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iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version

Description

iaf_psc_delta_ps is an implementation of a leaky integrate-and-fire model where the potential jumps on each spike arrival.

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

Spikes arriving while the neuron is refractory, are discarded by default. If the property “refractory_input” is set to true, such spikes are added to the membrane potential at the end of the refractory period, dampened according to the interval between arrival and end of refractoriness.

The linear subthreshold dynamics is integrated by the Exact Integration scheme 1. The neuron dynamics are solved exactly in time. Incoming and outgoing spike times are handled precisely 3.

An additional state variable and the corresponding differential equation represents a piecewise constant external current.

Spikes can occur either on receipt of an excitatory input spike, or be caused by a depolarizing input current. Spikes evoked by incoming spikes, will occur precisely at the time of spike arrival, since incoming spikes are modeled as instantaneous potential jumps. Times of spikes caused by current input are determined exactly by solving the membrane potential equation. Note that, in contrast to the neuron models discussed in 3 4, this model has so simple dynamics that no interpolation or iterative spike location technique is required at all.

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. sli/testsuite/nest contains a number of such tests.

The iaf_psc_delta_ps is the standard model used to check the consistency of the nest simulation kernel because it is at the same time complex enough to exhibit non-trivial dynamics and simple enough compute relevant measures analytically.

Parameters

The following parameters can be set in the status dictionary.

V_m

mV

Membrane potential

E_L

mV

Resting membrane potential

C_m

pF

Capacitance of the membrane

tau_m

ms

Membrane time constant

t_ref

ms

Duration of refractory period

V_th

ms

Spike threshold

V_reset

mV

Reset potential of the membrane

I_e

pA

Constant input current

V_min

mV

Absolute lower value for the membrane potential

refractory_input

(bool)

If true, keep input during refractory period (default: false)

Remarks

Please note that this node is capable of sending precise spike times to target nodes (on-grid spike time plus offset).

The iaf_psc_delta_ps neuron accepts connections transmitting CurrentEvents. These events transmit stepwise-constant currents which can only change at on-grid times.

For details about exact subthreshold integration, please see Integrating neural models using exact integration.

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.

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.

3(1,2)

Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact Subthreshold Integration with Continuous Spike Times in Discrete Time Neural Network Simulations. To appear in Neural Computation.

4

Hanuschkin A, Kunkel S, Helias M, Morrison A & Diesmann M (2010) A general and efficient method for incorporating exact spike times in globally time-driven simulations Front Neuroinformatics, 4:113

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest