wb_cond_multisyn

wb_cond_multisyn - Wang-Buzsaki model with multiple synapses

Description

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

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.

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

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

wb_cond_multisyn

Parameters

Name	Physical unit	Default value	Description
g_Na	nS	3500.0nS	Sodium peak conductance
g_K	nS	900.0nS	Potassium peak conductance
g_L	nS	10nS	Leak conductance
C_m	pF	100.0pF	Membrane Capacitance
E_Na	mV	55.0mV	Sodium reversal potential
E_K	mV	-90.0mV	Potassium reversal potentia
E_L	mV	-65.0mV	Leak reversal Potential (aka resting potential)
V_Tr	mV	-55.0mV	Spike Threshold
refr_T	ms	2ms	Duration of refractory period
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
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	-65.0mV	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
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
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

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

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

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

Source code

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

Characterisation