diff --git a/PySONIC/neurons/sundt.py b/PySONIC/neurons/sundt.py index 079c5db..6117501 100644 --- a/PySONIC/neurons/sundt.py +++ b/PySONIC/neurons/sundt.py @@ -1,308 +1,308 @@ # -*- 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: 2019-11-25 12:21:41 +# @Last Modified time: 2019-11-26 18:39:11 import numpy as np from ..core import PointNeuron from ..constants import CELSIUS_2_KELVIN, FARADAY, Rg, Z_Ca from ..utils import findModifiedEq, logger class Sundt(PointNeuron): ''' Unmyelinated C-fiber model. 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)* ''' # Neuron name name = 'sundt' # ------------------------------ 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 # gMbar = 3.1 # Slow non-inactivating Potassium (from MOD file, paper studies 2-8 S/m2 range) # gCaLbar = 30 # High-threshold Calcium (from MOD file, but only in soma !!!) # gKCabar = 2.0 # Calcium dependent Potassium (only in soma !!!) # 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) # iM parameters taupMax = 1.0 # Max. adaptation decay of slow non-inactivating Potassium current (s) # Ca2+ parameters # Cao = 2e-3 # Extracellular Calcium concentration (M) # Cai0 = 70e-9 # Intracellular Calcium concentration at rest (M) (Aradi 1999) # deff = 200e-9 # effective depth beneath membrane for intracellular [Ca2+] calculation (m) # taur_Cai = 20e-3 # decay time constant for intracellular Ca2+ dissolution (s) # iKCa parameters # Ca_factor = 1e6 # conversion factor for q-gate Calcium sensitivity (expressed in uM) # Ca_power = 3 # power exponent for q-gate Calcium sensitivity (-) # Additional parameters celsius = 35.0 # Temperature (Celsius) celsius_Traub = 30.0 # Temperature in Traub 1991 (Celsius) - celsius_Yamada = 23.5 # Temperature in Yamada 1989 (Celsius) celsius_BG = 30.0 # Temperature in Borg-Graham 1987 (Celsius) + # celsius_Yamada = 23.5 # Temperature in Yamada 1989 (Celsius) # ------------------------------ States names & descriptions ------------------------------ states = { 'm': 'iNa activation gate', 'h': 'iNa inactivation gate', 'n': 'iKd activation gate', 'l': 'iKd inactivation gate', # 'p': 'iM gate', # 'c': 'iCaL gate', # 'q': 'iKCa Calcium dependent gate', # 'Cai': 'Calcium intracellular concentration (M)' } def __new__(cls): cls.q10_Traub = 3**((cls.celsius - cls.celsius_Traub) / 10) - cls.q10_Yamada = 3**((cls.celsius - cls.celsius_Yamada) / 10) cls.q10_BG = 3**((cls.celsius - cls.celsius_BG) / 10) + # cls.q10_Yamada = 3**((cls.celsius - cls.celsius_Yamada) / 10) cls.T = cls.celsius + CELSIUS_2_KELVIN # cls.current_to_molar_rate_Ca = cls.currentToConcentrationRate(Z_Ca, cls.deff) # 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(Sundt, cls).__new__(cls) # @classmethod # def getPltScheme(cls): # pltscheme = super().getPltScheme() # pltscheme['[Ca^{2+}]_i'] = ['Cai'] # return pltscheme # @classmethod # def getPltVars(cls, wrapleft='df["', wrapright='"]'): # return {**super().getPltVars(wrapleft, wrapright), **{ # 'Cai': { # 'desc': 'sumbmembrane Ca2+ concentration', # 'label': '[Ca^{2+}]_i', # 'unit': 'uM', # 'factor': 1e6 # } # }} # ------------------------------ 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 # # iM kinetics: taken from Yamada 1989, with notable changes: # # - Q10 correction to account for temperature adaptation from 23.5 to 35 degrees # # - difference in normalization factor of positive exponential tau_p formulation vs. Yamada 1989 ref. (20 vs. 40) # @staticmethod # def pinf(Vm): # return 1.0 / (1 + np.exp(-(Vm + 35) / 10)) # @classmethod # def taup(cls, Vm): # tau = cls.taupMax / (3.3 * (np.exp((Vm + 35) / 20) + np.exp(-(Vm + 35) / 20))) # s # return tau * cls.q10_Yamada # # iCaL kinetics: from Migliore 1995 that itself refers to Jaffe 1994. # @classmethod # def alphac(cls, Vm): # return 15.69 * cls.vtrap((81.5 - Vm), 10.) * 1e3 # s-1 # @classmethod # def betac(cls, Vm): # return 0.29 * np.exp(-Vm / 10.86) * 1e3 # s-1 # # iKCa kinetics: from Aradi 1999, which uses equations from Yuen 1991 with a few modifications: # # - 12 mV (???) shift in activation curve # # - log10 instead of log for Ca2+ sensitivity # # - global dampening factor of 1.67 applied on both rates # # Sundt 2015 applies an extra modification: # # - higher Calcium sensitivity (third power of Ca concentration) # # Also, there is an error in the alphaq denominator in the paper: using -4 instead of -4.5 # @classmethod # def alphaq(cls, Cai): # return 0.00246 / np.exp((12 * np.log10((Cai * cls.Ca_factor)**cls.Ca_power) + 28.48) / -4.5) * 1e3 # s-1 # @classmethod # def betaq(cls, Cai): # return 0.006 / np.exp((12 * np.log10((Cai * cls.Ca_factor)**cls.Ca_power) + 60.4) / 35) * 1e3 # s-1 # ------------------------------ States derivatives ------------------------------ # @classmethod # def derCai(cls, c, Cai, Vm): # ''' Using accumulation-dissolution formalism as in Aradi, with # a longer Ca2+ intracellular dissolution time constant (20 ms vs. 9 ms). # ''' # return -cls.current_to_molar_rate_Ca * cls.iCaL(c, Cai, Vm) - (Cai - cls.Cai0) / cls.taur_Cai # M/s @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'], # 'p': lambda Vm, x: (cls.pinf(Vm) - x['p']) / cls.taup(Vm), # 'c': lambda Vm, x: cls.alphac(Vm) * (1 - x['c']) - cls.betac(Vm) * x['c'], # 'q': lambda Vm, x: cls.alphaq(x['Cai']) * (1 - x['q']) - cls.betaq(x['Cai']) * x['q'], # 'Cai': lambda Vm, x: cls.derCai(x['c'], x['Cai'], Vm) } # ------------------------------ Steady states ------------------------------ # @classmethod # def qinf(cls, Cai): # return cls.alphaq(Cai) / (cls.alphaq(Cai) + cls.betaq(Cai)) # @classmethod # def Caiinf(cls, c, Vm): # return findModifiedEq( # cls.Cai0, # lambda Cai, c, Vm: cls.derCai(c, Cai, Vm), # c, Vm # ) @classmethod def steadyStates(cls): lambda_dict = { '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)), # 'p': lambda Vm: cls.pinf(Vm), # 'c': lambda Vm: cls.alphac(Vm) / (cls.alphac(Vm) + cls.betac(Vm)), } # lambda_dict['Cai'] = lambda Vm: cls.Caiinf(lambda_dict['c'](Vm), Vm) # lambda_dict['q'] = lambda Vm: cls.qinf(lambda_dict['Cai'](Vm)) return lambda_dict # ------------------------------ Membrane currents ------------------------------ # Sodium current: inconsistency with 1991 ref: m2h vs. m3h @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 ''' 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 iM(cls, p, Vm): # ''' slow non-inactivating Potassium current ''' # return cls.gMbar * p * (Vm - cls.EK) # mA/m2 # @classmethod # def iCaL(cls, c, Cai, Vm): # ''' Calcium current ''' # ECa = cls.nernst(Z_Ca, Cai, cls.Cao, cls.T) # mV # return cls.gCaLbar * c**2 * (Vm - ECa) # mA/m2 # @classmethod # def iKCa(cls, q, Vm): # ''' Calcium-dependent Potassium current ''' # return cls.gKCabar * q**2 * (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), # 'iM': lambda Vm, x: cls.iM(x['p'], Vm), # 'iCaL': lambda Vm, x: cls.iCaL(x['c'], x['Cai'], Vm), # 'iKCa': lambda Vm, x: cls.iKCa(x['q'], Vm), 'iLeak': lambda Vm, _: cls.iLeak(Vm) } def chooseTimeStep(self): ''' neuron-specific time step for fast dynamics. ''' return super().chooseTimeStep() * 1e-2 \ No newline at end of file