gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron (GIF) model with multiple synaptic time constants (from the Gerstner lab)
========================================================================================================================================================
Description
+++++++++++
``gif_psc_exp_multisynapse`` is the generalized integrate-and-fire neuron
according to Mensi et al. (2012) [1]_ and Pozzorini et al. (2015) [2]_, 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:
.. math::
C \cdot dV(t)/dt = -g_L \cdot (V(t)-E_L) - \eta_1(t) - \eta_2(t) - \ldots
- \eta_n(t) + I(t)
where each :math:`\eta_i` is a spike-triggered current (stc), and the neuron
model can have arbitrary number of them.
Dynamic of each :math:`\eta_i` is described by:
.. math::
\tau_\eta{_i} \cdot d{\eta_i}/dt = -\eta_i
and in case of spike emission, its value increased by a constant (which can be
positive or negative):
.. math::
\eta_i = \eta_i + q_{\eta_i} \text{ (in case of spike emission).}
Neuron produces spikes stochastically according to a point process with the
firing intensity:
.. math::
\lambda(t) = \lambda_0 \cdot \exp (V(t)-V_T(t)) / \Delta_V
where :math:`V_T(t)` is a time-dependent firing threshold:
.. math::
V_T(t) = V_{T_{star}} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t)
where :math:`\gamma_i` is a kernel of spike-frequency adaptation (sfa), and the
neuron model can have arbitrary number of them.
Dynamic of each :math:`\gamma_i` is described by:
.. math::
\tau_{\gamma_i} \cdot d\gamma_i/dt = -\gamma_i
and in case of spike emission, its value increased by a constant (which can be
positive or negative):
.. math::
\gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).}
Note:
In the current implementation of the model, the values of
:math:`\eta_i` and :math:`\gamma_i` are affected immediately after spike
emission. However, `GIF toolbox `_, which
fits the model using experimental data, requires a different set of
:math:`\eta_i` and :math:`\gamma_i`. It applies the jump of
:math:`\eta_i` and :math:`\gamma_i` after the refractory period. One can
easily convert between :math:`q_\eta/\gamma` of these two approaches:
.. math::
q{_\eta}_{giftoolbox} = q_{\eta_{NEST}} \cdot (1 - \exp( -\tau_{ref} /
\tau_\eta ))
The same formula applies for :math:`q_{\gamma}`.
On the postsynaptic 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 postsynaptic current is exponential.
.. note::
If ``tau_m`` is very close to a synaptic time constant, the model
will numerically behave as if ``tau_m`` is equal to the synaptic
time constant, to avoid numerical instabilities.
For implementation details see the
`IAF Integration Singularity notebook <../model_details/IAF_Integration_Singularity.ipynb>`_.
Parameters
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The following parameters can be set in the status dictionary.
======== ====== =======================================================
**Membrane Parameters**
--------------------------------------------------------------------------
Delta_V mV Noise level of escape rate
tau_m ms Membrane time constant
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 list of ms Time constants of the synaptic currents
======= ================ ==================================================
References
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.. [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
Sends
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SpikeEvent
Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest
See also
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:doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `
Examples using this model
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.. listexamples:: gif_psc_exp_multisynapse