terub_gpe

terub_gpe - Terman Rubin neuron model

Description

terub_gpe is an implementation of a spiking neuron using the Terman Rubin model based on the Hodgkin-Huxley formalism.

  1. Post-syaptic currents: Incoming spike events induce a post-synaptic change of current modelled by an alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 pA.

  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

Parameters

Name

Physical unit

Default value

Description

E_L

mV

-55mV

Resting membrane potential

g_L

nS

0.1nS

Leak conductance

C_m

pF

1pF

Capacitance of the membrane

E_Na

mV

55mV

Sodium reversal potential

g_Na

nS

120nS

Sodium peak conductance

E_K

mV

-80.0mV

Potassium reversal potential

g_K

nS

30.0nS

Potassium peak conductance

E_Ca

mV

120mV

Calcium reversal potential

g_Ca

nS

0.15nS

Calcium peak conductance

g_T

nS

0.5nS

T-type Calcium channel peak conductance

g_ahp

nS

30nS

Afterpolarization current peak conductance

tau_syn_exc

ms

1ms

Rise time of the excitatory synaptic alpha function

tau_syn_inh

ms

12.5ms

Rise time of the inhibitory synaptic alpha function

E_gg

mV

-100mV

Reversal potential for inhibitory input (from GPe)

refr_T

ms

2ms

Duration of refractory period

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

gate_h

real

0.0

gating variable h

gate_n

real

0.0

gating variable n

gate_r

real

0.0

gating variable r

Ca_con

real

0.0

calcium concentration

Equations

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-(I_{Na} + I_{K} + I_{L} + I_{T} + I_{Ca} + I_{ahp}) \cdot \mathrm{pA} + I_{e} + I_{stim} + I_{exc,mod} \cdot \mathrm{pA} + I_{inh,mod} \cdot \mathrm{pA}) } \right)\]
\[\frac{ dgate_{h} } { dt }= \frac 1 { \mathrm{ms} } \left( { g_{\phi,h} \cdot (\frac{ (h_{\infty} - gate_{h}) } { \tau_{h} }) } \right)\]
\[\frac{ dgate_{n} } { dt }= \frac 1 { \mathrm{ms} } \left( { g_{\phi,n} \cdot (\frac{ (n_{\infty} - gate_{n}) } { \tau_{n} }) } \right)\]
\[\frac{ dgate_{r} } { dt }= \frac 1 { \mathrm{ms} } \left( { g_{\phi,r} \cdot (\frac{ (r_{\infty} - gate_{r}) } { \tau_{r} }) } \right)\]
\[\frac{ dCa_{con} } { dt }= g_{\epsilon} \cdot (-I_{Ca} - I_{T} - g_{k,Ca} \cdot Ca_{con})\]

Source code

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

Characterisation