# -*- coding: utf-8 -*-
# Copyright 2025 BrainX Ecosystem Limited. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""
This module implements voltage-dependent calcium channels.
"""
from typing import Union, Callable, Optional
import brainpy.math as bm
from brainpy.context import share
from brainpy.dyn.ions.calcium import Calcium, CalciumDyna
from brainpy.initialize import Initializer, parameter, variable
from brainpy.integrators.joint_eq import JointEq
from brainpy.integrators.ode.generic import odeint
from brainpy.types import Shape, ArrayType
from .base import IonChannel
__all__ = [
'CalciumChannel',
'ICaN_IS2008',
'ICaT_HM1992',
'ICaT_HP1992',
'ICaHT_HM1992',
'ICaHT_Re1993',
'ICaL_IS2008',
]
[docs]
class CalciumChannel(IonChannel):
"""Base class for Calcium ion channels."""
master_type = Calcium
'''The type of the master object.'''
def update(self, V, C, E):
raise NotImplementedError
def current(self, V, C, E):
raise NotImplementedError
def reset(self, V, C, E, batch_size: int = None):
self.reset_state(V, C, E, batch_size)
def reset_state(self, V, C, E, batch_size: int = None):
raise NotImplementedError('Must be implemented by the subclass.')
class _ICa_p2q_ss(CalciumChannel):
r"""The calcium current model of :math:`p^2q` current which described with steady-state format.
The dynamics of this generalized calcium current model is given by:
.. math::
I_{CaT} &= g_{max} p^2 q(V-E_{Ca}) \\
{dp \over dt} &= {\phi_p \cdot (p_{\infty}-p)\over \tau_p} \\
{dq \over dt} &= {\phi_q \cdot (q_{\infty}-q) \over \tau_q} \\
where :math:`\phi_p` and :math:`\phi_q` are temperature-dependent factors,
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
size: int, tuple of int
The size of the simulation target.
keep_size: bool
Keep size or flatten the size?
method: str
The numerical method
name: str
The name of the object.
g_max : float, ArrayType, Callable, Initializer
The maximum conductance.
phi_p : float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`p`.
phi_q : float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`q`.
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
phi_p: Union[float, ArrayType, Initializer, Callable] = 3.,
phi_q: Union[float, ArrayType, Initializer, Callable] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 2.,
method: str = 'exp_auto',
mode: Optional[bm.Mode] = None,
name: Optional[str] = None
):
super().__init__(size,
keep_size=keep_size,
name=name,
mode=mode, )
# parameters
self.phi_p = parameter(phi_p, self.varshape, allow_none=False)
self.phi_q = parameter(phi_q, self.varshape, allow_none=False)
self.g_max = parameter(g_max, self.varshape, allow_none=False)
# variables
self.p = variable(bm.zeros, self.mode, self.varshape)
self.q = variable(bm.zeros, self.mode, self.varshape)
# functions
self.integral = odeint(JointEq([self.dp, self.dq]), method=method)
def dp(self, p, t, V):
return self.phi_p * (self.f_p_inf(V) - p) / self.f_p_tau(V)
def dq(self, q, t, V):
return self.phi_q * (self.f_q_inf(V) - q) / self.f_q_tau(V)
def update(self, V, C, E):
self.p.value, self.q.value = self.integral(self.p.value, self.q.value, share['t'], V, share['dt'])
def current(self, V, C, E):
return self.g_max * self.p * self.p * self.q * (E - V)
def reset_state(self, V, C, E, batch_size=None):
self.p.value = self.f_p_inf(V)
self.q.value = self.f_q_inf(V)
if isinstance(batch_size, int):
assert self.p.shape[0] == batch_size
assert self.q.shape[0] == batch_size
def f_p_inf(self, V):
raise NotImplementedError
def f_p_tau(self, V):
raise NotImplementedError
def f_q_inf(self, V):
raise NotImplementedError
def f_q_tau(self, V):
raise NotImplementedError
class _ICa_p2q_markov(CalciumChannel):
r"""The calcium current model of :math:`p^2q` current which described with first-order Markov chain.
