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"""
Reproduces Figure 12 (simplified three-compartment model) from the following
paper:
Dendritic Low-Threshold Calcium Currents in Thalamic Relay Cells
Alain Destexhe, Mike Neubig, Daniel Ulrich, John Huguenard
Journal of Neuroscience 15 May 1998, 18 (10) 3574-3588
The original NEURON code is available on ModelDB: https://senselab.med.yale.edu/modeldb/ShowModel.cshtml?model=279
Reference for the original morphology:
Rat VB neuron (thalamocortical cell), given by J. Huguenard, stained with
biocytin and traced by A. Destexhe, December 1992. The neuron is described
in: J.R. Huguenard & D.A. Prince, A novel T-type current underlies prolonged
calcium-dependent burst firing in GABAergic neurons of rat thalamic reticular
nucleus. J. Neurosci. 12: 3804-3817, 1992.
Available at NeuroMorpho.org:
http://neuromorpho.org/neuron_info.jsp?neuron_name=tc200
NeuroMorpho.Org ID :NMO_00881
Notes
-----
* Completely removed the "Fast mechanism for submembranal Ca++ concentration
(cai)" -- it did not affect the results presented here
* Time constants for the I_T current are slightly different from the equations
given in the paper -- the paper calculation seems to be based on 36 degree
Celsius but the temperature that is used is 34 degrees.
* To reproduce Figure 12C, the "presence of dendritic shunt conductances" meant
setting g_L to 0.15 mS/cm^2 for the whole neuron.
* Other small discrepancies with the paper -- values from the NEURON code were
used whenever different from the values stated in the paper
"""
from brian2 import *
from brian2.units.constants import (zero_celsius, faraday_constant as F,
gas_constant as R)
defaultclock.dt = 0.01*ms
VT = -52*mV
El = -76.5*mV # from code, text says: -69.85*mV
E_Na = 50*mV
E_K = -100*mV
C_d = 7.954 # dendritic correction factor
T = 34*kelvin + zero_celsius # 34 degC (current-clamp experiments)
tadj_HH = 3.0**((34-36)/10.0) # temperature adjustment for Na & K (original recordings at 36 degC)
tadj_m_T = 2.5**((34-24)/10.0)
tadj_h_T = 2.5**((34-24)/10.0)
shift_I_T = -1*mV
gamma = F/(R*T) # R=gas constant, F=Faraday constant
Z_Ca = 2 # Valence of Calcium ions
Ca_i = 240*nM # intracellular Calcium concentration
Ca_o = 2*mM # extracellular Calcium concentration
eqs = Equations('''
Im = gl*(El-v) - I_Na - I_K - I_T: amp/meter**2
I_inj : amp (point current)
gl : siemens/meter**2
# HH-type currents for spike initiation
g_Na : siemens/meter**2
g_K : siemens/meter**2
I_Na = g_Na * m**3 * h * (v-E_Na) : amp/meter**2
I_K = g_K * n**4 * (v-E_K) : amp/meter**2
v2 = v - VT : volt # shifted membrane potential (Traub convention)
dm/dt = (0.32*(mV**-1)*(13.*mV-v2)/
(exp((13.*mV-v2)/(4.*mV))-1.)*(1-m)-0.28*(mV**-1)*(v2-40.*mV)/
(exp((v2-40.*mV)/(5.*mV))-1.)*m) / ms * tadj_HH: 1
dn/dt = (0.032*(mV**-1)*(15.*mV-v2)/
(exp((15.*mV-v2)/(5.*mV))-1.)*(1.-n)-.5*exp((10.*mV-v2)/(40.*mV))*n) / ms * tadj_HH: 1
dh/dt = (0.128*exp((17.*mV-v2)/(18.*mV))*(1.-h)-4./(1+exp((40.*mV-v2)/(5.*mV)))*h) / ms * tadj_HH: 1
# Low-threshold Calcium current (I_T) -- nonlinear function of voltage
I_T = P_Ca * m_T**2*h_T * G_Ca : amp/meter**2
P_Ca : meter/second # maximum Permeability to Calcium
G_Ca = Z_Ca**2*F*v*gamma*(Ca_i - Ca_o*exp(-Z_Ca*gamma*v))/(1 - exp(-Z_Ca*gamma*v)) : coulomb/meter**3
dm_T/dt = -(m_T - m_T_inf)/tau_m_T : 1
dh_T/dt = -(h_T - h_T_inf)/tau_h_T : 1
m_T_inf = 1/(1 + exp(-(v/mV + 56)/6.2)) : 1
h_T_inf = 1/(1 + exp((v/mV + 80)/4)) : 1
tau_m_T = (0.612 + 1.0/(exp(-(v/mV + 131)/16.7) + exp((v/mV + 15.8)/18.2))) * ms / tadj_m_T: second
tau_h_T = (int(v<-81*mV) * exp((v/mV + 466)/66.6) +
int(v>=-81*mV) * (28 + exp(-(v/mV + 21)/10.5))) * ms / tadj_h_T: second
''')
# Simplified three-compartment morphology
morpho = Cylinder(x=[0, 38.42]*um, diameter=26*um)
morpho.dend = Cylinder(x=[0, 12.49]*um, diameter=10.28*um)
morpho.dend.distal = Cylinder(x=[0, 84.67]*um, diameter=8.5*um)
neuron = SpatialNeuron(morpho, eqs, Cm=0.88*uF/cm**2, Ri=173*ohm*cm,
method='exponential_euler')
neuron.v = -74*mV
# Only the soma has Na/K channels
neuron.main.g_Na = 100*msiemens/cm**2
neuron.main.g_K = 100*msiemens/cm**2
