Intrinsic sodium currents and excitatory synaptic transmission influence spontaneous firing in up and down activities
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
For the inhibitory neurons, the main equation is given by
Where, the intrinsic currents, , , ,
Fast sodium current is critical to the generation of spontaneous neural firing during up and down activities
In this section, we chose neurons as the size of the model network, with the ratio of excitatory neurons to inhibitory neurons , 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).
References (27)
- et al.
Synchronous membrane potential fluctuations in neurons of the cat visual cortex
Neuron
(1999) - et al.
An introduction and guidance for neurodynamics
Science Bulletin
(2015) - et al.
Energy coding and energy functions for local activities of the brain
Neurocomputing
(2009) - et al.
Synchronous transitions of up and down states in a network model based on stimulations
Journal of Theoretical Biology
(2017) - et al.
The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network
Chaos, Solitons & Fractals
(2015) - et al.
Cellular and network mechanisms of slow oscillatory activity (1 hz) and wave propagations in a cortical network model
Journal of Neurophysiology
(2003) - et al.
Stimulus dependence of two-state fluctuations of membrane potential in cat visual cortex
Nature Neuroscience
(2000) - et al.
Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism
Journal of Computational Neuroscience
(1994) - et al.
Propagating neuronal discharges in neocortical slices: computational and experimental study
Journal of Neurophysiology
(1997) - et al.
A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model
Nonlinear Dynamics
(2015)
A review for dynamics of collective behaviors of network of neurons
Science China: Technological Sciences
Methods in neuronal modeling: from ions to networks
Analysis of stability of neural network with inhibitory neurons
Cognitive Neurodynamics
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