The dynamics of this generalized calcium current model is given by:
.. math::
I_{CaT} &= g_{max} p^2 q(V-E_{Ca}) \\
{dp \over dt} &= \phi_p (\alpha_p(V)(1-p) - \beta_p(V)p) \\
{dq \over dt} &= \phi_q (\alpha_q(V)(1-q) - \beta_q(V)q) \\
where :math:`\phi_p` and :math:`\phi_q` are temperature-dependent factors,
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
size: int, tuple of int
The size of the simulation target.
keep_size: bool
Keep size or flatten the size?
method: str
The numerical method
name: str
The name of the object.
g_max : float, ArrayType, Callable, Initializer
The maximum conductance.
phi_p : float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`p`.
phi_q : float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`q`.
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
phi_p: Union[float, ArrayType, Initializer, Callable] = 3.,
phi_q: Union[float, ArrayType, Initializer, Callable] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 2.,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
super().__init__(size,
keep_size=keep_size,
name=name,
mode=mode)
# parameters
self.phi_p = parameter(phi_p, self.varshape, allow_none=False)
self.phi_q = parameter(phi_q, self.varshape, allow_none=False)
self.g_max = parameter(g_max, self.varshape, allow_none=False)
# variables
self.p = variable(bm.zeros, self.mode, self.varshape)
self.q = variable(bm.zeros, self.mode, self.varshape)
# functions
self.integral = odeint(JointEq([self.dp, self.dq]), method=method)
def dp(self, p, t, V):
return self.phi_p * (self.f_p_alpha(V) * (1 - p) - self.f_p_beta(V) * p)
def dq(self, q, t, V):
return self.phi_q * (self.f_q_alpha(V) * (1 - q) - self.f_q_beta(V) * q)
def update(self, V, C, E):
self.p.value, self.q.value = self.integral(self.p.value, self.q.value, share['t'], V, share['dt'])
def current(self, V, C, E):
return self.g_max * self.p * self.p * self.q * (E - V)
def reset_state(self, V, C, E, batch_size=None):
alpha, beta = self.f_p_alpha(V), self.f_p_beta(V)
self.p.value = alpha / (alpha + beta)
alpha, beta = self.f_q_alpha(V), self.f_q_beta(V)
self.q.value = alpha / (alpha + beta)
if isinstance(batch_size, int):
assert self.p.shape[0] == batch_size
assert self.q.shape[0] == batch_size
def f_p_alpha(self, V):
raise NotImplementedError
def f_p_beta(self, V):
raise NotImplementedError
def f_q_alpha(self, V):
raise NotImplementedError
def f_q_beta(self, V):
raise NotImplementedError
[docs]
class ICaN_IS2008(CalciumChannel):
r"""The calcium-activated non-selective cation channel model
proposed by (Inoue & Strowbridge, 2008) [2]_.
The dynamics of the calcium-activated non-selective cation channel model [1]_ [2]_ is given by:
.. math::
\begin{aligned}
I_{CAN} &=g_{\mathrm{max}} M\left([Ca^{2+}]_{i}\right) p \left(V-E\right)\\
&M\left([Ca^{2+}]_{i}\right) ={[Ca^{2+}]_{i} \over 0.2+[Ca^{2+}]_{i}} \\
&{dp \over dt} = {\phi \cdot (p_{\infty}-p)\over \tau_p} \\
&p_{\infty} = {1.0 \over 1 + \exp(-(V + 43) / 5.2)} \\
&\tau_{p} = {2.7 \over \exp(-(V + 55) / 15) + \exp((V + 55) / 15)} + 1.6
\end{aligned}
where :math:`\phi` is the temperature factor.
Parameters::
g_max : float
The maximal conductance density (:math:`mS/cm^2`).
E : float
The reversal potential (mV).
phi : float
The temperature factor.
References::
.. [1] Destexhe, Alain, et al. "A model of spindle rhythmicity in the isolated
thalamic reticular nucleus." Journal of neurophysiology 72.2 (1994): 803-818.
.. [2] Inoue T, Strowbridge BW (2008) Transient activity induces a long-lasting
increase in the excitability of olfactory bulb interneurons.
J Neurophysiol 99: 187–199.
