gif_psc_exp - Current-based generalized integrate-and-fire neuron
model according to Mensi et al. (2012) and Pozzorini et al. (2015).
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:
@f[
C*dV(t)/dt = -g_L*(V(t)-E_L) - \eta_1(t) - \eta_2(t) - \ldots - \eta_n(t)
+ I(t)
@f]
where each \f$ \eta_i \f$ is a spike-triggered current (stc), and the neuron
model can have arbitrary number of them.
Dynamic of each \f$ \eta_i \f$ is described by:
@f[
\tau_{\eta_i}*d{\eta_i}/dt = -\eta_i
@f]
and in case of spike emission, its value increased by a constant (which can be
positive or negative):
@f[
\eta_i = \eta_i + q_{\eta_i} \text{ (in case of spike emission).}
@f]
Neuron produces spikes STOCHASTICALLY according to a point process with the
firing intensity:
@f[
\lambda(t) = \lambda_0 * \exp[ (V(t)-V_T(t)) / \Delta_V ]
@f]
where \f$ V_T(t) \f$ is a time-dependent firing threshold:
@f[
V_T(t) = V_{T_{star}} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t)
@f]
where \f$ \gamma_i \f$ is a kernel of spike-frequency adaptation (sfa), and the
neuron model can have arbitrary number of them.
Dynamic of each \f$ gamma_i \f$ is described by:
@f[
\tau_{\gamma_i}*d{\gamma_i}/dt = -\gamma_i
@f]
and in case of spike emission, its value increased by a constant (which can be
positive or negative):
@f[
\gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).}
@f]
Note that in the current implementation of the model (as described in [1] and
[2]) the values of \f$ eta_i \f$ and \f$ gamma_i \f$ 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
\f$ eta_i \f$ and \f$ gamma_i \f$. It applies the jump of \f$ eta_i \f$ and
\f$ gamma_i \f$ after the refractory period. One can easily convert between
\f$ q_eta/gamma \f$ of these two approaches:
\f$ q_eta_giftoolbox = q_eta_NEST * (1 - exp( -tau_ref / tau_eta )) /f$
The same formula applies for /f$ q_gamma /f$.
The shape of post synaptic current is exponential.
The following parameters can be set in the status dictionary.
\verbatim embed:rst
======== ======= ================================================
**Membrane Parameters**
-----------------------------------------------------------------
C_m pF Capacitance of the membrane
t_ref ms Duration of refractory period
V_reset mV Membrane potential is reset to this value after
a spike
E_L mV Resting potential
g_L nS Leak conductance
I_e pA Constant input current
======== ======= ================================================
========= ========== ====================================================
**Spike adaptation and firing intensity parameters**
--------------------------------------------------------------------------
q_stc list of nA Values added to spike-triggered currents (stc)
after each spike emission
tau_stc list of ms Time constants of stc variables
q_sfa list of mV Values added to spike-frequency adaptation
(sfa) after each spike emission
tau_sfa list of ms Time constants of sfa variables
Delta_V mV Stochasticity level
lambda_0 1/s Stochastic intensity at firing threshold V_T
V_T_star mV Base threshold
========= ========== ====================================================
=========== ======= ===========================================================
**Synaptic parameters**
-------------------------------------------------------------------------------
tau_syn_ex ms Time constant of excitatory synaptic conductance
tau_syn_in ms Time constant of the inhibitory synaptic conductance
=========== ======= ===========================================================
\endverbatim
SpikeEvent, CurrentEvent, DataLoggingRequest
SpikeEvent
\verbatim embed:rst
.. [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. Journal of
Neurophysiology, 107(6):1756-1775.
DOI: https://doi.org/10.1152/jn.00408.2011
.. [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 Computational Biology, 11(6), e1004275.
DOI: https://doi.org/10.1371/journal.pcbi.1004275
\endverbatim
March 2016, Setareh
/var/www/debian/nest/nest-simulator-2.20.0/models/gif_psc_exp.h