class brainpy.dyn.IAHP_De1994v2(size, keep_size=False, n=2, g_max=10.0, alpha=48.0, beta=0.09, phi=1.0, method='exp_auto', name=None, mode=None)[source]#

The calcium-dependent potassium current model proposed by (Destexhe, et al., 1994) [1].

Both in vivo (Contreras et al. 1993; Mulle et al. 1986) and in vitro recordings (Avanzini et al. 1989) show the presence of a marked after-hyper-polarization (AHP) after each burst of the RE cell. This slow AHP is mediated by a slow \(Ca^{2+}\)-dependent K+ current (Bal and McCormick 1993). (Destexhe, et al., 1994) adopted a modified version of a model of \(I_{KCa}\) introduced previously (Yamada et al. 1989) that requires the binding of \(nCa^{2+}\) to open the channel

\[(\text { closed })+n \mathrm{Ca}_{i}^{2+} \underset{\beta}{\stackrel{\alpha}{\rightleftharpoons}(\text { open })\]

where \(Ca_i^{2+}\) is the intracellular calcium and \(\alpha\) and \(\beta\) are rate constants. The ionic current is then given by

\[\begin{split}\begin{aligned} I_{AHP} &= g_{\mathrm{max}} p^2 (V - E_K) \\ {dp \over dt} &= \phi {p_{\infty}(V, [Ca^{2+}]_i) - p \over \tau_p(V, [Ca^{2+}]_i)} \\ p_{\infty} &=\frac{\alpha[Ca^{2+}]_i^n}{\left(\alpha[Ca^{2+}]_i^n + \beta\right)} \\ \tau_p &=\frac{1}{\left(\alpha[Ca^{2+}]_i +\beta\right)} \end{aligned}\end{split}\]

where \(E\) is the reversal potential, \(g_{max}\) is the maximum conductance, \([Ca^{2+}]_i\) is the intracellular Calcium concentration. The values \(n=2, \alpha=48 \mathrm{~ms}^{-1} \mathrm{mM}^{-2}\) and \(\beta=0.03 \mathrm{~ms}^{-1}\) yielded AHPs very similar to those RE cells recorded in vivo and in vitro.


g_max (float) – The maximal conductance density (\(mS/cm^2\)).



The type of the master object.

alias of JointType[Calcium, Potassium]