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

Description

aeif_cond_beta_multisynapse is a conductance-based adaptive exponential integrate-and-fire neuron model according to [1] with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by a beta function.

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

It allows an arbitrary number of synaptic rise time and decay time constants. Synaptic conductance is modeled by a beta function, as described in [2].

The membrane potential is given by the following differential equation:

\[C_m \frac{dV}{dt} = -g_L(V-E_L) + g_L\Delta_T \exp\left(\frac{V-V_{th}}{\Delta_T}\right) + I_{syn_{tot}}(V, t)- w + I_e\]

where:

\[I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V - E_{rev,i}) ,\]

the synapse i is excitatory or inhibitory depending on the value of \(E_{rev,i}\) and 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

The number of receptor ports must be specified at neuron creation (default value is 1) and the receptor index starts from 0 (and not from 1 as in NEST multisynapse models). The time constants are supplied by by two arrays, tau_rise and tau_decay for the synaptic rise time and decay time, respectively. The synaptic reversal potentials are supplied by the array E_rev. Port numbers are automatically assigned in the range 0 to n_receptors-1. During connection, the ports are selected with the synapse property receptor.

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
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	list of mV	Reversal potential
tau_rise	list of ms	Rise time constant of synaptic conductance
tau_decay	list of ms	Decay time constant of 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