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

TL;DR

This paper generalizes an event-based integration scheme for integrate-and-fire neuron models, relaxing previous constraints on synaptic time constants, thus broadening its applicability to various neuron and synapse types.

Contribution

It introduces a formal proof and a generalized Carnevale-Hines lemma to relax constraints on synaptic time constants in the integration scheme.

Findings

The generalized lemma allows for broader synaptic time constant ranges.

The integration scheme can now simulate diverse neuron and synapse types.

Constraints on decay time constants are effectively lifted.

Abstract

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.