doi: 10.3934/era.2021035
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Enhancement of gamma oscillations in E/I neural networks by increase of difference between external inputs

1. 

College of Information Science and Technology, Donghua University, Shanghai 201620, China

2. 

Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence, Ministry of Education, Fudan University, Shanghai 200433, China

* Corresponding author: Fang Han and Zhijie Wang

Received  December 2020 Revised  March 2021 Early access April 2021

Experimental observations suggest that gamma oscillations are enhanced by the increase of the difference between the components of external stimuli. To explain these experimental observations, we firstly construct a small excitatory/inhibitory (E/I) neural network of IAF neurons with external current input to E-neuron population differing from that to I-neuron population. Simulation results show that the greater the difference between the external inputs to excitatory and inhibitory neurons, the stronger gamma oscillations in the small E/I neural network. Furthermore, we construct a large-scale complicated neural network with multi-layer columns to explore gamma oscillations regulated by external stimuli which are simulated by using a novel CUDA-based algorithm. It is further found that gamma oscillations can be caused and enhanced by the difference between the external inputs in a large-scale neural network with a complicated structure. These results are consistent with the existing experimental findings well.

Citation: Xiaochun Gu, Fang Han, Zhijie Wang, Kaleem Kashif, Wenlian Lu. Enhancement of gamma oscillations in E/I neural networks by increase of difference between external inputs. Electronic Research Archive, doi: 10.3934/era.2021035
References:
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A. M. BastosF. BriggsH. J. AlittoG. R. Mangun and W. M. Usrey, Simultaneous recordings from the primary visual cortex and lateral geniculate nucleus reveal rhythmic interactions and a cortical source for gamma-band oscillations, Journal of Neuroscience, 34 (2014), 7639-7644.  doi: 10.1523/JNEUROSCI.4216-13.2014.  Google Scholar

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P. Guiraud and E. Tanre, Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 5183-5201.  doi: 10.3934/dcdsb.2019056.  Google Scholar

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Z. J. WangX. Peng and F. Han, A novel parallel clock-driven algorithm for simulation of neuronal networks based on virtual synapse, Simulation, 94 (2020), 415-427.   Google Scholar

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Z. J. WangX. Peng and F. Han, A novel time-event-driven algorithm for simulating spiking neural networks based on circular array, Neurocomputing, 292 (2018), 121-129.   Google Scholar

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Q. WangX. Shi and and G. Chen, Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 607-621.  doi: 10.3934/dcdsb.2011.16.607.  Google Scholar

[20]

B. Zhen, Z. Li and Z. Song, Influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo neurons, Applied Sciences, 9 (2019), 2159. doi: 10.3390/app9102159.  Google Scholar

[21]

B. Zhen, D. Zhang and Z. Son, Complexity induced by external stimulations in a neural network system with time delay, Math. Probl. Eng., 2020 (2020), 5472351, 9 pp. doi: 10.1155/2020/5472351.  Google Scholar

show all references

References:
[1]

P. AdjamianA. HadjipapasG. R. BarnesA. Hillebrand and I. E. Holliday, Induced gamma activity in primary visual cortex is related to luminance and not color contrast: An MEG study, Journal of Vision, 8 (2008), 1-7.  doi: 10.1167/8.7.4.  Google Scholar

[2]

A. M. BastosF. BriggsH. J. AlittoG. R. Mangun and W. M. Usrey, Simultaneous recordings from the primary visual cortex and lateral geniculate nucleus reveal rhythmic interactions and a cortical source for gamma-band oscillations, Journal of Neuroscience, 34 (2014), 7639-7644.  doi: 10.1523/JNEUROSCI.4216-13.2014.  Google Scholar

[3]

G. Buzsáki and X.-J. Wang, Mechanisms of gamma oscillations, Annu. Rev. Neurosci, 35 (2012), 203-225.  doi: 10.1146/annurev-neuro-062111-150444.  Google Scholar

