# Command: gif_psc_exp_multisynapse

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Name:

    gif_psc_exp_multisynapse - Current-based generalized
      integrate-and-fire neuron model with multiple synaptic time
      constants according to Mensi et al. (2012) and Pozzorini et al. (2015).

Description:

      gif_psc_exp_multisynapse 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.

      On the postsynapic side, there can be arbitrarily many synaptic time constants
      (gif_psc_exp has exactly two: tau_syn_ex and tau_syn_in). This can be reached
      by specifying separate receptor ports, each for a different time constant. The
      port number has to match the respective "receptor_type" in the connectors.

      The shape of post synaptic current is exponential.

Parameters:

      C_m	 double	- Capacity 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  vector of double	- Time constants of the synaptic currents 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:

- pp_psc_delta
- gif_psc_exp
- gif_cond_exp
- gif_cond_exp_multisynapse

Source:

    /opt/conda/conda-bld/nest_1524088722951/work/nest-2.14.0/models/gif_psc_exp_multisynapse.h

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