Source code for brainpy._src.dyn.channels.potassium_compatible

# -*- coding: utf-8 -*-

"""
This module implements voltage-dependent potassium channels.

"""

from typing import Union, Callable, Optional, Sequence

import brainpy.math as bm
from brainpy._src.context import share
from brainpy._src.dyn.channels.base import IonChannel
from brainpy._src.dyn.neurons.hh import HHTypedNeuron
from brainpy._src.initialize import Initializer, parameter, variable
from brainpy._src.integrators import odeint, JointEq
from brainpy.types import ArrayType

__all__ = [
  'IKDR_Ba2002',
  'IK_TM1991',
  'IK_HH1952',
  'IKA1_HM1992',
  'IKA2_HM1992',
  'IKK2A_HM1992',
  'IKK2B_HM1992',
  'IKNI_Ya1989',
  'IKL',
]


class _IK_p4_markov(IonChannel):
  r"""The delayed rectifier potassium channel of :math:`p^4`
  current which described with first-order Markov chain.

  This general potassium current model should have the form of

  .. math::

      \begin{aligned}
      I_{\mathrm{K}} &= g_{\mathrm{max}} * p^4 \\
      \frac{dp}{dt} &= \phi * (\alpha_p (1-p) - \beta_p p)
      \end{aligned}

  where :math:`\phi` is a temperature-dependent factor.

  Parameters
  ----------
  size: int, sequence of int
    The object size.
  keep_size: bool
    Whether we use `size` to initialize the variable. Otherwise, variable shape
    will be initialized as `num`.
  g_max : float, ArrayType, Initializer, Callable
    The maximal conductance density (:math:`mS/cm^2`).
  E : float, ArrayType, Initializer, Callable
    The reversal potential (mV).
  phi : float, ArrayType, Initializer, Callable
    The temperature-dependent factor.
  method: str
    The numerical integration method.
  name: str
    The object name.

  """
  master_type = HHTypedNeuron

  def __init__(
      self,
      size: Union[int, Sequence[int]],
      keep_size: bool = False,
      E: Union[float, ArrayType, Initializer, Callable] = -90.,
      g_max: Union[float, ArrayType, Initializer, Callable] = 10.,
      phi: Union[float, ArrayType, Initializer, Callable] = 1.,
      method: str = 'exp_auto',
      name: str = None,
      mode: bm.Mode = None,
  ):
    super().__init__(size,
                     keep_size=keep_size,
                     name=name,
                     mode=mode)

    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):
    return self.phi * (self.f_p_alpha(V) * (1. - p) - self.f_p_beta(V) * p)

  def update(self, V):
    self.p.value = self.integral(self.p.value, share['t'], V, share['dt'])

  def current(self, V):
    return self.g_max * self.p ** 4 * (self.E - V)

  def reset_state(self, V, batch_size=None):
    alpha = self.f_p_alpha(V)
    beta = self.f_p_beta(V)
    self.p.value = alpha / (alpha + beta)
    if isinstance(batch_size, int):
      assert self.p.shape[0] == batch_size