[4] P. Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, Cambridge: MIT Press, 2001.   Google Scholar
[5]

P. Guiraud and E. Tanre, Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 5183-5201.  doi: 10.3934/dcdsb.2019056.  Google Scholar

[6]

J. A. Henrie and R. Shapley, LFP power spectra in V1 cortex: The graded effect of stimulus contrast, Journal of Neurophysiology, 94 (2005), 479-490.  doi: 10.1152/jn.00919.2004.  Google Scholar

[7]

J. F. HippA. K. Engel and M. Siegel, Oscillatory synchronization in large-scale cortical networks predicts perception, Neuron, 69 (2011), 387-396.  doi: 10.1016/j.neuron.2010.12.027.  Google Scholar

[8]

M. P. Jadi and T. J. Sejnowski, Cortical oscillations arise from contextual interactions that regulate sparse coding, Proc. Nat. Acad. Sci. USA, 111 (2014), 6780-6785.  doi: 10.1073/pnas.1405300111.  Google Scholar

[9]

V. B. Mountcastle, The columnar organization of the neocortex, Brain, 120 (1997), 701-722.  doi: 10.1093/brain/120.4.701.  Google Scholar

[10]

J. M. NageswaranN. DuttJ. L. Krichmar and al. et, A configurable simulation environment for the efficient simulation of large-scale spiking neural networks on graphics processors, Neural Networks, 22 (2009), 791-800.  doi: 10.1016/j.neunet.2009.06.028.  Google Scholar

[11]

S. A. Neymotin, H. Lee, E. Park, A. A. Fenton and W. W. Lytton, Emergence of physiological oscillation frequencies in a computer model of neocortex, Front. Comput. Neurosci., 5 (2011), 19. doi: 10.3389/fncom. 2011.00019.  Google Scholar

[12]

C. C. H. Petersen and B. Sakmann, Functionally independent columns of rat somatosensory barrel cortex revealed with voltage-sensitive dye imaging, Journal of Neuroscience, 21 (2001), 8435-8446.  doi: 10.1523/JNEUROSCI.21-21-08435.2001.  Google Scholar

[13]

W. H. Press, S. A. Teukolsky and W. T. Vetterling, Numerical recipes in C: The art of scientific computing, IEEE Concurrency, 6 (1992), 79. Google Scholar

[14]

L. Sacerdote and M. T. Giraudo, Stochastic Integrate and Fire Models: A review on mathematical methods and their applications, Stochastic biomathematical models, Lecture Notes in Math., Math. Biosci. Subser., Springer, Heidelberg, 2058 (2013), 99–148. doi: 10.1007/978-3-642-32157-3_5.  Google Scholar

[15]

A. B. SaleemA. D. LienM. KruminB. HaiderM. R. RosónA. AyazK. ReinholdL. BussesM. Carandini and K. D. Harris, Subcortical source and modulation of the narrowband gamma oscillation in mouse visual cortex, Neuron, 93 (2017), 315-322.  doi: 10.1016/j.neuron.2016.12.028.  Google Scholar

[16]

E. Wallace, M. Benayoun, W. van Drongelen and J. D. Cowan, Emergent oscillations in networks of stochastic Spiking Neurons, PLOS ONE, 6 (2011). doi: 10.1371/journal. pone. 0014804.  Google Scholar

[17]

Z. J. WangX. Peng and F. Han, A novel parallel clock-driven algorithm for simulation of neuronal networks based on virtual synapse, Simulation, 94 (2020), 415-427.   Google Scholar

[18]

Z. J. WangX. Peng and F. Han, A novel time-event-driven algorithm for simulating spiking neural networks based on circular array, Neurocomputing, 292 (2018), 121-129.   Google Scholar

[19]

Q. WangX. Shi and and G. Chen, Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 607-621.  doi: 10.3934/dcdsb.2011.16.607.  Google Scholar

[20]

B. Zhen, Z. Li and Z. Song, Influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo neurons, Applied Sciences, 9 (2019), 2159. doi: 10.3390/app9102159.  Google Scholar

