# brainpy.dyn.channels.IH.Ih_De1996#

class brainpy.dyn.channels.IH.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=NormalMode)[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

1

Destexhe, Alain, et al. “Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices.” Journal of neurophysiology 76.3 (1996): 2049-2070.

__init__(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=NormalMode)[source]#

Methods

 __init__(size[, keep_size, E, k2, k4, V_sh, ...]) clear_input() current(V, C_Ca, E_Ca) dO(O, t, OL, V) dOL(OL, t, O, P1) dP1(P1, t, C_Ca) f_inf(V) f_tau(V) get_delay_data(identifier, delay_step, *indices) Get delay data according to the provided delay steps. load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. offline_fit(target, fit_record) offline_init() online_fit(target, fit_record) online_init() register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes, **named_nodes) register_implicit_vars(*variables, ...) reset(V, C_Ca, E_Ca[, batch_size]) Reset function which reset the whole variables in the model. reset_local_delays([nodes]) Reset local delay variables. reset_state(V, C_Ca, E_Ca[, batch_size]) Reset function which reset the states in the model. save_states(filename[, variables]) Save the model states. train_vars([method, level, include_self]) The shortcut for retrieving all trainable variables. unique_name([name, type_]) Get the unique name for this object. update(tdi, V, C_Ca, E_Ca) The function to specify the updating rule. update_local_delays([nodes]) Update local delay variables. vars([method, level, include_self]) Collect all variables in this node and the children nodes.

Attributes

 global_delay_data mode Mode of the model, which is useful to control the multiple behaviors of the model. name Name of the model. varshape