Field Effects in the CNS Play Functional Roles

An endogenous electrical field effect, i.e., ephaptic transmission, occurs when an electric field associated with activity occurring in one neuron polarizes the membrane of another neuron. It is well established that field effects occur during pathological conditions, such as epilepsy, but less clear if they play a functional role in the healthy brain. Here, we describe the principles of field effect interactions, discuss identified field effects in diverse brain structures from the teleost Mauthner cell to the mammalian cortex, and speculate on the function of these interactions. Recent evidence supports that relatively weak endogenous and exogenous field effects in laminar structures reach significance because they are amplified by network interactions. Such interactions may be important in rhythmogenesis for the cortical slow wave and hippocampal sharp wave–ripple, and also during transcranial stimulation.

reports of functional fi eld effect interactions in the mammalian brain suggest that they are more common than previously accepted and are also shaped by the temporal dynamics of neural activity especially when relatively homogeneous populations of neurons are synchronously active (Bracci et al., 1999;Grenier et al., 2003;Vreugdenhil et al., 2005;Foffani et al., 2007;Frohlich et al., 2009;Anastassiou et al., 2010). That is, when the dipoles produced by a group of individual neurons are similarly oriented in space, neuronal population activity that is synchronous or coherent in phase produces a larger fi eld and a more powerful effect. Here, we review the recent work on fi eld effects in the context of their functional roles in neuronal communication, rather than in pathology. As previously, new results with the M-cell system provide insights not otherwise accessible at the single cell level.

FIELDS GENERATED BY NEURAL ACTIVITY AND THE PRINCIPLES OF FIELD EFFECT INTERACTIONS
Electrical fi eld effects are generated when extracellular currents associated with electrical activity of the dendrites, soma or axon of one or more neurons are suffi ciently large that they are channeled across the membranes of adjacent inactive neurons. These effects are greatest when the extracellular resistance is high, a condition which favors the fl ow of current along an alternative parallel pathway. Figure 1 illustrates the case of two neighboring neurons with similar orientations, typical of many cortical structures. The difference between the two examples is that the extracellular resistance is higher in Figure 1A than Figure 1B. In both, an EPSP in Figure 1A is associated with an inward current at the soma and, because of charge conservation, outward currents at the dendrites. The fi eld in the somatic region will be negative and, as noted above, the fi eld effect will be greater in Figure 1A because more current will be channeled across the somatic membrane of the inactive cell on the right. Geometry also plays a role, as polarization along the longitudinal axis of a pyramidal neuron results in a dipole and an open fi eld with currents and associated fi eld effects detectable far from the generator (Holt and Koch, 1999;Gold et al., 2006).

