gif_cond_exp_multisynapse - Conductance-based generalized
integrate-and-fire neuron model with multiple synaptic time constants
according to Mensi et al. (2012) and Pozzorini et al. (2015).
gif_cond_exp_multisynapse 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 gamma_i 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$.
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 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**
------------------------------------------------------------------------------
tau_syn list of ms Time constants of the synaptic conductance
(same size as E_rev)
E_rev list of mV Reversal potentials (same size as tau_syn)
========= ============= ===================================================
============== ====== ======================================================
**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
Example:
neuron = nest.Create('gif_cond_exp_multisynapse',
params={'E_rev': [0.0, -85.0],
'tau_syn': [4.0, 8.0]})
spike = nest.Create('spike_generator', params={'spike_times':
np.array([10.0])})
delays = [1., 30.]
w = [1., 5.]
for syn in range(2):
nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse',
'receptor_type': 1 + syn,
'weight': w[syn],
'delay': delays[syn]})
nest.Simulate(100.)
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_multisynapse.h