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. 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 :math:`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 :math:`g_{ij}( V_i - V_j)`. .. note:: In this model, a spike is emitted if :math:`V_m \geq V_T + 30` mV and :math:`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 :math:`t_{ref} = 3` ms ([1]_, p 118), while we used :math:`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] 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 ++++++++ :doc:`Neuron `, :doc:`Hodgkin-Huxley `, :doc:`Conductance-Based `