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 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 hh_psc_alpha : public Archiving_Node
#include <hh_psc_alpha.h>

Name: hh_psc_alpha - Hodgkin-Huxley neuron model.

Description:

hh_psc_alpha is an implementation of a spiking neuron using the Hodgkin-Huxley formalism.

  1. Post-synaptic currents Incoming spike events induce a post-synaptic 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 threshold-and-local-maximum 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

Inact_h

real

Inactivation variable h

Act_n

real

Activation 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 - Hodgkin-Huxley neuron model with support for the Clopath synapse.

Description:

hh_psc_alpha_clopath is an implementation of a spiking neuron using the Hodgkin-Huxley formalism and that is capable of connecting to a Clopath synapse.

(1) Post-synaptic currents Incoming spike events induce a post-synaptic 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 threshold-and-local-maximum 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

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

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

Inact_h

real

Inactivation variable h

Act_n

real

Activation 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 voltage-based STDP with homeostasis. Nature Neuroscience 13(3):344-352. 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

Voltage-based STDP synapse (Clopath et al. 2010) connected to a Hodgkin-Huxley 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 - Hodgkin-Huxley neuron model with gap-junction support.

Description:

hh_psc_alpha_gap is an implementation of a spiking neuron using the Hodgkin-Huxley formalism. In contrast to hh_psc_alpha the implementation additionally supports gap junctions.

  1. Post-synaptic currents Incoming spike events induce a post-synaptic 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 threshold-and-local-maximum search: if there is a local maximum above a certain threshold of the membrane potential, it is considered a spike.

  3. 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

Inact_h

real

Inactivation variable h

Act_n

real

Activation 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, 27:2058-2073 DOI: https://doi.org/10.1523/JNEUROSCI.2715-06.2007 (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 gap-junction 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