Adaptive Exponential Integrate-and-Fire (aEIF) neuron models¶

class aeif_cond_alpha : public Archiving_Node¶

#include <aeif_cond_alpha.h>

Name: aeif_cond_alpha - Conductance based exponential integrate-and-fire neuron model according to Brette and Gerstner (2005). Description:

aeif_cond_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances are modelled as alpha-functions.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive step size to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split} C_m \frac{dV}{dt} = -g_L(V-E_L)+g_L\Delta_T\exp\left(\frac{V-V_{th}}{\Delta_T}\right) - g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w \frac{dw}{dt} = a(V-E_L) - w \]

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
g_ex	nS	Excitatory synaptic conductance
dg_ex	nS/ms	First derivative of g_ex
g_in	nS	Inhibitory synaptic conductance
dg_in	nS/ms	First derivative of g_in
w	pA	Spike-adaptation current

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 parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Synaptic parameters
E_ex	mV	Excitatory reversal potential
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
E_in	mV	Inhibitory reversal potential
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Authors: Marc-Oliver Gewaltig; full revision by Tanguy Fardet on December 2016

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642 DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_cond_alpha, aeif_cond_exp

class aeif_cond_alpha_multisynapse : public Archiving_Node¶

#include <aeif_cond_alpha_multisynapse.h>

Name: aeif_cond_alpha_multisynapse - Conductance based adaptive exponential integrate-and-fire neuron model according to Brette and Gerstner (2005) with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by an alpha function.

Description:

aeif_cond_alpha_multisynapse is a conductance-based adaptive exponential integrate-and-fire neuron model. It allows an arbitrary number of synaptic time constants. Synaptic conductance is modeled by an alpha function, as described by A. Roth and M.C.W. van Rossum in Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6.

The time constants are supplied by an array, “tau_syn”, and the pertaining synaptic reversal potentials are supplied by the array “E_rev”. Port numbers are automatically assigned in the range from 1 to n_receptors. During connection, the ports are selected with the property “receptor_type”.

The membrane potential is given by the following differential equation:

\[ C dV/dt = -g_L(V-E_L) + g_L*\Delta_T*\exp((V-V_T)/\Delta_T) + I_{syn_{tot}}(V, t)- w + I_e \]

where

\[ I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V - E_{rev,i}) , \]

the synapse i is excitatory or inhibitory depending on the value of \( E_{rev,i}\) and the differential equation for the spike-adaptation current w is:

\[ \tau_w * dw/dt = a(V - E_L) - w \]

When the neuron fires a spike, the adaptation current w <- w + b.

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
w	pA	Spike-adaptation current

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
Delta_T	mV	Slope factor
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Spike adaptation parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
tau_w	ms	Adaptation time constant

Synaptic parameters
E_rev	list of mV	Reversal potential
tau_syn	list of ms	Time constant of synaptic conductance

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Examples:

import nest
import numpy as np

neuron = nest.Create('aeif_cond_alpha_multisynapse')
nest.SetStatus(neuron, {"V_peak": 0.0, "a": 4.0, "b":80.5})
nest.SetStatus(neuron, {'E_rev':[0.0, 0.0, 0.0, -85.0],
                        'tau_syn':[1.0, 5.0, 10.0, 8.0]})

spike = nest.Create('spike_generator', params = {'spike_times':
                                                np.array([10.0])})

voltmeter = nest.Create('voltmeter', 1, {'withgid': True})

delays=[1.0, 300.0, 500.0, 700.0]
w=[1.0, 1.0, 1.0, 1.0]
for syn in range(4):
    nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse',
                                          'receptor_type': 1 + syn,
                                          'weight': w[syn],
                                          'delay': delays[syn]})

nest.Connect(voltmeter, neuron)

nest.Simulate(1000.0)
dmm = nest.GetStatus(voltmeter)[0]
Vms = dmm["events"]["V_m"]
ts = dmm["events"]["times"]
import pylab
pylab.figure(2)
pylab.plot(ts, Vms)
pylab.show()

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Author: Hans Ekkehard Plesser, based on aeif_cond_beta_multisynapse

SeeAlso: aeif_cond_alpha_multisynapse

class aeif_cond_alpha_RK5 : public Archiving_Node¶

#include <aeif_cond_alpha_RK5.h>

Name: aeif_cond_alpha_RK5 - Conductance based exponential integrate-and-fire neuron model according to Brette and Gerstner (2005)

Description:

aeif_cond_alpha_RK5 is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances are modelled as alpha-functions.