"""
'''The type of the master object.'''
master_type = CalciumDyna
def __init__(
self,
size: Shape,
keep_size: bool = False,
E: Union[float, ArrayType, Initializer, Callable] = 10.,
g_max: Union[float, ArrayType, Initializer, Callable] = 1.,
phi: Union[float, ArrayType, Initializer, Callable] = 1.,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
super().__init__(size,
keep_size=keep_size,
name=name,
mode=mode)
# parameters
self.E = parameter(E, self.varshape, allow_none=False)
self.g_max = parameter(g_max, self.varshape, allow_none=False)
self.phi = parameter(phi, self.varshape, allow_none=False)
# variables
self.p = variable(bm.zeros, self.mode, self.varshape)
# function
self.integral = odeint(self.derivative, method=method)
def derivative(self, p, t, V):
phi_p = 1.0 / (1 + bm.exp(-(V + 43.) / 5.2))
p_inf = 2.7 / (bm.exp(-(V + 55.) / 15.) + bm.exp((V + 55.) / 15.)) + 1.6
return self.phi * (phi_p - p) / p_inf
def update(self, V, C, E):
self.p.value = self.integral(self.p.value, share['t'], V, share['dt'])
def current(self, V, C, E):
M = C / (C + 0.2)
g = self.g_max * M * self.p
return g * (self.E - V)
def reset_state(self, V, C, E, batch_size=None):
self.p.value = 1.0 / (1 + bm.exp(-(V + 43.) / 5.2))
if isinstance(batch_size, int):
assert self.p.shape[0] == batch_size
[docs]
class ICaT_HM1992(_ICa_p2q_ss):
r"""The low-threshold T-type calcium current model proposed by (Huguenard & McCormick, 1992) [1]_.
The dynamics of the low-threshold T-type calcium current model [1]_ is given by:
.. math::
I_{CaT} &= g_{max} p^2 q(V-E_{Ca}) \\
{dp \over dt} &= {\phi_p \cdot (p_{\infty}-p)\over \tau_p} \\
&p_{\infty} = {1 \over 1+\exp [-(V+59-V_{sh}) / 6.2]} \\
&\tau_{p} = 0.612 + {1 \over \exp [-(V+132.-V_{sh}) / 16.7]+\exp [(V+16.8-V_{sh}) / 18.2]} \\
{dq \over dt} &= {\phi_q \cdot (q_{\infty}-q) \over \tau_q} \\
&q_{\infty} = {1 \over 1+\exp [(V+83-V_{sh}) / 4]} \\
& \begin{array}{l} \tau_{q} = \exp \left(\frac{V+467-V_{sh}}{66.6}\right) \quad V< (-80 +V_{sh})\, mV \\
\tau_{q} = \exp \left(\frac{V+22-V_{sh}}{-10.5}\right)+28 \quad V \geq (-80 + V_{sh})\, mV \end{array}
where :math:`\phi_p = 3.55^{\frac{T-24}{10}}` and :math:`\phi_q = 3^{\frac{T-24}{10}}`
are temperature-dependent factors (:math:`T` is the temperature in Celsius),
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
T : float, ArrayType
The temperature.
T_base_p : float, ArrayType
The brainpy_object temperature factor of :math:`p` channel.
T_base_q : float, ArrayType
The brainpy_object temperature factor of :math:`q` channel.
g_max : float, ArrayType, Callable, Initializer
The maximum conductance.
V_sh : float, ArrayType, Callable, Initializer
The membrane potential shift.
phi_p : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`p`.
phi_q : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`q`.
References::
.. [1] Huguenard JR, McCormick DA (1992) Simulation of the currents involved in
rhythmic oscillations in thalamic relay neurons. J Neurophysiol 68:1373–1383.
