The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result

• Published in: Neural computation 2000-05, Vol.12 (5), p.1045-1055
• Main Authors: Knight, B. W., Omurtag, A., Sirovich, L.
• Format: Article
• Language: English
• Subjects: Algorithms; Animal and plant ecology; Animal, plant and microbial ecology; Applied sciences; Artificial intelligence; Biological and medical sciences; Computer science; control theory; systems; Connectionism. Neural networks; Control theory. Systems; Demecology; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; General aspects. Models. Methods; Modelling and identification; Models, Neurological; Neurons - physiology; Population Dynamics; Synapses - physiology; Vertebrates: nervous system and sense organs
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/089976600300015493

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.