INTRODUCTION
The electrical fi eld produced by neural activity is commonly viewed as a measure of that activity rather than as a mechanism for infl uencing it. However, an infl uence can be exerted when currents associated with an extracellular fi eld (Ve) cross a region of cell membrane. In that case, the transmembrane potential, Vm, differs from the intracellular potential (Vi) and instead equals the difference Vi − Ve (Furukawa and Furshpan, 1963;Faber and Korn, 1989) (Figure 1). This notion is straightforward and is based upon fi rst principles, and thus, so called fi eld effects or ephaptic interactions, are well known to be theoretically feasible (Arvanitaki, 1942;Katz and Schmitt, 1942). However, they are most often treated as being of negligible magnitude and to be nonspecifi c. Indeed, a current generated across the membrane of one neuron will produce a fi eld that decays with distance and may affect all points at a fi xed distance equally. On this basis, it is diffi cult to imagine how an electrical fi eld effect might be useful in neural computations involving neurons interconnected with discrete and plastic synapses. Rather, fi eld effects, when recognized, are usually associated with dysfunction in neural circuits brought on by hypersynchrony, for example. They are thought to contribute to epileptic activity (Jefferys and Haas, 1982;Haas and Jefferys, 1984;Traub et al., 1985a,b;Jefferys, 1995;Dudek et al., 1998;Bikson et al., 2003;Grenier et al., 2003;Fox et al., 2004;Haglund and Hochman, 2005;Jiruska et al., 2010) and to crosstalk between demyelinated axons (Rasminsky, 1980) in multiple sclerosis (Smith and McDonald, 1999), and in trigeminal neuralgia (Love and Coakham, 2001;Prasad and Galetta, 2009).
There is an alternative view, namely that fi eld effects are not epiphenomena, but are specialized forms of neurotransmission that in some cases are known to mediate computations in neural circuits. Until recently, evidence for fi eld effects in the CNS, which depend upon structural features, such as the orientation and proximity of neurons, as well as the uniformity, anisotropy, and impedance in the extracellular medium, was restricted to a few systems, most notably that of the teleost Mauthner cell (Furukawa and Furshpan, 1963;Korn and Faber, 1975;Weiss et al., 2008). However, recent population activity (Autere et al., 1999), increases the extracellular resistivity, and increases the strength of fi eld effects in hippocampal slices . Notably, the administration of furosemide and mannitol, two agents that act by different mechanisms to prevent tissue swelling, suppresses epileptic activity in human cortex, perhaps by reducing fi eld effect interactions (Haglund and Hochman, 2005).
Another consideration is the superposition principle, that the fi elds produced by individual neurons spatially summate in space. On this basis, the orientation of neurons is a critical factor governing fi eld effect interactions. If multiple neurons are oriented in a parallel laminar orientation, such as pyramidal neurons in the neocortex and hippocampus, the electrical fi elds produced by synaptic currents can be additive, and an inactive neuron oriented in parallel with these neurons will experience depolarizations and hyperpolarizations of spatially separated regions due to interneuronal current fl ow.
A key factor in discerning the functional consequences of a fi eld effect interaction is the electrotonic properties of the neurons affected (Chan and Nicholson, 1986;Tranchina and Nicholson, 1986;Anastassiou et al., 2010). Cable and multicompartment In contrast, in radially symmetric neurons, such as stellate cells, somatic polarization produces a closed fi eld, and an extracellular potential restricted to the space within the range of the dendrites (Bishop and O'Leary, 1942;Lorente de No, 1947).
Recently, the extracellular fi elds produced by action currents of neurons with complex geometries have been estimated with multicompartment models and line source approximations using Coulomb's law extended to three-dimensional conducting media (Holt and Koch, 1999). Results from these simulations demonstrate that the type and distribution of ion channels outweighs dendritic morphology in determining the spatial orientation and amplitude of the fi eld generated by an action potential in modeled CA1 pyramidal neurons (Gold et al., 2006(Gold et al., , 2007, and that close to the axon hillock fi eld potentials can be several millivolts in magnitude, which may be strong enough to infl uence conduction at a node of Ranvier in a neighboring axon via a fi eld effect (Holt and Koch, 1999).
The importance of extracellular resistivity in determining how an electric fi eld produced by a neuron(s) affects its neighbor, as illustrated in Figure 1, has also been demonstrated experimentally. Tissue swelling, which occurs during pronounced neuronal  simulations have proved helpful for investigating these relationships, particularly the simple case of a cylinder with passive membrane properties in a constant or spatially inhomogenous fi eld. When the length of the cylinder is greater than the space constant (λ) the maximum polarization at the sealed ends approaches a constant value of λ multiplied by the magnitude of the electric fi eld (Chan and Nicholson, 1986; Figure 2A). If however this length is less than λ the polarization is decreased and is more linearly related to the position along the cylinder. When the cylinder is in an oscillatory spatially inhomogenous fi eld oriented along the dendro-somatic axis, the transmembrane polarization is maximized if the electronic length of the cylinder exceeds the distance between periodic values of fi eld strength, or in other words the spatial frequency of the fi eld. Also, polarization is strongest when the diameter of the cylinder is relatively large (Anastassiou et al., 2010). In such simulations the transients across the membrane have a more rapid rate of rise than when current is injected intracellularly ( Figure 2B) (Cartee and Plonsey, 1992;Svirskis et al., 1997a,b;Vigmond et al., 1997;Anastassiou et al., 2010). The reason is that with fi eld stimulation each line of the fi eld crosses the membrane in both directions and the total net charge on the membrane capacitance is zero at all times. In this case, the kinetics of the transient are due to the redistribution of charge and hence are proportional to the intracellular and extracellular conductivities.
These spatial and temporal properties of constant fi eld polarization have been experimentally verifi ed in isolated neurons (Svirskis et al., 1997a), and hippocampal slices using electrophysiological recordings, voltage sensitive dyes , and cell reconstructions (Radman et al., 2009). Both models and experiments show that electrotonic properties dictate how specifi c types of neurons will respond to an applied fi eld or a fi eld occurring in vivo.