This implementation uses a 5th order Runge-Kutta solver with adaptive stepsize to integrate the differential equation (see Numerical Recipes 3rd Edition, Press et al. 2007, Ch. 17.2).

The membrane potential is given by the following differential equation:

\[\begin{split} C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w * dw/dt= a(V-E_L) -w \]

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
g_ex	nS	Excitatory synaptic conductance
dg_ex	nS/ms	First derivative of g_ex
g_in	nS	Inhibitory synaptic conductance
dg_in	nS/ms	First derivative of g_in
w	pA	Spike-adaptation current

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 parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Synaptic parameters
E_ex	mV	Excitatory reversal potential
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
E_in	mV	Inhibitory reversal potential
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

Numerical integration parameters
HMIN	ms	Minimal stepsize for numerical integration (default 0.001ms)
MAXERR	mV	Error estimate tolerance for adaptive stepsize control (steps accepted if err<=MAXERR). Note that the error refers to the difference between the 4th and 5th order RK terms. Default 1e-10 mV.

Authors: Stefan Bucher, Marc-Oliver Gewaltig.

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_cond_alpha, aeif_cond_exp, aeif_cond_alpha

class aeif_cond_beta_multisynapse : public Archiving_Node¶

#include <aeif_cond_beta_multisynapse.h>

Name: aeif_cond_beta_multisynapse - Conductance based adaptive exponential integrate-and-fire neuron model according to Brette and Gerstner (2005) with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by a beta function.

Description:

aeif_cond_beta_multisynapse is a conductance-based adaptive exponential integrate-and-fire neuron model. It allows an arbitrary number of synaptic rise time and decay time constants. Synaptic conductance is modeled by a beta function, as described by A. Roth and M.C.W. van Rossum in Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6.

The time constants are supplied by two arrays, “tau_rise” and “tau_decay” for the synaptic rise time and decay time, respectively. The synaptic reversal potentials are supplied by the array “E_rev”. The port numbers are automatically assigned in the range from 1 to n_receptors. During connection, the ports are selected with the property “receptor_type”.

The membrane potential is given by the following differential equation:

\[ C dV/dt = -g_L(V-E_L) + g_L*\Delta_T*\exp((V-V_T)/\Delta_T) + I_{syn_{tot}}(V, t) - w + I_e \]

where:

\[ I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V - E_{rev,i}) , \]

the synapse i is excitatory or inhibitory depending on the value of \( E_{rev,i} \) and the differential equation for the spike-adaptation current w is:

\[ \tau_w * dw/dt = a(V - E_L) - w \]

When the neuron fires a spike, the adaptation current w <- w + b.

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

Dynamic state variables:
V_m	mV	Membrane potential
w	pA	Spike-adaptation current

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
Delta_T	mV	Slope factor
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Spike adaptation parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
tau_w	ms	Adaptation time constant

Synaptic parameters
E_rev	list of mV	Reversal potential
tau_syn	list of ms	Time constant of synaptic conductance

