# 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 $$V_m \geq V_T + 30$$ mV and $$V_m$$ 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 chose a sufficiently long refractory period. Traub and Miles used $$t_{ref} = 3$$ ms (2, p 118), while we used $$t_{ref} = 2$$ ms in 2.

## 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_syn_ex ms Time constant of the excitatory synaptic exponential function tau_syn_in ms Time constant of the inhibitory synaptic exponential function 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)

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(1,2,3,4,5)

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

3

http://modeldb.yale.edu/83319

SpikeEvent