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Research ArticleResearch Article: New Research, Integrative Systems

A Network Model of the Modulation of γ Oscillations by NMDA Receptors in Cerebral Cortex

Eduarda Susin and Alain Destexhe
eNeuro 8 November 2023, 10 (11) ENEURO.0157-23.2023; https://doi.org/10.1523/ENEURO.0157-23.2023
Eduarda Susin
Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Centre National de la Recherche Scientifique (CNRS), Saclay, France 91400
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Alain Destexhe
Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Centre National de la Recherche Scientifique (CNRS), Saclay, France 91400
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  • Figure 1.
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    Figure 1.

    Parameter space of NMDA synaptic weights in RS and FS cells. A, Average spiking rate in RS cells. B, Average spiking rate in FS cells. C, Population activity Power Spectrum pick. D, Population activity Power Spectrum amplitude. The parameter space of weights in NMDA synapses (QNMDA ) was explored for RS and FS cells in the developed network model. QRSNMDA and QFSNMDA varied from 0 to 1 nS in steps of 0.05 nS. Each point in the color maps corresponds to the average of 10 simulations of 5 s. Points in which QRSNMDA =QFSNMDA are highlighted. Small squares indicate a possible trajectory in the parameter space (in the direction of the arrow) generated by the action of NMDAR antagonists.

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    Figure 2.

    Excitatory synaptic currents. A, Average AMPA current of one randomly picked RS (green) and one randomly picked FS (red) neuron. B, Average NMDA current of one randomly picked RS (green) and one randomly picked FS (red) neuron. C, Ratio of NMDA and AMPA charges for RS and FS cells. The synaptic charge ratio of each neuron was calculated separately. The Bars indicate the mean and the SD among the RS and FS population. The NMDA synaptic strengths in RS and FS cells are QRSNMDA = 0.8 nS and QFSNMDA = 1 nS (which, in our model, describes a healthy condition).

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    Figure 3.

    Network dynamics with respect to different levels of NMDA channels block in the network. A, Possible trajectory in the parameter space of QRSNMDA versus QFSNMDA (NMDA synaptic strengths in RS and FS cells), mimicking the action of NMDA receptor (NMDAR) antagonists (the higher the intensity of the NMDAR antagonists, the smaller the NMDA synaptic strengths; same trajectory as that indicated in Fig. 1). The thin line indicates the identity for reference. The arrow indicates the progressive action of NMDAR antagonists. Points of higher synaptic strengths are associated with healthy conditions, while points with lower synaptic strengths are associated to pathologic conditions supposedly similar to the schizophrenic brain. B, C, Raster plots indicating the activity of only 1000 cells of each type (FS in red and RS in green), for two parameter sets. B, QRSNMDA = 0.8 nS and QFSNMDA = 1 nS. C, QRSNMDA = 0.213 nS and QFSNMDA = 0.2 nS. D, Average normalized Power Spectrum of the network LFP for different NMDA synaptic strength. The synaptic strengths follow the curve indicated in A, but only the values in FS cells (QFSNMDA ) are indicated in the color scale. Notice the shift of the Power Spectrum peak toward smaller frequencies with the increase of NMDA channel block. E, Power Spectrum peak amplitude with respect to the levels of NMDA channels block. Only the values of the NMDA synaptic strengths in FS cells (QFSNMDA ) are indicated in the x-axis. The color scheme (presented for better visualization) is the same as in D. SEMs are indicated as error bars. F, Average firing rate of RS (green) and FS cells (red) with respect to the trajectory in parameter space depicted in A. Like in E, only QFSNMDA are indicated in the x-axis. SEMs are indicated as error bars. Results expressed in D–F are the outcome of 50 simulations average. In all simulations, an external drive of 3 Hz was used to maintain network activity in γ regime. See Materials and Methods.

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    Figure 4.

    Excitatory synaptic currents with respect to different levels of NMDA channels block. As in Figure 3, higher values of synaptic strengths are associated with healthy conditions, while lower values of synaptic strengths are associated to pathologic conditions supposedly similar to the schizophrenic brain. A, Average AMPA current (for healthy and pathologic conditions) of two randomly picked neurons: RS (green) and FS (red). B, Average NMDA current (for healthy and pathologic conditions) of two randomly picked neurons: RS (green) and FS (red). C, Ratio of NMDA and AMPA charges for RS and FS cells (for healthy and pathologic conditions). The synaptic charge ratio of each neuron was calculated separately. The bars indicate the mean and the SD among the RS and FS population.

