Leaky Integrate-and-Fire Neuron Model

How synaptic input is integrated into spikes

: 22 px


Cell, passive properties



Cell, active properties












Short-term plasticity



How to use this simulation

The model

The leaky integrate-and-fire neuron treats the membrane as a resistor-capacitor circuit. Current drives the membrane potential toward threshold while the leak pulls it toward Eleak. On crossing threshold, the model draws an action-potential peak and resets the voltage. The peak and reset make spikes easy to see, but they do not represent voltage-gated Na+ and K+ currents.

Explore integration and firing

Use Current injection to see how input resistance, capacitance, and the membrane time constant control the rate and extent of voltage change. Then enable the Synapse and an Externally defined train. Change synaptic conductance, reversal potential, pulse frequency, and threshold to test when separate responses summate enough to trigger spikes.

The lower plots show the depression and facilitation variables. After each presynaptic pulse, d multiplies the available synaptic efficacy, so smaller values produce stronger depression, while f adds facilitation. The corresponding time constants set recovery toward baseline. These are phenomenological variables: they reproduce useful short-term dynamics without explicitly modelling vesicle pools or presynaptic Ca2+.

Try it

  1. Inject the same current while changing Rinput or CM. Compare the steady voltage change and charging speed.
  2. With a synaptic train, raise the frequency until temporal summation crosses threshold.
  3. Compare depressing, facilitating, and no-plasticity settings. Ask whether the first or later inputs dominate spike generation.
  4. Use Keep last sweep to compare one parameter change at a time.

References

For the history and interpretation of the integrate-and-fire model, see Brunel & van Rossum (2007), Lapicque’s 1907 paper: from frogs to integrate-and-fire. The short-term-plasticity controls are related to phenomenological descriptions by Varela et al. (1997), A Quantitative Description of Short-Term Plasticity at Excitatory Synapses in Layer 2/3 of Rat Primary Visual Cortex, and Tsodyks & Markram (1997), The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.