EIF_cond_alpha_isfa_ista

models.Neurons.EIF_cond_alpha_isfa_ista(
    self,
    v_rest=-70.6,
    cm=0.281,
    tau_m=9.3667,
    tau_refrac=0.1,
    tau_syn_E=5.0,
    tau_syn_I=5.0,
    e_rev_E=0.0,
    e_rev_I=-80.0,
    tau_w=144.0,
    a=4.0,
    b=0.0805,
    i_offset=0.0,
    delta_T=2.0,
    v_thresh=-50.4,
    v_reset=-70.6,
    v_spike=-40.0,
)

Exponential integrate-and-fire neuron with spike triggered and sub-threshold adaptation conductances (isfa, ista reps.).

Definition according to:

Brette R and Gerstner W (2005) Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642

Parameters:

• v_rest = -70.6 : Resting membrane potential (mV)
• cm = 0.281 : Capacity of the membrane (nF)
• tau_m = 9.3667 : Membrane time constant (ms)
• tau_refrac = 0.1 : Duration of refractory period (ms)
• tau_syn_E = 5.0 : Decay time of excitatory synaptic current (ms)
• tau_syn_I = 5.0 : Decay time of inhibitory synaptic current (ms)
• e_rev_E = 0.0 : Reversal potential for excitatory input (mV)
• e_rev_I = -80.0 : Reversal potential for inhibitory input (mv)
• tau_w = 144.0 : Time constant of the adaptation variable (ms)
• a = 4.0 : Scaling of the adaptation variable
• b = 0.0805 : Increment on the adaptation variable after a spike
• i_offset = 0.0 : Offset current (nA)
• delta_T = 2.0 : Speed of the exponential (mV)
• v_thresh = -50.4 : Spike threshold for the exponential (mV)
• v_reset = -70.6 : Reset potential after a spike (mV)
• v_spike = -40.0 : Spike threshold (mV)

Variables:

• I : input current (nA):

  I = g_exc * (e_rev_E - v) + g_inh * (e_rev_I - v) + i_offset

• v : membrane potential in mV (init=-70.6):

  tau_m * dv/dt = (v_rest - v + delta_T * exp((v-v_thresh)/delta_T)) + tau_m/cm*(I - w)

• w : adaptation variable (init=0.0):

  tau_w * dw/dt = a * (v - v_rest) / 1000.0 - w

• g_exc : excitatory current (init = 0.0):

  tau_syn_E * dg_exc/dt = - g_exc

• g_inh : inhibitory current (init = 0.0):

  tau_syn_I * dg_inh/dt = - g_inh

• alpha_exc : alpha function of excitatory current (init = 0.0):

  tau_syn_E * dalpha_exc/dt = exp((tau_syn_E - dt/2.0)/tau_syn_E) * g_exc - alpha_exc

• alpha_inh: alpha function of inhibitory current (init = 0.0):

  tau_syn_I * dalpha_inh/dt = exp((tau_syn_I - dt/2.0)/tau_syn_I) * g_inh - alpha_inh

Spike emission:

v > v_spike

Reset:

v = v_reset
u += b

The ODEs are solved using the explicit Euler method.

Equivalent code:

EIF_cond_alpha_isfa_ista = Neuron(
    parameters = """
        v_rest = -70.6
        cm = 0.281 
        tau_m = 9.3667 
        tau_syn_E = 5.0 
        tau_syn_I = 5.0 
        e_rev_E = 0.0 
        e_rev_I = -80.0
        tau_w = 144.0 
        a = 4.0
        b = 0.0805
        i_offset = 0.0
        delta_T = 2.0 
        v_thresh = -50.4
        v_reset = -70.6
        v_spike = -40.0 
    """, 
    equations = """
        gmax_exc = exp((tau_syn_E - dt/2.0)/tau_syn_E)
        gmax_inh = exp((tau_syn_I - dt/2.0)/tau_syn_I)                
        I = alpha_exc * (e_rev_E - v) + alpha_inh * (e_rev_I - v) + i_offset
        tau_m * dv/dt = (v_rest - v +  delta_T * exp((v-v_thresh)/delta_T)) + tau_m/cm*(I - w) : init=-70.6
        tau_w * dw/dt = a * (v - v_rest) / 1000.0 - w 
        tau_syn_E * dg_exc/dt = - g_exc : exponential
        tau_syn_I * dg_inh/dt = - g_inh : exponential
        tau_syn_E * dalpha_exc/dt = gmax_exc * g_exc - alpha_exc  : exponential
        tau_syn_I * dalpha_inh/dt = gmax_inh * g_inh - alpha_inh  : exponential
    """,
    spike = "v > v_spike",
    reset = """
        v = v_reset
        w += b
    """,
    refractory = 0.1
)