# brainpy.channels.Ih_De1996#

class brainpy.channels.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

__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=None)[source]#

Methods

 __init__(size[, keep_size, E, k2, k4, V_sh, ...]) clear_input() cpu() Move all variable into the CPU device. cuda() Move all variables into the GPU device. 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_state_dict(state_dict[, warn, compatible]) Copy parameters and buffers from state_dict into this module and its descendants. load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes[, node_cls]) register_implicit_vars(*variables[, var_cls]) 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. state_dict() Returns a dictionary containing a whole state of the module. to(device) Moves all variables into the given device. tpu() Move all variables into the TPU device. train_vars([method, level, include_self]) The shortcut for retrieving all trainable variables. tree_flatten() Flattens the object as a PyTree. tree_unflatten(aux, dynamic_values) Unflatten the data to construct an object of this class. 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 Global delay data, which stores the delay variables and corresponding delay targets. mode Mode of the model, which is useful to control the multiple behaviors of the model. name Name of the model. varshape