier

Neural Networks

Volume 98, February 2018, Pages 42-50
Neural Networks

Intrinsic sodium currents and excitatory synaptic transmission influence spontaneous firing in up and down activities

https://doi.org/10.1016/j.neunet.2017.10.008Get rights and content

Abstract

Periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity. These kinds of oscillations always accompany with some spontaneous firing in up state. Our previous theoretical studies mainly looked at the subthreshold up and down transitions and characteristics of up and down dynamics. In this paper, we focus on suprathreshold spontaneous firing of up and down transitions based on improved network model and its stimulations. The simulated results indicate that fast sodium current is critical to the generation of spontaneous neural firing. While persistent sodium current plays a part in spontaneous fluctuation. Both intrinsic fast and persistent sodium dynamics influence spontaneous firing rate and synchronous activity in up and down behavior. Meanwhile, blocking excitatory synaptic transmission decreases neural firing and reveals spontaneous firing. These simulated results are basically in accordance with experimental results. Through the observation and analysis of the findings, we prove the validity of the model so we can further adopt this model to study other properties and characteristics of the network, laying the foundation for further work on cortex activity.

Introduction

Periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity. Neural electrophysiology experiments have shown that membrane potentials make spontaneous transitions between two different levels called up and down states (Parga & Abbott, 2007) in the primary visual cortex of anesthetized animals Anderson et al. (2000), Lampl et al. (1999), Steriade et al. (1993) and also in the somatosensory cortex of unanesthetized animals (Petersen, Hahn, Mehta, Grinvald, & Sakmann, 2003).

These two states characterize the bistability of the membrane potentials, which is an important feature of neural system, accompanying with complex nonlinear dynamics Jun & Tang (2015), Ma & Tang (2017), Ma & Xu (2015). Further, recordings in vivo show up and down transitions occur synchronously Lampl et al. (1999), Stern et al. (1998). In neurodynamical system, synchronized transition often indicates formation of spatial pattern Gu & Pan (2015), Tao et al. (2017), Xiao et al. (2016), Zhao & Gu (2015).

Another characteristic of up and down transitions is that these kinds of oscillations always accompany with some spontaneous firing in up state. Intracellular recordings in vivo showed that the slow oscillationis mediated by two phases: a period in which nearly all cell types within the cerebral cortex are depolarized and generate action potentials at a low rate (the so-called up state) interdigitated with a period of hyperpolarization and relative inactivity (the down state) (A, MV, DA, & X-J, 2003). So in this paper, our study adds to the literature describing the spontaneous firing of up and down activities.

We previously worked on spontaneous up and down transitions and tried to explain the dynamic mechanism involved in these transitions at the ionic channel level. At the single neuron level, we introduced three significant characteristics – bistability, directivity and spontaneity – of a single neuron up and down transitions (Xu & Wang, 2014) [p] and at the network level with constant connections, the cortical average membrane potential adopted as the local field potential (LFP) also showed up and down transitions over time (Xu & Wang, 2013). LFP is often used to describe the state of the whole cortex Liu et al. (2010), Wang & Zhang (2007), Wang et al. (2009). Further, we put forward a neural network model of spontaneous up and down transitions, which reflects the in vivo mechanism better (Xu, Ni, & Wang, 2016). Using this model, we explored the factors that influence spontaneous periodic up and down transitions and synchronous transitions of up and down activities based on stimulations Xu et al. (2016), Xu et al. (2017).

In this paper, we focused on the spontaneous firing during up and down transitions and improved our previous work by adding fast sodium current to model neurons, to simulate the small amount of action potentials during up state. We found that the fast sodium dynamics was critical to the generation of spontaneous neural firing during up and down activities. While persistent sodium current played a role in spontaneous fluctuation. Both intrinsic fast and persistent sodium dynamics influence spontaneous firing rate and synchronous activity in up and down behavior. Meanwhile, blocking excitatory synaptic transmission decreased neural firing and revealed spontaneous firing. These simulated results are basically in accordance with experimental results.

Section snippets

Model neurons

In this paper, we considered a neural network connected by both excitatory and inhibitory neurons.

For the excitatory neurons, the main dynamical equation is described by CdVidt=INaF(Vi)INaP(Vi)Ih(Vi,hi)IK(Vi,bi)Il(Vi)IAMPA(Vi,sAMPAi)INMDA(Vi,sNMDAi)IGABAA(Vi,sGABAAi).

For the inhibitory neurons, the main equation is given by CdVidt=INaF(Vi)INaP(Vi)Ih(Vi,hi)IK(Vi,bi)Il(Vi)IAMPA(Vi,sAMPAi)INMDA(Vi,sNMDAi).

Where, the intrinsic currents, INaF, INaP, Ih,

Fast sodium current is critical to the generation of spontaneous neural firing during up and down activities

In this section, we chose 1000 neurons as the size of the model network, with the ratio of excitatory neurons to inhibitory neurons 4:1, and the topology introduced in section above. According to the network model, the simulation results exhibited spontaneous up and down transitions of membrane potential of a single neuron without any external stimulation or noise, as shown in Fig. 2. The difference between Fig. 2 (A)(B) and Fig. 2 (C)(D) is whether the neurons in the network have fast sodium

Conclusion

In a summary, this paper mainly discussed about the factors that influence the spontaneous firing of up and down states of neurons in the network by adopting an improved dynamic network model based on our previous research.

The first factor studied with the model was the intrinsic sodium dynamics. Fast sodium current was critical to the generation of spontaneous neural firing. While persistent sodium current was critical in spontaneous fluctuation without any stimulation or noise. With presence

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11232005 and 11702096) and the Fundamental Research Funds for the Central Universities (No. 222201714020).

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