glif_psc_double_alpha – Current-based generalized leaky integrate-and-fire (GLIF) models with double alpha-function (from the Allen Institute)
==============================================================================================================================================
Description
+++++++++++
``glif_psc_double_alpha`` provides five generalized leaky integrate-and-fire
(GLIF) models [1]_ with double alpha-function shaped synaptic currents.
Incoming spike events induce a postsynaptic change of current modeled
by the sum of two alpha functions (fast and slow components) for each receptor [2]_.
This function is normalized such that an event of weight 1.0 results in a peak current
of the fast component of the alpha function to be 1 pA at
:math:`t = \tau_\text{syn, fast}`.
The relative peak current of the slow component is given as ``amp_slow``, at
:math:`t = \tau_\text{syn, slow}`. Namely,
.. math::
I_\text{syn} = \text{alpha_function} \left( \tau_\text{syn} = \tau_\text{syn, fast} \right) + \text{amp_slow} \cdot
\text{alpha_function} \left( \tau_\text{syn} = \tau_\text{syn, slow} \right).
Therefore if ``amp_slow`` is not 0, the peak current of the total synaptic current is larger
than the specified weight. By default, ``glif_psc_double_alpha`` has a single synapse that
is accessible through ``receptor_port`` 1. An arbitrary number of synapses with different
time constants and ``amp_slow`` can be configured by setting the desired parameters of
``tau_syn_fast``, ``tau_syn_slow``, and ``amp_slow`` arrays. The resulting synapses are addressed
through ``receptor_port`` 1, 2, 3, ....
The five GLIF models are:
* **GLIF Model 1** - Traditional leaky integrate and fire (LIF)
* **GLIF Model 2** - Leaky integrate and fire with biologically defined reset rules
(LIF_R)
* **GLIF Model 3** - Leaky integrate and fire with after-spike currents (LIF_ASC)
* **GLIF Model 4** - Leaky integrate and fire with biologically defined reset rules
and after-spike currents (LIF_R_ASC)
* **GLIF Model 5** - Leaky integrate and fire with biologically defined reset rules,
after-spike currents and a voltage dependent threshold (LIF_R_ASC_A)
GLIF model mechanism setting is based on three parameters
(``spike_dependent_threshold``, ``after_spike_currents``, ``adapting_threshold``).
The settings of these three parameters for the five GLIF models are listed
below. Other combinations of these parameters will not be supported.
+--------+---------------------------+----------------------+--------------------+
| Model | spike_dependent_threshold | after_spike_currents | adapting_threshold |
+========+===========================+======================+====================+
| GLIF1 | False | False | False |
+--------+---------------------------+----------------------+--------------------+
| GLIF2 | True | False | False |
+--------+---------------------------+----------------------+--------------------+
| GLIF3 | False | True | False |
+--------+---------------------------+----------------------+--------------------+
| GLIF4 | True | True | False |
+--------+---------------------------+----------------------+--------------------+
| GLIF5 | True | True | True |
+--------+---------------------------+----------------------+--------------------+
Typical parameter setting of different levels of GLIF models for different cells
can be found and downloaded in the `Allen Cell Type Database
`_. For example, the default parameter setting of this
``glif_psc_double_alpha`` neuron model was from the parameter values of GLIF Model 5 of
Cell 490626718, which can be retrieved from the `Allen Brain Atlas
`_, with units being converted from SI units (i.e., V, S (1/Ohm),
F, s, A) to NEST used units (i.e., mV, nS (1/GOhm), pF, ms, pA) and values
being rounded to appropriate digits for simplification.
For models with spike dependent threshold (i.e., GLIF2, GLIF4 and GLIF5),
parameter setting of ``voltage_reset_fraction`` and ``voltage_reset_add`` may lead to the
situation that voltage is bigger than threshold after reset. In this case, the neuron
will continue to spike until the end of the simulation regardless the stimulated inputs.
We recommend the setting of the parameters of these three models to follow the
condition of
.. math::
E_L + \mathrm{voltage\_reset\_fraction} \cdot \left( V_\mathrm{th} - E_L \right)
+ \mathrm{voltage\_reset\_add} < V_\mathrm{th} + \mathrm{th\_spike\_add}
.. 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 <../model_details/IAF_Integration_Singularity.ipynb>`_ notebook.
Parameters
++++++++++
The following parameters can be set in the status dictionary.
========= ======== ============================================================
**Membrane parameters**
-------------------------------------------------------------------------------
V_m double Membrane potential in mV (absolute value)
V_th double Instantaneous threshold in mV
g double Membrane conductance in nS
E_L double Resting membrane potential in mV
C_m double Capacitance of the membrane in pF
t_ref double Duration of refractory time in ms
V_reset double Reset potential of the membrane in mV (GLIF 1 or GLIF 3)
========= ======== ============================================================
========================= =============== =====================================
**Spike adaptation and firing intensity parameters**
-------------------------------------------------------------------------------
th_spike_add double Threshold addition following spike
in mV (delta_theta_s in Equation (6)
in [1]_)
th_spike_decay double Spike-induced threshold time
constant in 1/ms (bs in Equation (2)
in [1]_)
voltage_reset_fraction double Voltage fraction coefficient
following spike (fv in Equation (5)
in [1]_)
voltage_reset_add double Voltage addition following spike in
mV (-delta_V (sign flipped) in
Equation (5) in [1]_)
asc_init double vector Initial values of after-spike
currents in pA
asc_decay double vector After-spike current time constants
in 1/ms (kj in Equation (3) in [1]_)
asc_amps double vector After-spike current amplitudes in
pA (deltaIj in Equation (7) in [1]_)
asc_r double vector Current fraction following spike
coefficients for fj in Equation (7)
in [1]_
th_voltage_index double Adaptation index of threshold - A
'leak-conductance' for the
voltage-dependent component of the
threshold in 1/ms (av in Equation
(4) in [1]_)
th_voltage_decay double Voltage-induced threshold time
constant - Inverse of which is the
time constant of the
voltage-dependent component of the
threshold in 1/ms (bv in Equation
(4) in [1]_)
tau_syn_fast double vector Time constants of the faster
synaptic alpha function in ms
tau_syn_slow double vector Time constants of the slower
synaptic alpha function in ms
amp_slow double vector Relative amplitude of the slower
synaptic alpha function
E_rev double vector Reversal potential in mV
spike_dependent_threshold bool flag whether the neuron has
biologically defined reset rules
with a spike dependent threshold
component
after_spike_currents bool flag whether the neuron has after
spike currents
adapting_threshold bool flag whether the neuron has a
voltage dependent threshold component
========================= =============== =====================================
References
++++++++++
.. [1] Teeter C, Iyer R, Menon V, Gouwens N, Feng D, Berg J, Szafer A,
Cain N, Zeng H, Hawrylycz M, Koch C, & Mihalas S (2018)
Generalized leaky integrate-and-fire models classify multiple neuron
types. Nature Communications 9:709.
.. [2] Meffin, H., Burkitt, A. N., & Grayden, D. B. (2004). An analytical
model for the large, fluctuating synaptic conductance state typical of
neocortical neurons in vivo. J. Comput. Neurosci., 16, 159-175.
See also
++++++++
:doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `
Examples using this model
+++++++++++++++++++++++++
.. listexamples:: glif_psc_double_alpha