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