ANNarchy 5.0.0
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On this page

  • EIF_cond_alpha_isfa_ista
    • Parameters

EIF_cond_alpha_isfa_ista

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.), 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 Type 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
HH_cond_exp
EIF_cond_exp_isfa_ista
 

Copyright Julien Vitay, Helge Ülo Dinkelbach, Fred Hamker