  def f_p_alpha(self, V):
    raise NotImplementedError

  def f_p_beta(self, V):
    raise NotImplementedError


[docs] class IKDR_Ba2002(_IK_p4_markov): r"""The delayed rectifier potassium channel current. The potassium current model is adopted from (Bazhenov, et, al. 2002) [1]_. It's dynamics is given by: .. math:: \begin{aligned} I_{\mathrm{K}} &= g_{\mathrm{max}} * p^4 \\ \frac{dp}{dt} &= \phi * (\alpha_p (1-p) - \beta_p p) \\ \alpha_{p} &=\frac{0.032\left(V-V_{sh}-15\right)}{1-\exp \left(-\left(V-V_{sh}-15\right) / 5\right)} \\ \beta_p &= 0.5 \exp \left(-\left(V-V_{sh}-10\right) / 40\right) \end{aligned} where :math:`\phi` is a temperature-dependent factor, which is given by :math:`\phi=3^{\frac{T-36}{10}}` (:math:`T` is the temperature in Celsius). Parameters ---------- size: int, sequence of int The object size. keep_size: bool Whether we use `size` to initialize the variable. Otherwise, variable shape will be initialized as `num`. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). T_base : float, ArrayType The brainpy_object of temperature factor. T : float, ArrayType, Initializer, Callable The temperature (Celsius, :math:`^{\circ}C`). V_sh : float, ArrayType, Initializer, Callable The shift of the membrane potential to spike. method: str The numerical integration method. name: str The object name. References ---------- .. [1] Bazhenov, Maxim, et al. "Model of thalamocortical slow-wave sleep oscillations and transitions to activated states." Journal of neuroscience 22.19 (2002): 8691-8704. """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., V_sh: Union[float, ArrayType, Initializer, Callable] = -50., T_base: Union[float, ArrayType] = 3., T: Union[float, ArrayType] = 36., phi: Optional[Union[float, ArrayType, Initializer, Callable]] = None, method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): phi = T_base ** ((T - 36) / 10) if phi is None else phi super(IKDR_Ba2002, self).__init__(size, keep_size=keep_size, name=name, method=method, g_max=g_max, phi=phi, E=E, mode=mode) # parameters self.T = parameter(T, self.varshape, allow_none=False) self.T_base = parameter(T_base, self.varshape, allow_none=False) self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_alpha(self, V): tmp = V - self.V_sh - 15. return 0.032 * tmp / (1. - bm.exp(-tmp / 5.)) def f_p_beta(self, V): return 0.5 * bm.exp(-(V - self.V_sh - 10.) / 40.)
[docs] class IK_TM1991(_IK_p4_markov): r"""The potassium channel described by (Traub and Miles, 1991) [1]_. The dynamics of this channel is given by: .. math:: \begin{aligned} I_{\mathrm{K}} &= g_{\mathrm{max}} * p^4 \\ \frac{dp}{dt} &= \phi * (\alpha_p (1-p) - \beta_p p) \\ \alpha_{p} &= 0.032 \frac{(15 - V + V_{sh})}{(\exp((15 - V + V_{sh}) / 5) - 1.)} \\ \beta_p &= 0.5 * \exp((10 - V + V_{sh}) / 40) \end{aligned} where :math:`V_{sh}` is the membrane shift (default -63 mV), and :math:`\phi` is the temperature-dependent factor (default 1.). Parameters ---------- size: int, sequence of int The geometry size. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). method: str The numerical integration method. name: str The object name. References ---------- .. [1] Traub, Roger D., and Richard Miles. Neuronal networks of the hippocampus. Vol. 777. Cambridge University Press, 1991. See Also -------- INa_TM1991 """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., phi: Union[float, ArrayType, Initializer, Callable] = 1., V_sh: Union[int, float, ArrayType, Initializer, Callable] = -60., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IK_TM1991, self).__init__(size, keep_size=keep_size, name=name, method=method, phi=phi, E=E, g_max=g_max, mode=mode) self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_alpha(self, V): c = 15 - V + self.V_sh return 0.032 * c / (bm.exp(c / 5) - 1.) def f_p_beta(self, V): return 0.5 * bm.exp((10 - V + self.V_sh) / 40)
