Neuron models with conductance-based synapses

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 gif_cond_exp : public Archiving_Node

#include <gif_cond_exp.h>

Name: gif_cond_exp - Conductance-based generalized integrate-and-fire neuron model according to Mensi et al. (2012) and Pozzorini et al. (2015).

Description:

gif_psc_exp is the generalized integrate-and-fire neuron according to Mensi et al. (2012) and Pozzorini et al. (2015), with post-synaptic conductances in the form of truncated exponentials.

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:

\[ C*dV(t)/dt = -g_L*(V(t)-E_L) - \eta_1(t) - \eta_2(t) - \ldots - \eta_n(t) + I(t) \]

where each \( \eta_i \) is a spike-triggered current (stc), and the neuron model can have arbitrary number of them. Dynamic of each \( \eta_i \) is described by:

\[ \tau_\eta{_i}*d{\eta_i}/dt = -\eta_i \]

and in case of spike emission, its value increased by a constant (which can be positive or negative):

\[ \eta_i = \eta_i + q_{\eta_i} \text{ (in case of spike emission).} \]

Neuron produces spikes STOCHASTICALLY according to a point process with the firing intensity:

\[ \lambda(t) = \lambda_0 * \exp (V(t)-V_T(t)) / \Delta_V \]

where \( V_T(t) \) is a time-dependent firing threshold:

\[ V_T(t) = V_{T_star} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t) \]

where \( \gamma_i \) is a kernel of spike-frequency adaptation (sfa), and the neuron model can have arbitrary number of them. Dynamic of each \( \gamma_i \) is described by:

\[ \tau_{\gamma_i}*d\gamma_i/dt = -\gamma_i \]

and in case of spike emission, its value increased by a constant (which can be positive or negative):

\[ \gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).} \]

Note:

In the current implementation of the model (as described in [1] and [2]), the values of \( \eta_i \) and \( \gamma_i \) are affected immediately after spike emission. However, GIF toolbox (http://wiki.epfl.ch/giftoolbox) which fits the model using experimental data, requires a different set of \( \eta_i \) and \( \gamma_i\) . It applies the jump of \( \eta_i \) and \( \gamma_i \) after the refractory period. One can easily convert between \( q_\eta/\gamma \) of these two approaches: \( q{_\eta}_{giftoolbox} = q_{\eta_{NEST}} * (1 - \exp( -\tau_{ref} / \tau_\eta )) \) The same formula applies for \( q_{\gamma} \).

The shape of synaptic conductance is exponential.

Parameters:

The following parameters can be set in the status dictionary.

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 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	real	Stochastic intensity at firing threshold V_T i n 1/s.
V_T_star	mV	Base threshold

Synaptic parameters
E_ex	mV	Excitatory reversal potential
tau_syn_ex	ms	Decay time of excitatory synaptic conductance
E_in	mV	Inhibitory reversal potential
tau_syn_in	ms	Decay time of the inhibitory 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.

References:

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: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Author: March 2016, Setareh

SeeAlso: pp_psc_delta, gif_cond_exp_multisynapse, gif_psc_exp, gif_psc_exp_multisynapse

class hh_cond_beta_gap_traub : public Archiving_Node

#include <hh_cond_beta_gap_traub.h>

Name: hh_cond_beta_gap_traub - modified Hodgkin-Huxley neuron as featured in Brette et al (2007) review with added gap junction support and beta function synaptic conductance.

Description:

hh_cond_beta_gap_traub is an implementation of a modified Hodgkin-Huxley model that also supports gap junctions.

This model was specifically developed for a major review of simulators [1], based on a model of hippocampal pyramidal cells by Traub and Miles[2]. The key differences between the current model and the model in [2] are:

• This model is a point neuron, not a compartmental model.

• This model includes only I_Na and I_K, with simpler I_K dynamics than in [2], so it has only three instead of eight gating variables; in particular, all Ca dynamics have been removed.

• Incoming spikes induce an instantaneous conductance change followed by exponential decay instead of activation over time.

This model is primarily provided as reference implementation for hh_coba example of the Brette et al (2007) review. Default parameter values are chosen to match those used with NEST 1.9.10 when preparing data for [1]. Code for all simulators covered is available from ModelDB [3].

Note: In this model, a spike is emitted if

\[ V_m >= V_T + 30 mV and V_m has fallen during the current time step \]

To avoid that this leads to multiple spikes during the falling flank of a spike, it is essential to chose a sufficiently long refractory period. Traub and Miles used \( t_ref = 3 ms \) [2, p 118], while we used \( t_ref = 2 ms \) in [2].

