wb_cond_exp_neuron

wb_cond_exp - Wang-Buzsaki model

Description

wb_cond_exp is an implementation of a modified Hodkin-Huxley model.

(1) Post-synaptic currents: Incoming spike events induce a post-synaptic change of conductance modeled by an exponential function.

(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]

Wang, X.J. and Buzsaki, G., (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. Journal of neuroscience, 16(20), pp.6402-6413.

See Also

hh_cond_exp_traub, wb_cond_multisyn

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
C_m	pF	100pF	Membrane capacitance
g_Na	nS	3500nS	Sodium peak conductance
g_K	nS	900nS	Potassium peak conductance
g_L	nS	10nS	Leak conductance
E_Na	mV	55mV	Sodium reversal potential
E_K	mV	-90mV	Potassium reversal potential
E_L	mV	-65mV	Leak reversal potential (a.k.a. resting potential)
V_Tr	mV	-55mV	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	10ms	Rise time of the inhibitory synaptic alpha function
E_exc	mV	0mV	Excitatory synaptic reversal potential
E_inh	mV	-75mV	Inhibitory synaptic reversal potential
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
Inact_h	real	alpha_h_init / (alpha_h_init + beta_h_init)
Act_n	real	alpha_n_init / (alpha_n_init + beta_n_init)

Equations

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

\[\frac{ dAct_{n} } { dt }= (\text{alpha_n}(V_{m}) \cdot (1 - Act_{n}) - \text{beta_n}(V_{m}) \cdot Act_{n})\]

\[\frac{ dInact_{h} } { dt }= (\text{alpha_h}(V_{m}) \cdot (1 - Inact_{h}) - \text{beta_h}(V_{m}) \cdot Inact_{h})\]

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

Source code

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