The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result.
The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.
Knight
B W
BW
Rockefeller University, New York, NY 10021, USA.
Omurtag
A
A
Sirovich
L
L
D000465:Algorithms; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D011157:Population Dynamics; D013569:Synapses / Q000502:physiology