aeif_cond_beta – Conductance-based adaptive exponential integrate-and-fire neuron model

Description

aeif_cond_beta is a conductance-based adaptive exponential integrate-and-fire neuron model according to [1] with synaptic conductance modeled by a beta function, as described in [2].

This implementation uses the 5th order Runge-Kutta solver with adaptive step size to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[C_m \frac{dV}{dt} = -g_L(V-E_L) + g_L\Delta_T \exp\left(\frac{V-V_{th}}{\Delta_T}\right) + g_{ex}(t) (V - E_{rev\_ ex,i}) + g_{in}(t) (V - E_{rev\_ in,i}) - w + I_e\]

The differential equation for the spike-adaptation current w is

\[\tau_w dw/dt = a(V - E_L) - w\]

When the neuron fires a spike, the adaptation current w <- w + b.

Note

Although this model is not multisynapse, the port (excitatory or inhibitory) to be chosen must be specified using the synapse property receptor. The excitatory port has index 0, whereas the inhibitory one has index 1. Differently from NEST, the connection weights related to the inhibitory port must be positive.

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
g_ex	nS	Excitatory synaptic conductance
g_in	nS	Inhibitory synaptic conductance
w	pA	Spike-adaptation current

Membrane Parameters
V_th	mV	Spike initiation threshold
Delta_T	mV	Slope factor
g_L	nS	Leak conductance
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
I_e	pA	Constant external input current
V_peak	mV	Spike detection threshold
V_reset	mV	Reset value for V_m after a spike
t_ref	ms	Duration of refractory period
den_delay	ms	Dendritic delay

Spike adaptation parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
tau_w	ms	Adaptation time constant

Synaptic parameters
E_rev_ex	mV	Excitatory reversal potential
E_rev_in	mV	Inhibitory reversal potential
tau_rise_ex	ms	Rise time constant of excitatory synaptic conductance
tau_rise_in	ms	Rise time constant of inhibitory synaptic conductance
tau_decay_ex	ms	Decay time constant of excitatory synaptic conductance
tau_decay_in	ms	Decay time constant of inhibitory synaptic conductance

Integration parameters
h0_rel	real	Starting step in ODE integration relative to time resolution
h_min_rel	real	Minimum step in ODE integration relative to time resolution

References

[1]

Brette R and Gerstner W (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005

[2]

A. Roth and M. C. W. van Rossum, Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6. DOI: https://doi.org/10.7551/mitpress/9780262013277.003.0007

See also

Neuron, Adaptive Threshold, Integrate-And-Fire, Conductance-Based