hh_cond_exp_destexhe_neuron

hh_cond_exp_destexhe - Hodgin Huxley based model, Traub, Destexhe and Mainen modified

Description

hh_cond_exp_destexhe is an implementation of a modified Hodkin-Huxley model, which is based on the hh_cond_exp_traub model.

Differences to hh_cond_exp_traub:

1. Additional background noise: A background current whose conductances were modeled as an Ornstein-Uhlenbeck process is injected into the neuron.

2. Additional non-inactivating K+ current: A non-inactivating K+ current was included, which is responsible for spike frequency adaptation.

References

[1]

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

[2]

Destexhe, A. and Pare, D. (1999) Impact of Network Activity on the Integrative Properties of Neocortical Pyramidal Neurons In Vivo. Journal of Neurophysiology

[3]

1. Destexhe, M. Rudolph, J.-M. Fellous and T. J. Sejnowski (2001) Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience

[4]

26. Mainen, J. Joerges, J. R. Huguenard and T. J. Sejnowski (1995) A Model of Spike Initiation in Neocortical Pyramidal Neurons. Neuron

See also

hh_cond_exp_traub

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	17318.0nS	Na Conductance
g_K	nS	3463.6nS	K Conductance
g_L	nS	15.5862nS	Leak Conductance
C_m	pF	346.36pF	Membrane capacitance
E_Na	mV	60mV	Reversal potential
E_K	mV	-90mV	Potassium reversal potential
E_L	mV	-80mV	Leak reversal potential (a.k.a. resting potential)
V_T	mV	-58mV	Voltage offset that controls dynamics. For default
tau_syn_exc	ms	2.7ms	parameters, V_T = -63mV results in a threshold around -50mV.Synaptic time constant for excitatory synapse
tau_syn_inh	ms	10.5ms	Synaptic time constant for inhibitory synapse
E_exc	mV	0mV	Excitatory synaptic reversal potential
E_inh	mV	-75mV	Inhibitory synaptic reversal potential
g_M	nS	173.18nS	Conductance of non-inactivating K+ channel
g_noise_exc0	uS	0.012uS	Conductance OU noiseMean of the excitatory noise conductance
g_noise_inh0	uS	0.057uS	Mean of the inhibitory noise conductance
sigma_noise_exc	uS	0.003uS	Standard deviation of the excitatory noise conductance
sigma_noise_inh	uS	0.0066uS	Standard deviation of the inhibitory noise conductance
alpha_n_init	1 / ms	0.032 / (ms * mV) * (15mV - V_m) / (exp((15mV - V_m) / 5mV) - 1)
beta_n_init	1 / ms	0.5 / ms * exp((10mV - V_m) / 40mV)
alpha_m_init	1 / ms	0.32 / (ms * mV) * (13mV - V_m) / (exp((13mV - V_m) / 4mV) - 1)
beta_m_init	1 / ms	0.28 / (ms * mV) * (V_m - 40mV) / (exp((V_m - 40mV) / 5mV) - 1)
alpha_h_init	1 / ms	0.128 / ms * exp((17mV - V_m) / 18mV)
beta_h_init	1 / ms	(4 / (1 + exp((40mV - V_m) / 5mV))) / ms
alpha_p_init	1 / ms	0.0001 / (ms * mV) * (V_m + 30mV) / (1 - exp(-(V_m + 30mV) / 9mV))
beta_p_init	1 / ms	-0.0001 / (ms * mV) * (V_m + 30mV) / (1 - exp((V_m + 30mV) / 9mV))
refr_T	ms	2ms	Duration of refractory period
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
g_noise_exc	uS	g_noise_exc0
g_noise_inh	uS	g_noise_inh0
V_m	mV	E_L	Membrane potential
V_m_old	mV	E_L	Membrane potential at the 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)
Noninact_p	real	alpha_p_init / (alpha_p_init + beta_p_init)

Equations

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

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

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

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

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

\[\frac{ dNoninact_{p} } { dt }= (\alpha_{p} - (\alpha_{p} + \beta_{p}) \cdot Noninact_{p})\]

Source code

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