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hh.py
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# -*- coding: utf-8 -*-
# @Author: Theo Lemaire
# @Email: theo.lemaire@epfl.ch
# @Date: 2020-07-21 14:53:30
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2020-07-21 16:14:22
import numpy as np
from ..core import PointNeuron, addSonicFeatures
@addSonicFeatures
class HodgkinHuxleySegment(PointNeuron):
''' Unmyelinated giant squid axon segment.
Reference:
*A quantitative description of membrane current and its application to conduction
and excitation in nerve. J.Physiol. 117:500-544 (1952).*
'''
# Neuron name
name = 'HHseg'
# ------------------------------ Biophysical parameters ------------------------------
# Resting parameters
Cm0 = 1e-2 # Membrane capacitance (F/m2)
Vm0 = -65.0 # Membrane potential (mV)
# Reversal potentials (mV)
ENa = 50. # Sodium
EK = -77. # Potassium
ELeak = -54.3 # Non-specific leakage
# Maximal channel conductances (S/m2)
gNabar = 1200.0 # Sodium
gKdbar = 360.0 # Delayed-rectifier Potassium
gLeak = 3.0 # Non-specific leakage
# Additional parameters
celsius_HH = 6.3 # Temperature in Hodgkin Huxley 1952 (Celsius)
# celsius = 6.3 # Temperature (Celsius)
# ------------------------------ States names & descriptions ------------------------------
states = {
'm': 'iNa activation gate',
'h': 'iNa inactivation gate',
'n': 'iKd gate'
}
# ------------------------------ Gating states kinetics ------------------------------
def __new__(cls):
cls.q10 = 3**((cls.celsius - cls.celsius_HH) / 10.) # from Hodgkin Huxley 1952
return super(HodgkinHuxleySegment, cls).__new__(cls)
@classmethod
def alpham(cls, Vm):
return cls.q10 * 0.1 * cls.vtrap(-(Vm + 40), 10) * 1e3 # s-1
@classmethod
def betam(cls, Vm):
return cls.q10 * 4 * np.exp(-(Vm + 65) / 18) * 1e3 # s-1
@classmethod
def alphah(cls, Vm):
return cls.q10 * 0.07 * np.exp(-(Vm + 65) / 20) * 1e3 # s-1
@classmethod
def betah(cls, Vm):
return cls.q10 * 1.0 / (np.exp(-(Vm + 35) / 10) + 1) * 1e3 # s-1
@classmethod
def alphan(cls, Vm):
return cls.q10 * 0.01 * cls.vtrap(-(Vm + 55), 10) * 1e3 # s-1
@classmethod
def betan(cls, Vm):
return cls.q10 * 0.125 * np.exp(-(Vm + 65) / 80) * 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'],
'n': lambda Vm, x: cls.alphan(Vm) * (1 - x['n']) - cls.betan(Vm) * x['n']
}
# ------------------------------ 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)),
'n': lambda Vm: cls.alphan(Vm) / (cls.alphan(Vm) + cls.betan(Vm))
}
# ------------------------------ Membrane currents ------------------------------
@classmethod
def iNa(cls, m, h, Vm):
''' Sodium current '''
return cls.gNabar * m**3 * h * (Vm - cls.ENa) # mA/m2
@classmethod
def iKd(cls, n, Vm):
''' delayed-rectifier Potassium current '''
return cls.gKdbar * n**4 * (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 {
'iNa': lambda Vm, x: cls.iNa(x['m'], x['h'], Vm),
'iKd': lambda Vm, x: cls.iKd(x['n'], Vm),
'iLeak': lambda Vm, _: cls.iLeak(Vm)
}
def chooseTimeStep(self):
''' neuron-specific time step for fast dynamics. '''
return super().chooseTimeStep() * 1e-1

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