**Name:**

gif_psc_exp - Current-based generalized integrate-and-fire neuron

model according to Mensi et al. (2012) and Pozzorini et al. (2015).

**Description:**

gif_psc_exp is the generalized integrate-and-fire neuron according to

Mensi et al. (2012) and Pozzorini et al. (2015), with exponential shaped

postsynaptic currents.

This model features both an adaptation current and a dynamic threshold for

spike-frequency adaptation. The membrane potential (V) is described by the

differential equation:

C*dV(t)/dt = -g_L*(V(t)-E_L) - eta_1(t) - eta_2(t) - ... - eta_n(t) + I(t)

where each eta_i is a spike-triggered current (stc), and the neuron model can

have arbitrary number of them.

Dynamic of each eta_i is described by:

tau_eta_i*d{eta_i}/dt = -eta_i

and in case of spike emission, its value increased by a constant (which can be

positive or negative):

eta_i = eta_i + q_eta_i (in case of spike emission).

Neuron produces spikes STOCHASTICALLY according to a point process with the

firing intensity:

lambda(t) = lambda_0 * exp[ (V(t)-V_T(t)) / Delta_V ]

where V_T(t) is a time-dependent firing threshold:

V_T(t) = V_T_star + gamma_1(t) + gamma_2(t) + ... + gamma_m(t)

where gamma_i is a kernel of spike-frequency adaptation (sfa), and the neuron

model can have arbitrary number of them.

Dynamic of each gamma_i is described by:

tau_gamma_i*d{gamma_i}/dt = -gamma_i

and in case of spike emission, its value increased by a constant (which can be

positive or negative):

gamma_i = gamma_i + q_gamma_i (in case of spike emission).

Note that in the current implementation of the model (as described in [1] and

[2]) the values of eta_i and gamma_i are affected immediately after spike

emission. However, GIF toolbox (http://wiki.epfl.ch/giftoolbox) which fits

the model using experimental data, requires a different set of eta_i and

gamma_i. It applies the jump of eta_i and gamma_i after the refractory period.

One can easily convert between q_eta/gamma of these two approaches:

q_eta_giftoolbox = q_eta_NEST * (1 - exp( -tau_ref / tau_eta ))

The same formula applies for q_gamma.

The shape of post synaptic current is exponential.

**Parameters:**

C_m double - Capacitance of the membrane in pF

t_ref double - Duration of refractory period in ms.

V_reset double - Reset value after a spike in mV.

E_L double - Leak reversal potential in mV.

g_L double - Leak conductance in nS.

I_e double - Constant external input current in pA.

Spike adaptation and firing intensity parameters:

q_stc vector of double - Values added to spike-triggered currents (stc)

after each spike emission in nA.

tau_stc vector of double - Time constants of stc variables in ms.

q_sfa vector of double - Values added to spike-frequency adaptation

(sfa) after each spike emission in mV.

tau_sfa vector of double - Time constants of sfa variables in ms.

Delta_V double - Stochasticity level in mV.

lambda_0 double - Stochastic intensity at firing threshold V_T in 1/s.

V_T_star double - Base threshold in mV

Synaptic parameters

tau_syn_ex double - Time constant of the excitatory synaptic current in ms.

tau_syn_in double - Time constant of the inhibitory synaptic current in ms.

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**References:**

[1] Mensi S, Naud R, Pozzorini C, Avermann M, Petersen CC, Gerstner W (2012)

Parameter extraction and classification of three cortical neuron types

reveals two distinct adaptation mechanisms. J. Neurophysiol., 107(6),

1756-1775.

[2] Pozzorini C, Mensi S, Hagens O, Naud R, Koch C, Gerstner W (2015)

Automated High-Throughput Characterization of Single Neurons by Means of

Simplified Spiking Models. PLoS Comput. Biol., 11(6), e1004275.

**Author:**

March 2016, Setareh

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/gif_psc_exp.h