This is a controversial issue, but some light is starting to be shone in this direction. Many neuroscientists assume that the electric fields generated by neurons are too weak to have any effect on their neighbours. However, recent research (Radman et al., 2007) has shown that weak electric fields (<5 V/m) within a broad spectrum of operating brain frequencies affect the firing properties of individual neurons. The researchers show that the nonlinear properties of an individual neuron can 'amplify' the effects of such small fields, effectively 'resonating' with the extracellular field.
"when concurrent to suprathreshold synaptic input, small electric fields can have significant effects on spike timing. For low-frequency fields, our theory predicts a linear dependency of spike timing changes on field strength. For high-frequency fields (relative to the synaptic input), the theory predicts coherent firing, with mean firing phase and coherence each increasing monotonically with field strength. Importantly, in both cases, the effects of fields on spike timing are amplified with decreasing synaptic input slope and increased cell susceptibility (millivolt membrane polarization per field amplitude). We confirmed these predictions experimentally using CA1 hippocampal neurons in vitro exposed to static (direct current) and oscillating (alternating current) uniform electric fields. In addition, we develop a robust method to quantify cell susceptibility using spike timing. Our results provide a precise mechanism for a functional role of endogenous field oscillations (e.g., gamma) in brain function and introduce a framework for considering the effects of environmental fields and design of low-intensity therapeutic neurostimulation technologies."
The researchers are thus fully aware of the importance of their findings in that they provide a framework within which others can develop neuro-therapies, as well as for researchers looking at the effects of environmental electromagnetic radiation. Add to that the not insignificant contribution to how the brain really functions! So much so that an open letter is appended to the research paper by David M. Alexander, RIKEN Brain Science Institute, Japan. "As reported by Massimini et al. (2004), slow-wave sleep EEG has been shown to take the form of a global spatio-temporal wave. Such waves are able to act as an 'external' source of electric fields to individual minicolumns in the cortex. There is now sufficient evidence to outline the case that large-scale electrical field dynamics do indeed play a causal role in brain activity, and to propose confirmatory experiments." The letter is also interesting in that it lists other papers that add weight to the Radman experiments, one paper going all the way back to 1984. Alexander sounds like a converted skeptic as he also quotes:"our [Radman et al.] results challenge the common view that extracellular slow potential oscillations represent mere epiphenomena without physiological significance per se."

Indeed, when a uniform AC electric field was applied the neuron fired coherently with the extracellular field, even at low field strengths of 1 V/m. The choice of a 30 Hz AC corresponds to the brain activity known as gamma waves (25-100Hz), although I'm not sure why they didn't pick the archetypical 40 Hz. This range of brain waves has been associated with a number of cognitive functions including consciousness itself. "Electric field-induced changes in spike timing would be particularly relevant for temporal coding during coherent (synchronous) network activity. For example, theta-modulated gamma activity in the hippocampus has been identified as a physiological correlate for a number of phenomena, including spatial navigation, memory, etc." Theta waves oscillate at 4-10 Hz so that combined with gamma activity they may collaborate in a kind of internal clock or a "pay attention!" mechanism.

I think this is an important step forward in a coherent theory of the brain and the mind.
References:
Spike Timing Amplifies the Effect of Electric Fields on Neurons: Implications for Endogenous Field Effects Thomas Radman, Yuzhuo Su, Je Hi An, Lucas C. Parra, and Marom Bikson. The Journal of Neuroscience, March 14, 2007
Is the EEG an epiphenomenon? David M. Alexander (21 October 2007)
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