[docs] class IK_HH1952(_IK_p4_markov): r"""The potassium channel described by Hodgkin–Huxley model [1]_. The dynamics of this channel is given by: .. math:: \begin{aligned} I_{\mathrm{K}} &= g_{\mathrm{max}} * p^4 \\ \frac{dp}{dt} &= \phi * (\alpha_p (1-p) - \beta_p p) \\ \alpha_{p} &= \frac{0.01 (V -V_{sh} + 10)}{1-\exp \left(-\left(V-V_{sh}+ 10\right) / 10\right)} \\ \beta_p &= 0.125 \exp \left(-\left(V-V_{sh}+20\right) / 80\right) \end{aligned} where :math:`V_{sh}` is the membrane shift (default -45 mV), and :math:`\phi` is the temperature-dependent factor (default 1.). Parameters ---------- size: int, sequence of int The geometry size. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). method: str The numerical integration method. name: str The object name. References ---------- .. [1] Hodgkin, Alan L., and Andrew F. Huxley. "A quantitative description of membrane current and its application to conduction and excitation in nerve." The Journal of physiology 117.4 (1952): 500. See Also -------- INa_HH1952 """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., phi: Union[float, ArrayType, Initializer, Callable] = 1., V_sh: Union[int, float, ArrayType, Initializer, Callable] = -45., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IK_HH1952, self).__init__(size, keep_size=keep_size, name=name, method=method, phi=phi, E=E, g_max=g_max, mode=mode) self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_alpha(self, V): temp = V - self.V_sh + 10 return 0.01 * temp / (1 - bm.exp(-temp / 10)) def f_p_beta(self, V): return 0.125 * bm.exp(-(V - self.V_sh + 20) / 80)
class _IKA_p4q_ss(IonChannel): r"""The rapidly inactivating Potassium channel of :math:`p^4q` current which described with steady-state format. This model is developed according to the average behavior of rapidly inactivating Potassium channel in Thalamus relay neurons [2]_ [3]_. .. math:: &IA = g_{\mathrm{max}} p^4 q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [3] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. """ master_type = HHTypedNeuron def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: 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_p = parameter(phi_p, self.varshape, allow_none=False) self.phi_q = parameter(phi_q, 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 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): self.p.value, self.q.value = self.integral(self.p.value, self.q.value, share['t'], V, share['dt']) def current(self, V): return self.g_max * self.p ** 4 * self.q * (self.E - V) def reset_state(self, V, 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
[docs] class IKA1_HM1992(_IKA_p4q_ss): r"""The rapidly inactivating Potassium channel (IA1) model proposed by (Huguenard & McCormick, 1992) [2]_. This model is developed according to the average behavior of rapidly inactivating Potassium channel in Thalamus relay neurons [2]_ [1]_. .. math:: &IA = g_{\mathrm{max}} p^4 q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &p_{\infty} = \frac{1}{1+ \exp[-(V -V_{sh}+ 60)/8.5]} \\ &\tau_{p}=\frac{1}{\exp \left(\frac{V -V_{sh}+35.8}{19.7}\right)+ \exp \left(\frac{V -V_{sh}+79.7}{-12.7}\right)}+0.37 \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ &q_{\infty} = \frac{1}{1+ \exp[(V -V_{sh} + 78)/6]} \\ &\begin{array}{l} \tau_{q} = \frac{1}{\exp((V -V_{sh}+46)/5.) + \exp((V -V_{sh}+238)/-37.5)} \quad V<(-63+V_{sh})\, mV \\ \tau_{q} = 19 \quad V \geq (-63 + V_{sh})\, mV \end{array} where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [1] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. See Also -------- IKA2_HM1992 """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 30., V_sh: Union[float, ArrayType, Initializer, Callable] = 0., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IKA1_HM1992, self).