hh_cond_exp_traub

hh_cond_exp_traub - Hodgkin-Huxley model for Brette et al (2007) review

Description

hh_cond_exp_traub is an implementation of a modified Hodgkin-Huxley model.

This model was specifically developed for a major review of simulators [1], based on a model of hippocampal pyramidal cells by Traub and Miles [2]. The key differences between the current model and the model in [2] are:

  • This model is a point neuron, not a compartmental model.

  • This model includes only I_Na and I_K, with simpler I_K dynamics than in [2], so it has only three instead of eight gating variables; in particular, all Ca dynamics have been removed.

  • Incoming spikes induce an instantaneous conductance change followed by exponential decay instead of activation over time.

This model is primarily provided as reference implementation for hh_coba example of the Brette et al (2007) review. Default parameter values are chosen to match those used with NEST 1.9.10 when preparing data for [1]. Code for all simulators covered is available from ModelDB [3].

Note: In this model, a spike is emitted if \(V_m >= V_T + 30\) mV and \(V_m\) has fallen during the current time step.

To avoid that this leads to multiple spikes during the falling flank of a spike, it is essential to choose a sufficiently long refractory period. Traub and Miles used \(t_{ref} = 3\) ms [2, p 118], while we used \(t_{ref} = 2\) ms in [2].

References

See also

hh_psc_alpha

Parameters

Name

Physical unit

Default value

Description

g_Na

nS

20000nS

Na Conductance

g_K

nS

6000nS

K Conductance

g_L

nS

10nS

Leak Conductance

C_m

pF

200pF

Membrane Capacitance

E_Na

mV

50mV

Reversal potentials

E_K

mV

-90mV

Potassium reversal potential

E_L

mV

-60mV

Leak reversal potential (aka resting potential)

V_T

mV

-63mV

Voltage offset that controls dynamics. For default

tau_syn_exc

ms

5ms

parameters, V_T = -63 mV results in a threshold around -50 mV.Synaptic time constant of excitatory synapse

tau_syn_inh

ms

10ms

Synaptic time constant of inhibitory synapse

refr_T

ms

2ms

Duration of refractory period

E_exc

mV

0mV

Excitatory synaptic reversal potential

E_inh

mV

-80mV

Inhibitory synaptic reversal potential

alpha_n_init

1 / ms

0.032 / (ms * mV) * (15.0mV - E_L) / (exp((15.0mV - E_L) / 5.0mV) - 1.0)

beta_n_init

1 / ms

0.5 / ms * exp((10.0mV - E_L) / 40.0mV)

alpha_m_init

1 / ms

0.32 / (ms * mV) * (13.0mV - E_L) / (exp((13.0mV - E_L) / 4.0mV) - 1.0)

beta_m_init

1 / ms

0.28 / (ms * mV) * (E_L - 40.0mV) / (exp((E_L - 40.0mV) / 5.0mV) - 1.0)

alpha_h_init

1 / ms

0.128 / ms * exp((17.0mV - E_L) / 18.0mV)

beta_h_init

1 / ms

(4.0 / (1.0 + exp((40.0mV - E_L) / 5.0mV))) / ms

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

refr_t

ms

0ms

Refractory period timer

is_refractory

boolean

false

Act_m

real

alpha_m_init / (alpha_m_init + beta_m_init)

Act_h

real

alpha_h_init / (alpha_h_init + beta_h_init)

Inact_n

real

alpha_n_init / (alpha_n_init + beta_n_init)

Equations

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

Source code

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

Characterisation

Synaptic response

hh_cond_exp_traub_neuron

f-I curve

hh_cond_exp_traub_neuron