See Also::
ICa_p2q_form
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
T: Union[float, ArrayType] = 36.,
T_base_p: Union[float, ArrayType] = 3.55,
T_base_q: Union[float, ArrayType] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 2.,
V_sh: Union[float, ArrayType, Initializer, Callable] = -3.,
phi_p: Union[float, ArrayType, Initializer, Callable] = None,
phi_q: Union[float, ArrayType, Initializer, Callable] = None,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
phi_p = T_base_p ** ((T - 24) / 10) if phi_p is None else phi_p
phi_q = T_base_q ** ((T - 24) / 10) if phi_q is None else phi_q
super().__init__(size,
keep_size=keep_size,
name=name,
method=method,
g_max=g_max,
phi_p=phi_p,
phi_q=phi_q,
mode=mode)
# parameters
self.T = parameter(T, self.varshape, allow_none=False)
self.T_base_p = parameter(T_base_p, self.varshape, allow_none=False)
self.T_base_q = parameter(T_base_q, self.varshape, allow_none=False)
self.V_sh = parameter(V_sh, self.varshape, allow_none=False)
def f_p_inf(self, V):
return 1. / (1 + bm.exp(-(V + 59. - self.V_sh) / 6.2))
def f_p_tau(self, V):
return 1. / (bm.exp(-(V + 132. - self.V_sh) / 16.7) +
bm.exp((V + 16.8 - self.V_sh) / 18.2)) + 0.612
def f_q_inf(self, V):
return 1. / (1. + bm.exp((V + 83. - self.V_sh) / 4.0))
def f_q_tau(self, V):
return bm.where(V >= (-80. + self.V_sh),
bm.exp(-(V + 22. - self.V_sh) / 10.5) + 28.,
bm.exp((V + 467. - self.V_sh) / 66.6))
[docs]
class ICaT_HP1992(_ICa_p2q_ss):
r"""The low-threshold T-type calcium current model for thalamic
reticular nucleus proposed by (Huguenard & Prince, 1992) [1]_.
The dynamics of the low-threshold T-type calcium current model in thalamic
reticular nucleus neurons [1]_ is given by:
.. math::
I_{CaT} &= g_{max} p^2 q(V-E_{Ca}) \\
{dp \over dt} &= {\phi_p \cdot (p_{\infty}-p)\over \tau_p} \\
&p_{\infty} = {1 \over 1+\exp [-(V+52-V_{sh}) / 7.4]} \\
&\tau_{p} = 3+{1 \over \exp [(V+27-V_{sh}) / 10]+\exp [-(V+102-V_{sh}) / 15]} \\
{dq \over dt} &= {\phi_q \cdot (q_{\infty}-q) \over \tau_q} \\
&q_{\infty} = {1 \over 1+\exp [(V+80-V_{sh}) / 5]} \\
& \tau_q = 85+ {1 \over \exp [(V+48-V_{sh}) / 4]+\exp [-(V+407-V_{sh}) / 50]}
where :math:`\phi_p = 5^{\frac{T-24}{10}}` and :math:`\phi_q = 3^{\frac{T-24}{10}}`
are temperature-dependent factors (:math:`T` is the temperature in Celsius),
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
T : float, ArrayType
The temperature.
T_base_p : float, ArrayType
The brainpy_object temperature factor of :math:`p` channel.
T_base_q : float, ArrayType
The brainpy_object temperature factor of :math:`q` channel.
g_max : float, ArrayType, Callable, Initializer
The maximum conductance.
V_sh : float, ArrayType, Callable, Initializer
The membrane potential shift.
phi_p : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`p`.
phi_q : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`q`.
References::
.. [1] Huguenard JR, Prince DA (1992) A novel T-type current underlies
prolonged Ca2+- dependent burst firing in GABAergic neurons of rat
thalamic reticular nucleus. J Neurosci 12: 3804–3817.
See Also::
ICa_p2q_form
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
T: Union[float, ArrayType] = 36.,
T_base_p: Union[float, ArrayType] = 5.,
T_base_q: Union[float, ArrayType] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 1.75,
V_sh: Union[float, ArrayType, Initializer, Callable] = -3.,
phi_p: Union[float, ArrayType, Initializer, Callable] = None,
phi_q: Union[float, ArrayType, Initializer, Callable] = None,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
phi_p = T_base_p ** ((T - 24) / 10) if phi_p is None else phi_p
phi_q = T_base_q ** ((T - 24) / 10) if phi_q is None else phi_q
super().__init__(size,
keep_size=keep_size,
name=name,
method=method,
g_max=g_max,
phi_p=phi_p,
phi_q=phi_q,
mode=mode)
# parameters
self.T = parameter(T, self.varshape, allow_none=False)
self.T_base_p = parameter(T_base_p, self.varshape, allow_none=False)
self.T_base_q = parameter(T_base_q, self.varshape, allow_none=False)
self.V_sh = parameter(V_sh, self.varshape, allow_none=False)
def f_p_inf(self, V):
return 1. / (1. + bm.exp(-(V + 52. - self.V_sh) / 7.4))
def f_p_tau(self, V):
return 3. + 1. / (bm.exp((V + 27. - self.V_sh) / 10.) +
bm.exp(-(V + 102. - self.V_sh) / 15.))