Post-synaptic currents Incoming spike events induce a post-synaptic change of conductance modelled by a beta function as outlined in [4,5]. The beta function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_rise_xx \) where xx is ex or in.

Spike Detection Spike detection is done by a combined threshold-and-local-maximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.

Gap Junctions Gap Junctions are implemented by a gap current of the form \( g_ij( V_i - V_j) \).

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
V_T	mV	Voltage offset that controls dynamics. For default parameters, V_T = -63mV results in a threshold around -50mV
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
g_L	nS	Leak conductance
tau_rise_ex	ms	Excitatory synaptic beta function rise time
tau_decay_ex	ms	Excitatory synaptic beta function decay time
tau_rise_in	ms	Inhibitory synaptic beta function rise time
tau_decay_in	ms	Inhibitory synaptic beta function decay time
t_ref	ms	Duration of refractory period (see Note)
E_ex	mV	Excitatory synaptic reversal potential
E_in	mV	Inhibitory synaptic reversal potential
E_Na	mV	Sodium reversal potential
g_Na	nS	Sodium peak conductance
E_K	mV	Potassium reversal potential
g_K	nS	Potassium peak conductance
I_e	pA	External input current

References:

1

Brette R et al (2007). Simulation of networks of spiking neurons: A review of tools and strategies. Journal of Computational Neuroscience 23:349-98. DOI: https://doi.org/10.1007/s10827-007-0038-6

2

Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge UK.

3

http://modeldb.yale.edu/83319

4

Rotter S and Diesmann M (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biological Cybernetics 81:381 DOI: https://doi.org/10.1007/s004220050570

5

Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Author: Daniel Naoumenko (modified hh_cond_exp_traub by Schrader and hh_psc_alpha_gap by Jan Hahne, Moritz Helias and Susanne Kunkel)

SeeAlso: hh_psc_alpha_gap, hh_cond_exp_traub, gap_junction, iaf_cond_beta

class iaf_chxk_2008 : public Archiving_Node

#include <iaf_chxk_2008.h>

Name: iaf_chxk_2008 - Conductance based leaky integrate-and-fire neuron model used in Casti et al 2008.

Description:

iaf_chxk_2008 is an implementation of a spiking neuron using IAF dynamics with conductance-based synapses [1]. It is modeled after iaf_cond_alpha with the addition of after hyper-polarization current instead of a membrane potential reset. Incoming spike events induce a post-synaptic change of conductance modeled by an alpha function. The alpha function is normalized such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_{syn} \).

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
V_th	mV	Spike threshold
E_ex	mV	Excitatory reversal potential
E_in	mV	Inhibitory reversal potential
g_L	nS	Leak conductance
tau_ex	ms	Rise time of the excitatory synaptic alpha function
tau_in	ms	Rise time of the inhibitory synaptic alpha function
I_e	pA	Constant input current
tau_ahp	ms	Afterhyperpolarization (AHP) time constant
E_ahp	mV	AHP potential
g_ahp	nS	AHP conductance
ahp_bug	boolean	Defaults to false. If true, behaves like original model implementation

References:

1

Casti A, Hayot F, Xiao Y, Kaplan E (2008) A simple model of retina-LGN transmission. Journal of Computational Neuroscience 24:235-252. DOI: https://doi.org/10.1007/s10827-007-0053-7

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent

Author: Heiberg

SeeAlso: iaf_cond_alpha

class iaf_cond_alpha : public Archiving_Node

#include <iaf_cond_alpha.h>

Name: iaf_cond_alpha - Simple conductance based leaky integrate-and-fire neuron model.

Description:

iaf_cond_alpha is an implementation of a spiking neuron using IAF dynamics with conductance-based synapses. Incoming spike events induce a post-synaptic change of conductance modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \( t = tau_{syn} \).

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold
V_reset	mV	Reset potential of the membrane
E_ex	mV	Excitatory reversal potential
E_in	mV	Inhibitory reversal potential
g_L	nS	Leak conductance
tau_syn_ex	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in	ms	Rise time of the inhibitory synaptic alpha function
I_e	pA	Constant input current

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Remarks:

References:

Note

Per 2009-04-17, this class has been revised to our newest insights into class design. Please use THIS CLASS as a reference when designing your own models with nonlinear dynamics. One weakness of this class is that it distinguishes between inputs to the two synapses by the sign of the synaptic weight. It would be better to use receptor_types, cf iaf_cond_alpha_mc.

