Synchronization and wave propagation in neuronal network under field coupling

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SCIENCE CHINA Technological Sciences, Volume 62, Issue 3: 448-457(2019) https://doi.org/10.1007/s11431-018-9268-2

Synchronization and wave propagation in neuronal network under field coupling

Mi LV1, Jun MA1,2,*, YuanGen YAO3, Faris ALZAHRANI4
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  • ReceivedJan 29, 2018
  • AcceptedApr 23, 2018
  • PublishedJul 3, 2018
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Abstract

Electric and chemical synapse play important role in connecting neurons and thus signal propagation can be realized between neurons. External electric stimulus can change the excitability of neuron and then the electrical activities can be modulated completely. Continuous fluctuation of ion concentration in cell can induce complex time-varying electromagnetic field during the exchange of charged ions across the membrane of neuron. Polarization and magnetization in the media (and neuron), which exposed to electromagnetic radiation, can modulate the dynamical response and mode transition in electrical activities of neurons. In this paper, magnetic flux is used to describe the effect of electromagnetic field, and the three-variable Hindmarsh-Rose neuron model is updated to propose a four-variable neuron model that the effect of electromagnetic induction and radiation can be explained. Based on the physical law of electromagnetic induction, exchange of charged ions and flow of ion currents will change the distribution of electromagnetic filed in cell, and each neuron will be exposed to the superimposed field triggered by other neurons. Therefore, signal exchange could occur even synapse coupling between neurons is removed in the case of field coupling. A chain network is proposed to investigate the signal exchange between neurons under field coupling when synapse coupling is not available. It is found that field coupling between neurons can change the collective behaviors in electrical activities. A statistical factor of synchronization and spatial patterns are calculated, these results confirmed that field coupling is effective for signal communication between neurons. In the end, open problems are suggested for readers’ extensive guidance in this field.


Funded by

the National Natural Science Foundation of China(Grant,Nos.,11672122,11765011)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11672122 & 11765011).


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  • Click to view Download high-quality image

    Figure 1

    Sampled time series for membrane potential and magnetic flux of neurons (i=5, 25, 48). Evolution of membrane potentials is shown in (a), (c), (e); magnetic flux shown in (b), (d), (f). (a), (b) i=25, I=1.1; i=5, 48, I=0.0. (c), (d) i=25, I=1.35; i=5, 48, I=0.0. (e), (f) i=25, I=2.0; i=5, 48, I=0.0. k=0.9, k1=0.4, k2=0.5, k3=0.001. The field coupling is considered from t>500 time units.

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    Figure 2

    Evolution of spatial patterns is calculated for membrane potentials of N neurons. (a), (d) i=21, 22, 23, 24, 25 neuron, the external stimuli I=1.1, other neurons I=0.0; for (b), (e) i=21, 22, 23, 24, 25 neuron, the external stimuli I=1.35, other neurons I=0.0; for (c), (f) i=21, 22, 23, 24, 25 neuron, the external stimuli I=2.0, other neurons I=0.0. The snapshots are shown in color scale. k=0.9, k1=0.4, k2=0.5, k3=0.001.

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    Figure 3

    Sampled time series for membrane potential and magnetic flux of neurons (i=5, 25, 48) are calculated when field coupling is activated from t=500 time units. Evolution of membrane potentials is shown in (a), (c), (e); magnetic flux shown in (b), (d), (f). (a), (b) i=25, I=2.0; i=5, 48, I=1.2. (c), (d) i=25, I=2.0; i=5, 48, I=1.3. (e), (f) i=25, I=2.0; i=5, 48, I=1.4. k=0.9, k1=0.4, k2=0.5, k3=0.001.

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    Figure 4

    Evolution of spatial patterns is calculated for membrane potentials and magnetic flux of N neurons. (a), (d) i=21, 22, 23, 24, 25 neuron, the external stimuli I=2.0, other neurons I=1.2; (b), (e) i=21, 22, 23, 24, 25 neuron, the external stimuli I=2.0, other neurons I=1.3; (c), (f) i=21, 22, 23, 24, 25 neuron, the external stimuli I=2.0, other neurons I=1.4. The snapshots are shown in color scale. k=0.9, k1=0.4, k2=0.5, k3=0.001.

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    Figure 5

    Sampled time series for membrane potentials of neurons (node 5, i=5) when different intensities of field coupling are considered. Neurons on node (i=21, 22, 23, 24, 25) are imposed the same external stimulus as I=2.0, the other neurons are driven by the same stimulus as I=1.4. The parameters are set as k=0.9, k1=0.4, k2=0.5.

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    Figure 6

    Distribution for factors of synchronization is calculated by applying different intensities in field coupling. Neurons on node (i=21, 22, 23, 24, 25) are imposed on the same external stimulus as I=2.0, the other neurons are driven the same stimulus as I=1.4. k=0.9, k1=0.4, k2=0.5.

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