HH_cond_exp
HH_cond_exp(self,
=20.0,
gbar_Na=6.0,
gbar_K=0.01,
gleak=0.2,
cm=-63.0,
v_offset=50.0,
e_rev_Na=-90.0,
e_rev_K=-65.0,
e_rev_leak=0.0,
e_rev_E=-80.0,
e_rev_I=0.2,
tau_syn_E=2.0,
tau_syn_I=0.0,
i_offset=0.0,
v_thresh )
Single-compartment Hodgkin-Huxley-type neuron with transient sodium and delayed-rectifier potassium currents using the ion channel models from Traub.
The ODEs for n, m, h and v are solved using the midpoint method, while the conductances g_exc and g_inh are solved using the exponential Euler method.
Equivalent code:
= Neuron(
HH_cond_exp = dict(
parameters = 20.0
gbar_Na = 6.0
gbar_K = 0.01
gleak = 0.2
cm = -63.0
v_offset = 50.0
e_rev_Na = -90.0
e_rev_K = -65.0
e_rev_leak = 0.0
e_rev_E = -80.0
e_rev_I = 0.2
tau_syn_E = 2.0
tau_syn_I = 0.0
i_offset = 0.0
v_thresh
), = [
equations # Previous membrane potential
'prev_v = v',
# Voltage-dependent rate constants
'an = 0.032 * (15.0 - v + v_offset) / (exp((15.0 - v + v_offset)/5.0) - 1.0)',
'am = 0.32 * (13.0 - v + v_offset) / (exp((13.0 - v + v_offset)/4.0) - 1.0)',
'ah = 0.128 * exp((17.0 - v + v_offset)/18.0)',
'bn = 0.5 * exp ((10.0 - v + v_offset)/40.0)',
'bm = 0.28 * (v - v_offset - 40.0) / (exp((v - v_offset - 40.0)/5.0) - 1.0)',
'bh = 4.0/(1.0 + exp (( 10.0 - v + v_offset )) )',
# Activation variables
'dn/dt = an * (1.0 - n) - bn * n', init = 0.0, method="exponential")
ann.Variable('dm/dt = am * (1.0 - m) - bm * m', init = 0.0, method="exponential")
ann.Variable('dh/dt = ah * (1.0 - h) - bh * h', init = 1.0, method="exponential")
ann.Variable(
# Membrane equation
'cm * dv/dt = gleak*(e_rev_leak -v) + gbar_K * n**4 * (e_rev_K - v) + gbar_Na * m**3 * h * (e_rev_Na - v)
ann.Variable( + g_exc * (e_rev_E - v) + g_inh * (e_rev_I - v) + i_offset', method="exponential", init=-65.0),
# Exponentially-decaying conductances
'tau_syn_E * dg_exc/dt = - g_exc', method="exponential")
ann.Variable('tau_syn_I * dg_inh/dt = - g_inh', method="exponential")
ann.Variable(
],= "(v > v_thresh) and (prev_v <= v_thresh)",
spike = ""
reset )
Parameters
Name | Type | Description | Default |
---|---|---|---|
gbar_Na | Maximal conductance of the Sodium current. | 20.0 |
|
gbar_K | Maximal conductance of the Potassium current. | 6.0 |
|
gleak | Conductance of the leak current (nF) | 0.01 |
|
cm | Capacity of the membrane (nF) | 0.2 |
|
v_offset | Threshold for the rate constants (mV) | -63.0 |
|
e_rev_Na | Reversal potential for the Sodium current (mV) | 50.0 |
|
e_rev_K | Reversal potential for the Potassium current (mV) | -90.0 |
|
e_rev_leak | Reversal potential for the leak current (mV) | -65.0 |
|
e_rev_E | Reversal potential for excitatory input (mV) | 0.0 |
|
e_rev_I | Reversal potential for inhibitory input (mV) | -80.0 |
|
tau_syn_E | Decay time of excitatory synaptic current (ms) | 0.2 |
|
tau_syn_I | Decay time of inhibitory synaptic current (ms) | 2.0 |
|
i_offset | Offset current (nA) | 0.0 |
|
v_thresh | Threshold for spike emission | 0.0 |