ELECTRICAL INHIBITION IN SENSORIMOTOR INTEGRATION IN THE M-CELL SYSTEM
The teleost M-cell system that initiates the C-start escape behavior has served as the prototype for demonstrating fi eld effects in vivo (Furukawa and Furshpan, 1963). Monosynaptic inputs from ipsilateral inner ear afferents have mixed electrotonic and chemical excitatory synapses on the M-cell lateral dendrite (Pereda et al., 2004) and also have electrotonic synapses on interneurons which inhibit the M-cells. The inhibitory interneurons release glycine and also inhibit the M-cells via a fi eld effect Faber, 1975, 2005).
The latter occurs in a specialized region called the axon cap, with an extracellular volume resistivity that is approximately ninefold greater than the surrounding medium (Korn and Faber, 1975;Weiss et al., 2008). The axon cap surrounds the M-cell axon hillock and is penetrated by the unmyelinated axons of the feed-forward inhibitory interneurons (Figure 3). Action currents in these axons fl ow passively out at the terminals in the axon cap and some current fl ows inward across the M-cell axon hillock due to the high resistance of the axon cap, this inward current produces a signifi cant hyperpolarization of the M-cell, i.e., the M-cell is electrically inhibited.
We investigated the functional role of this electrical inhibition, using loud sounds to simulate a predatory strike. The auditory stimulus elicits synchronized action potentials in as many as 20 or more inhibitory interneurons, and the resulting action currents coincide with and counteract the sound evoked monosynaptic electrotonic excitation of the M-cell (Weiss et al., 2008). The amplitude of this electrical inhibition was ∼30-40% the size of the electrotonic excitation, and it was strong enough to prevent the M-cell from reaching threshold. Functional inhibition was confi rmed by showing that the same sound could elicit an M-spike when the electrical inhibition was neutralized by a cathodal current pulse produced by a second electrode in the axon cap. Furthermore, since a single M-spike initiates the C-start behavior by activating neural networks in the spinal cord (Korn and Faber, 2005) and sound evoked electrical inhibition coincides with the M-spike in ∼45% of trials in free swimming fi sh (Weiss et al., 2008), we concluded that electrical inhibition regulates the behavioral threshold.
The functional role of the electrical inhibition is best understood in the context of the extremely short utilization time of the M-cell, as little as 400 µs, which serves to ensure survival by triggering a rapid escape (Catania, 2009). Within this very short interval two important computations must take place. First, in order to determine whether an escape is warranted, the M-cell system must determine if the auditory stimulus is salient, as would be the case if it were produced by an attacking predator. Second, in order for the escape to be directed away from the sound source its location must be identifi ed and the appropriate left or right M-cell activated. Experimental results (Oda et al., 1998;Weiss et al., 2009) and neural simulations (Guzik et al., 1999) support the notion that these computations involve excitatory-inhibitory integration. Therefore, electrical inhibition, in complementing the electrotonic excitation, minimizes the escape latency while preserving the functionality of the neural circuit.
A similar type of electrical inhibition may occur between basket cells and Purkinje cells in the cerebellar cortex (Korn and Axelrad, 1980). However, electrical inhibitory synapses are less effi cient than classical chemical synapses, because a higher portion of the current fl ows extracellularly (Bennett, 1968). If electrical inhibition in the cerebellar cortex is indeed a reality, presumably only conditions in which a substantial number of inhibitory fi bers are synchronously active will result in a meaningful inhibition.