__init__(size, keep_size=keep_size, name=name, method=method, E=E, g_max=g_max, phi_p=phi_p, phi_q=phi_q, mode=mode) # parameters self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_inf(self, V): return 1. / (1. + bm.exp(-(V - self.V_sh + 60.) / 8.5)) def f_p_tau(self, V): return 1. / (bm.exp((V - self.V_sh + 35.8) / 19.7) + bm.exp(-(V - self.V_sh + 79.7) / 12.7)) + 0.37 def f_q_inf(self, V): return 1. / (1. + bm.exp((V - self.V_sh + 78.) / 6.)) def f_q_tau(self, V): return bm.where(V < -63 + self.V_sh, 1. / (bm.exp((V - self.V_sh + 46.) / 5.) + bm.exp(-(V - self.V_sh + 238.) / 37.5)), 19.)
[docs] class IKA2_HM1992(_IKA_p4q_ss): r"""The rapidly inactivating Potassium channel (IA2) model proposed by (Huguenard & McCormick, 1992) [2]_. This model is developed according to the average behavior of rapidly inactivating Potassium channel in Thalamus relay neurons [2]_ [1]_. .. math:: &IA = g_{\mathrm{max}} p^4 q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &p_{\infty} = \frac{1}{1+ \exp[-(V -V_{sh}+ 36)/20.]} \\ &\tau_{p}=\frac{1}{\exp \left(\frac{V -V_{sh}+35.8}{19.7}\right)+ \exp \left(\frac{V -V_{sh}+79.7}{-12.7}\right)}+0.37 \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ &q_{\infty} = \frac{1}{1+ \exp[(V -V_{sh} + 78)/6]} \\ &\begin{array}{l} \tau_{q} = \frac{1}{\exp((V -V_{sh}+46)/5.) + \exp((V -V_{sh}+238)/-37.5)} \quad V<(-63+V_{sh})\, mV \\ \tau_{q} = 19 \quad V \geq (-63 + V_{sh})\, mV \end{array} where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [1] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. See Also -------- IKA1_HM1992 """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 20., V_sh: Union[float, ArrayType, Initializer, Callable] = 0., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IKA2_HM1992, self).__init__(size, keep_size=keep_size, name=name, method=method, E=E, g_max=g_max, phi_q=phi_q, phi_p=phi_p, mode=mode) # parameters self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_inf(self, V): return 1. / (1. + bm.exp(-(V - self.V_sh + 36.) / 20.)) def f_p_tau(self, V): return 1. / (bm.exp((V - self.V_sh + 35.8) / 19.7) + bm.exp(-(V - self.V_sh + 79.7) / 12.7)) + 0.37 def f_q_inf(self, V): return 1. / (1. + bm.exp((V - self.V_sh + 78.) / 6.)) def f_q_tau(self, V): return bm.where(V < -63 + self.V_sh, 1. / (bm.exp((V - self.V_sh + 46.) / 5.) + bm.exp(-(V - self.V_sh + 238.) / 37.5)), 19.)
class _IKK2_pq_ss(IonChannel): r"""The slowly inactivating Potassium channel of :math:`pq` current which described with steady-state format. The dynamics of the model is given as [2]_ [3]_. .. math:: &IK2 = g_{\mathrm{max}} p q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [3] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. """ master_type = HHTypedNeuron def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: 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_p = parameter(phi_p, self.varshape, allow_none=False) self.phi_q = parameter(phi_q, 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 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): self.p.value, self.q.value = self.integral(self.p.value, self.q.value, share['t'], V, share['dt']) def current(self, V): return self.g_max * self.p * self.q * (self.E - V) def reset_state(self, V, 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
