# brainpy.channels.IAHP_De1994#

class brainpy.channels.IAHP_De1994(size, keep_size=False, E=-95.0, 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.

Parameters:
• g_max (float) – The maximal conductance density ($$mS/cm^2$$).

• E (float) – The reversal potential (mV).

References

__init__(size, keep_size=False, E=-95.0, n=2, g_max=10.0, alpha=48.0, beta=0.09, phi=1.0, method='exp_auto', name=None, mode=None)[source]#

Methods

 __init__(size[, keep_size, E, n, g_max, ...]) clear_input() cpu() Move all variable into the CPU device. cuda() Move all variables into the GPU device. current(V, C_Ca, E_Ca) dp(p, t, C_Ca) 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. pass_shared varshape