mat2_psc_exp

mat2_psc_exp - Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

Description

mat2_psc_exp is an implementation of a leaky integrate-and-fire model with exponential-kernel postsynaptic currents (PSCs). Thus, postsynaptic currents have an infinitely short rise time.

The threshold is lifted when the neuron is fired and then decreases in a fixed time scale toward a fixed level [3].

The threshold crossing is followed by a total refractory period during which the neuron is not allowed to fire, even if the membrane potential exceeds the threshold. The membrane potential is NOT reset, but continuously integrated.

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]

Rotter S and 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]

Kobayashi R, Tsubo Y and Shinomoto S (2009). Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold. Frontiers in Computuational Neuroscience 3:9. DOI: https://doi.org/10.3389/neuro.10.009.2009

Parameters

Name	Physical unit	Default value	Description
tau_m	ms	5ms	Membrane time constant
C_m	pF	100pF	Capacitance of the membrane
refr_T	ms	2ms	Duration of refractory period
E_L	mV	-70mV	Resting potential
tau_syn_exc	ms	1ms	Time constant of postsynaptic excitatory currents
tau_syn_inh	ms	3ms	Time constant of postsynaptic inhibitory currents
tau_1	ms	10ms	Short time constant of adaptive threshold
tau_2	ms	200ms	Long time constant of adaptive threshold
alpha_1	mV	37mV	Amplitude of short time threshold adaption [3]
alpha_2	mV	2mV	Amplitude of long time threshold adaption [3]
omega	mV	19mV	Resting spike threshold (absolute value, not relative to E_L)
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_th_alpha_1	mV	0mV	Two-timescale adaptive threshold
V_th_alpha_2	mV	0mV	Two-timescale adaptive threshold
V_m	mV	E_L	Absolute membrane potential.
refr_t	ms	0ms	Refractory period timer
is_refractory	boolean	false

Equations

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

Source code

The model source code can be found in the NESTML models repository here: mat2_psc_exp.

Characterisation