# Apply the correction factor to the dendrites
neuron.dend.Cm *= C_d
neuron.m_T = 'm_T_inf'
neuron.h_T = 'h_T_inf'
mon = StateMonitor(neuron, ['v'], record=True)
store('initial state')
def do_experiment(currents, somatic_density, dendritic_density,
dendritic_conductance=0.0379*msiemens/cm**2,
HH_currents=True):
restore('initial state')
voltages = []
neuron.P_Ca = somatic_density
neuron.dend.distal.P_Ca = dendritic_density * C_d
# dendritic conductance (shunting conductance used for Fig 12C)
neuron.gl = dendritic_conductance
neuron.dend.gl = dendritic_conductance * C_d
if not HH_currents:
# Shut off spiking (for Figures 12B and 12C)
neuron.g_Na = 0*msiemens/cm**2
neuron.g_K = 0*msiemens/cm**2
run(180*ms)
store('before current')
for current in currents:
restore('before current')
neuron.main.I_inj = current
print('.', end='')
run(320*ms)
voltages.append(mon[morpho].v[:]) # somatic voltage
return voltages
## Run the various variants of the model to reproduce Figure 12
mpl.rcParams['lines.markersize'] = 3.0
fig, axes = plt.subplots(2, 2)
print('Running experiments for Figure A1 ', end='')
voltages = do_experiment([50, 75]*pA, somatic_density=1.7e-5*cm/second,
dendritic_density=1.7e-5*cm/second)
print(' done.')
cut_off = 100*ms # Do not display first part of simulation
axes[0, 0].plot((mon.t - cut_off) / ms, voltages[0] / mV, color='gray')
axes[0, 0].plot((mon.t - cut_off) / ms, voltages[1] / mV, color='black')
axes[0, 0].set(xlim=(0, 400), ylim=(-80, 40), xticks=[],
title='A1: Uniform T-current density', ylabel='Voltage (mV)')
axes[0, 0].spines['right'].set_visible(False)
axes[0, 0].spines['top'].set_visible(False)
axes[0, 0].spines['bottom'].set_visible(False)
print('Running experiments for Figure A2 ', end='')
voltages = do_experiment([50, 75]*pA, somatic_density=1.7e-5*cm/second,
dendritic_density=9.5e-5*cm/second)
print(' done.')
cut_off = 100*ms # Do not display first part of simulation
axes[1, 0].plot((mon.t - cut_off) / ms, voltages[0] / mV, color='gray')
axes[1, 0].plot((mon.t - cut_off) / ms, voltages[1] / mV, color='black')
axes[1, 0].set(xlim=(0, 400), ylim=(-80, 40),
title='A2: High T-current density in dendrites',
xlabel='Time (ms)', ylabel='Voltage (mV)')
axes[1, 0].spines['right'].set_visible(False)
axes[1, 0].spines['top'].set_visible(False)
print('Running experiments for Figure B ', end='')
currents = np.linspace(0, 200, 41)*pA
voltages_somatic = do_experiment(currents, somatic_density=56.36e-5*cm/second,
dendritic_density=0*cm/second,
HH_currents=False)
voltages_somatic_dendritic = do_experiment(currents, somatic_density=1.7e-5*cm/second,
dendritic_density=9.5e-5*cm/second,
HH_currents=False)
print(' done.')
maxima_somatic = Quantity(voltages_somatic).max(axis=1)
maxima_somatic_dendritic = Quantity(voltages_somatic_dendritic).max(axis=1)
axes[0, 1].yaxis.tick_right()
axes[0, 1].plot(currents/pA, maxima_somatic/mV,
'o-', color='black', label='Somatic only')
axes[0, 1].plot(currents/pA, maxima_somatic_dendritic/mV,
's-', color='black', label='Somatic & dendritic')
axes[0, 1].set(xlabel='Injected current (pA)', ylabel='Peak LTS (mV)',
ylim=(-80, 0))
axes[0, 1].legend(loc='best', frameon=False)
print('Running experiments for Figure C ', end='')
currents = np.linspace(200, 400, 41)*pA
voltages_somatic = do_experiment(currents, somatic_density=56.36e-5*cm/second,
dendritic_density=0*cm/second,
dendritic_conductance=0.15*msiemens/cm**2,
HH_currents=False)
voltages_somatic_dendritic = do_experiment(currents, somatic_density=1.7e-5*cm/second,
dendritic_density=9.5e-5*cm/second,
dendritic_conductance=0.15*msiemens/cm**2,
HH_currents=False)
print(' done.')
maxima_somatic = Quantity(voltages_somatic).max(axis=1)
maxima_somatic_dendritic = Quantity(voltages_somatic_dendritic).max(axis=1)
axes[1, 1].yaxis.tick_right()
axes[1, 1].plot(currents/pA, maxima_somatic/mV,
'o-', color='black', label='Somatic only')
axes[1, 1].plot(currents/pA, maxima_somatic_dendritic/mV,
's-', color='black', label='Somatic & dendritic')
axes[1, 1].set(xlabel='Injected current (pA)', ylabel='Peak LTS (mV)',
ylim=(-80, 0))
axes[1, 1].legend(loc='best', frameon=False)
plt.tight_layout()
plt.show()
|