[21]

B. Zhen, D. Zhang and Z. Son, Complexity induced by external stimulations in a neural network system with time delay, Math. Probl. Eng., 2020 (2020), 5472351, 9 pp. doi: 10.1155/2020/5472351.  Google Scholar

Figure 1.  The structure of the small E/I network with external stimuli. Wiring among E- and I- neurons are all-to-all and only three cells of the E-neuron population (red dots) and I-neuron population (blue dots) are depicted here. Directed wiring is red for excitatory and blue for inhibitory connections. $ w_{\rm{EE}} $, $ w_{\rm{II}} $, $ w_{\rm{EI}} $ and $ w_{\rm{IE}} $ are the synaptic weights ($ g_{{\mathrm{max}}} $) of E to E, I to I, I to E, and E to I connections, respectively
Figure 2.  Gamma oscillations are caused by the typical input that $ S1 $ is 0.6 and $ S2 $ is zero (50ms-450ms in a 1s simulation). (a) Raster plots of the spiking times of neurons. (b) Average population activity. (c) The power spectrum of the population activity
Figure 3.  Gamma oscillations are caused by the typical input that $ S2 $ is 0.2 and $ S1 $ is zero (50ms-450ms in a 1s simulation). (a) Raster plots of the spiking times of neurons. (b) Average population activity. (c) The power spectrum of the population activity
Figure 4.  Increase of the peak power of gamma oscillations in the small E/I neural network with the increasing of the difference between $ S1 $ and $ S2 $. The increase of the peak power in the second case (blue curve) is more evident than that in the first case (green curve)
Figure 5.  Intra-layer and inter-layer connections in a single column
Figure 6.  The framework of simulation for the large-scale complicated network with multi-layer columns. $ t_{0} $ is the initial time. $ \Delta{t} $ is the time step
Figure 7.  The pseudo-code of constructing the multi-layer column structure of the large-scale complicated network. The variable $ m\_uiNumCell\_per\_column $ denotes the number of neurons in each column, the variables $ idx\_column $, and $ jdx\_column $ denote the IDs of columns and the variables $ ii\_idx\_column $ and $ jj\_jdx\_column $ denote the IDs of neurons
Figure 8.  Gamma oscillations are generated in the large-scale complicated neural network. (a) Raster plots of the spiking times of neurons in each layer of columns when $ S1 = 0.3, S2 = 0 $. (b) Raster plots of the spiking times of neurons in each layer of columns when $ S1 = 0, S2 = 0.3 $. (c) Power spectrums of average population activities with the two input cases
Figure 9.  Increase of the peak power of gamma oscillations in the large-scale complicated network with the increasing of the difference between $ S1 $ and $ S2 $
Table 2.  Connection Types and parameters of neurons within a column
