hh_cond_exp_destexhe

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

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 potentials
E_K	mV	-90.0mV	Potassium reversal potential
E_L	mV	-80.0mV	Leak reversal Potential (aka resting potential)
V_T	mV	-58.0mV	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 Excitatory Synapse
tau_syn_inh	ms	10.5ms	Synaptic Time Constant for Inhibitory Synapse
E_exc	mV	0.0mV	Excitatory synaptic reversal potential
E_inh	mV	-75.0mV	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) * (15.0mV - V_m) / (exp((15.0mV - V_m) / 5.0mV) - 1.0)
beta_n_init	1 / ms	0.5 / ms * exp((10.0mV - V_m) / 40.0mV)
alpha_m_init	1 / ms	0.32 / (ms * mV) * (13.0mV - V_m) / (exp((13.0mV - V_m) / 4.0mV) - 1.0)
beta_m_init	1 / ms	0.28 / (ms * mV) * (V_m - 40.0mV) / (exp((V_m - 40.0mV) / 5.0mV) - 1.0)
alpha_h_init	1 / ms	0.128 / ms * exp((17.0mV - V_m) / 18.0mV)
beta_h_init	1 / ms	(4.0 / (1.0 + exp((40.0mV - V_m) / 5.0mV))) / ms
alpha_p_init	1 / ms	0.0001 / (ms * mV) * (V_m + 30.0mV) / (1.0 - exp(-(V_m + 30.0mV) / 9.0mV))
beta_p_init	1 / ms	-0.0001 / (ms * mV) * (V_m + 30.0mV) / (1.0 - exp((V_m + 30.0mV) / 9.0mV))
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
is_refractory	boolean	false
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

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

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

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

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

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

Source code

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

Characterisation