Hodgkin Huxley (HH) neuron models¶

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
hh_psc_alpha
: public Archiving_Node  #include <hh_psc_alpha.h>
Name: hh_psc_alpha  HodgkinHuxley neuron model.
Description:
hh_psc_alpha is an implementation of a spiking neuron using the HodgkinHuxley formalism.
Postsynaptic currents Incoming spike events induce a postsynaptic change of current 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 pA.
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.
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
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
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_K
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
Problems/Todo:
better spike detection initial wavelet/spike at simulation onset
References:
 1
Gerstner W, Kistler W (2002). Spiking neuron models: Single neurons, populations, plasticity. New York: Cambridge University Press
 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>
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Authors: Schrader
SeeAlso: hh_cond_exp_traub

class
hh_psc_alpha_clopath
: public Clopath_Archiving_Node  #include <hh_psc_alpha_clopath.h>
Name: hh_psc_alpha_clopath  HodgkinHuxley neuron model with support for the Clopath synapse.
Description:
hh_psc_alpha_clopath is an implementation of a spiking neuron using the HodgkinHuxley formalism and that is capable of connecting to a Clopath synapse.
(1) Postsynaptic currents Incoming spike events induce a postsynaptic change of current 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 pA.
(2) 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.
Parameters:
The following parameters can be set in the status dictionary.
Dynamic state variables
V_m
mV
Membrane potential
u_bar_plus
mV
Lowpass filtered Membrane potential
u_bar_minus
mV
Lowpass filtered Membrane potential
u_bar_bar
mV
Lowpass filtered u_bar_minus
Membrane Parameters
E_L
mV
Leak reversal potential
C_m
pF
Capacity of the membrane
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
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_K
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
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.
Problems/Todo:
better spike detection initial wavelet/spike at simulation onset
References:
 1
Gerstner W and Kistler WM (2002). Spiking neuron models: Single neurons, populations, plasticity. New York: Cambridge university press.
 2
Dayan P and Abbott L (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
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
 4
Clopath et al. (2010). Connectivity reflects coding: a model of voltagebased STDP with homeostasis. Nature Neuroscience 13(3):344352. DOI: https://doi.org/10.1038/nn.2479
 5
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
 6
Voltagebased STDP synapse (Clopath et al. 2010) connected to a HodgkinHuxley neuron on ModelDB: https://senselab.med.yale.edu/ModelDB/showmodel.cshtml?model=144566&file =%2fmodeldb_package%2fstdp_cc.mod
Sends: SpikeEvent
Receives: SpikeEvent, CurrentEvent, DataLoggingRequest
Author: Jonas Stapmanns, David Dahmen, Jan Hahne (adapted from hh_psc_alpha by Schrader)
SeeAlso: hh_psc_alpha, clopath_synapse, aeif_psc_delta_clopath

class
hh_psc_alpha_gap
: public Archiving_Node  #include <hh_psc_alpha_gap.h>
Name: hh_psc_alpha_gap  HodgkinHuxley neuron model with gapjunction support.
Description:
hh_psc_alpha_gap is an implementation of a spiking neuron using the HodgkinHuxley formalism. In contrast to hh_psc_alpha the implementation additionally supports gap junctions.
Postsynaptic currents Incoming spike events induce a postsynaptic change of current 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 pA.
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.
tau_ex
ms
Rise time of the excitatory synaptic alpha function
tau_in
ms
Rise time of the inhibitory synaptic alpha function
g_K
nS
Potassium peak conductance
V_m
mV
Membrane potential
E_L
mV
Leak reversal potential
g_L
nS
Leak conductance
C_m
pF
Capacity of the membrane
tau_syn_ex
ms
Rise time of the excitatory synaptic alpha function
tau_syn_in
ms
Rise time of the inhibitory synaptic alpha function
E_Na
mV
Sodium reversal potential
g_Na
nS
Sodium peak conductance
E_K
mV
Potassium reversal potential
g_Kv1
nS
Potassium peak conductance
g_Kv3
nS
Potassium peak conductance
Act_m
real
Activation variable m
Act_h
real
Activation variable h
Inact_n
real
Inactivation variable n
I_e
pA
External input current
References:
 1
Gerstner W, Kistler W. Spiking neuron models: Single neurons, populations, plasticity. Cambridge University Press
 2
Mancilla JG, Lewis TG, Pinto DJ, Rinzel J, Connors BW (2007). Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex, Journal of Neurosciece, 27:20582073 DOI: https://doi.org/10.1523/JNEUROSCI.271506.2007 (parameters taken from here)
 3
Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764
 4
Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gapjunction interactions in distributed neuronal netowrk simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022
Sends: SpikeEvent, GapJunctionEvent
Receives: SpikeEvent, GapJunctionEvent, CurrentEvent, DataLoggingRequest
Author: Jan Hahne, Moritz Helias, Susanne Kunkel
SeeAlso: hh_psc_alpha, hh_cond_exp_traub, gap_junction