gif_cond_exp - Conductance-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 post-synaptic
conductances in the form of truncated exponentials.
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:
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 synaptic conductance is exponential.
The following parameters can be set in the status dictionary.
\verbatim embed:rst
======== ======= =======================================
**Membrane Parameters**
--------------------------------------------------------
C_m pF Capacity of the membrane
t_ref ms Duration of refractory period
V_reset mV Reset value for V_m after a spike
E_L mV Leak reversal potential
g_L nS Leak conductance
I_e pA Constant external 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 real Stochastic intensity at firing threshold V_T i
n 1/s.
V_T_star mV Base threshold
========= ================= ===============================================
=========== ======= ===========================================================
**Synaptic parameters**
-------------------------------------------------------------------------------
E_ex mV Excitatory reversal potential
tau_syn_ex ms Decay time of excitatory synaptic conductance
E_in mV Inhibitory reversal potential
tau_syn_in ms Decay time of the inhibitory synaptic conductance
=========== ======= ===========================================================
============= ======= =========================================================
**Integration parameters**
-------------------------------------------------------------------------------
gsl_error_tol real This parameter controls the admissible error of the
GSL integrator. Reduce it if NEST complains about
numerical instabilities.
============= ======= =========================================================
\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_cond_exp.h