IF_curr_alpha

IF_curr_alpha(
    self,
    v_rest=-65.0,
    cm=1.0,
    tau_m=20.0,
    tau_refrac=0.0,
    tau_syn_E=5.0,
    tau_syn_I=5.0,
    v_thresh=-50.0,
    v_reset=-65.0,
    i_offset=0.0,
)

Leaky integrate-and-fire model with fixed threshold and alpha post-synaptic currents.

Separate synaptic currents for excitatory and inhibitory synapses.

The alpha currents are calculated through a system of two linears ODEs. After a spike is received at t_spike, it peaks at t_spike + tau_syn_X, with a maximum equal to the synaptic efficiency.

The ODEs are solved using the exponential Euler method.

Equivalent code:

IF_curr_alpha = Neuron(
    parameters = dict(
        v_rest = ann.Parameter(-65.0),
        cm  = ann.Parameter(1.0),
        tau_m  = ann.Parameter(20.0),
        tau_syn_E = ann.Parameter(5.0),
        tau_syn_I = ann.Parameter(5.0),
        v_thresh = ann.Parameter(-50.0),
        v_reset = ann.Parameter(-65.0),
        i_offset = ann.Parameter(0.0),
    ), 
    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)',

        # Membrane potential
        ann.Variable(
            'cm * dv/dt = cm/tau_m*(v_rest -v)   + alpha_exc - alpha_inh + i_offset',
            method='exponential', init=-65.0),

        # 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_thresh",
    reset = "v = v_reset",
    refractory = 0.0
)

Parameters

Name	Description	Default
v_rest	Resting membrane potential (mV)	`-65.0`
cm	Capacity of the membrane (nF)	`1.0`
tau_m	Membrane time constant (ms)	`20.0`
tau_refrac	Duration of refractory period (ms)	`0.0`
tau_syn_E	Rise time of excitatory synaptic current (ms)	`5.0`
tau_syn_I	Rise time of inhibitory synaptic current (ms)	`5.0`
v_thresh	Spike threshold (mV)	`-50.0`
v_reset	Reset potential after a spike (mV)	`-65.0`
i_offset	Offset current (nA)	`0.0`