Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments

doi:10.1016/j.neucom.2006.10.047

Neurocomputing

Volume 70, Issues 10–12, June 2007, Pages 1668-1673

https://doi.org/10.1016/j.neucom.2006.10.047 Get rights and content

Abstract

An adaptive Exponential Integrate-and-Fire (aEIF) model was used to predict the activity of layer-V-pyramidal neurons of rat neocortex under random current injection. A new protocol has been developed to extract the parameters of the aEIF model using an optimal filtering technique combined with a black-box numerical optimization. We found that the aEIF model is able to accurately predict both subthreshold fluctuations and the exact timing of spikes, reasonably close to the limits imposed by the intrinsic reliability of pyramidal neurons.

Introduction

Electrophysiological data can be described by detailed conductance-based models (Hodgkin–Huxley-type models [6]). However, those models are rather complex, which implies that they are difficult to analyze and costly to implement numerically. Moreover, it is unclear how many details of conductance-based models are really necessary for the reproduction of experimental spike patterns [4], [13]. For those reasons, simple phenomenological spiking neurons such as Integrate-and-Fire models are highly popular.

The adaptive Exponential Integrate-and-Fire (aEIF) model used in this paper generalizes the standard leaky Integrate-and-Fire model in several directions: the strict threshold is replaced by a more realistic smooth threshold zone as in the Exponential Integrate-and-Fire neuron [2]. Furthermore, addition of a second variable captures subthreshold resonance or adaptation [7], [15]. The aEIF model showed convincing performances when compared to more detailed models [1], but so far, has never been tested on recordings of real neuron.

In this report, we will test the performances of the aEIF model on layer-V neocortical pyramidal neurons under random current injection.

Section snippets

Model

The aEIF is defined by [1] $C \frac{d u (t)}{d t} = - g_{L} (u (t) - E_{L}) + g_{L} Δ_{T} \exp (\frac{u (t) - V_{T}}{Δ_{T}}) - w + I,$ $τ_{w} \frac{d w (t)}{d t} = a (u (t) - E_{L}) - w (t),$ where $C$ is the membrane capacitance, $g_{L}$ the leak conductance, $E_{L}$ the resting potential, $Δ_{T}$ the slope factor and $V_{T}$ the threshold potential (Fig. 1). Note that formally, $E_{L}$ is not exactly the resting potential because of the exponential term. The variable $w$ describes the level of adaptation of the neuron and $a$ represents the relevance of subthreshold adaptation. The exponential term describes the early

Parameter fitting

Recordings of layer-V pyramidal neurons of rat neocortex were used to determine parameters of the model. The neurons were recorded intracellularly in vitro while stimulated at the soma by a randomly fluctuating current generated by an Ornstein–Uhlenbeck (OU) process (autocorrelation time 1 ms). Both mean and variance of the OU process were varied in order to sample the response of the neurons to various levels of tonic and time-dependent inputs. Details of the experimental procedure can be found

Results

The data set consists of four different neurons. For each cell, a set of 10 different input currents with different means and variances are injected. Each input trace is repeated four times. Fig. 3 shows a direct comparison between predicted and recorded spike trains for a typical neuron. Both spike trains are almost indistinguishable (Fig. 3A; for clarity reasons, the predicted spike train has been shifted upward). Even when zooming in the subthreshold regime, differences are in the range of a

Discussion and conclusion

We tested the aEIF model on experimental electrophysiology recordings and found a prediction of the spike times $Γ_{eff}$ up to 96% (average of 60%). With the same data set, a Spike Response Model with dynamic threshold has been evaluated and the performances were $Γ_{eff}$ up to 75% (average 65%) [8].

We remark that the protocol used for the recordings is not the most suitable for characterizing our model: in our extraction method, we had to set the subthreshold adaptation $a$ to 0. In addition, data

Acknowledgments

This work was supported by Swiss National Science Foundation Grant number SNF 200020-108093/1.

Claudia Clopath has obtained her M.Sc. in physics from the EPFL, in April 2005. She is now a Ph.D. in the Laboratory of Computational Neuroscience at the EPFL and her current research interest is to describe neuronal activity with simple Integrate-and-Fire type models.

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Renaud Jolivet obtained his Ph.D. in theoretical neuroscience at EPFL, in 2005, after studies in biophysics at the University of Lausanne (M.Sc.). He is now a postdoc in the laboratory of Prof. Pierre Magistretti at the University of Lausanne where his research is focused on neuro-astrocytic interactions in the context of brain metabolism and signal processing.

Alexander Rauch obtained his M.D., in 2003, at the University of Bern after studies in medicine at the University of Basel. His clinical experience includes surgery and neurorehabilitation. Between 1999 and 2003, he has worked as an electrophysiologist at the University of Bern focusing his research on links between cortical pyramidal neurons and simple models of neuronal activity. He is now a research assistant in the laboratory of Prof. Nikos Logothetis at the Max-Planck-Institute where his research is focused on BOLD signal and brain imaging techniques.

Hans-Rudolf Lüscher is Director of the Department of Physiology, University of Bern, Switzerland. He has a Medical Degree from the University of Zürich, Switzerland. He did his postdoctoral training with Elwood Henneman at the Department of Physiology and Biophysics, Harvard Medical School, Boston, USA. He spent extended time periods at the Division of Neuroscience, John Curtin School of Medical Research, Canberra, Australia. Hans-Rudolf Lüscher served as Dean and Vice-Dean of the Medical Faculty, University of Bern. He is a member of the Science Council of the Swiss National Science Foundation and of the Swiss Academy of Medical Sciences.

Wulfram Gerstner received his Ph.D. degree in theoretical physics from the TU Munich, Germany, in 1993, after studies in Tübingen, Berkeley, and Munich. He is a Professor and Head of Laboratory of Computational Neuroscience, EPFL, Switzerland.

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Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments

Abstract

Introduction

Section snippets

Model

Parameter fitting

Results

Discussion and conclusion

Acknowledgments

Adaptive exponential integrate-and-fire model as an effective description of neuronal activity

J. Neurophysiol.

How spike generation mechanisms determine the neuronal response to fluctuating inputs

J. Neurosci.

Spiking neuron Models: Single Neurons

Global structure

robustness and modulation of neuronal models, J. Neurosci.

A quantitative description of membrane current and its application to conduction and excitation in nerve

J. Physiol.

Which model to use for cortical spiking neurons IEEE Trans. Neural Networks

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

J. Comput. Neurosci.