def f_q_inf(self, V):
return 1. / (1. + bm.exp((V + 80. - self.V_sh) / 5.))
def f_q_tau(self, V):
return 85. + 1. / (bm.exp((V + 48. - self.V_sh) / 4.) +
bm.exp(-(V + 407. - self.V_sh) / 50.))
[docs]
class ICaHT_HM1992(_ICa_p2q_ss):
r"""The high-threshold T-type calcium current model proposed by (Huguenard & McCormick, 1992) [1]_.
The high-threshold T-type calcium current model is adopted from [1]_.
Its dynamics is given by
.. math::
\begin{aligned}
I_{\mathrm{Ca/HT}} &= g_{\mathrm{max}} p^2 q (V-E_{Ca})
\\
{dp \over dt} &= {\phi_{p} \cdot (p_{\infty} - p) \over \tau_{p}} \\
&\tau_{p} =\frac{1}{\exp \left(\frac{V+132-V_{sh}}{-16.7}\right)+\exp \left(\frac{V+16.8-V_{sh}}{18.2}\right)}+0.612 \\
& p_{\infty} = {1 \over 1+exp[-(V+59-V_{sh}) / 6.2]}
\\
{dq \over dt} &= {\phi_{q} \cdot (q_{\infty} - h) \over \tau_{q}} \\
& \begin{array}{l} \tau_q = \exp \left(\frac{V+467-V_{sh}}{66.6}\right) \quad V< (-80 +V_{sh})\, mV \\
\tau_q = \exp \left(\frac{V+22-V_{sh}}{-10.5}\right)+28 \quad V \geq (-80 + V_{sh})\, mV \end{array} \\
&q_{\infty} = {1 \over 1+exp[(V+83 -V_{shift})/4]}
\end{aligned}
where :math:`phi_p = 3.55^{\frac{T-24}{10}}` and :math:`phi_q = 3^{\frac{T-24}{10}}`
are temperature-dependent factors (:math:`T` is the temperature in Celsius),
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
T : float, ArrayType
The temperature.
T_base_p : float, ArrayType
The brainpy_object temperature factor of :math:`p` channel.
T_base_q : float, ArrayType
The brainpy_object temperature factor of :math:`q` channel.
g_max : float, ArrayType, Initializer, Callable
The maximum conductance.
V_sh : float, ArrayType, Initializer, Callable
The membrane potential shift.
References::
.. [1] Huguenard JR, McCormick DA (1992) Simulation of the currents involved in
rhythmic oscillations in thalamic relay neurons. J Neurophysiol 68:1373–1383.
See Also::
ICa_p2q_form
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
T: Union[float, ArrayType] = 36.,
T_base_p: Union[float, ArrayType] = 3.55,
T_base_q: Union[float, ArrayType] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 2.,
V_sh: Union[float, ArrayType, Initializer, Callable] = 25.,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
super().__init__(size,
keep_size=keep_size,
name=name,
method=method,
g_max=g_max,
phi_p=T_base_p ** ((T - 24) / 10),
phi_q=T_base_q ** ((T - 24) / 10),
mode=mode)
# parameters
self.T = parameter(T, self.varshape, allow_none=False)
self.T_base_p = parameter(T_base_p, self.varshape, allow_none=False)
self.T_base_q = parameter(T_base_q, self.varshape, allow_none=False)
self.V_sh = parameter(V_sh, self.varshape, allow_none=False)
# variables
self.p = variable(bm.zeros, self.mode, self.varshape)
self.q = variable(bm.zeros, self.mode, self.varshape)
# function
self.integral = odeint(JointEq([self.dp, self.dq]), method=method)
def f_p_inf(self, V):
return 1. / (1. + bm.exp(-(V + 59. - self.V_sh) / 6.2))
def f_p_tau(self, V):
return 1. / (bm.exp(-(V + 132. - self.V_sh) / 16.7) +
bm.exp((V + 16.8 - self.V_sh) / 18.2)) + 0.612
def f_q_inf(self, V):
return 1. / (1. + bm.exp((V + 83. - self.V_sh) / 4.))
