iaf_psc_exp – Leaky integrate-and-fire neuron model with exponential PSCs
=========================================================================
Description
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``iaf_psc_exp`` is an implementation of a leaky integrate-and-fire model
with exponential shaped postsynaptic currents (PSCs) according to [1]_.
Thus, postsynaptic currents have an infinitely short rise time.
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 neuron dynamics is solved on the time grid given by the computation step
size. Incoming as well as emitted spikes are forced to that grid.
The linear subthreshold dynamics is integrated by the Exact
Integration scheme [2]_, which is more precise, but different from the
implementation in [1]_, which uses the forward Euler integration scheme.
This precludes an exact numerical reproduction of the results from [1]_.
An additional state variable and the corresponding differential
equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with
neuron like dynamics interacting by point events is described in
[2]_. A flow chart can be found in [3]_.
Spiking in this model can be either deterministic (delta=0) or stochastic (delta
> 0). In the stochastic case this model implements a type of spike response
model with escape noise [4]_.
.. note::
If ``tau_m`` is very close to ``tau_syn_ex`` or ``tau_syn_in``, the model
will numerically behave as if ``tau_m`` is equal to ``tau_syn_ex`` or
``tau_syn_in``, respectively, to avoid numerical instabilities.
For implementation details see the
`IAF Integration Singularity notebook <../model_details/IAF_Integration_Singularity.ipynb>`_.
``iaf_psc_exp`` can handle current input in two ways:
1. Current input through ``receptor_type`` 0 is handled as a stepwise constant
current input as in other iaf models, that is, this current directly enters the
membrane potential equation.
2. In contrast, current input through ``receptor_type`` 1 is filtered through an
exponential kernel with the time constant of the excitatory synapse,
``tau_syn_ex``.
For an example application, see [4]_.
**Warning:** this current input is added to the state variable
``i_syn_ex_``. If this variable is being recorded, its numerical value
will thus not correspond to the excitatory synaptic input current, but to
the sum of excitatory synaptic input current and the contribution from
receptor type 1 currents.
For conversion between postsynaptic potentials (PSPs) and PSCs,
please refer to the ``postsynaptic_potential_to_current`` function in
:doc:`PyNEST Microcircuit: Helper Functions <../auto_examples/Potjans_2014/helpers>`.
Parameters
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The following parameters can be set in the status dictionary.
=========== ======= ========================================================
E_L mV Resting membrane potential
C_m pF Capacity of the membrane
tau_m ms Membrane time constant
tau_syn_ex ms Exponential decay time constant of excitatory synaptic
current kernel
tau_syn_in ms Exponential decay time constant of inhibitory synaptic
current kernel
t_ref ms Duration of refractory period (V_m = V_reset)
V_m mV Membrane potential in mV
V_th mV Spike threshold in mV
V_reset mV Reset membrane potential after a spike
I_e pA Constant input current
t_spike ms Point in time of last spike
=========== ======= ========================================================
References
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.. [1] Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent
networks with frequency-dependent synapses. The Journal of Neuroscience,
20,RC50:1-5. URL: https://infoscience.epfl.ch/record/183402
.. [2] 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
.. [3] Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001). State
space analysis of synchronous spiking in cortical neural
networks. Neurocomputing 38-40:565-571.
DOI: https://doi.org/10.1016/S0925-2312(01)00409-X
.. [4] Schuecker J, Diesmann M, Helias M (2015). Modulated escape from a
metastable state driven by colored noise. Physical Review E 92:052119
DOI: https://doi.org/10.1103/PhysRevE.92.052119
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:: iaf_psc_exp