iaf_psc_exp_neuron

iaf_psc_exp - Leaky integrate-and-fire neuron model

Description

iaf_psc_exp is an implementation of a leaky integrate-and-fire model with exponentially decaying synaptic currents according to [1]. Thus, postsynaptic currents have an infinitely short rise time.

The threshold crossing is followed by an absolute refractory period during which the membrane potential is clamped to the resting potential and spiking is prohibited.

The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].

Critical tests for the formulation of the neuron model are the comparisons of simulation results for different computation step sizes.

Note

If tau_m is very close to tau_syn_exc or tau_syn_inh, numerical problems may arise due to singularities in the propagator matrics. If this is the case, replace equal-valued parameters by a single parameter.

For details, please see IAF_neurons_singularity.ipynb in the NEST source code (docs/model_details).

References

[1] (1,2)

Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570

[2]

Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 38-40:565-571. DOI: https://doi.org/10.1016/S0925-2312(01)00409-X

[3]

Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Computation, in press DOI: https://doi.org/10.1162/neco.2007.19.1.47

See also

iaf_psc_delta, iaf_psc_alpha, iaf_cond_exp

Copyright statement

This file is part of NEST.

Copyright (C) 2004 The NEST Initiative

NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with NEST. If not, see <http://www.gnu.org/licenses/>.

Parameters

Name	Physical unit	Default value	Description
C_m	pF	250pF	Capacitance of the membrane
tau_m	ms	10ms	Membrane time constant
tau_syn_inh	ms	2ms	Time constant of inhibitory synaptic current
tau_syn_exc	ms	2ms	Time constant of excitatory synaptic current
refr_T	ms	2ms	Duration of refractory period
E_L	mV	-70mV	Resting potential
V_reset	mV	-70mV	Reset value of the membrane potential
V_th	mV	-55mV	Spike threshold potential
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	E_L	Membrane potential
refr_t	ms	0ms	Refractory period timer
I_syn_exc	pA	0pA
I_syn_inh	pA	0pA

Equations

\[\frac{ dI_{syn,exc} } { dt }= \frac{ -I_{syn,exc} } { \tau_{syn,exc} }\]

\[\frac{ dI_{syn,inh} } { dt }= \frac{ -I_{syn,inh} } { \tau_{syn,inh} }\]

\[\frac{ dV_{m} } { dt }= \frac{ -(V_{m} - E_{L}) } { \tau_{m} } + \frac 1 { C_{m} } \left( { (I_{syn,exc} - I_{syn,inh} + I_{e} + I_{stim}) } \right)\]

\[\frac{ drefr_{t} } { dt }= \frac{ -1000.0 \cdot \mathrm{ms} } { \mathrm{s} }\]

Source code

The model source code can be found in the NESTML models repository here: iaf_psc_exp_neuron.

Synaptic response

Response to pulse current injection

f-I curve