def f_q_tau(self, V):
return bm.where(V >= (-80. + self.V_sh),
bm.exp(-(V + 22. - self.V_sh) / 10.5) + 28.,
bm.exp((V + 467. - self.V_sh) / 66.6))
[docs]
class ICaHT_Re1993(_ICa_p2q_markov):
r"""The high-threshold T-type calcium current model proposed by (Reuveni, et al., 1993) [1]_.
HVA Calcium current was described for neocortical neurons by Sayer et al. (1990).
Its dynamics is given by (the rate functions are measured under 36 Celsius):
.. math::
\begin{aligned}
I_{L} &=\bar{g}_{L} q^{2} r\left(V-E_{\mathrm{Ca}}\right) \\
\frac{\mathrm{d} q}{\mathrm{~d} t} &= \phi_p (\alpha_{q}(V)(1-q)-\beta_{q}(V) q) \\
\frac{\mathrm{d} r}{\mathrm{~d} t} &= \phi_q (\alpha_{r}(V)(1-r)-\beta_{r}(V) r) \\
\alpha_{q} &=\frac{0.055(-27-V+V_{sh})}{\exp [(-27-V+V_{sh}) / 3.8]-1} \\
\beta_{q} &=0.94 \exp [(-75-V+V_{sh}) / 17] \\
\alpha_{r} &=0.000457 \exp [(-13-V+V_{sh}) / 50] \\
\beta_{r} &=\frac{0.0065}{\exp [(-15-V+V_{sh}) / 28]+1},
\end{aligned}
Parameters::
size: int, tuple of int
The size of the simulation target.
keep_size: bool
Keep size or flatten the size?
method: str
The numerical method
name: str
The name of the object.
g_max : float, ArrayType, Callable, Initializer
The maximum conductance.
V_sh : float, ArrayType, Callable, Initializer
The membrane potential shift.
T : float, ArrayType
The temperature.
T_base_p : float, ArrayType
The brainpy_object temperature factor of :math:`p` channel.
T_base_q : float, ArrayType
The brainpy_object temperature factor of :math:`q` channel.
phi_p : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`p`.
If `None`, :math:`\phi_p = \mathrm{T_base_p}^{\frac{T-23}{10}}`.
phi_q : optional, float, ArrayType, Callable, Initializer
The temperature factor for channel :math:`q`.
If `None`, :math:`\phi_q = \mathrm{T_base_q}^{\frac{T-23}{10}}`.
References::
.. [1] Reuveni, I., et al. "Stepwise repolarization from Ca2+ plateaus
in neocortical pyramidal cells: evidence for nonhomogeneous
distribution of HVA Ca2+ channels in dendrites." Journal of
Neuroscience 13.11 (1993): 4609-4621.
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
T: Union[float, ArrayType] = 36.,
T_base_p: Union[float, ArrayType] = 2.3,
T_base_q: Union[float, ArrayType] = 2.3,
phi_p: Union[float, ArrayType, Initializer, Callable] = None,
phi_q: Union[float, ArrayType, Initializer, Callable] = None,
g_max: Union[float, ArrayType, Initializer, Callable] = 1.,
V_sh: Union[float, ArrayType, Initializer, Callable] = 0.,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
phi_p = T_base_p ** ((T - 23.) / 10.) if phi_p is None else phi_p
phi_q = T_base_q ** ((T - 23.) / 10.) if phi_q is None else phi_q
super().__init__(size,
keep_size=keep_size,
name=name,
method=method,
g_max=g_max,
phi_p=phi_p,
phi_q=phi_q,
mode=mode)
self.T = parameter(T, self.varshape, allow_none=False)
self.T_base_p = parameter(T_base_p, self.varshape, allow_none=False)
self.T_base_q = parameter(T_base_q, self.varshape, allow_none=False)
self.V_sh = parameter(V_sh, self.varshape, allow_none=False)
def f_p_alpha(self, V):
temp = -27 - V + self.V_sh
return 0.055 * temp / (bm.exp(temp / 3.8) - 1)
def f_p_beta(self, V):
return 0.94 * bm.exp((-75. - V + self.V_sh) / 17.)
def f_q_alpha(self, V):
return 0.000457 * bm.exp((-13. - V + self.V_sh) / 50.)
def f_q_beta(self, V):
return 0.0065 / (bm.exp((-15. - V + self.V_sh) / 28.) + 1.)