ELECTRICAL INTERACTIONS AT CHEMICAL SYNAPSES: VARIATIONS ON A THEME
In addition to the concept of electrical synapses involving fi eld effect transmission, there are suggestions that fi elds can modify chemical synaptic transmission, for example, by clearing negatively charged requires revisions since according to an equivalent circuit model this inhibition is of minimal amplitude, performs better in the dark, and is more effective in mediating positive rather than negative feedback (Dmitriev and Mangel, 2006) but see rebuttal by Fahrenfort et al. (2009).

FIELD EFFECTS IN THE HIPPOCAMPUS AND NEOCORTEX ASSOCIATED WITH SYNCHRONOUS ACTIVITY
Whereas in the example of the M-cell, sizeable fi eld effects can be generated by, or exerted on a single neuron, in the cortex and hippocampus tens of thousands of neurons per cubic millimeter of brain have multiple generators, such as chemical synapses and active conductances, that produce intercellular currents that are pooled together. The local fi eld potential (LFP) results from the sum of these intercellular currents and contains structure that correlates with attention, perception, movement, and memory (for example see, Wehr and Laurent, 1996;Buzsaki, 2002;Perez-Orive et al., 2002;Pesaran et al., 2002;Mehring et al., 2003;Womelsdorf et al., 2006;Fries et al., 2007). The LFP is estimated to represent a region with a radius of 100-250 µm in which neurons may share some common inputs and computational features (Katzner et al., 2009;Xing et al., 2009). On this basis, it is popular to regard the LFP as a sign of the underlying synchronous dynamics and computations in the neurons that produce the currents with which the LFP is associated. Here we instead ask whether glutamate molecules from the cleft by electrodiffusion (Sylantyev et al., 2008) or by infl uencing voltage gated channels involved in exocytosis (Voronin et al., 1999;Kasyanov et al., 2000;Voronin, 2000;Kamermans et al., 2001;Kamermans and Fahrenfort, 2004;Fahrenfort et al., 2009). Voronin and colleagues concluded that, at synapses in visual cortex and hippocampus, synaptic currents may be directed across the membrane of the pre-synaptic cell because of the high intracleft resistance resulting in a positive feedback loop (Voronin et al., 1999;Kasyanov et al., 2000;Voronin, 2000). A similar mechanism has been proposed to occur in Type I hair cells (Goldberg, 1996) and in synapses in the electrosensory system of Gymnarchus (Carr, 2004;Matsushita and Kawasaki, 2005).
It has been postulated that a synaptic fi eld effect mediates feedback between horizontal cells and cones in the retina (Kamermans and Fahrenfort, 2004). This feedback may contribute to establishing the center-surround organization of bipolar cells and ganglion cells (Kamermans et al., 2001;Kamermans and Fahrenfort, 2004;Fahrenfort et al., 2009). In this case, it is thought that currents fl owing into the horizontal cell at one cone-horizontal cell synapse passively fl ow out through gap junction hemichannels localized to another cone-horizontal cell synapse. The current is then directed across the pre-synaptic membrane of the cone and infl uences the opening of voltage gated calcium channels. Modeling studies suggest, however, that this proposed mechanism These studies have found that extremely weak fi elds (<0.5 mV/mm) are capable of signifi cantly modulating activity at the network and single cell level.
In one such study hippocampal slices were bathed in high K + to elicit spontaneous seizure-like activity. This spontaneous activity could be entrained to an exogenous pulsed electric fi eld produced by parallel plate electrodes oriented perpendicular to the somadendritic axis of area CA1 (Figure 2A). The threshold for inducing this entrainment, in area CA1, was ∼295 µV/mm (Francis et al., 2003), far lower than many extracellular fi eld gradients evident in vivo (Figure 4). In a similar study, hippocampal slices were bathed in kainate to elicit spontaneous activity in the beta and gamma frequency ranges (Deans et al., 2007). In the presence of an AC fi eld as small as 1 mV/mm, oriented as described above, the peak of the spontaneous oscillation frequency shifted from the spontaneous frequency to the frequency of the applied fi eld, ∼50 Hz, or its subharmonic.
These effects are remarkable considering that applied uniform DC fi elds alter the transmembrane potential in individual neurons by 0.18 mV/mm, and AC fi elds are even less effective (Deans et al., 2007). One explanation is that the small infl uence that a fi eld effect exerts across a large population of laminar neurons is amplifi ed by network interactions between the affected neurons (Purpura and McMurtry, 1965). For example, in spontaneously fi ring interconnected neurons a fi eld effect may induce small changes in spike timing (Radman et al., 2007;Anastassiou et al., 2010) that can increase synchronicity in excitatory chemical synaptic transmission thereby signifi cantly impacting network dynamics (Fujisawa et al., 2004). Theoretically, this amplifi cation would be maximized by a network confi guration of laminarly arranged neurons interconnected by chemical synapses, and also if spike timing in this network is suffi ciently synchronous to generate strong fi elds (Figure 5). Although, this amplifi cation also occurs in more complex network structures such as in the hippocampus (Francis et al., 2003;Fujisawa et al., 2004;Deans et al., 2007) and when ongoing spiking is relatively random (Francis et al., 2003).