1

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

2

Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):11569-11573. DOI: https://doi.org/10.1073/pnas.88.24.11569

3

Kuhn A, Rotter S (2004) Neuronal integration of synaptic input in the fluctuation- driven regime. Journal of Neuroscience, 24(10):2345-2356 DOI: https://doi.org/10.1523/JNEUROSCI.3349-03.2004

Author: Schrader, Plesser

SeeAlso: iaf_cond_exp, iaf_cond_alpha_mc

class iaf_cond_alpha_mc : public Archiving_Node

#include <iaf_cond_alpha_mc.h>

Name: iaf_cond_alpha_mc - PROTOTYPE Multi-compartment conductance-based leaky integrate-and-fire neuron model.

Description:

THIS MODEL IS A PROTOTYPE FOR ILLUSTRATION PURPOSES. IT IS NOT YET FULLY TESTED. USE AT YOUR OWN PERIL!

iaf_cond_alpha_mc is an implementation of a multi-compartment spiking neuron using IAF dynamics with conductance-based synapses. It serves mainly to illustrate the implementation of multicompartment models in NEST.

The model has three compartments: soma, proximal and distal dendrite, labeled as s, p, and d, respectively. Compartments are connected through passive conductances as follows

\[\begin{split} C_{m.s} d/dt V_{m.s} = \ldots - g_{sp} ( V_{m.s} - V_{m.p} ) \\ C_{m.p} d/dt V_{m.p} = \ldots - g_{sp} ( V_{m.p} - V_{m.s} ) - g_{pd} ( V_{m.p} - V_{m.d} ) \\ C_{m.d} d/dt V_{m.d} = \ldots \qquad - g_{pd} ( V_{m.d} - V_{m.p} ) \end{split}\]

A spike is fired when the somatic membrane potential exceeds threshold, \( V_{m.s} >= V_{th} \). After a spike, somatic membrane potential is clamped to a reset potential, \( V_{m.s} == V_{reset} \), for the refractory period. Dendritic membrane potentials are not manipulated after a spike.

There is one excitatory and one inhibitory conductance-based synapse onto each compartment, with alpha-function time course. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at t = tau_syn. Each compartment can also receive current input from a current generator, and an external (rheobase) current can be set for each compartment.

Synapses, including those for injection external currents, are addressed through the receptor types given in the receptor_types entry of the state dictionary. Note that in contrast to the single-compartment iaf_cond_alpha model, all synaptic weights must be positive numbers!

Parameters:

The following parameters can be set in the status dictionary. Parameters for each compartment are collected in a sub-dictionary; these sub-dictionaries are called “soma”, “proximal”, and “distal”, respectively. In the list below, these parameters are marked with an asterisk.

V_m*	mV	Membrane potential
E_L*	mV	Leak reversal potential
C_m*	pF	Capacity of the membrane
E_ex*	mV	Excitatory reversal potential
E_in*	mV	Inhibitory reversal potential
g_L*	nS	Leak conductance
tau_syn_ex*	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in*	ms	Rise time of the inhibitory synaptic alpha function
I_e*	pA	Constant input current
g_sp	nS	Conductance connecting soma and proximal dendrite
g_pd	nS	Conductance connecting proximal and distal dendrite
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold in mV
V_reset	mV	Reset potential of the membrane

Example: See pynest/examples/mc_neuron.py.

Remarks:

This is a prototype for illustration which has undergone only limited testing. Details of the implementation and user-interface will likely change. USE AT YOUR OWN PERIL!

Sends: SpikeEvent

Note

All parameters that occur for both compartments and dendrite are stored as C arrays, with index 0 being soma.

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

2

Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):11569-11573. DOI: https://doi.org/10.1073/pnas.88.24.11569

Author: Plesser

SeeAlso: iaf_cond_alpha

class iaf_cond_beta : public Archiving_Node

#include <iaf_cond_beta.h>

Name: iaf_cond_beta - Simple conductance based leaky integrate-and-fire neuron model.

Description:

iaf_cond_beta is an implementation of a spiking neuron using IAF dynamics with conductance-based synapses. Incoming spike events induce a post-synaptic change of conductance modelled by an beta function. The beta function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at t = tau_rise_[ex|in].