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Examples:

import nest
import numpy as np

neuron = nest.Create('aeif_cond_beta_multisynapse')
nest.SetStatus(neuron, {"V_peak": 0.0, "a": 4.0, "b":80.5})
nest.SetStatus(neuron, {'E_rev':[0.0,0.0,0.0,-85.0],
                        'tau_decay':[50.0,20.0,20.0,20.0],
                        'tau_rise':[10.0,10.0,1.0,1.0]})

spike = nest.Create('spike_generator', params = {'spike_times':
                                                np.array([10.0])})

voltmeter = nest.Create('voltmeter', 1, {'withgid': True})

delays=[1.0, 300.0, 500.0, 700.0]
w=[1.0, 1.0, 1.0, 1.0]
for syn in range(4):
    nest.Connect(spike, neuron, syn_spec={'model': 'static_synapse',
                                          'receptor_type': 1 + syn,
                                          'weight': w[syn],
                                          'delay': delays[syn]})

nest.Connect(voltmeter, neuron)

nest.Simulate(1000.0)
dmm = nest.GetStatus(voltmeter)[0]
Vms = dmm["events"]["V_m"]
ts = dmm["events"]["times"]
import pylab
pylab.figure(2)
pylab.plot(ts, Vms)
pylab.show()

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Author: Bruno Golosio 07/10/2016

SeeAlso: aeif_cond_alpha_multisynapse

class aeif_cond_exp : public Archiving_Node¶

#include <aeif_cond_exp.h>

Name: aeif_cond_exp - Conductance based exponential integrate-and-fire neuron model according to Brette and Gerstner (2005).

Description:

aeif_cond_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with post-synaptic conductances in the form of truncated exponentials.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split} C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w * dw/dt= a(V-E_L) -W \]

Note that the spike detection threshold V_peak is automatically set to \( V_th+10 mV \) to avoid numerical instabilites that may result from setting V_peak too high.

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

Dynamic state variables:
V_m	mV	Membrane potential
g_ex	nS	Excitatory synaptic conductance
g_in	nS	Inhibitory synaptic conductance
w	pA	Spike-adaptation current

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 parameters
a	nS	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Synaptic parameters
E_ex	mV	Excitatory reversal potential
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
E_in	mV	Inhibitory reversal potential
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Author: Adapted from aeif_cond_alpha by Lyle Muller; full revision by Tanguy Fardet on December 2016

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_cond_exp, aeif_cond_alpha

class aeif_psc_alpha : public Archiving_Node¶

#include <aeif_psc_alpha.h>

Name: aeif_psc_alpha - Current-based exponential integrate-and-fire neuron model according to Brette and Gerstner (2005).

Description:

aeif_psc_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic currents are modelled as alpha-functions.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive step size to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split} C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w * dw/dt= a(V-E_L) -W \]

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
I_ex	pA	Excitatory synaptic current
dI_ex	pA/ms	First derivative of I_ex
I_in	pA	Inhibitory synaptic current
dI_in	pA/ms	First derivative of I_in
w	pA	Spike-adaptation current
g	pa	Spike-adaptation current

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 parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Synaptic parameters
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities

Author: Tanguy Fardet

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_psc_alpha, aeif_cond_exp

class aeif_psc_delta : public Archiving_Node¶

#include <aeif_psc_delta.h>

Name: aeif_psc_delta - Current-based adaptive exponential integrate-and-fire neuron model according to Brette and Gerstner (2005) with delta synapse.

Description:

aeif_psc_delta is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with post-synaptic currents in the form of delta spikes.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split} C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w * dw/dt= a(V-E_L) -W \]

\[ I(t) = J \sum_k \delta(t - t^k). \]

Here delta is the dirac delta function and k indexes incoming spikes. This is implemented such that V_m will be incremented/decremented by the value of J after a spike.

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables
V_m	mV	Membrane potential
w	pA	Spike-adaptation current

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 parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
tau_w	ms	Adaptation time constant
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_th	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Author: Mikkel Elle Lepperød adapted from aeif_psc_exp and iaf_psc_delta

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_psc_delta, aeif_cond_exp, aeif_psc_exp

class aeif_psc_delta_clopath : public Clopath_Archiving_Node¶

#include <aeif_psc_delta_clopath.h>

Name: aeif_psc_delta_clopath - Exponential integrate-and-fire neuron model according to Clopath et al. (2010).

Description:

aeif_psc_delta_clopath is an implementation of the neuron model as it is used in [1]. It is an extension of the aeif_psc_delta model and capable of connecting to a Clopath synapse.

