Effects of a Spatial and Temporal Non-Uniform Extracellular Potential Distribution on the Activity of Single Neurones and Neuronal Populations

What impact have local electric field fluctuations on neuronal activity? Recording extracellular action potential is one of the primary methods to study brain function in the living animal. Understanding and quantifying the effect of the local field potential on the transmembrane potential of neurones is crucial for determining whether and when a given synaptic input will cause neurones to initiate an action potential. Since the days of Hodgkin-Huxley and their equations, neuronal membrane and extended dendritic as well as axonal structures have been modelled using one-dimensional cable theory in combination with linear or nonlinear time, voltage- and ligand-gated membrane conductances. In this entire body of work a common assumption was that the extracellular potential (Ve) is uniform, i.e. it does not depend on space, and is constant in time. Both assumptions, however, are known to be wrong - otherwise one could not record action potentials from outside neurones - but were justified by arguing that contributions of a non-uniform Ve(x, t) could be neglected. We propose to study theoretically the effect of a non-uniform and dynamic Ve on different levels of neuronal complexity: (a) on a single, unbranched cable model of a neurone, (b) on hippocampal pyramidal neurones with realistic dendritic morphology and electrophysiological signature and (c) on a population of simplified cortical cells exhibiting typical morphology and activity. In the first two stages, existing simulators from Prof. Christof Koch's lab (California Institute of Technology, USA) will be implemented as well as experimentally measured spatial and temporal Ve distributions from electrode arrays from Prof. Gyorgy Buzsaki's lab (Rutgers, USA). Recent in vitro studies indicate that in hippocampus electric field effects play a crucial role on neuronal synchronization. Based on these results, in the third stage, a reduced model will help us study the same effects on a neuronal population where features of small-world dynamics and synchronization will be investigated. All our theoretical conclusions will be compared to detailed experimental measurements.What effects do large excursions of Ve (up to 10 mV/mm for hippocampal sharp waves) have on the spiking activity of individual hippocampal pyramidal neurones? Will the firing of the neurone become entrained to the electric field through direct, so-called ephaptic, effects? How are these phenomena reflected upon a population of neurones firing? Are these effects manifested differently on the typical oscillatory frequencies that are attributed to diverse behavioural states? These are just a few of the questions we seek to investigate with this proposal.