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
andI_K
, with simplerI_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.
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