# -*- coding: utf-8 -*-
"""
This module implements voltage-dependent calcium channels.
"""
from typing import Union, Callable, Optional
import brainpy.math as bm
from brainpy._src.context import share
from brainpy._src.dyn.ions.calcium import Calcium, CalciumDyna
from brainpy._src.initialize import Initializer, parameter, variable
from brainpy._src.integrators.joint_eq import JointEq
from brainpy._src.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',
'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, self.q, 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, self.q, 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))