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold
V_reset	mV	Reset potential of the membrane
E_ex	mV	Excitatory reversal potential
E_in	mV	Inhibitory reversal potential
g_L	nS	Leak conductance
tau_syn_ex	ms	Rise time of the excitatory synaptic alpha function
tau_decay_ex	ms	Rise time of the excitatory synaptic beta function
tau_syn_in	ms	Rise time of the inhibitory synaptic alpha function
tau_decay_in	ms	Rise time of the inhibitory synaptic beta function
I_e	pA	Constant input current

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

Remarks:

References:

Note

Per 2009-04-17, this class has been revised to our newest insights into class design. Please use THIS CLASS as a reference when designing your own models with nonlinear dynamics. One weakness of this class is that it distinguishes between inputs to the two synapses by the sign of the synaptic weight. It would be better to use receptor_types, cf iaf_cond_alpha_mc.

1

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

2

Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):11569-11573. DOI: https://doi.org/10.1073/pnas.88.24.11569

3

Kuhn A, Rotter S (2004) Neuronal integration of synaptic input in the fluctuation- driven regime. Journal of Neuroscience, 24(10):2345-2356 DOI: https://doi.org/10.1523/JNEUROSCI.3349-03.2004

4

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

5

Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.

Author: Daniel Naoumenko (modified iaf_cond_alpha by Schrader, Plesser)

SeeAlso: iaf_cond_exp, iaf_cond_alpha, iaf_cond_alpha_mc

class iaf_cond_exp : public Archiving_Node

#include <iaf_cond_exp.h>

Name: iaf_cond_exp - Simple conductance based leaky integrate-and-fire neuron model.

Description:

iaf_cond_exp is an implementation of a spiking neuron using IAF dynamics with conductance-based synapses. Incoming spike events induce a post-synaptic change of conductance modelled by an exponential function. The exponential function is normalised such that an event of weight 1.0 results in a peak conductance of 1 nS.

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold
V_reset	mV	Reset potential of the membrane
E_ex	mV	Excitatory reversal potential
E_in	mV	Inhibitory reversal potential
g_L	nS	Leak conductance
tau_syn_ex	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in	ms	Rise time of the inhibitory synaptic alpha function
I_e	pA	Constant input current

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

Author: Sven Schrader

SeeAlso: iaf_psc_delta, iaf_psc_exp, iaf_cond_exp

class iaf_cond_exp_sfa_rr : public Archiving_Node

#include <iaf_cond_exp_sfa_rr.h>

Name: iaf_cond_exp_sfa_rr - Simple conductance based leaky integrate-and-fire neuron model.

Description:

iaf_cond_exp_sfa_rr is an iaf_cond_exp_sfa_rr i.e. an implementation of a spiking neuron using IAF dynamics with conductance-based synapses, with additional spike-frequency adaptation and relative refractory mechanisms as described in Dayan+Abbott, 2001, page 166.

As for the iaf_cond_exp_sfa_rr, Incoming spike events induce a post-synaptic change of conductance modelled by an exponential function. The exponential function is normalised such that an event of weight 1.0 results in a peak current of 1 nS.

Outgoing spike events induce a change of the adaptation and relative refractory conductances by q_sfa and q_rr, respectively. Otherwise these conductances decay exponentially with time constants tau_sfa and tau_rr, respectively.

Parameters:

The following parameters can be set in the status dictionary.

V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold
V_reset	mV	Reset potential of the membrane
E_ex	mV	Excitatory reversal potential
E_in	mV	Inhibitory reversal potential
g_L	nS	Leak conductance
tau_syn_ex	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in	ms	Rise time of the inhibitory synaptic alpha function
q_sfa	nS	Outgoing spike activated quantal spike-frequency adaptation conductance increase in nS
q_rr	nS	Outgoing spike activated quantal relative refractory conductance increase in nS
tau_sfa	ms	Time constant of spike-frequency adaptation in ms
tau_rr	ms	Time constant of the relative refractory mechanism in ms
E_sfa	mV	Spike-frequency adaptation conductance reversal potential in mV
E_rr	mV	Relative refractory mechanism conductance reversal potential in mV
I_e	pA	Constant input current

Sends: SpikeEvent

Receives: SpikeEvent, CurrentEvent, DataLoggingRequest

References:

1

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

2

Dayan P, Abbott LF (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press. https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=

item_3006127

Author: Sven Schrader, Eilif Muller

SeeAlso: iaf_cond_exp_sfa_rr, aeif_cond_alpha, iaf_psc_delta, iaf_psc_exp, iaf_cond_alpha