[docs]
class ICaL_IS2008(_ICa_p2q_ss):
r"""The L-type calcium channel model proposed by (Inoue & Strowbridge, 2008) [1]_.
The L-type calcium channel model is adopted from (Inoue, et, al., 2008) [1]_.
Its dynamics is given by:
.. math::
I_{CaL} &= g_{max} p^2 q(V-E_{Ca}) \\
{dp \over dt} &= {\phi_p \cdot (p_{\infty}-p)\over \tau_p} \\
& p_{\infty} = {1 \over 1+\exp [-(V+10-V_{sh}) / 4.]} \\
& \tau_{p} = 0.4+{0.7 \over \exp [(V+5-V_{sh}) / 15]+\exp [-(V+5-V_{sh}) / 15]} \\
{dq \over dt} &= {\phi_q \cdot (q_{\infty}-q) \over \tau_q} \\
& q_{\infty} = {1 \over 1+\exp [(V+25-V_{sh}) / 2]} \\
& \tau_q = 300 + {100 \over \exp [(V+40-V_{sh}) / 9.5]+\exp [-(V+40-V_{sh}) / 9.5]}
where :math:`phi_p = 3.55^{\frac{T-24}{10}}` and :math:`phi_q = 3^{\frac{T-24}{10}}`
are temperature-dependent factors (:math:`T` is the temperature in Celsius),
:math:`E_{Ca}` is the reversal potential of Calcium channel.
Parameters::
T : float
The temperature.
T_base_p : float
The brainpy_object temperature factor of :math:`p` channel.
T_base_q : float
The brainpy_object temperature factor of :math:`q` channel.
g_max : float
The maximum conductance.
V_sh : float
The membrane potential shift.
References::
.. [1] Inoue, Tsuyoshi, and Ben W. Strowbridge. "Transient activity induces a long-lasting
increase in the excitability of olfactory bulb interneurons." Journal of
neurophysiology 99, no. 1 (2008): 187-199.
See Also::
ICa_p2q_form
"""
def __init__(
self,
size: Shape,
keep_size: bool = False,
T: Union[float, ArrayType, Initializer, Callable] = 36.,
T_base_p: Union[float, ArrayType, Initializer, Callable] = 3.55,
T_base_q: Union[float, ArrayType, Initializer, Callable] = 3.,
g_max: Union[float, ArrayType, Initializer, Callable] = 1.,
V_sh: Union[float, ArrayType, Initializer, Callable] = 0.,
method: str = 'exp_auto',
name: Optional[str] = None,
mode: Optional[bm.Mode] = None,
):
super().__init__(size,
keep_size=keep_size,
name=name,
method=method,
g_max=g_max,
phi_p=T_base_p ** ((T - 24) / 10),
phi_q=T_base_q ** ((T - 24) / 10),
mode=mode)
# parameters
self.T = parameter(T, self.varshape, allow_none=False)
self.T_base_p = parameter(T_base_p, self.varshape, allow_none=False)
self.T_base_q = parameter(T_base_q, self.varshape, allow_none=False)
self.V_sh = parameter(V_sh, self.varshape, allow_none=False)
def f_p_inf(self, V):
return 1. / (1 + bm.exp(-(V + 10. - self.V_sh) / 4.))
def f_p_tau(self, V):
return 0.4 + .7 / (bm.exp(-(V + 5. - self.V_sh) / 15.) +
bm.exp((V + 5. - self.V_sh) / 15.))
def f_q_inf(self, V):
return 1. / (1. + bm.exp((V + 25. - self.V_sh) / 2.))
def f_q_tau(self, V):
return 300. + 100. / (bm.exp((V + 40 - self.V_sh) / 9.5) +
bm.exp(-(V + 40 - self.V_sh) / 9.5))