[docs] class IKK2A_HM1992(_IKK2_pq_ss): r"""The slowly inactivating Potassium channel (IK2a) model proposed by (Huguenard & McCormick, 1992) [2]_. The dynamics of the model is given as [2]_ [3]_. .. math:: &IK2 = g_{\mathrm{max}} p q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &p_{\infty} = \frac{1}{1+ \exp[-(V -V_{sh}+ 43)/17]} \\ &\tau_{p}=\frac{1}{\exp \left(\frac{V -V_{sh}-81.}{25.6}\right)+ \exp \left(\frac{V -V_{sh}+132}{-18}\right)}+9.9 \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ &q_{\infty} = \frac{1}{1+ \exp[(V -V_{sh} + 59)/10.6]} \\ & \tau_{q} = \frac{1}{\exp((V -V_{sh}+1329)/200.) + \exp((V -V_{sh}+130)/-7.1)} + 120 \\ where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [3] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., V_sh: Union[float, ArrayType, Initializer, Callable] = 0., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IKK2A_HM1992, self).__init__(size, keep_size=keep_size, name=name, method=method, phi_p=phi_p, phi_q=phi_q, g_max=g_max, E=E, mode=mode) # parameters self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_inf(self, V): return 1. / (1. + bm.exp(-(V - self.V_sh + 43.) / 17.)) def f_p_tau(self, V): return 1. / (bm.exp((V - self.V_sh - 81.) / 25.6) + bm.exp(-(V - self.V_sh + 132) / 18.)) + 9.9 def f_q_inf(self, V): return 1. / (1. + bm.exp((V - self.V_sh + 58.) / 10.6)) def f_q_tau(self, V): return 1. / (bm.exp((V - self.V_sh - 1329.) / 200.) + bm.exp(-(V - self.V_sh + 130.) / 7.1))
[docs] class IKK2B_HM1992(_IKK2_pq_ss): r"""The slowly inactivating Potassium channel (IK2b) model proposed by (Huguenard & McCormick, 1992) [2]_. The dynamics of the model is given as [2]_ [3]_. .. math:: &IK2 = g_{\mathrm{max}} p q (E-V) \\ &\frac{dp}{dt} = \phi_p \frac{p_{\infty} - p}{\tau_p} \\ &p_{\infty} = \frac{1}{1+ \exp[-(V -V_{sh}+ 43)/17]} \\ &\tau_{p}=\frac{1}{\exp \left(\frac{V -V_{sh}-81.}{25.6}\right)+ \exp \left(\frac{V -V_{sh}+132}{-18}\right)}+9.9 \\ &\frac{dq}{dt} = \phi_q \frac{q_{\infty} - q}{\tau_q} \\ &q_{\infty} = \frac{1}{1+ \exp[(V -V_{sh} + 59)/10.6]} \\ &\begin{array}{l} \tau_{q} = \frac{1}{\exp((V -V_{sh}+1329)/200.) + \exp((V -V_{sh}+130)/-7.1)} + 120 \quad V<(-70+V_{sh})\, mV \\ \tau_{q} = 8.9 \quad V \geq (-70 + V_{sh})\, mV \end{array} where :math:`\phi_p` and :math:`\phi_q` are the temperature dependent factors (default 1.). Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). 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 ---------- .. [2] Huguenard, John R., and David A. McCormick. "Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons." Journal of neurophysiology 68.4 (1992): 1373-1383. .. [3] Huguenard, J. R., and D. A. Prince. "Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons." Journal of neurophysiology 66.4 (1991): 1316-1328. """ def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 10., V_sh: Union[float, ArrayType, Initializer, Callable] = 0., phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IKK2B_HM1992, self).__init__(size, keep_size=keep_size, name=name, method=method, phi_p=phi_p, phi_q=phi_q, g_max=g_max, E=E, mode=mode) # parameters self.V_sh = parameter(V_sh, self.varshape, allow_none=False) def f_p_inf(self, V): return 1. / (1. + bm.exp(-(V - self.V_sh + 43.) / 17.)) def f_p_tau(self, V): return 1. / (bm.exp((V - self.V_sh - 81.) / 25.6) + bm.exp(-(V - self.V_sh + 132) / 18.)) + 9.9 def f_q_inf(self, V): return 1. / (1. + bm.exp((V - self.V_sh + 58.) / 10.6)) def f_q_tau(self, V): return bm.where(V < -70 + self.V_sh, 1. / (bm.exp((V - self.V_sh - 1329.) / 200.) + bm.exp(-(V - self.V_sh + 130.) / 7.1)), 8.9)
