hh_cond_exp_traub_neuron

hh_cond_exp_traub - Hodgkin-Huxley model for Brette et al (2007) review

Description

hh_cond_exp_traub is an implementation of a modified Hodgkin-Huxley model.

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 choose 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].

References

[1] (1,2)

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] (1,2,3,4)

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

[3]

http://modeldb.yale.edu/83319

See also

hh_psc_alpha

Copyright statement

This file is part of NEST.

Copyright (C) 2004 The NEST Initiative

NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with NEST. If not, see <http://www.gnu.org/licenses/>.

Parameters

Name	Physical unit	Default value	Description
g_Na	nS	20000nS	Na conductance
g_K	nS	6000nS	K conductance
g_L	nS	10nS	Leak conductance
C_m	pF	200pF	Membrane capacitance
E_Na	mV	50mV	Sodium reversal potential
E_K	mV	-90mV	Potassium reversal potential
E_L	mV	-60mV	Leak reversal potential (a.k.a. resting potential)
V_T	mV	-63mV	Voltage offset that controls dynamics. For default
tau_syn_exc	ms	5ms	parameters, V_T = -63 mV results in a threshold around -50 mV.Synaptic time constant of excitatory synapse
tau_syn_inh	ms	10ms	Synaptic time constant of inhibitory synapse
refr_T	ms	2ms	Duration of refractory period
E_exc	mV	0mV	Excitatory synaptic reversal potential
E_inh	mV	-80mV	Inhibitory synaptic reversal potential
alpha_n_init	1 / ms	0.032 / (ms * mV) * (15mV - E_L) / (exp((15mV - E_L) / 5mV) - 1)
beta_n_init	1 / ms	0.5 / ms * exp((10mV - E_L) / 40mV)
alpha_m_init	1 / ms	0.32 / (ms * mV) * (13mV - E_L) / (exp((13mV - E_L) / 4mV) - 1)
beta_m_init	1 / ms	0.28 / (ms * mV) * (E_L - 40mV) / (exp((E_L - 40mV) / 5mV) - 1)
alpha_h_init	1 / ms	0.128 / ms * exp((17mV - E_L) / 18mV)
beta_h_init	1 / ms	(4 / (1 + exp((40mV - E_L) / 5mV))) / ms
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	E_L	Membrane potential
V_m_old	mV	E_L	Membrane potential at previous timestep
refr_t	ms	0ms	Refractory period timer
Act_m	real	alpha_m_init / (alpha_m_init + beta_m_init)
Act_h	real	alpha_h_init / (alpha_h_init + beta_h_init)
Inact_n	real	alpha_n_init / (alpha_n_init + beta_n_init)

Equations

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-I_{Na} - I_{K} - I_{L} - I_{syn,exc} - I_{syn,inh} + I_{e} + I_{stim}) } \right)\]

\[\frac{ drefr_{t} } { dt }= \frac{ -1000.0 \cdot \mathrm{ms} } { \mathrm{s} }\]

\[\frac{ dAct_{m} } { dt }= (\alpha_{m} - (\alpha_{m} + \beta_{m}) \cdot Act_{m})\]

\[\frac{ dAct_{h} } { dt }= (\alpha_{h} - (\alpha_{h} + \beta_{h}) \cdot Act_{h})\]

\[\frac{ dInact_{n} } { dt }= (\alpha_{n} - (\alpha_{n} + \beta_{n}) \cdot Inact_{n})\]

Source code

The model source code can be found in the NESTML models repository here: hh_cond_exp_traub_neuron.

Synaptic response

Response to pulse current injection

f-I curve