Special issue on quantitative neuron modeling

Abstract

Single neurons are the fundamental constituents of all nervous systems. Understanding the properties and dynamics of single neurons is therefore one of the key challenges in modern neuroscience. Since the work of Lapicque (1907) [see also the recent translation by Brunel and van Rossum (2007)], single neuron models have enjoyed great popularity and have been the subject of many theoretical studies. Two broad categories of spiking neuron models have been extensively studied and used: Hodgkin-Huxley-type neuron models and simplified phenomenological neuron models, of which the integrate-and-fire model is the most famous representative. Each model type presents its own set of advantages and drawbacks. The Hodgkin-Huxley framework permits the design of detailed, biophysically realistic models, which can be used to study the effects of different types of ion channels including their distribution along dendrites. However, these models are computationally expensive and their analysis is usually difficult. Simple phenomenological neuron models, on the other hand, are analytically tractable and computationally cheap, but their realism is questionable. Both types of models have been used in countless studies of single neurons and network models, with the ultimate aim of understanding how information processing in single neurons and neural circuits gives rise to behaviour.Despite the tremendous popularity both types of models enjoy, the question of their quantitative accuracy in reproducing experimentally measured neuronal dynamics has been barely addressed until recently. It was implicitly assumed that Hodgkin-Huxley-type neuron models are the most realistic, while simplified phenomenological neuron models were overlooked in that regard but extensively used because of their simplicity. However, are either of these models able to predict the rate and timing of output spikes of a real neuron, given arbitrary patterns of synaptic input? Can they correctly predict the result of the interactions between dendrites and soma? And can they quantitatively predict the effect of various intrinsic neuronal mechanisms, for example those underlying adaptation or bursting? With recent initiatives such as the Blue Brain Project (Markram 2006) or the recent large-scale model by Izhikevich and Edelman (2008), it is now time to try to answer these questions. In order to provide the community with a benchmark to address these questions, we set up an international scholarly challenge on quantitative single neuron modeling 1 . The present Special Issue comprises a selection of papers that address precisely these questions, and extensively describe the challenge: can Hodgkin-Huxley-type neuron models or simplified phenomenological neuron models predict the activity of real neurons? What is the minimal level of description required to achieve a reasonable accuracy of predictions made by 1

Elemental Spiking Neuron Model for Reproducing Diverse Firing Patterns and Predicting Precise Firing Times

“…The adaptive capability of the model in predicting spike times was assessed using a coefficient measuring the fraction of spikes that coincided in 4 ms between a model spike train and a real biological spike train. Among various measures (including Victor and Purpura, 1996; Tsubo et al, 2004), we adopted coincidence factor Γ as introduced in the competition (Jolivet et al, 2004, 2006, 2008; Kobayashi and Shinomoto, 2007). …”

“…In the competition, spike neuron models were assessed based on their quantitative performance in accurately predicting spike times (Mainen and Sejnowski, 1995; Jolivet et al, 2008; Gerstner and Naud, 2009). The simplistic integrate-and-fire models described above displayed higher performance than the complicated biophysical neuron models of Hodgkin–Huxley type (Hodgkin and Huxley, 1952).…”

Leaky Integrate and Fire Models Coupled through Copulas: Association Properties of the Interspike Intervals

“…This determines the copulas catching the different coupling between the epochs of excitatory (inhibitory) inputs. When the continuous limit of Stein's equations [15] is performed one gets [8] and [9] (10, 15) and the increments of the processes exhibit a dependence due to the dependence between the arrival times of the inputs. The copula expression between the increments should then be determined from the copula between the arrival times.…”

“…According to the classical assumptions on LIF models, eqs. [8] and [9] describe the subthreshold behavior while the interspike intervals of the two neurons are described by the first passage time of the processes through a boundary S:…”

“…This fact has allowed the use of single neuron models to describe the role of the noise in signal transmission and to study input-output relationships. In this framework Leaky Integrate and Fire (LIF) models owe their popularity to the existence of specific mathematical methods and to their ability to reproduce a set of experimental features (4,5,9).…”