aeif_psc_delta_clopath – Adaptive exponential integrate-and-fire neuron

Description

aeif_psc_delta_clopath is an implementation of the neuron model as it is used in [1]. It is an extension of the aeif_psc_delta model and capable of connecting to a Clopath synapse.

Note that there are two points that are not mentioned in the paper but present in a MATLAB implementation by Claudia Clopath [3]. The first one is the clamping of the membrane potential to a fixed value after a spike occurred to mimic a real spike and not just the upswing. This is important since the finite duration of the spike influences the evolution of the convolved versions (u_bar_[plus/minus]) of the membrane potential and thus the change of the synaptic weight. Secondly, there is a delay with which u_bar_[plus/minus] are used to compute the change of the synaptic weight.

Note: Neither the clamping nor the delayed processing of u_bar_[plus/minus] are mentioned in [1]. However, they are part of an reference implementation by Claudia Clopath et al. that can be found on ModelDB [3]. The clamping is important to mimic a spike which is otherwise not described by the aeif neuron model.

For implementation details see the aeif_models_implementation notebook.

See also [2].

Note

The default refractory period for aeif models is zero, consistent with the model definition in Brette & Gerstner [4]. Thus, an aeif neuron with default parameters can fire multiple spikes in a single time step, which can lead to exploding spike numbers and extreme slow-down of simulations.

To avoid such unphysiological behavior, you should set a refractory time t_ref > 0.

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables
V_m	mV	Membrane potential
w	pA	Spike-adaptation current
z	pA	Spike-adaptation current
V_th	mV	Adaptive spike initiation threshold
u_bar_plus	mV	Low-pass filtered Membrane potential
u_bar_minus	mV	Low-pass filtered Membrane potential
u_bar_bar	mV	Low-pass filtered u_bar_minus

Membrane Parameters
C_m	pF	Capacity of the membrane
t_ref	ms	Duration of refractory period
V_reset	mV	Reset value for V_m after a spike
E_L	mV	Leak reversal potential
g_L	nS	Leak conductance
I_e	pA	Constant external input current
tau_u_bar_plus	ms	Time constant of u_bar_plus
tau_u_bar_minus	ms	Time constant of u_bar_minus
tau_u_bar_bar	ms	Time constant of u_bar_bar

Spike adaptation parameters
a	nS	Subthreshold adaptation
b	pA	Spike-triggered adaptation
Delta_T	mV	Slope factor
tau_w	ms	Adaptation time constant
tau_z	ms	Spike afterpotential current time constant
I_sp	pA	Depolarizing spike afterpotential current magnitude
V_peak	mV	Spike detection threshold
V_th_max	mV	Value of V_th after a spike
V_th_rest	mV	Resting value of V_th

Clopath rule parameters
A_LTD	1/mV	Amplitude of depression
A_LTP	1/mV^2	Amplitude of facilitation
theta_plus	mV	Threshold for u
theta_minus	mV	Threshold for u_bar_[plus/minus]
A_LTD_const	boolean	Flag that indicates whether A_LTD_ should be constant (true, default) or multiplied by u_bar_bar^2 / u_ref_squared (false).
delay_u_bars	real	Delay with which u_bar_[plus/minus] are processed to compute the synaptic weights.
U_ref_squared	real	Reference value for u_bar_bar_^2.

Other parameters
t_clamp	ms	Duration of clamping of Membrane potential after a spike
V_clamp	mV	Value to which the Membrane potential is clamped

Integration parameters
gsl_error_tol	real	This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

References

[1] (1,2)

Clopath et al. (2010). Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nature Neuroscience 13(3):344-352. DOI: https://doi.org/10.1038/nn.2479

[2]

Clopath and Gerstner (2010). Voltage and spike timing interact in STDP – a unified model. Frontiers in Synaptic Neuroscience. 2:25 DOI: https://doi.org/10.3389/fnsyn.2010.00025

[3] (1,2)

Voltage-based STDP synapse (Clopath et al. 2010) on ModelDB https://modeldb.science/144566?tab=1

[4]

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

See also

aeif_psc_delta, clopath_synapse, hh_psc_alpha_clopath

Examples using this model

• Clopath Rule: Bidirectional connections

• Clopath Rule: Spike pairing experiment