hh_cond_exp_traub_neuron
########################

hh_cond_exp_traub - Hodgkin-Huxley model for Brette et al (2007) review


Description
+++++++++++

hh_cond_exp_traub is an implementation of a modified Hodgkin-Huxley model.

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 :math:`V_m >= V_T + 30` mV and
:math:`V_m` has fallen during the current time step.

To avoid that this leads to multiple spikes during the falling flank of a
spike, it is essential to choose a sufficiently long refractory period.
Traub and Miles used :math:`t_{ref} = 3` ms [2, p 118], while we used
:math:`t_{ref} = 2` ms in [2]_.

References
++++++++++

.. [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


See also
++++++++

hh_psc_alpha

Copyright statement
+++++++++++++++++++

This file is part of NEST.

Copyright (C) 2004 The NEST Initiative

NEST is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.

NEST is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with NEST.  If not, see <http://www.gnu.org/licenses/>.


Parameters
++++++++++
.. csv-table::
    :header: "Name", "Physical unit", "Default value", "Description"
    :widths: auto

    
    "g_Na", "nS", "20000nS", "Na conductance"    
    "g_K", "nS", "6000nS", "K conductance"    
    "g_L", "nS", "10nS", "Leak conductance"    
    "C_m", "pF", "200pF", "Membrane capacitance"    
    "E_Na", "mV", "50mV", "Sodium reversal potential"    
    "E_K", "mV", "-90mV", "Potassium reversal potential"    
    "E_L", "mV", "-60mV", "Leak reversal potential (a.k.a. resting potential)"    
    "V_T", "mV", "-63mV", "Voltage offset that controls dynamics. For default"    
    "tau_syn_exc", "ms", "5ms", "parameters, V_T = -63 mV results in a threshold around -50 mV.Synaptic time constant of excitatory synapse"    
    "tau_syn_inh", "ms", "10ms", "Synaptic time constant of inhibitory synapse"    
    "refr_T", "ms", "2ms", "Duration of refractory period"    
    "E_exc", "mV", "0mV", "Excitatory synaptic reversal potential"    
    "E_inh", "mV", "-80mV", "Inhibitory synaptic reversal potential"    
    "alpha_n_init", "1 / ms", "0.032 / (ms * mV) * (15mV - E_L) / (exp((15mV - E_L) / 5mV) - 1)", ""    
    "beta_n_init", "1 / ms", "0.5 / ms * exp((10mV - E_L) / 40mV)", ""    
    "alpha_m_init", "1 / ms", "0.32 / (ms * mV) * (13mV - E_L) / (exp((13mV - E_L) / 4mV) - 1)", ""    
    "beta_m_init", "1 / ms", "0.28 / (ms * mV) * (E_L - 40mV) / (exp((E_L - 40mV) / 5mV) - 1)", ""    
    "alpha_h_init", "1 / ms", "0.128 / ms * exp((17mV - E_L) / 18mV)", ""    
    "beta_h_init", "1 / ms", "(4 / (1 + exp((40mV - E_L) / 5mV))) / ms", ""    
    "I_e", "pA", "0pA", "constant external input current"



State variables
+++++++++++++++

.. csv-table::
    :header: "Name", "Physical unit", "Default value", "Description"
    :widths: auto

    
    "V_m", "mV", "E_L", "Membrane potential"    
    "V_m_old", "mV", "E_L", "Membrane potential at previous timestep"    
    "refr_t", "ms", "0ms", "Refractory period timer"    
    "Act_m", "real", "alpha_m_init / (alpha_m_init + beta_m_init)", ""    
    "Act_h", "real", "alpha_h_init / (alpha_h_init + beta_h_init)", ""    
    "Inact_n", "real", "alpha_n_init / (alpha_n_init + beta_n_init)", ""




Equations
+++++++++



.. math::
   \frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-I_{Na} - I_{K} - I_{L} - I_{syn,exc} - I_{syn,inh} + I_{e} + I_{stim}) } \right) 

.. math::
   \frac{ drefr_{t} } { dt }= \frac{ -1000.0 \cdot \mathrm{ms} } { \mathrm{s} }

.. math::
   \frac{ dAct_{m} } { dt }= (\alpha_{m} - (\alpha_{m} + \beta_{m}) \cdot Act_{m})

.. math::
   \frac{ dAct_{h} } { dt }= (\alpha_{h} - (\alpha_{h} + \beta_{h}) \cdot Act_{h})

.. math::
   \frac{ dInact_{n} } { dt }= (\alpha_{n} - (\alpha_{n} + \beta_{n}) \cdot Inact_{n})



Source code
+++++++++++

The model source code can be found in the NESTML models repository here: `hh_cond_exp_traub_neuron <https://github.com/nest/nestml/tree/main/models/neurons/hh_cond_exp_traub_neuron.nestml>`_.

.. include:: hh_cond_exp_traub_neuron_characterisation.rst


.. footer::

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