Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.
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.
Jolivet
Renaud
R
Laboratory of Computational Neuroscience, Swiss Federal Institute of Technology, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. renaud.jolivet@epfl.ch
Lewis
Timothy J
TJ
Gerstner
Wulfram
W
D000200:Action Potentials; D000818:Animals; D002540:Cerebral Cortex / Q000166:cytology / Q000502:physiology*; D004056:Differential Threshold; D004553:Electric Conductivity; D004558:Electric Stimulation; D006801:Humans; D008564:Membrane Potentials; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D017729:Presynaptic Terminals / Q000502:physiology; D013269:Stochastic Processes; D013997:Time Factors