Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models.

Josef Ladenbauer,Klaus Obermayer,Lyle J Graham

doi:10.1371/journal.pcbi.1006974

Abstract

Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.

Highlights

The interaction between weak electric fields and neuronal activity in the brain has gained increased attention over the past decade [1,2,3]
Modeling studies at the population level greatly contribute to our mechanistic understanding but face a methodological challenge because
The PY model neurons consist of two compartments, one for the soma and one for the dendrite, for which we consider trans-membrane capacitive currents, ionic leak currents, an approximation of the somatic Na+ current at spike initiation, an internal current, synaptic input currents and an extracellular electric field

Summary

Introduction

The interaction between weak electric fields and neuronal activity in the brain has gained increased attention over the past decade [1,2,3]. Two-compartment neuron models feature a suitable compromise between biological rigor and analytical tractability in this regard, with minimal level of spatial detail necessary to biophysically take into account an extracellular electric field. Models of this type have proven useful to study the effects of constant fields on the activity of single neurons and synchronization of neuronal pairs [34,35,36]. Powerful methods to study the spiking dynamics of these model neurons, at the levels of single cells and populations in a noisy, cortical setting, have been lacking

Methods

Results

Discussion

Conclusion