Article Figures & Data
Figures
- Figure 1.
Structure of the population model. A, Scheme of interacting neural populations. E, I: excitatory and inhibitory populations;
,
: excitatory to excitatory and excitatory to inhibitory maximal conductances;
,
: inhibitory-to-inhibitory and inhibitory-to-excitatory maximal conductance; gAHP: adaptation conductance in the excitatory population;
: synaptic noise input to the excitatory population; AHP, afterhyperpolarization current (Buchin and Chizhov, 2010b). B, LFP model:
: contribution of a single excitatory cell; N: the number of neurons;
: the average membrane potential in the excitatory population. C, D, Sigmoid approximation of potential-to-rate function (Johannesma, 1968) of the excitatory (C) and inhibitory population (D). - Figure 2.
Neural mass model in various excitatory regimes. A, Activity of a neural population in the resting state. B, Seizure state. C, Disinhibited state. LFP is present together with intracellular recording from the pyramidal cell. Each plot contains the model scheme, power spectrum, and time traces provided by the excitatory population
as well as experimental LFP. Red traces correspond to the model, blue traces to the experiment, and green traces to the intracellular recordings from the pyramidal cells. Model parameters for (A):
= 1.5 mS/cm2;
= 1 mS/cm2;
= 2 mS/cm2;
= 0.2 mS/cm2;
= 1.6 mS/cm2; (B):
= 1.5 mS/cm2;
= 1 mS/cm2;
= 0.5 mS/cm2;
= 0.2 mS/cm2;
= 1.6 mS/cm2; (C):
= 1.5 mS/cm2;
= 1 mS/cm2;
= 0 mS/cm2;
= 0.2 mS/cm2;
= 1.6 mS/cm2. - Figure 3.
Oscillatory frequencies of the population model. A–D, Oscillatory frequencies of the population model in the absence of the synaptic noise (
= 0) as a function of the synaptic conductance,
. E, Simultaneous intracellular recording from single pyramidal cell, LFP, and population model during transition from the resting state toward seizure. States marked by dotted lines. The green trace corresponds to the model’s resting state (Fig. 2A,
), red corresponds to early seizure (Fig. 2B,
), yellow corresponds to late seizure (
), and purple corresponds to the disinhibition state (Fig. 2C,
). - Figure 4.
Analysis of the population model. A–D, Bifurcation diagrams for the variations of the maximal synaptic conductances, including recurrent excitation
, excitation from excitatory to inhibitory population
, inhibition from inhibitory to excitatory population
, and the recurrent inhibition in the inhibitory population
, respectively. E, F, Bifurcation diagrams for adaptation in the excitatory population
and GABA reversal potential
from the inhibitory-to-excitatory current,
. Diagrams A–D were calculated for
= 2 mS/cm2; E, gIE = 0.5 mS/cm2; and F, gIE 1 mS/cm2. The value of
characterizes the average membrane potential in the resting state and maximal/minimal values of
during the oscillations. Red and green dots correspond to the supercritical and subcritical Andronov–Hopf bifurcations. Solid and dotted lines depict the stable and unstable solutions.
Tables
Excitatory population Parameter Value Interpretation 1 mF/cm2 Membrane capacitance (Buchin and Chizhov, 2010b) 0.02 mS/cm2 Sodium leak conductance (Krishnan and Bazhenov, 2011) 0.044 mS/cm2 Potassium leak conductance (Krishnan and Bazhenov, 2011) 0.01 mS/cm2 Chloride leak conductance (Krishnan and Bazhenov, 2011) 1.6 mS/cm2 AHP-current conductance (Buchin and Chizhov, 2010b) 1.5 mS/cm2 Excitatory-to-excitatory conductance 1 mS/cm2 Excitatory-to-inhibitory conductance 2; 0.5; 1 mS/cm2 Inhibitory-to-excitatory conductance 0.2 mS/cm2 Inhibitory-to-inhibitory conductance –65 mV Reset membrane potential (Chizhov and Graham, 2007; Buchin and Chizhov, 2010b) –55 mV Threshold membrane potential (Chizhov and Graham, 2007; Buchin and Chizhov, 2010b) 2.84 × 104 Sigmoid fit parameter 0.19 mV-1 Sigmoid fit parameter 1.23 × 104 Sigmoid fit parameter –10 mV Sigmoid fit parameter (threshold) 3 μA/cm2 Input current variance 5.4 ms AMPA current correlation time (Buchin et al., 2016a,b) 4 mV Membrane potential dispersion 50 mV Sodium reversal potential (Krishnan and Bazhenov, 2011) –75 mV Potassium reversal potential (Krishnan and Bazhenov, 2011) –93 mV Chloride reversal potential (Krishnan and Bazhenov, 2011) –75 mV GABA reversal potential (Huberfeld et al., 2007) 0 mV AMPA reversal potential (Brunel and Wang, 2001) –70 mV AHP reversal potential (Brunel and Wang, 2001) 1 ms AHP rise time (Brunel and Wang, 2001) 320 ms AHP decay time (Brunel and Wang, 2001) 1 ms AMPA rise time (Chizhov, 2002) 5.4 ms AMPA decay time (Chizhov, 2002) Inhibitory population Parameter Value Interpretation 1 mS/cm2 Membrane capacitance (Buchin and Chizhov, 2010b) 0.02 mS/cm2 Sodium leak conductance (Krishnan and Bazhenov, 2011) 0.04 mS/cm2 Potassium leak conductance (Krishnan and Bazhenov, 2011) 0.03 mS/cm2 Chloride leak conductance (Krishnan and Bazhenov, 2011) 2 mS/cm2 Inhibitory-excitatory synaptic conductance 0.2 mS/cm2 Excitatory-inhibitory synaptic conductance –65 mV Reset membrane potential –55 mV Threshold membrane potential 2.84 × 104 Sigmoid fit parameter 0.19 mV-1 Sigmoid fit parameter 1.23 × 104 Sigmoid fit parameter –10 mV Sigmoid fit parameter (threshold) 4 mV Membrane potential dispersion 50 mV Sodium reversal potential (Krishnan and Bazhenov, 2011) –75 mV Potassium reversal potential (Krishnan and Bazhenov, 2011) –82 mV Chloride reversal potential (Krishnan and Bazhenov, 2011) 8.3 ms GABA-A decay time (Chizhov et al., 2002) 0.2 ms GABA-A rise time (Chizhov, 2002) Variable Interpretation
, mVAverage membrane potential of the excitatorypopulation
, mVAverage membrane potential of the inhibitory population e Excitatory population synaptic gating variable i Inhibitory population synaptic gating variable a Excitatory population adaptation gating variable
, μA/cm2Random excitatory input
, HzFiring rate of the excitatory population
, HzFiring rate of the inhibitory population Model, peak amplitude, Hz Experiment, peak amplitude, Hz Model, spectrum linear fit, 1/Hz Experiment, spectrum linear fit, 1/Hz Rest - - -0.005—-0.002 -0.005—-0.002 Seizure 3.01—3.52 2.95—3.75 -0.005—-0.002 -0.003—-0.002 Pre-ictal state 1.33—1.43 1.21—1.79 -0.007—-0.003 -0.01—-0.008
Extended Data 1
The code is available as Extended Data. Download Extended Data, ZIP file
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