traub_psc_alpha_neuron

traub_psc_alpha - Traub model according to Borgers 2017

Reduced Traub-Miles Model of a Pyramidal Neuron in Rat Hippocampus [1]. Parameters obtained from reference [2].

Incoming spike events induce a post-synaptic change of current, modelled by an alpha function.

References

[1]

18. 4. Traub and R. Miles, Neuronal Networks of the Hippocampus,Cam- bridge University Press, Cambridge, UK, 1991.

[2]

Borgers, C., 2017. An introduction to modeling neuronal dynamics (Vol. 66). Cham: Springer.

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
V_m_init	mV	-70mV	Initial membrane potential
C_m	pF	100pF	Membrane capacitance
g_Na	nS	10000nS	Sodium peak conductance
g_K	nS	8000nS	Potassium peak conductance
g_L	nS	10nS	Leak conductance
E_Na	mV	50mV	Sodium reversal potential
E_K	mV	-100mV	Potassium reversal potential
E_L	mV	-67mV	Leak reversal potential (a.k.a. resting potential)
V_Tr	mV	-20mV	Spike threshold
refr_T	ms	2ms	Duration of refractory period
tau_syn_exc	ms	0.2ms	Rise time of the excitatory synaptic alpha function
tau_syn_inh	ms	2ms	Rise time of the inhibitory synaptic alpha function
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	V_m_init	Membrane potential
V_m_old	mV	V_m_init	Membrane potential at previous timestep for threshold check
refr_t	ms	0ms	Refractory period timer
Act_m	real	alpha_m_init / (alpha_m_init + beta_m_init)	Activation variable m for Na
Inact_h	real	alpha_h_init / (alpha_h_init + beta_h_init)	Inactivation variable h for Na
Act_n	real	alpha_n_init / (alpha_n_init + beta_n_init)	Activation variable n for K

Equations

\[\frac{ dAct_{n} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{n} \cdot (1 - Act_{n}) - \beta_{n} \cdot Act_{n}) } \right)\]

\[\frac{ dAct_{m} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{m} \cdot (1 - Act_{m}) - \beta_{m} \cdot Act_{m}) } \right)\]

\[\frac{ dInact_{h} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{h} \cdot (1 - Inact_{h}) - \beta_{h} \cdot Inact_{h}) } \right)\]

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

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

Source code

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