[docs] class IKNI_Ya1989(IonChannel): r"""A slow non-inactivating K+ current described by Yamada et al. (1989) [1]_. This slow potassium current can effectively account for spike-frequency adaptation. .. math:: \begin{aligned} &I_{M}=\bar{g}_{M} p\left(V-E_{K}\right) \\ &\frac{\mathrm{d} p}{\mathrm{~d} t}=\left(p_{\infty}(V)-p\right) / \tau_{p}(V) \\ &p_{\infty}(V)=\frac{1}{1+\exp [-(V-V_{sh}+35) / 10]} \\ &\tau_{p}(V)=\frac{\tau_{\max }}{3.3 \exp [(V-V_{sh}+35) / 20]+\exp [-(V-V_{sh}+35) / 20]} \end{aligned} where :math:`\bar{g}_{M}` was :math:`0.004 \mathrm{mS} / \mathrm{cm}^{2}` and :math:`\tau_{\max }=4 \mathrm{~s}`, unless stated otherwise. Parameters ---------- size: int, sequence of int The geometry size. method: str The numerical integration method. name: str The object name. g_max : float, ArrayType, Initializer, Callable The maximal conductance density (:math:`mS/cm^2`). E : float, ArrayType, Initializer, Callable The reversal potential (mV). V_sh : float, ArrayType, Callable, Initializer The membrane potential shift. phi_p : optional, float, ArrayType, Callable, Initializer The temperature factor for channel :math:`p`. tau_max: float, ArrayType, Callable, Initializer The :math:`tau_{\max}` parameter. References ---------- .. [1] Yamada, Walter M. "Multiple channels and calcium dynamics." Methods in neuronal modeling (1989): 97-133. """ master_type = HHTypedNeuron def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, E: Union[float, ArrayType, Initializer, Callable] = -90., g_max: Union[float, ArrayType, Initializer, Callable] = 0.004, phi_p: Union[float, ArrayType, Initializer, Callable] = 1., phi_q: Union[float, ArrayType, Initializer, Callable] = 1., tau_max: Union[float, ArrayType, Initializer, Callable] = 4e3, V_sh: Union[float, ArrayType, Initializer, Callable] = 0., method: str = 'exp_auto', name: str = None, mode: bm.Mode = None, ): super(IKNI_Ya1989, self).__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.tau_max = parameter(tau_max, self.varshape, allow_none=False) self.V_sh = parameter(V_sh, self.varshape, allow_none=False) self.phi_p = parameter(phi_p, self.varshape, allow_none=False) self.phi_q = parameter(phi_q, self.varshape, allow_none=False) # variables self.p = variable(bm.zeros, self.mode, self.varshape) # function self.integral = odeint(self.dp, method=method) def dp(self, p, t, V): return self.phi_p * (self.f_p_inf(V) - p) / self.f_p_tau(V) def update(self, V): self.p.value = self.integral(self.p.value, share['t'], V, share['dt']) def current(self, V): return self.g_max * self.p * (self.E - V) def reset_state(self, V, batch_size=None): self.p.value = self.f_p_inf(V) if isinstance(batch_size, int): assert self.p.shape[0] == batch_size def f_p_inf(self, V): return 1. / (1. + bm.exp(-(V - self.V_sh + 35.) / 10.)) def f_p_tau(self, V): temp = V - self.V_sh + 35. return self.tau_max / (3.3 * bm.exp(temp / 20.) + bm.exp(-temp / 20.))
[docs] class IKL(IonChannel): """The potassium leak channel current. Parameters ---------- g_max : float The potassium leakage conductance which is modulated by both acetylcholine and norepinephrine. E : float The reversal potential. """ master_type = HHTypedNeuron def __init__( self, size: Union[int, Sequence[int]], keep_size: bool = False, g_max: Union[int, float, ArrayType, Initializer, Callable] = 0.005, E: Union[int, float, ArrayType, Initializer, Callable] = -90., method: str = None, name: str = None, mode: bm.Mode = None, ): super().__init__(size, keep_size=keep_size, name=name, mode=mode) self.E = parameter(E, self.varshape, allow_none=False) self.g_max = parameter(g_max, self.varshape, allow_none=False) self.method = method def reset_state(self, V, batch_size=None): pass def update(self, V): pass def current(self, V): return self.g_max * (self.E - V)