wb_cond_exp

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

See Also

hh_cond_exp_traub, wb_cond_multisyn

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 (aka 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

is_refractory

boolean

false

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

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-(I_{Na} + I_{K} + I_{L}) + I_{e} + I_{stim} + I_{syn,exc} - I_{syn,inh}) } \right)\]
\[\frac{ dAct_{n} } { dt }= (\text{alpha_n}(V_{m}) \cdot (1 - Act_{n}) - \text{beta_n}(V_{m}) \cdot Act_{n})\]
\[\frac{ dInact_{h} } { dt }= (\text{alpha_h}(V_{m}) \cdot (1 - Inact_{h}) - \text{beta_h}(V_{m}) \cdot Inact_{h})\]

Source code

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

Characterisation