terub_stn

terub_stn - Terman Rubin neuron model

Description

terub_stn is an implementation of a spiking neuron using the Terman Rubin model based on the Hodgkin-Huxley formalism.

1. Post-syaptic 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.

References

[1]

Terman, D. and Rubin, J.E. and Yew, A.C. and Wilson, C.J. Activity Patterns in a Model for the Subthalamopallidal Network of the Basal Ganglia. The Journal of Neuroscience, 22(7), 2963-2976 (2002)

[2]

Rubin, J.E. and Terman, D. High Frequency Stimulation of the Subthalamic Nucleus Eliminates Pathological Thalamic Rhythmicity in a Computational Model Journal of Computational Neuroscience, 16, 211-235 (2004)

Parameters

Name	Physical unit	Default value	Description
E_L	mV	-60mV	Resting membrane potential
g_L	nS	2.25nS	Leak conductance
C_m	pF	1pF	Capacity of the membrane
E_Na	mV	55mV	Sodium reversal potential
g_Na	nS	37.5nS	Sodium peak conductance
E_K	mV	-80mV	Potassium reversal potential
g_K	nS	45nS	Potassium peak conductance
E_Ca	mV	140mV	Calcium reversal potential
g_Ca	nS	0.5nS	Calcium peak conductance
g_T	nS	0.5nS	T-type Calcium channel peak conductance
g_ahp	nS	9nS	Afterpolarization current peak conductance
tau_syn_exc	ms	1ms	Rise time of the excitatory synaptic alpha function
tau_syn_inh	ms	0.08ms	Rise time of the inhibitory synaptic alpha function
E_gs	mV	-85mV	Reversal potential for inhibitory input (from GPe)
refr_T	ms	2ms	Duration of refractory period
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 for threshold check
refr_t	ms	0ms	Refractory period timer
is_refractory	boolean	false
gate_h	real	0.0	gating variable h
gate_n	real	0.0	gating variable n
gate_r	real	0.0	gating variable r
Ca_con	real	0.0	calcium concentration

Equations

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

\[\frac{ dgate_{h} } { dt }= \phi_{h} \cdot (\frac{ (h_{\infty} - gate_{h}) } { \tau_{h} })\]

\[\frac{ dgate_{n} } { dt }= \phi_{n} \cdot (\frac{ (n_{\infty} - gate_{n}) } { \tau_{n} })\]

\[\frac{ dgate_{r} } { dt }= \phi_{r} \cdot (\frac{ (r_{\infty} - gate_{r}) } { \tau_{r} })\]

\[\frac{ dCa_{con} } { dt }= \epsilon \cdot (\frac{ (-I_{Ca} - I_{T}) } { \mathrm{pA} } - k_{Ca} \cdot Ca_{con})\]

Source code

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

Characterisation