presynaptic neuron postsynaptic neuron $ \mathit{\boldsymbol{\alpha}} $ $ \mathit{\boldsymbol{\beta}} $ $ \mathit{\boldsymbol{g_{{\mathrm{max}}}}} $ $ \mathit{\boldsymbol{d(ms)}} $
E23 E23, E4, E5, I23 0.9 0.003 0.004 2
I23 E23, E5, E6, I23, I5, I6 0.9 0.003 0.05 1
E4 E4, E5, E6, I4 0.9 0.003 0.004 2
I4 E4, I4 0.9 0.003 0.05 1
E5 E23, E4, E5, E6, I5 0.9 0.003 0.004 2
I5 E23, E5, E6, I23, I5, I6 0.9 0.003 0.05 1
E6 E6, I6 0.9 0.003 0.004 2
I6 E23, E5, E6, I5, I6 0.9 0.003 0.05 1
presynaptic neuron postsynaptic neuron $ \mathit{\boldsymbol{\alpha}} $ $ \mathit{\boldsymbol{\beta}} $ $ \mathit{\boldsymbol{g_{{\mathrm{max}}}}} $ $ \mathit{\boldsymbol{d(ms)}} $
E23 E23, E4, E5, I23 0.9 0.003 0.004 2
I23 E23, E5, E6, I23, I5, I6 0.9 0.003 0.05 1
E4 E4, E5, E6, I4 0.9 0.003 0.004 2
I4 E4, I4 0.9 0.003 0.05 1
E5 E23, E4, E5, E6, I5 0.9 0.003 0.004 2
I5 E23, E5, E6, I23, I5, I6 0.9 0.003 0.05 1
E6 E6, I6 0.9 0.003 0.004 2
I6 E23, E5, E6, I5, I6 0.9 0.003 0.05 1
Table 1.  Parameters and counts of different types of neurons within a column
Type $ \mathit{\boldsymbol{N}} $ $ \mathit{\boldsymbol{V_{\rm{th}}(mV)}} $ $ \mathit{\boldsymbol{V_{\rm{reset}}(mV)}} $ $ \mathit{\boldsymbol{E_{\rm{syn}}(mV)}} $ $ \mathit{\boldsymbol{\tau(ms)}} $ $ \mathit{\boldsymbol{R(k\Omega)}} $ $ \mathit{\boldsymbol{V_{\rm{L}}(mV) }}$
E23 200 -47 -65 0 5 10 -65
I23 50 -45 -65 -75 1 10 -65
E4 200 -47 -65 0 5 10 -65
I4 50 -45 -65 -75 1 10 -65
E5 200 -47 -65 0 5 10 -65
I5 50 -45 -65 -75 1 10 -65
E6 200 -47 -65 0 5 10 -65
I6 50 -45 -65 -75 1 10 -65
Type $ \mathit{\boldsymbol{N}} $ $ \mathit{\boldsymbol{V_{\rm{th}}(mV)}} $ $ \mathit{\boldsymbol{V_{\rm{reset}}(mV)}} $ $ \mathit{\boldsymbol{E_{\rm{syn}}(mV)}} $ $ \mathit{\boldsymbol{\tau(ms)}} $ $ \mathit{\boldsymbol{R(k\Omega)}} $ $ \mathit{\boldsymbol{V_{\rm{L}}(mV) }}$
E23 200 -47 -65 0 5 10 -65
I23 50 -45 -65 -75 1 10 -65
E4 200 -47 -65 0 5 10 -65
I4 50 -45 -65 -75 1 10 -65
E5 200 -47 -65 0 5 10 -65
I5 50 -45 -65 -75 1 10 -65
E6 200 -47 -65 0 5 10 -65
I6 50 -45 -65 -75 1 10 -65
Table 3.  Connection types and parameters of neurons between columns
presynaptic neuron postsynaptic neuron $ \mathit{\boldsymbol{\alpha}} $ $ \mathit{\boldsymbol{\beta}} $ $ \mathit{\boldsymbol{g_{{\mathrm{max}}}}} $ $ \mathit{\boldsymbol{d(ms)}} $
E23 I23 0.8 0.001 0.98 1
E4 I4 0.8 0.001 0.98 1
E5 E5 0.8 0.001 0.16 1
E5 I5 0.8 0.001 0.98 1
E5 E23 0.8 0.001 0.16 1
E5 I23 0.8 0.001 0.98 1
E6 I6 0.8 0.001 0.98 1
presynaptic neuron postsynaptic neuron $ \mathit{\boldsymbol{\alpha}} $ $ \mathit{\boldsymbol{\beta}} $ $ \mathit{\boldsymbol{g_{{\mathrm{max}}}}} $ $ \mathit{\boldsymbol{d(ms)}} $
E23 I23 0.8 0.001 0.98 1
E4 I4 0.8 0.001 0.98 1
E5 E5 0.8 0.001 0.16 1
E5 I5 0.8 0.001 0.98 1
E5 E23 0.8 0.001 0.16 1
E5 I23 0.8 0.001 0.98 1
E6 I6 0.8 0.001 0.98 1
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