Neuron models with conductancebased synapses¶

class
aeif_cond_alpha
: public Archiving_Node  #include <aeif_cond_alpha.h>
Name: aeif_cond_alpha  Conductance based exponential integrateandfire 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 alphafunctions.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive step size to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C_m \frac{dV}{dt} = g_L(VE_L)+g_L\Delta_T\exp\left(\frac{VV_{th}}{\Delta_T}\right)  g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w \frac{dw}{dt} = a(VE_L)  w \]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
Spikeadaptation 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
Spiketriggered 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: MarcOliver 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 IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642 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 integrateandfire 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 conductancebased adaptive exponential integrateandfire 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:
\[ C dV/dt = g_L(VE_L) + g_L*\Delta_T*\exp((VV_T)/\Delta_T) + I_{syn_{tot}}(V, t) w + I_e \]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 spikeadaptation 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
Spikeadaptation 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
Spiketriggered 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 integrateandfire 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 alphafunctions.
This implementation uses a 5th order RungeKutta 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:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and\[ \tau_w * dw/dt= a(VE_L) w \]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
Spikeadaptation 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
Spiketriggered 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 1e10 mV.
Authors: Stefan Bucher, MarcOliver Gewaltig.
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
 1
Brette R and Gerstner W (2005). Adaptive Exponential IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. 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 integrateandfire 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 conductancebased adaptive exponential integrateandfire 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:
\[ C dV/dt = g_L(VE_L) + g_L*\Delta_T*\exp((VV_T)/\Delta_T) + I_{syn_{tot}}(V, t)  w + I_e \]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 spikeadaptation 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
Spikeadaptation 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
Spiketriggered 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 integrateandfire 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 postsynaptic conductances in the form of truncated exponentials.
This implementation uses the embedded 4th order RungeKuttaFehlberg solver with adaptive stepsize to integrate the differential equation.
The membrane potential is given by the following differential equation:
\[\begin{split} C dV/dt= g_L(VE_L)+g_L*\Delta_T*\exp((VV_T)/\Delta_T)g_e(t)(VE_e) \\ g_i(t)(VE_i)w +I_e \end{split}\]and
\[ \tau_w * dw/dt= a(VE_L) W \]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
Spikeadaptation 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
Spiketriggered 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 IntegrateandFire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:36373642. 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  Conductancebased generalized integrateandfire neuron model according to Mensi et al. (2012) and Pozzorini et al. (2015).
Description:
gif_psc_exp is the generalized integrateandfire neuron according to Mensi et al. (2012) and Pozzorini et al. (2015), with postsynaptic conductances in the form of truncated exponentials.
This model features both an adaptation current and a dynamic threshold for spikefrequency 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 spiketriggered 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 timedependent 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 spikefrequency 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 spiketriggered currents (stc) after each spike emission
tau_stc
list of ms
Time constants of stc variables
q_sfa
list of mV
Values added to spikefrequency 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):17561775. DOI: https://doi.org/10.1152/jn.00408.2011
 2
Pozzorini C, Mensi S, Hagens O, Naud R, Koch C, Gerstner W (2015). Automated highthroughput 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 HodgkinHuxley 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 HodgkinHuxley 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].
Postsynaptic currents Incoming spike events induce a postsynaptic 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 thresholdandlocalmaximum 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 23:34998. DOI: https://doi.org/10.1007/s1082700700386
 2
Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge UK.
 3
 4
Rotter S and Diesmann M (1999). Exact digital simulation of timeinvariant 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.
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 integrateandfire neuron model used in Casti et al 2008.
Description:
iaf_chxk_2008 is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses [1]. It is modeled after iaf_cond_alpha with the addition of after hyperpolarization current instead of a membrane potential reset. Incoming spike events induce a postsynaptic 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 retinaLGN transmission. Journal of Computational Neuroscience 24:235252. DOI: https://doi.org/10.1007/s1082700700537
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 integrateandfire neuron model.
Description:
iaf_cond_alpha is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic 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 20090417, 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, 16:159175. 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):1156911573. 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):23452356 DOI: https://doi.org/10.1523/JNEUROSCI.334903.2004
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 Multicompartment conductancebased leaky integrateandfire 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 multicompartment spiking neuron using IAF dynamics with conductancebased 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 conductancebased synapse onto each compartment, with alphafunction 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 singlecompartment 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 subdictionary; these subdictionaries 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 userinterface 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, 16:159175. 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):1156911573. 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 integrateandfire neuron model.
Description:
iaf_cond_beta is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic 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_[exin].
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 20090417, 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, 16:159175. 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):1156911573. 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):23452356 DOI: https://doi.org/10.1523/JNEUROSCI.334903.2004
 4
Rotter S, Diesmann M (1999). Exact simulation of timeinvariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381402. 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 integrateandfire neuron model.
Description:
iaf_cond_exp is an implementation of a spiking neuron using IAF dynamics with conductancebased synapses. Incoming spike events induce a postsynaptic 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, 16:159175. 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 integrateandfire 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 conductancebased synapses, with additional spikefrequency 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 postsynaptic 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 spikefrequency adaptation conductance increase in nS
q_rr
nS
Outgoing spike activated quantal relative refractory conductance increase in nS
tau_sfa
ms
Time constant of spikefrequency adaptation in ms
tau_rr
ms
Time constant of the relative refractory mechanism in ms
E_sfa
mV
Spikefrequency 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, 16:159175. 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