def BIO_model_threshold_in_CC(ais_start, ais_end, gna_tot):
print('AIS start:', ais_start, 'Gna:', gna_tot)
params = params_model_description #params_all
pulse_length = 50. * ms
neuron = model_Na_Kv1(params=params,
resting_vm=-75. * mV,
Na_start=ais_start,
Na_end=ais_end,
gna_tot=gna_tot,
density=False)
i_rheo = measure_current_threshold(params, neuron, -75. * mV,
ais_start, ais_end, pulse_length)
print('Rheobase:', i_rheo)
neuron = model_Na_Kv1(params=params,
resting_vm=-75. * mV,
Na_start=ais_start,
Na_end=ais_end,
gna_tot=gna_tot,
density=False)
v_thres, _, _, _ = measure_voltage_threshold(params, neuron, -75. * mV,
ais_start, ais_end,
i_rheo, pulse_length)
print('Voltage threshold:', v_thres)
return v_thres
def BIO_model_threshold_in_CC(x_star, length, gna_tot):
defaultclock.dt = 0.005*ms
resting_vm = -75.*mV
pulse_length = 50.*ms
# AIS start
start = round(x_star, 2)*um - length/2
# AIS end
end = start + length
# Removing impossible geometries: the length can not be bigger than two times the middle position
if length/2 <= round(x_star, 2)*um:
print ('x1/2:', round(x_star, 2)*um, 'AIS length:', length, 'AIS start:', start, 'AIS end:', end)
# current threshold
neuron = model_Na_Kv1(params, resting_vm, Na_start = start, Na_end = end, density=False, gna_tot=gna_tot, morpho=morpho)
i_rheo = measure_current_threshold(params, neuron, resting_vm=resting_vm, ais_start=start, ais_end=end, pulse_length = pulse_length)
print ('Rheobase:', i_rheo)
# voltage threshold
neuron = model_Na_Kv1(params, resting_vm, Na_start = start, Na_end = end, density=False, gna_tot=gna_tot, morpho=morpho)
vs, va, _, _ = measure_voltage_threshold(params, neuron, resting_vm=resting_vm, ais_start=start, ais_end=end, i_rheo = i_rheo, pulse_length = pulse_length)
print ('Threshold:', vs)
res = vs
else: # bottom right triangle
res = nan
return res
def BIO_model_in_CC_constant_density(ais_start, ais_end):
defaultclock.dt = 0.005*ms
resting_vm = -75.*mV
pulse_length = 50.*ms
print ('AIS start:', ais_start, 'AIS end:', ais_end)
# current threshold
neuron = model_Na_Kv1(params, resting_vm, ais_start, ais_end, density = True)
i_rheo = measure_current_threshold(params, neuron, resting_vm, ais_start, ais_end, pulse_length = pulse_length)
print ('Rheobase:', i_rheo)
# voltage threshold
neuron = model_Na_Kv1(params, resting_vm, ais_start, ais_end, density=True)
vs, va, _, _ = measure_voltage_threshold(params, neuron, resting_vm, ais_start, ais_end, i_rheo = i_rheo, pulse_length = pulse_length)
print ('Threshold:', vs)
return vs
def measure_different_thresholds(gna_ais, i_inj, gL_soma):
'''
A function to measure the charge, current and voltage thresholds at the soma.
Variables: the somatic leak conductance, the total Na conductance at the AIS and the amount of hyperpolarizing current injected at the AIS.
'''
# current threshold
neuron = model_Na_Kv1(params, resting_vm, start, end, density=False, gna_tot=gna_ais, gk_tot=params.Gk, gL_soma = gL_soma)
i_rheo = measure_current_threshold_no_VC(params, neuron, resting_vm, start, end, pulse_length = 50.*ms, i_inj = i_inj, plot_v = False)
print ('Current threshold:', i_rheo)
# voltage threshold
neuron = model_Na_Kv1(params, resting_vm, start, end, density=False, gna_tot=gna_ais, gk_tot=params.Gk, gL_soma = gL_soma)
vs, va, _, _, v0, v0_ais= measure_voltage_threshold_no_VC(params, neuron, resting_vm,start, end, i_rheo = i_rheo, pulse_length = 50.*ms, i_inj = i_inj)
print ('Threshold:', vs)
# input resistance
neuron = model_Na_Kv1(params, resting_vm, start, end, density=False, gna_tot=gna_ais, gk_tot=params.Gk)
rs,_,_ = measure_input_resistance(params, neuron, resting_vm)
print (rs)
return i_rheo, vs, va, rs, v0, v0_ais
import matplotlib.image as mpimg
import matplotlib.patches as patches
defaultclock.dt = 0.005*ms
### AIS geometry and parameters
start =5.*um # AIS start position
end = 35.*um # AIS end position
params = params_model_description
### Model
# The total conductances at the AIS is fixed:
#neuron = model_Na_Kv1(params, -75.*mV, start, end, density=False, gna_tot=350.*nS, gk_tot=150.*nS, morpho=params.morpho)
# The conductance densities at the AIS is fixed:
neuron = model_Na_Kv1(params, -75.*mV, start, end, density=True, morpho=params.morpho)
M = StateMonitor(neuron, ('v','I_VC', 'INa', 'IK'), record = 0) # recording at the soma
M_AIS = StateMonitor(neuron, ('v', 'm', 'h', 'n', 'INa', 'IK'), record = neuron.morphology.axon[end-1*um]) # recording at AIS end
### Simulation
# Protocol to elicit an AP with fixed initial voltage
neuron.V_VC[0] = -75.*mV
neuron.VC_on[0] = 1
run(20*ms)
neuron.VC_on[0] = 0
neuron.I_CC[0] = 1.5*nA
run(2*ms)
neuron.VC_on[0] = 0
neuron.I_CC[0] = 0*amp
run(20*ms)