Note that there are two points that are not mentioned in the paper but present in a MATLAB implementation by Claudia Clopath [3]. The first one is the clamping of the membrane potential to a fixed value after a spike occured to mimik a real spike and not just the upswing. This is important since the finite duration of the spike influences the evolution of the convolved versions (u_bar_[plus/minus]) of the membrane potential and thus the change of the synaptic weight. Secondly, there is a delay with which u_bar_[plus/minus] are used to compute the change of the synaptic weight.

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables
V_m	mV	Membrane potential
w	pA	Spike-adaptation current
z	pA	Spike-adaptation current
V_th	mV	Adaptive spike initiation threshold
u_bar_plus	mV	Low-pass filtered Membrane potential
u_bar_minus	mV	Low-pass filtered Membrane potential
u_bar_bar	mV	Low-pass filtered u_bar_minus

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
tau_plus	ms	Time constant of u_bar_plus
tau_minus	ms	Time constant of u_bar_minus
tau_bar_bar	ms	Time constant of u_bar_bar

Spike adaptation parameters
a	nS	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_peak	mV	Spike detection threshold
V_th_max	mV	Value of V_th afer a spike
V_th_rest	mV	Resting value of V_th

Clopath rule parameters
A_LTD	1/mV	Amplitude of depression
A_LTP	1/mV^2	Amplitude of facilitation
theta_plus	mV	Threshold for u
theta_minus	mV	Threshold for u_bar_[plus/minus]
A_LTD_const	boolean	Flag that indicates whether A_LTD_ should be constant (true, default) or multiplied by u_bar_bar^2 / u_ref_squared (false).
delay_u_bars	real	Delay with which u_bar_[plus/minus] are processed to compute the synaptic weights.
U_ref_squared	real	Reference value for u_bar_bar_^2.

Other parameters
t_clamp	ms	Duration of clamping of Membrane potential after a spike
V_clamp	mV	Value to which the Membrane potential is clamped

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Note:

Neither the clamping nor the delayed processing of u_bar_[plus/minus] are mentioned in [1]. However, they are part of an reference implementation by Claudia Clopath et al. that can be found on ModelDB [3]. The clamping is important to mimic a spike which is otherwise not described by the aeif neuron model.

Author: Jonas Stapmanns, David Dahmen, Jan Hahne

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1: Clopath et al. (2010). Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nature Neuroscience 13(3):344-352. DOI: https://doi.org/10.1038/nn.2479
2: Clopath and Gerstner (2010). Voltage and spike timing interact in STDP – a unified model. Frontiers in Synaptic Neuroscience. 2:25 DOI: https://doi.org/10.3389/fnsyn.2010.00025
3: Voltage-based STDP synapse (Clopath et al. 2010) on ModelDB https://senselab.med.yale.edu/ModelDB/showmodel.cshtml?model=144566&file=%2f modeldb_package%2fVoTriCode%2faEIF.m

SeeAlso: aeif_psc_delta, clopath_synapse, hh_psc_alpha_clopath

class aeif_psc_exp : public Archiving_Node¶

#include <aeif_psc_exp.h>

Name: aeif_psc_exp - Current-based exponential integrate-and-fire neuron model according to Brette and Gerstner (2005).

Description:

aeif_psc_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with post-synaptic currents in the form of truncated exponentials.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split} C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e \end{split}\]

and

\[ \tau_w * dw/dt= a(V-E_L) -W \]

Note that the spike detection threshold V_peak is automatically set to \( V_th+10 \) mV to avoid numerical instabilites that may result from setting V_peak too high.

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
I_ex	pA	Excitatory synaptic current
I_in	pA	Inhibitory synaptic current
w	pA	Spike-adaptation current

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 parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
V_t	mV	Spike initiation threshold
V_peak	mV	Spike detection threshold

Synaptic parameters
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities

Author: Tanguy Fardet

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1: Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

SeeAlso: iaf_psc_exp, aeif_cond_exp