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mrg.py
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# -*- coding: utf-8 -*-
# @Author: Mariia Popova
# @Email: theo.lemaire@epfl.ch
# @Date: 2020-02-27 21:24:05
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2020-03-31 18:13:32
import numpy as np
from ..core import PointNeuron, addSonicFeatures
@addSonicFeatures
class MRGNode(PointNeuron):
''' Mammalian myelinated fiber node.
Reference:
*McIntyre, C.C., Richardson, A.G., and Grill, W.M. (2002). Modeling the excitability
of mammalian nerve fibers: influence of afterpotentials on the recovery cycle.
J. Neurophysiol. 87, 995–1006.*
'''
# Mechanism name
name = 'MRGnode'
# ------------------------------ Biophysical parameters ------------------------------
# Resting parameters
Cm0 = 2e-2 # Membrane capacitance (F/m2)
Vm0 = -80. # Membrane potential (mV)
# Reversal potentials (mV)
ENa = 50. # Sodium
EK = -90. # Potassium
ELeak = -90. # Non-specific leakage
# Maximal channel conductances (S/m2)
gNafbar = 3e4 # Fast Sodium
gNapbar = 100. # Persistent Sodium
gKsbar = 800. # Slow Potassium
gLeak = 70. # Non-specific leakage
# Additional parameters
celsius = 36.0 # Temperature (Celsius)
celsius_Schwarz = 20.0 # Temperature in Schwarz 1995 (Celsius)
celsius_Ks = 36.0 # Temperature iused for Ks channels (unknown ref.)
mhshift = 3. # m and h gates voltage shift (mV)
vtraub = -80. # Reference voltage for the definition of the s rate constants (mV)
# ------------------------------ States names & descriptions ------------------------------
states = {
'm': 'iNaf activation gate',
'h': 'iNaf inactivation gate',
'p': 'iNap activation gate',
's': 'iKs activation gate',
}
# ------------------------------ Gating states kinetics ------------------------------
def __new__(cls):
cls.q10_mp = 2.2**((cls.celsius - cls.celsius_Schwarz) / 10) # from Schwarz 1987
cls.q10_h = 2.9**((cls.celsius - cls.celsius_Schwarz) / 10) # from Schwarz 1987
cls.q10_s = 3.0**((cls.celsius - cls.celsius_Ks) / 10) # from ???
return super(MRGNode, cls).__new__(cls)
# iNaf kinetics: adapted from Schwarz 1995, with notable changes:
# - Q10 correction to account for temperature adaptation from 20 degrees reference
# - 3 mV offset to m and h gates to shift voltage dependence in the hyperpolarizing direction,
# to increase the conduction velocity and strength-duration time constant (from McIntyre 2002)
# - increase in tau_h to slow down inactivation (achieved through alphah?)
@classmethod
def alpham(cls, Vm):
Vm += cls.mhshift
return cls.q10_mp * 1.86 * cls.vtrap(-(Vm + 18.4), 10.3) * 1e3 # s-1
@classmethod
def betam(cls, Vm):
Vm += cls.mhshift
return cls.q10_mp * 0.086 * cls.vtrap(Vm + 22.7, 9.16) * 1e3 # s-1
@classmethod
def alphah(cls, Vm):
Vm += cls.mhshift
return cls.q10_h * 0.062 * cls.vtrap(Vm + 111.0, 11.0) * 1e3 # s-1
@classmethod
def betah(cls, Vm):
Vm += cls.mhshift
return cls.q10_h * 2.3 / (1 + np.exp(-(Vm + 28.8) / 13.4)) * 1e3 # s-1
# iNap kinetics: adapted from ???, with notable changes:
# - Q10 correction to account for temperature adaptation from 20 degrees reference
# - increase in tau_p in order to extend the duration and amplitude of the DAP.
@classmethod
def alphap(cls, Vm):
return cls.q10_mp * 0.01 * cls.vtrap(-(Vm + 27.), 10.2) * 1e3 # s-1
@classmethod
def betap(cls, Vm):
return cls.q10_mp * 0.00025 * cls.vtrap(Vm + 34., 10.) * 1e3 # s-1
# iKs kinetics: adapted from ???, with notable changes:
# - Q10 correction to account for temperature adaptation from 36 degrees reference
# - increase in tau_s in order to to create an AHP that matches experimental records.
@classmethod
def alphas(cls, Vm):
Vm -= cls.vtraub
return cls.q10_s * 0.3 / (1 + np.exp(-(Vm - 27.) / 5.)) * 1e3 # s-1
@classmethod
def betas(cls, Vm):
Vm -= cls.vtraub
return cls.q10_s * 0.03 / (1 + np.exp(-(Vm + 10.) / 1.)) * 1e3 # s-1
# ------------------------------ States derivatives ------------------------------
@classmethod
def derStates(cls):
return {
'm': lambda Vm, x: cls.alpham(Vm) * (1 - x['m']) - cls.betam(Vm) * x['m'],
'h': lambda Vm, x: cls.alphah(Vm) * (1 - x['h']) - cls.betah(Vm) * x['h'],
'p': lambda Vm, x: cls.alphap(Vm) * (1 - x['p']) - cls.betap(Vm) * x['p'],
's': lambda Vm, x: cls.alphas(Vm) * (1 - x['s']) - cls.betas(Vm) * x['s'],
}
# ------------------------------ Steady states ------------------------------
@classmethod
def steadyStates(cls):
return {
'm': lambda Vm: cls.alpham(Vm) / (cls.alpham(Vm) + cls.betam(Vm)),
'h': lambda Vm: cls.alphah(Vm) / (cls.alphah(Vm) + cls.betah(Vm)),
'p': lambda Vm: cls.alphap(Vm) / (cls.alphap(Vm) + cls.betap(Vm)),
's': lambda Vm: cls.alphas(Vm) / (cls.alphas(Vm) + cls.betas(Vm)),
}
# ------------------------------ Membrane currents ------------------------------
@classmethod
def iNaf(cls, m, h, Vm):
''' fast Sodium current. '''
return cls.gNafbar * m**3 * h * (Vm - cls.ENa) # mA/m2
@classmethod
def iNap(cls, p, Vm):
''' persistent Sodium current. '''
return cls.gNapbar * p**3 * (Vm - cls.ENa) # mA/m2
@classmethod
def iKs(cls, s, Vm):
''' slow Potassium current '''
return cls.gKsbar * s * (Vm - cls.EK) # mA/m2
@classmethod
def iLeak(cls, Vm):
''' non-specific leakage current '''
return cls.gLeak * (Vm - cls.ELeak) # mA/m2
@classmethod
def currents(cls):
return {
'iNaf': lambda Vm, x: cls.iNaf(x['m'], x['h'], Vm),
'iNap': lambda Vm, x: cls.iNap(x['p'], Vm),
'iKs': lambda Vm, x: cls.iKs(x['s'], Vm),
'iLeak': lambda Vm, _: cls.iLeak(Vm)
}
def chooseTimeStep(self):
''' neuron-specific time step for fast dynamics. '''
return super().chooseTimeStep() * 1e-2

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