Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy

J Neurophysiol. 2004 Aug;92(2):959-76. doi: 10.1152/jn.00190.2004.


We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70-80 percent of the spikes in the full model (with temporal precision of +/-2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

Publication types

  • Comparative Study

MeSH terms

  • Action Potentials
  • Animals
  • Cerebral Cortex / cytology
  • Cerebral Cortex / physiology*
  • Differential Threshold
  • Electric Conductivity
  • Electric Stimulation
  • Humans
  • Membrane Potentials
  • Models, Neurological*
  • Neurons / physiology*
  • Nonlinear Dynamics
  • Presynaptic Terminals / physiology
  • Stochastic Processes
  • Time Factors