Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models

Details Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models

2008-05-12

arxiv.org/abs/0805.1561v1

Neural Computation, July 2009, Vol. 21, No. 7, Pages 1913-1930

Biology

Quantitative Biology

Neurons and Cognition

11 pages with 2 figures included in main text

Scientific paper

10.1162/neco.2009.07-08-815

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has recently been introduced by Carnevale and Hines. This integration scheme imposes non-physiological constraints on the time constants of the synaptic currents it attempts to model which hamper the general applicability. This paper addresses this problem in two ways. First, we provide physical arguments to show why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. This proof rests on a generalization of the Carnevale-Hines lemma, which is a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems including receptor-neurotransmitter dissociation followed by channel closing. We show that this lemma can be generalized and subsequently used for lifting most of the original constraints on the time constants. Thus we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse type combinations than is apparent from the original treatment.

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