# -*- coding: utf-8 -*-
"""
This is parameter module for Averaged Neuron (AN) model.
These parameters are identical to those in Tatsuki et al., 2016
and Yoshida et al., 2018.
"""
__author__ = 'Fumiya Tatsuki, Kensuke Yoshida, Tetsuya Yamada, \
Takahiro Katsumata, Shoi Shi, Hiroki R. Ueda'
__status__ = 'Published'
__version__ = '1.0.0'
__date__ = '15 May 2020'
class Constants:
""" Constant values needed for AN model.
These constant values are based on previous researches. See Tatsuki et al., 2016,
Yoshida et al., 2018 and Compte et al., 2003.
Attributes
----------
cm : float
membrane capacitance (uF/cm2)
area : float
area of neuron (mm2)
tauA : float
time constant of inactivation variable for fast A-type potassium channel
s_a_ampar : float
coefficient of f(V)
s_tau_ampar : float
time constant of gating variable differential equation of AMPAR
x_a_nmdar : float
coefficient of f(V)
x_tau_nmdar : float
time constant for differential equation of second-order gating variable x
s_a_nmdar : float
coefficient of (1 - s)
s_tau_nmdar : float
time constant for differential equation of gating variable s
s_a_gabar : float
coefficient of f(V)
s_tau_gabar : float
time constant for differential equation of gating variable s
vL : float
equilibrium potential of leak channel (mV)
vNaL : float
equilibrium potential of leak sodium channel (mV)
vNa : float
equilibrium potential of sodium ion (mV)
vK : float
equilibrium potential of potassium ion (mV)
vCa : float
equilibrium potential of calcium channel (mV)
vAMPAR : float
equilibrium potential of AMPA receptor (mV)
vNMDAR : float
equilibrium potential of NMDA receptor (mV)
vGABAR : float
equilibrium potential of GABA receptor (mV)
an_ini : list (float)
initial parameters for differential equations of AN model:
v : membrane potential
h_nav : inactivation variable of voltage-gated sodium channel
n_kvhh : activation variable of HH-type voltage-gated
potassium channel
h_kva : inactivation variable of fast A-type potassium channel
m_kvsi : activation variable of slowly inactivating potassium channel
s_ampar : gating variable of AMPA recptor
x_nmdar : second-order gating variable of NMDA receptor
s_nmdar : gating variable of NMDA receptor
s_gabar : gating variable of GABA receptor
ca : intracellular calcium concentration
san_ini : list (float)
initial parameters for differential equations of SAN model:
v : membrane potential
n_kvhh : activation variable of HH-type voltage-gated
potassium channel
ca : intracellular calcium concentration
"""
def __init__(self) -> None:
self.cm = 1.0
self.area = 0.02
self.a_ca = 0.5
self.kd_ca = 30.0
self.tau_a = 15.0
self.s_a_ampar = 3.48
self.s_tau_ampar = 2.0
self.s_a_nmdar = 0.5
self.s_tau_nmdar = 100.0
self.x_a_nmdar = 3.48
self.x_tau_nmdar = 2.0
self.s_a_gabar = 1.0
self.s_tau_gabar = 10.0
self.vL = -60.95
self.vNaL = 0.
self.vNa = 55.0
self.vK = -100.0
self.vCa = 120.0
self.vAMPAR = 0.
self.vNMDAR = 0.
self.vGABAR = -70.0
self.an_ini = [
-45., # 0 : v
0.045, # 1 : h_nav
0.54, # 2 : n_kvhh
0.045, # 3 : h_kva
0.34, # 4 : m_kvsi
0.01, # 5 : s_ampar
0.01, # 6 : x_nmdar
0.01, # 7 : s_nmdar
0.01, # 8 : s_gabar
1., # 9 : Ca
]
self.san_ini = [
-45., # 0 : v
0.54, # 1 : n_kvhh
1., # 2 : Ca
]
class Ion:
""" Constant values needed for AN model with ion and typical ion concentrations.
These constant values are based on Ramussen et al., 2017.
Attributes
---------
r : float
gas constant (J/K/mol)
t : float
body temprature (K)
f : float
Faraday constant (C/mol)
awake_ion : dictionary (float)
typical ion concentrations which recapitulates awake firing pattern
sleep_ion : dictionary (float)
typical ion concentrations which recapitulates sleep (SWS) firing pattern
"""
def __init__(self) -> None:
self.r = 8.314472
self.t = 310.
self.f = 9.64853399 * 10000
self.awake_ion = {
'ex_na': 140,
'in_na': 7.0,
'ex_k': 4.4,
'in_k': 140,
'ex_cl': 140,
'in_cl': 7.0,
'ex_ca': 1.2,
'in_ca': 0.001,
'ex_mg': 0.7,
}
self.sleep_ion = {
'ex_na': 140.0,
'in_na': 7.0,
'ex_k': 3.9,
'in_k': 140.0,
'ex_cl': 140.0,
'in_cl': 7.0,
'ex_ca': 1.35,
'in_ca': 0.001,
'ex_mg': 0.8,
}
class TypicalParam:
""" Typical parameter set that recapitulate a cirtain firing pattern.
Attributes
----------
an_sws : dictionary (float)
typical parameter set which recapitulate SWS firing pattern in AN model
See : Tatsuki et al., 2016
san_sws : dictionary (float)
typical parameter set which recapitulate SWS firing patter in SAN model
See : Yoshida et al., 2018 figure 1L.
"""
def __init__(self) -> None:
self.an_sws = {
'g_leak': 0.03573,
'g_nav': 12.2438,
'g_kvhh': 2.61868,
'g_kva': 1.79259,
'g_kvsi': 0.0350135,
'g_cav': 0.0256867,
'g_kca': 2.34906,
'g_nap': 0.0717984,
'g_kir': 0.0166454,
'g_ampar': 0.513425,
'g_nmdar': 0.00434132,
'g_gabar': 0.00252916,
't_ca': 121.403,
}
self.san_sws = {
'g_leak': 0.016307,
'g_kvhh': 19.20436,
'g_cav': 0.1624,
'g_kca': 0.7506,
'g_nap': 0.63314,
't_ca': 739.09,
}