hh_cond_beta_gap_traub – Hodgkin-Huxley neuron with gap junction support and beta function synaptic conductances

Description

hh_cond_beta_gap_traub is an implementation of a modified Hodgkin-Huxley model that also supports gap junctions.

This model is derived from the hh_conda_exp model, but supports double-exponential-shaped (beta-shaped) synaptic conductances and also supports gap junctions. The model is originally based on a model of hippocampal pyramidal cells by Traub and Miles [1]. The key differences between the current model and the model in [1] 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 [1], 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.

Postsynaptic currents

Incoming spike events induce a postsynaptic change of conductance modelled by a beta function as outlined in [3] [4]. The beta function is normalized such that an event of weight 1.0 results in a peak current of 1 nS at \(t = \tau_{rise,xx}\) where xx is ex or in.

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.

Gap Junctions

Gap Junctions are implemented by a gap current of the form \(g_{ij}( V_i - V_j)\).

Note

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

To avoid multiple spikes from occurring 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 ([1], p 118), while we used \(t_{ref} = 2\) ms in [1].

Parameters

The following parameters can be set in the status dictionary.

V_m

mV

Membrane potential

V_T

mV

Voltage offset that controls dynamics. For default parameters, V_T = -63mV results in a threshold around -50mV

E_L

mV

Leak reversal potential

C_m

pF

Capacity of the membrane

g_L

nS

Leak conductance

tau_rise_ex

ms

Excitatory synaptic beta function rise time

tau_decay_ex

ms

Excitatory synaptic beta function decay time

tau_rise_in

ms

Inhibitory synaptic beta function rise time

tau_decay_in

ms

Inhibitory synaptic beta function decay time

t_ref

ms

Duration of refractory period (see Note)

E_ex

mV

Excitatory synaptic reversal potential

E_in

mV

Inhibitory synaptic reversal potential

E_Na

mV

Sodium reversal potential

g_Na

nS

Sodium peak conductance

E_K

mV

Potassium reversal potential

g_K

nS

Potassium peak conductance

I_e

pA

External input current

References

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

See also

Neuron, Hodgkin-Huxley, Conductance-Based