# 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.

For details on asynchronicity in spike and firing events with Hodgkin Huxley models see here.

See also [2].

### 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