# 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