Page MenuHomec4science
Files F60644262

sundt.py
No OneTemporary
Actions

File Metadata

Created
Wed, May 1, 16:36

sundt.py
View Options

# -*- coding: utf-8 -*-
# @Author: Mariia Popova
# @Email: theo.lemaire@epfl.ch
# @Date: 2019-10-03 15:58:38
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2021-06-05 17:36:34
import numpy as np
from ..core import PointNeuron, addSonicFeatures
from ..utils import logger
from ..postpro import detectSpikes
@addSonicFeatures
class SundtSegment(PointNeuron):
''' Unmyelinated C-fiber segment.
Reference:
*Sundt D., Gamper N., Jaffe D. B., Spike propagation through the dorsal
root ganglia in an unmyelinated sensory neuron: a modeling study.
Journal of Neurophysiology (2015)*
'''
# Mechanism name
name = 'SUseg'
# ------------------------------ Biophysical parameters ------------------------------
# Resting parameters
Cm0 = 1e-2 # Membrane capacitance (F/m2)
Vm0 = -60. # Membrane potential (mV)
# Reversal potentials (mV)
ENa = 55.0 # Sodium
EK = -90.0 # Potassium
# Maximal channel conductances (S/m2)
gNabar = 400.0 # Sodium
gKdbar = 400.0 # Delayed-rectifier Potassium
gLeak = 1.0 # Non-specific leakage
# Na+ current parameters
Vrest_Traub = -65. # Resting potential in Traub 1991 (mV), used as reference for m & h rates
mshift = -6.0 # m-gate activation voltage shift, from ModelDB file (mV)
hshift = 6.0 # h-gate activation voltage shift, from ModelDB file (mV)
# Additional parameters
# celsius = 35.0 # Temperature in ModelDB file (Celsius)
celsius_Traub = 30.0 # Temperature in Traub 1991 (Celsius)
celsius_BG = 30.0 # Temperature in Borg-Graham 1987 (Celsius)
# ------------------------------ States names & descriptions ------------------------------
states = {
'm': 'iNa activation gate',
'h': 'iNa inactivation gate',
'n': 'iKd activation gate',
'l': 'iKd inactivation gate'
}
def __new__(cls):
cls.q10_Traub = 3**((cls.celsius - cls.celsius_Traub) / 10)
cls.q10_BG = 3**((cls.celsius - cls.celsius_BG) / 10)
# Compute Eleak such that iLeak cancels out the net current at resting potential
sstates = {k: cls.steadyStates()[k](cls.Vm0) for k in cls.statesNames()}
i_dict = cls.currents()
del i_dict['iLeak']
iNet = sum([cfunc(cls.Vm0, sstates) for cfunc in i_dict.values()]) # mA/m2
cls.ELeak = cls.Vm0 + iNet / cls.gLeak # mV
logger.debug(f'Eleak = {cls.ELeak:.2f} mV')
return super(SundtSegment, cls).__new__(cls)
# ------------------------------ Gating states kinetics ------------------------------
# iNa kinetics: adapted from Traub 1991, with 2 notable changes:
# - Q10 correction to account for temperature adaptation from 30 to 35 degrees
# - 65 mV voltage offset to account for Traub 1991 relative voltage definition (Vm = v - Vrest)
# - voltage offsets in the m-gate (+6mV) and h-gate (-6mV) to shift iNa voltage dependence
# approximately midway between values reported for Nav1.7 and Nav1.8 currents.
@classmethod
def alpham(cls, Vm):
Vm -= cls.Vrest_Traub
Vm += cls.mshift
return cls.q10_Traub * 0.32 * cls.vtrap((13.1 - Vm), 4) * 1e3 # s-1
@classmethod
def betam(cls, Vm):
Vm -= cls.Vrest_Traub
Vm += cls.mshift
return cls.q10_Traub * 0.28 * cls.vtrap((Vm - 40.1), 5) * 1e3 # s-1
@classmethod
def alphah(cls, Vm):
Vm -= cls.Vrest_Traub
Vm += cls.hshift
return cls.q10_Traub * 0.128 * np.exp((17.0 - Vm) / 18) * 1e3 # s-1
@classmethod
def betah(cls, Vm):
Vm -= cls.Vrest_Traub
Vm += cls.hshift
return cls.q10_Traub * 4 / (1 + np.exp((40.0 - Vm) / 5)) * 1e3 # s-1
# iKd kinetics: using Migliore 1995 values, with Borg-Graham 1991 formalism, with:
# - Q10 correction to account for temperature adaptation from 30 to 35 degrees
@classmethod
def alphan(cls, Vm):
return cls.q10_BG * cls.alphaBG(0.03, -5, 0.4, -32., Vm) * 1e3 # s-1
@classmethod
def betan(cls, Vm):
return cls.q10_BG * cls.betaBG(0.03, -5, 0.4, -32., Vm) * 1e3 # s-1
@classmethod
def alphal(cls, Vm):
return cls.q10_BG * cls.alphaBG(0.001, 2, 1., -61., Vm) * 1e3 # s-1
@classmethod
def betal(cls, Vm):
return cls.q10_BG * cls.betaBG(0.001, 2, 1., -61., Vm) * 1e3 # s-1
@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'],
'l': lambda Vm, x: cls.alphal(Vm) * (1 - x['l']) - cls.betal(Vm) * x['l']
}
# ------------------------------ 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)),
'l': lambda Vm: cls.alphal(Vm) / (cls.alphal(Vm) + cls.betal(Vm))
}
# ------------------------------ Membrane currents ------------------------------
@classmethod
def iNa(cls, m, h, Vm):
''' Sodium current.
Gating formalism from Migliore 1995, using 3rd power for m
to reproduce 1 ms AP half-width
..Note: inconsistency with 1991 ref: m2h vs. m3h
'''
return cls.gNabar * m**3 * h * (Vm - cls.ENa) # mA/m2
@classmethod
def iKd(cls, n, l, Vm):
''' delayed-rectifier Potassium current '''
return cls.gKdbar * n**3 * l * (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'], x['l'], Vm),
'iLeak': lambda Vm, _: cls.iLeak(Vm)
}
def chooseTimeStep(self):
''' neuron-specific time step for fast dynamics. '''
return super().chooseTimeStep() * 1e-2
@staticmethod
def getNSpikes(data):
return detectSpikes(data, mph=-8.0e-5)[0].size

Event Timeline

c4science · Help