hill_tononi

hill_tononi - Neuron model after Hill & Tononi (2005)

Description

This model neuron implements a slightly modified version of the neuron model described in [1]. The most important properties are:

• Integrate-and-fire with threshold adaptive threshold.

• Repolarizing potassium current instead of hard reset.

• AMPA, NMDA, GABA_A, and GABA_B conductance-based synapses with beta-function (difference of exponentials) time course.

• Voltage-dependent NMDA with instantaneous or two-stage unblocking [1], [2].

• Intrinsic currents I_h, I_T, I_Na(p), and I_KNa.

• Synaptic “minis” are not implemented.

Documentation and examples can be found on the NEST Simulator repository (https://github.com/nest/nest-simulator/) at the following paths: - docs/model_details/HillTononiModels.ipynb - pynest/examples/intrinsic_currents_spiking.py - pynest/examples/intrinsic_currents_subthreshold.py

References

[1] (1,2)

Hill S, Tononi G (2005). Modeling sleep and wakefulness in the thalamocortical system. Journal of Neurophysiology. 93:1671-1698. DOI: https://doi.org/10.1152/jn.00915.2004

[2]

Vargas-Caballero M, Robinson HPC (2003). A slow fraction of Mg2+ unblock of NMDA receptors limits their contribution to spike generation in cortical pyramidal neurons. Journal of Neurophysiology 89:2778-2783. DOI: https://doi.org/10.1152/jn.01038.2002

Parameters

Name	Physical unit	Default value	Description
E_Na	mV	30.0mV
E_K	mV	-90.0mV
g_NaL	nS	0.2nS
g_KL	nS	1.0nS	1.0 - 1.85
Tau_m	ms	16.0ms	membrane time constant applying to all currents but repolarizing K-current (see [1, p 1677])
Theta_eq	mV	-51.0mV	equilibrium value
Tau_theta	ms	2.0ms	time constant
Tau_spike	ms	1.75ms	membrane time constant applying to repolarizing K-current
t_spike	ms	2.0ms	duration of re-polarizing potassium current
AMPA_g_peak	nS	0.1nS	Parameters for synapse of type AMPA, GABA_A, GABA_B and NMDApeak conductance
AMPA_E_rev	mV	0.0mV	reversal potential
AMPA_Tau_1	ms	0.5ms	rise time
AMPA_Tau_2	ms	2.4ms	decay time, Tau_1 < Tau_2
NMDA_g_peak	nS	0.075nS	peak conductance
NMDA_Tau_1	ms	4.0ms	rise time
NMDA_Tau_2	ms	40.0ms	decay time, Tau_1 < Tau_2
NMDA_E_rev	mV	0.0mV	reversal potential
NMDA_Vact	mV	-58.0mV	inactive for V << Vact, inflection of sigmoid
NMDA_Sact	mV	2.5mV	scale of inactivation
GABA_A_g_peak	nS	0.33nS	peak conductance
GABA_A_Tau_1	ms	1.0ms	rise time
GABA_A_Tau_2	ms	7.0ms	decay time, Tau_1 < Tau_2
GABA_A_E_rev	mV	-70.0mV	reversal potential
GABA_B_g_peak	nS	0.0132nS	peak conductance
GABA_B_Tau_1	ms	60.0ms	rise time
GABA_B_Tau_2	ms	200.0ms	decay time, Tau_1 < Tau_2
GABA_B_E_rev	mV	-90.0mV	reversal potential for intrinsic current
NaP_g_peak	nS	1.0nS	parameters for intrinsic currentspeak conductance for intrinsic current
NaP_E_rev	mV	30.0mV	reversal potential for intrinsic current
KNa_g_peak	nS	1.0nS	peak conductance for intrinsic current
KNa_E_rev	mV	-90.0mV	reversal potential for intrinsic current
T_g_peak	nS	1.0nS	peak conductance for intrinsic current
T_E_rev	mV	0.0mV	reversal potential for intrinsic current
h_g_peak	nS	1.0nS	peak conductance for intrinsic current
h_E_rev	mV	-40.0mV	reversal potential for intrinsic current
KNa_D_EQ	pA	0.001pA
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
potassium_refr_t	ms	0ms
is_refractory	boolean	false
g_spike	boolean	false
V_m	mV	(g_NaL * E_Na + g_KL * E_K) / (g_NaL + g_KL)	membrane potential
Theta	mV	Theta_eq	Threshold
IKNa_D	nS	0.0nS
IT_m	nS	0.0nS
IT_h	nS	0.0nS
Ih_m	nS	0.0nS
g_AMPA	real	0
g_NMDA	real	0
g_GABAA	real	0
g_GABAB	real	0
g_AMPA$	real	AMPAInitialValue
g_NMDA$	real	NMDAInitialValue
g_GABAA$	real	GABA_AInitialValue
g_GABAB$	real	GABA_BInitialValue

Equations

\[\frac{ dV_{m} } { dt }= \frac 1 { \mathrm{nF} } \left( { (\frac 1 { \Tau_{m} } \left( { (I_{Na} + I_{K} + I_{syn} + I_{NaP} + I_{KNa} + I_{T} + I_{h} + I_{e} + I_{stim}) } \right) + \frac{ I_{spike} \cdot \mathrm{pA} } { (\mathrm{ms} \cdot \mathrm{mV}) }) \cdot \mathrm{s} } \right)\]

\[\frac{ d\Theta } { dt }= \frac{ -(\Theta - \Theta_{eq}) } { \Tau_{\theta} }\]

\[\frac{ dIKNa_{D} } { dt }= \frac 1 { \mathrm{ms} } \left( { (D_{influx,peak} \cdot D_{influx} \cdot \mathrm{nS} - \frac 1 { \tau_{D} } \left( { (IKNa_{D} - \frac{ KNa_{D,EQ} } { \mathrm{mV} }) } \right) ) } \right)\]

\[\frac{ dIT_{m} } { dt }= \frac 1 { \mathrm{ms} } \left( { \frac 1 { \tau_{m,T} } \left( { (m_{\infty,T} \cdot \mathrm{nS} - IT_{m}) } \right) } \right)\]

\[\frac{ dIT_{h} } { dt }= \frac 1 { \mathrm{ms} } \left( { \frac 1 { \tau_{h,T} } \left( { (h_{\infty,T} \cdot \mathrm{nS} - IT_{h}) } \right) } \right)\]

\[\frac{ dIh_{m} } { dt }= \frac 1 { \mathrm{ms} } \left( { \frac 1 { \tau_{m,h} } \left( { (m_{\infty,h} \cdot \mathrm{nS} - Ih_{m}) } \right) } \right)\]

Source code

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

Characterisation