Command: hh_cond_beta_gap_traub

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Name:
hh_cond_beta_gap_traub - modified Hodgkin-Huxley neuron as featured in
Brette et al (2007) review with added gap junction support and beta function
synaptic conductance.
Description:
hh_cond_beta_gap_traub is an implementation of a modified Hodgkin-Huxley model
that also supports gap junctions.

This model was specifically developed for a major review of simulators [1],
based on a model of hippocampal pyramidal cells by Traub and Miles[2].
The key differences between the current model and the model in [2] 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 [2], 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.

This model is primarily provided as reference implementation for hh_coba
example of the Brette et al (2007) review. Default parameter values are chosen
to match those used with NEST 1.9.10 when preparing data for [1]. Code for all
simulators covered is available from ModelDB [3].

Note:
In this model, a spike is emitted if

@f[ V_m >= V_T + 30 mV and V_m has fallen during the current time step @f]

To avoid that this leads to multiple spikes during the falling flank of a
spike, it is essential to chose a sufficiently long refractory period.
Traub and Miles used \f$ t_ref = 3 ms \f$ [2, p 118], while we used
\f$ t_ref = 2 ms \f$ in [2].

Post-synaptic currents
Incoming spike events induce a post-synaptic change of conductance modelled by a
beta function as outlined in [4,5]. The beta function is normalised such that an
event of weight 1.0 results in a peak current of 1 nS at \f$ t = tau_rise_xx \f$
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
\f$ g_ij( V_i - V_j) \f$.
Parameters:
The following parameters can be set in the status dictionary.

\verbatim embed:rst
============ ====== =======================================================
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
============ ====== =======================================================
\endverbatim
Receives:
SpikeEvent, CurrentEvent, DataLoggingRequest
Sends:
SpikeEvent
References:
\verbatim embed:rst
.. [1] Brette R et al (2007). Simulation of networks of spiking neurons: A
review of tools and strategies. Journal of Computational Neuroscience
23:349-98. DOI: https://doi.org/10.1007/s10827-007-0038-6
.. [2] Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus.
Cambridge University Press, Cambridge UK.
.. [3] http://modeldb.yale.edu/83319
.. [4] 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
.. [5] Roth A and van Rossum M (2010). Chapter 6: Modeling synapses.
in De Schutter, Computational Modeling Methods for Neuroscientists,
MIT Press.
\endverbatim
Author:
Daniel Naoumenko (modified hh_cond_exp_traub by Schrader and
hh_psc_alpha_gap by Jan Hahne, Moritz Helias and Susanne Kunkel)
SeeAlso:
Source:
/var/www/debian/nest/nest-simulator-2.18.0/models/hh_cond_beta_gap_traub.h
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