EIF_cond_alpha_isfa_ista

EIF_cond_alpha_isfa_ista(
    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.), alpha post-synaptic conductances.

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

Equivalent code:


EIF_cond_alpha_isfa_ista = Neuron(
    parameters = dict(
        v_rest = ann.Parameter(-70.6),
        cm = ann.Parameter(0.281), 
        tau_m = ann.Parameter(9.3667), 
        tau_syn_E = ann.Parameter(5.0),
        tau_syn_I = ann.Parameter(5.0), 
        e_rev_E = ann.Parameter(0.0),
        e_rev_I = ann.Parameter(-80.0),
        tau_w = ann.Parameter(144.0), 
        a = ann.Parameter(4.0),
        b = ann.Parameter(0.0805),
        i_offset = ann.Parameter(0.0),
        delta_T = ann.Parameter(2.0),
        v_thresh = ann.Parameter(-50.4),
        v_reset = ann.Parameter(-70.6),
        v_spike = ann.Parameter(-40.0),
    ), 
    equations = [
        # Scaling
        'gmax_exc = exp((tau_syn_E - dt/2.0)/tau_syn_E)',
        'gmax_inh = exp((tau_syn_I - dt/2.0)/tau_syn_I)',

        # Input current
        'I = alpha_exc * (e_rev_E - v) + alpha_inh * (e_rev_I - v) + i_offset',    

        # Membrane potential     
        ann.Variable('tau_m * dv/dt = (v_rest - v +  delta_T * exp((v-v_thresh)/delta_T)) + tau_m/cm*(I - w)', init=-70.6),   

        # Recovery variable 
        'tau_w * dw/dt = a * (v - v_rest) / 1000.0 - w',    

        # Alpha-shaped conductance
        ann.Variable('tau_syn_E * dg_exc/dt = - g_exc', method='exponential'),
        ann.Variable('tau_syn_I * dg_inh/dt = - g_inh', method='exponential'),

        ann.Variable('tau_syn_E * dalpha_exc/dt = gmax_exc * g_exc - alpha_exc', method='exponential'),
        ann.Variable('tau_syn_I * dalpha_inh/dt = gmax_inh * g_inh - alpha_inh', method='exponential'),
    ],
    spike = "v > v_spike",
    reset = """
        v = v_reset
        w += b
    """,
    refractory = 0.1
)

Parameters

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