iaf_psc_exp_g – Leaky integrate-and-fire neuron model with exponential PSCs and same parameters within a population
===================================================================================================================

Description
+++++++++++

iaf_psc_exp_g is an implementation of a leaky integrate-and-fire model
with exponential shaped postsynaptic currents (PSCs) according to
equations 1, 2, 4 and 5 of [1]_ and equation 3 of [2]_.
Thus, postsynaptic currents have an infinitely short rise time.

This model enables only the change of parameters for the whole
population of neurons created within a single Create command.
For having the possibility of changing the parameters for single
neurons belonging to a neuron population please chose the
iaf_psc_exp neuron model.

The threshold crossing is followed by an absolute refractory period (t_ref)
during which the membrane potential is clamped to the resting potential
and spiking is prohibited.

The linear subthreshold dynamics is integrated by the Exact
Integration scheme [3]_. The neuron dynamics are solved on the time
grid given by the computational step size. Incoming as well as emitted
spikes are forced into that grid.

An additional state variable and the corresponding differential
equation represent a piecewise constant external current.

For conversion between postsynaptic potentials (PSPs) and PSCs,
please refer to the ``postsynaptic_potential_to_current`` function in
the ``helpers.py`` script of the Cortical Microcircuit model of [4]_.


Parameters
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The following parameters can be set in the status dictionary.

============  =======  ========================================================
 V_m_rel       mV      Membrane potential in mV (relative to resting potential)
 I_syn_ex      pA      Excitatory synaptic current
 I_syn_in      pA      Inhibitory synaptic current
 tau_m         ms      Membrane time constant
 C_m           pF      Capacity of the membrane
 E_L           mV      Resting membrane potential
 I_e           pA      Constant input current
 Theta_rel     mV      Spike threshold in mV (relative to resting potential)
 V_reset_rel   mV      Reset membrane potential after a spike
 tau_ex        ms      Exponential decay time constant of excitatory synaptic
                       current kernel
 tau_in        ms      Exponential decay time constant of inhibitory synaptic
                       current kernel
 t_ref         ms      Duration of refractory period (V_m = V_reset)
 den_delay     ms      Dendritic delay
============  =======  ========================================================

References
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.. [1] Burkitt A N (2006). A review of the integrate-and-fire neuron model:
       I. Homogeneous synaptic input. Biologial Cybernetics 95:1-19.
       DOI: https://doi.org/10.1007/s00422-006-0068-6
.. [2] Hanuschkin A, Kunkel S, Helias M, Morrison A, Diesmann M (2010).
       A general and efficient methof for incorporating precise spike
       times in globally time-driven simulations. Frontiers in Neuroinformatics.
       DOI: https://doi.org/10.3389/fninf.2010.00113
.. [3] Rotter S,  Diesmann M (1999). Exact simulation of
       time-invariant linear systems with applications to neuronal
       modeling. Biologial Cybernetics 81:381-402.
       DOI: https://doi.org/10.1007/s004220050570
.. [4] Potjans TC. and Diesmann M. 2014. The cell-type specific cortical
       microcircuit: relating structure and activity in a full-scale spiking
       network model. Cerebral Cortex. 24(3):785–806.
       DOI: https://doi.org/10.1093/cercor/bhs358.

See also
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:doc:`Neuron <index_neuron>`, :doc:`Integrate-And-Fire <index_integrate-and-fire>`, :doc:`Current-Based <index_current-based>`