iaf_psc_alpha – Leaky integrateandfire model with alphashaped input currents¶
Description¶
iaf_psc_alpha
is a leaky integrateandfire neuron model with
a hard threshold,
a fixed refractory period,
no adaptation mechanisms,
\(\alpha\)shaped synaptic input currents.
The membrane potential evolves according to
where the synaptic input current \(I_{\text{syn}}(t)\) is discussed below and \(I_\text{e}\) is a constant input current set as a model parameter.
A spike is emitted at time step \(t^*=t_{k+1}\) if
Subsequently,
that is, the membrane potential is clamped to \(V_{\text{reset}}\) during the refractory period.
The synaptic input current has an excitatory and an inhibitory component
where
where \(j\) indexes either excitatory (\(\text{X} = \text{ex}\)) or inhibitory (\(\text{X} = \text{in}\)) presynaptic neurons, \(k\) indexes the spike times of neuron \(j\), and \(d_j\) is the delay from neuron \(j\).
The individual postsynaptic currents (PSCs) are given by
where \(\Theta(x)\) is the Heaviside step function. The PSCs are normalized to unit maximum, that is,
As a consequence, the total charge \(q\) transferred by a single PSC depends on the synaptic time constant according to
By default, \(V_\text{m}\) is not bounded from below. To limit hyperpolarization to biophysically plausible values, set parameter \(V_{\text{min}}\) as lower bound of \(V_\text{m}\).
Note
NEST uses exact integration [1], [2] to integrate subthreshold membrane dynamics with maximum precision; see also [3].
If \(\tau_\text{m}\approx \tau_{\text{syn, ex}}\) or \(\tau_\text{m}\approx \tau_{\text{syn, in}}\), the model will numerically behave as if \(\tau_\text{m} = \tau_{\text{syn, ex}}\) or \(\tau_\text{m} = \tau_{\text{syn, in}}\), respectively, to avoid numerical instabilities.
For implementation details see the IAF Integration Singularity notebook.
Parameters¶
The following parameters can be set in the status dictionary.
Parameter 
Unit 
Math equivalent 
Description 


mV 
\(V_{\text{m}}\) 
Membrane potential 

mV 
\(E_\text{L}\) 
Resting membrane potential 

pF 
\(C_{\text{m}}\) 
Capacity of the membrane 

ms 
\(\tau_{\text{m}}\) 
Membrane time constant 

ms 
\(t_{\text{ref}}\) 
Duration of refractory period 

mV 
\(V_{\text{th}}\) 
Spike threshold 

mV 
\(V_{\text{reset}}\) 
Reset potential of the membrane 

ms 
\(\tau_{\text{syn, ex}}\) 
Rise time of the excitatory synaptic alpha function 

ms 
\(\tau_{\text{syn, in}}\) 
Rise time of the inhibitory synaptic alpha function 

pA 
\(I_\text{e}\) 
Constant input current 

mV 
\(V_{\text{min}}\) 
Absolute lower value for the membrane potenial (default \(\infty\)) 
References¶
Sends¶
SpikeEvent
Receives¶
SpikeEvent, CurrentEvent, DataLoggingRequest
See also¶
Examples using this model¶
Random balanced network (alpha synapses) connected with NEST
Spatial networks: 4x3 grid with pyramidal cells and interneurons
Spatial networks: A spatial network in 3D with Gaussian connection probabilities
Spatial networks: A spatial network in 3D with exponential connection probabilities
Spatial networks: Circular mask and flat probability, with edge wrap
Spatial networks: Convergent projection and rectangular mask, from source perspective
Spatial networks: Convergent projection and rectangular mask, from target perspective
Spatial networks: Showcase of PlotTargets, PlotSources, GetTargetNodes, GetSourceNodes
Use evolution strategies to find parameters for a random balanced network (alpha synapses)