Table 1 Descriptions and values of the neuron–astrocyte mass model parameters
Parameter | Interpretation | Value |
|---|---|---|
Neuronal compartment | ||
A | Average excitatory synaptic gain | \(3.25~\mbox{mV}\) |
B | Average inhibitory synaptic gain | \(22~\mbox{mV}\) |
\(\frac{1}{a}\) | Time constant of excitatory postsynaptic potentials | \(\frac{1}{100}~\mbox{s}\) |
\(\frac{1}{b}\) | Time constant of inhibitory postsynaptic potentials | \(\frac{1}{50}~\mbox{s}\) |
\(e_{0}\) | Half of the maximum discharge rate of a neuronal population | \(2.5~\mbox{s}^{-1}\) |
\(v_{0}\) | Basic excitability threshold for neurons | \(6~\mbox{mV}\) |
r | Stiffness of neuronal excitability | \(0.56~\mbox{mV}^{-1}\) |
\(C_{1}\) | Strength of the synaptic connections from P to \(P'\) | 135 |
\(C_{2}\) | Strength of the synaptic connections from \(P'\) to P | 108 |
\(C_{3}\) | Strength of the synaptic connections from P to I | 33.75 |
\(C_{4}\) | Strength of the synaptic connections from I to P | 33.75 |
G | Gain of the direct excitatory feedback from P to itself | 40 |
Glial compartment | ||
W | Tunes the peak amplitude of glutamate concentrations | \(53.6~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
Z | Tunes the peak amplitude of GABA concentrations | \(53.6~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(w_{1}\) | Tune the rise and decay times of glutamate release transfer function | \(90~\mbox{s}^{-1}\) |
\(w_{2}\) | \(33~\mbox{s}^{-1}\) | |
\(z_{1}\) | Tune the rise and decay times of GABA release transfer function | \(90~\mbox{s}^{-1}\) |
\(z_{2}\) | \(33~\mbox{s}^{-1}\) | |
\(V_{G}^{{\mathrm{ne}}}\) | Maximal rate of glutamate uptake by neurons | \(0.5~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(V_{G}^{{\mathrm{ae}}}\) | Maximal rate of glutamate uptake by astrocytes | \(4.5~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(s_{g}\) | Activation threshold of sigmoid glutamate uptakes | \(6~\mu\mbox{M}\) |
\(r_{g}\) | Stiffness of sigmoid glutamate uptakes | \(0.9~\mu\mbox{M}^{-1}\) |
\(V_{\gamma}^{{\mathrm{ae}}}\) | Maximal rate of astrocyte GABA uptake | \(2~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(K_{\gamma}^{{\mathrm{ae}}}\) | Maximal concentration for Hill dynamics of astrocyte GABA uptake | \(8~\mu\mbox{M}\) |
\(V_{\gamma}^{{\mathrm{ne}}}\) | Maximal rate of neuronal GABA uptake | \(5~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(K_{\gamma}^{{\mathrm{ne}}}\) | Maximal concentration for Hill dynamics of neuronal GABA uptake | \(24~\mu\mbox{M}\) |
\(V_{G}^{c}\) | Rate of glutamate degradation by astrocytes | \(9~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
\(V_{\gamma}^{c}\) | Rate of GABA degradation by astrocytes | \(9~\mu\mbox{M}\cdot\mbox{s}^{-1}\) |
Neuron excitability modulations by neurotransmitter concentrations (feedbacks) | ||
\(v_{G}\) | Excitability threshold of glutamate feedback function | \(30~\mu\mbox{M}\) |
\(r_{G}\) | Stiffness of sigmoid glutamate feedback function induced by glutamate | \(0.15~\mu\mbox{M}^{-1}\) |
\(m_{G}^{P}\) | Maximal coupling gain of glutamate feedback on pyramidal neurons | \(2.5~\mbox{mV}\) |
\(m_{G}^{I}\) | Maximal coupling gain of glutamate feedback on interneurons | \(1~\mbox{mV}\) |
\(v_{\gamma}\) | Excitability threshold of GABA feedback function | \(25~\mu\mbox{M}^{-1}\) |
\(r_{\gamma}\) | Stiffness of sigmoid GABA feedback function | \(0.12~\mu\mbox{M}^{-1}\) |
\(m_{\gamma}\) | Maximal coupling gain of GABA feedback | \(1~\mbox{mV}\) |