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Anton Chizhov edited untitled.tex
almost 8 years ago
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\begin{equation} \label{e2}
\varphi_G(t)=k_G \Biggl[ {d[K^+]_e \over dt} \Biggr]_{Glia},
\end{equation}
where
$\Biggl[ $\Bigl[ {d[K^+]_e \over dt}
\Biggr]_{Glia}$ \Bigr]_{Glia}$ is the potassium concentration change due to glia; $k_G$ is a coefficient.
Potassium currents through neuronal membranes are most pronounced during the spiking activity. That is why, approximately the currents are just proportional to the firing rate of principal neurons, $\nu(t)$. The increase of $[K^+]_e$ is then filtered by glial cells. Thus, the equation for the potassium concentration change due to glia should look like the refractory equation
\begin{equation} \label{e3}
\tau {\varphi_G(t) \over dt } = - \varphi_G(t) + c
\nu(t), ~\nu(t),
\end{equation}
where $\tau$ is the characteristic time constant; $c$ is a coefficient.
The time constant cumulatively express the kinetics of neuronal and glial voltage-gated channels, as well as the scales of glial intracellular processes evoked by neuronal activity.