hh_psc_alpha_gap – Hodgkin-Huxley neuron model with gap-junction support

Description

hh_psc_alpha_gap is an implementation of a spiking neuron using the Hodgkin-Huxley formalism. In contrast to hh_psc_alpha the implementation additionally supports gap junctions.

1. Postsynaptic currents Incoming spike events induce a postsynaptic change of current modelled by an alpha function. The alpha function is normalized such that an event of weight 1.0 results in a peak current of 1 pA.

2. 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.

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

See also [1], [2], [3], [4].

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

Parameters

The following parameters can be set in the status dictionary.

tau_ex	ms	Rise time of the excitatory synaptic alpha function
tau_in	ms	Rise time of the inhibitory synaptic alpha function
g_K	nS	Potassium peak conductance
V_m	mV	Membrane potential
E_L	mV	Leak reversal potential
g_L	nS	Leak conductance
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
tau_syn_ex	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in	ms	Rise time of the inhibitory synaptic alpha function
E_Na	mV	Sodium reversal potential
g_Na	nS	Sodium peak conductance
E_K	mV	Potassium reversal potential
g_Kv1	nS	Potassium peak conductance
g_Kv3	nS	Potassium peak conductance
Act_m	real	Activation variable m
Inact_h	real	Inactivation variable h
Act_n	real	Activation variable n
I_e	pA	External input current

References

[1]

Gerstner W, Kistler W. Spiking neuron models: Single neurons, populations, plasticity. Cambridge University Press

[2]

Mancilla JG, Lewis TG, Pinto DJ, Rinzel J, Connors BW (2007). Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex, Journal of Neurosciece, 27:2058-2073 DOI: https://doi.org/10.1523/JNEUROSCI.2715-06.2007 (parameters taken from here)

[3]

Hodgkin AL and Huxley A F (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117. DOI: https://doi.org/10.1113/jphysiol.1952.sp004764

[4]

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gap-junction interactions in distributed neuronal netowrk simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022

Sends

SpikeEvent, GapJunctionEvent

Receives

SpikeEvent, GapJunctionEvent, CurrentEvent, DataLoggingRequest

See also

Neuron, Current-Based, Hodgkin-Huxley, Gap Junction

Examples using this model

• Gap Junctions: Inhibitory network example

• Gap Junctions: Two neuron example