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    Figure 5.

    Network responsiveness to broad Gaussian inputs in different levels of NMDA channel blocked during γ rhythms. A, Responsiveness protocol scheme. The total number of spikes generated by the network were measured during an external stimulus and in its absence in a time window of 500 ms. The stimulus consisted of a Gaussian fluctuation in the firing rate of the external noise input. Responsiveness was calculated according to Equation 6. B, Gaussian input amplitude variation. The Gaussian amplitude varied from 0.05 to 2.5 Hz (step of 0.05 Hz), always keeping the same SD of 50 ms. C and D depict, respectively, the responsiveness of RS (C) and FS (D) neurons for different Gaussian amplitudes in different levels of NMDAR block, when the network was displaying γ activity. The color scheme indicates the synaptic weights of NMDA synapses (QNMDA ) in RS and FS cells. The arrow indicates the sense of the simulated action of NMDA antagonist (decreasing synaptic strength). Every point corresponds to the average responsiveness measured in 15 simulations. SEMs are indicated by the shaded region around each curve.

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    Figure 6.

    Membrane potential polarization as a function of NMDA receptor block. The average membrane potential of RS (green, left y-axis) and FS (red, right y-axis) is expressed as function of NMDA synaptic weights of RS and FS cells. The values of QRSNMDA and QFSNMDA follow the same trajectory in the parameter space, as indicated in Figure 3A. Only the values of QFSNMDA are indicated in the x-axis. The average was performed first in between neurons (〈〉N ), obtaining an average curve as a function of time, and subsequently with respect time (〈〉t ). The values plotted correspond to the average of 〈〈V〉N〉t in between 10 simulations. The error bars indicate the SEM between these simulations.

  • Figure 7.
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    Figure 7.

    Network responsiveness to broad Gaussian inputs of different amplitudes during γ and AI states. The responsiveness of RS neurons, because of different Gaussian amplitudes stimuli (same as in the protocol of Fig. 5), was measured in different states AI and γ for NMDA synaptic parameter sets: QRSNMDA = 0.8 nS and QFSNMDA = 1 nS (γ: black, AI: gray), and QRSNMDA = 0.36 nS and QFSNMDA = 0.4 nS (γ: blue, AI: light blue). The Gaussian amplitude varied from 0.05 to 2.5 Hz (step of 0.05 Hz), always keeping the same SD of 50 ms.

  • Figure 8.
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    Figure 8.

    Network responsiveness with faster NMDA decay time constant. As in Figure 7, the network responsiveness to broad Gaussian inputs of different amplitudes during γ and AI states are displayed. In this case, the used NMDA synaptic times constant used in Equation 5 are τriseNMDA = 2 ms and τdecayNMDA = 50 ms. The responsiveness of RS neurons, was measured in different states AI and γ for NMDA synaptic parameter sets: QRSNMDA = 0.8 nS and QFSNMDA = 1 nS (γ: black, AI: gray), and QRSNMDA = 0.36 nS and QFSNMDA = 0.4 nS (γ: blue, AI: light blue). The Gaussian amplitude varied from 0.25 to 2.5 Hz (step of 0.25 Hz), always keeping the same SD of 50 ms. Every point corresponds to the average responsiveness measured in 10 simulations. SEMs are indicated by the shaded region around each curve.

Tables

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    Table 1

    Specific neuron model parameters

    ParameterRSFS
     Vth −40 mV−47.5 mV
      Δ2 mV0.5 mV
     Tref 5 ms5 ms
     τw 500 ms500 ms
    a4 nS0 nS
    b20 pA0 pA
    C150 pF150 pF
     gL 10 nS10 nS
     EL −65 mV−65 mV
     EE 0 mV0 mV
     EI −80 mV−80 mV
     Vrest −65 mV−65 mV
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A Network Model of the Modulation of γ Oscillations by NMDA Receptors in Cerebral Cortex
Eduarda Susin, Alain Destexhe
eNeuro 8 November 2023, 10 (11) ENEURO.0157-23.2023; DOI: 10.1523/ENEURO.0157-23.2023

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A Network Model of the Modulation of γ Oscillations by NMDA Receptors in Cerebral Cortex
Eduarda Susin, Alain Destexhe
eNeuro 8 November 2023, 10 (11) ENEURO.0157-23.2023; DOI: 10.1523/ENEURO.0157-23.2023
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Keywords

  • γ oscillations
  • hallucinations
  • ketamine
  • Network model
  • NMDA receptors
  • schizophrenia

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