Ih_De1996#
- class brainpy.dyn.Ih_De1996(size, keep_size=False, E=-40.0, k2=0.0004, k4=0.001, V_sh=0.0, g_max=0.02, g_inc=2.0, Ca_half=0.002, T=36.0, T_base=3.0, phi=None, method='exp_auto', name=None, mode=None)[source]#
The hyperpolarization-activated cation current model propsoed by (Destexhe, et al., 1996) [1].
The full kinetic schema was
\[\begin{split}\begin{gathered} C \underset{\beta(V)}{\stackrel{\alpha(V)}{\rightleftarrows}} O \\ P_{0}+2 \mathrm{Ca}^{2+} \underset{k_{2}}{\stackrel{k_{1}}{\rightleftarrows}} P_{1} \\ O+P_{1} \underset{k_{4}}{\rightleftarrows} O_{\mathrm{L}} \end{gathered}\end{split}\]where the first reaction represents the voltage-dependent transitions of \(I_h\) channels between closed (C) and open (O) forms, with \(\alpha\) and \(\beta\) as transition rates. The second reaction represents the biding of intracellular \(\mathrm{Ca^{2+}}\) ions to a regulating factor (\(P_0\) for unbound and \(P_1\) for bound) with four binding sites for calcium and rates of \(k_1 = 2.5e^7\, mM^{-4} \, ms^{-1}\) and \(k_2=4e-4 \, ms^{-1}\) (half-activation of 0.002 mM \(Ca^{2+}\)). The calcium-bound form \(P_1\) associates with the open form of the channel, leading to a locked open form \(O_L\), with rates of \(k_3=0.1 \, ms^{-1}\) and \(k_4 = 0.001 \, ms^{-1}\).
The current is the proportional to the relative concentration of open channels
\[I_h = g_h (O+g_{inc}O_L) (V - E_h)\]with a maximal conductance of \(\bar{g}_{\mathrm{h}}=0.02 \mathrm{mS} / \mathrm{cm}^{2}\) and a reversal potential of \(E_{\mathrm{h}}=-40 \mathrm{mV}\). Because of the factor \(g_{\text {inc }}=2\), the conductance of the calcium-bound open state of \(I_{\mathrm{h}}\) channels is twice that of the unbound open state. This produces an augmentation of conductance after the binding of \(\mathrm{Ca}^{2+}\), as observed in sino-atrial cells (Hagiwara and Irisawa 1989).
The rates of \(\alpha\) and \(\beta\) are:
\[\begin{split}& \alpha = m_{\infty} / \tau_m \\ & \beta = (1-m_{\infty}) / \tau_m \\ & m_{\infty} = 1/(1+\exp((V+75-V_{sh})/5.5)) \\ & \tau_m = (5.3 + 267/(\exp((V+71.5-V_{sh})/14.2) + \exp(-(V+89-V_{sh})/11.6)))\end{split}\]and the temperature regulating factor \(\phi=2^{(T-24)/10}\).
References