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

[1] (1,2,3,4,5)

Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge UK.

[2]

http://modeldb.yale.edu/83319

[3]

Rotter S and Diesmann M (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biological Cybernetics 81:381 DOI: https://doi.org/10.1007/s004220050570

[4]

Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

See also

Neuron, Hodgkin-Huxley, Conductance-Based

Examples using this model

None