hh_psc_alpha

hh_psc_alpha - Hodgkin-Huxley neuron model

Description

hh_psc_alpha is an implementation of a spiking neuron using the Hodgkin-Huxley formalism.

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.

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.

Problems/Todo

  • better spike detection

  • initial wavelet/spike at simulation onset

References

See also

hh_cond_exp_traub

Parameters

Name

Physical unit

Default value

Description

t_ref

ms

2ms

Refractory period

g_Na

nS

12000nS

Sodium peak conductance

g_K

nS

3600nS

Potassium peak conductance

g_L

nS

30nS

Leak conductance

C_m

pF

100pF

Membrane Capacitance

E_Na

mV

50mV

Sodium reversal potential

E_K

mV

-77mV

Potassium reversal potential

E_L

mV

-54.402mV

Leak reversal Potential (aka resting potential)

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

V_m_init

mV

-65mV

Initial membrane potential

alpha_n_init

real

(0.01 * (V_m_init / mV + 55.0)) / (1.0 - exp(-(V_m_init / mV + 55.0) / 10.0))

beta_n_init

real

0.125 * exp(-(V_m_init / mV + 65.0) / 80.0)

alpha_m_init

real

(0.1 * (V_m_init / mV + 40.0)) / (1.0 - exp(-(V_m_init / mV + 40.0) / 10.0))

beta_m_init

real

4.0 * exp(-(V_m_init / mV + 65.0) / 18.0)

alpha_h_init

real

0.07 * exp(-(V_m_init / mV + 65.0) / 20.0)

beta_h_init

real

1.0 / (1.0 + exp(-(V_m_init / mV + 35.0) / 10.0))

I_e

pA

0pA

constant external input current

State variables

Name

Physical unit

Default value

Description

r

integer

0

number of steps in the current refractory phase

V_m

mV

V_m_init

Membrane potential

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

\[\frac{ dAct_{n} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{n} \cdot (1 - Act_{n}) - \beta_{n} \cdot Act_{n}) } \right)\]
\[\frac{ dAct_{m} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{m} \cdot (1 - Act_{m}) - \beta_{m} \cdot Act_{m}) } \right)\]
\[\frac{ dInact_{h} } { dt }= \frac 1 { \mathrm{ms} } \left( { (\alpha_{h} \cdot (1 - Inact_{h}) - \beta_{h} \cdot Inact_{h}) } \right)\]
\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-(I_{Na} + I_{K} + I_{L}) + I_{e} + I_{stim} + I_{syn,exc} - I_{syn,inh}) } \right)\]

Source code

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

Characterisation

Synaptic response

hh_psc_alpha_nestml

f-I curve

hh_psc_alpha_nestml