EVIDENCE FOR A ROLE OF FIELD EFFECTS IN RHYTHMOGENESIS IN CORTEX AND HIPPOCAMPUS
Several studies support the notion that endogenous fi elds are involved in generating and maintaining neural oscillations (Bracci et al., 1999;Grenier et al., 2003;Park et al., 2005;Richardson et al., 2005;Vreugdenhil et al., 2005;Foffani et al., 2007;Frohlich et al., 2009). DC fi elds with intensities comparable to those of endogenous fi elds (<1 mV/mm) can accelerate the neocortical slow wave oscillation associated with deep sleep (Steriade et al., 1993), by uniformly depolarizing the soma of layer 5 pyramidal neurons and decreasing the time spent in the down state. Similarly, amplitude matched AC sine waves (<1 Hz), and waves identical to those recorded in vivo, can entrain and amplify the slow oscillation (Frohlich et al., 2009).
Field effects have also been implicated in rhythmogenesis in tetanus-induced gamma oscillations recorded in hippocampal slices. In this case intercellular action currents entrain pyramidal neurons to fi re at gamma frequency (Bracci et al., 1999;Vreugdenhil et al., 2005). Paroxysmal events with characteristics of high-frequency oscillations in the neocortex may be generated currents associated with the LFP can infl uence neural dynamics and participate in neural computation via fi eld effects (Jefferys, 1995;Bullock, 1997).
One obstacle to investigating the infl uence of the electric fi eld associated with the LFP is that it is technically challenging to experimentally manipulate the fi elds, to test for effects on network function because of the complex spatial structures of endogenous fi elds and the fi ltering characteristics of brain tissue (Bédard et al., 2004;Logothetis et al., 2007). With this shortcoming in mind, one experimental approach has been to measure the threshold electric fi eld strength at which fi eld effects are induced in vitro in hippocampus and cortex, and compare it to electric fi eld strength measured in vivo (Figure 4) (Francis et al., 2003;Fujisawa et al., 2004;Deans et al., 2007;Radman et al., 2007;Frohlich et al., 2009).

FIGURE 4 | A comparison of the strength of endogenous electric fi elds with that of exogenous fi elds shown to alter spike timing in vitro.
Approximate strength of endogenous electrical fi elds resulting from normal activity in the cortex and hippocampus (blue arrows), as well as the in the M-cell system (yellow arrow, vertical line indicates range). The approximate fi eld strength of epileptic discharges (green arrow and vertical line). Spike timing in hippocampal slices (red arrows) is altered by exogenous fi elds that are considerably weaker in strength.
Nevertheless, fi eld effects are ideal to mediate synchronization of fast oscillations, such as paroxysmal events and the sharp waveripple complex, since temporal constraints imposed by membrane capacitance are reduced ( Figure 2B) (Cartee and Plonsey, 1992;Svirskis et al., 1997a;Anastassiou et al., 2010). For example, modeling demonstrates that, due to a fi eld effect, an action potential in one pyramidal neuron is transmitted to a neighboring pyramidal cell as a biphasic spikelet, lasting 1-2 ms (Vigmond et al., 1997). Similar spikelets can also result from action currents conducted across gap junctions between pyramidal neurons in the hippocampus (Bennett and Pereda, 2006;Mercer et al., 2006). Field effects may be able to mediate neurotransmission even more rapidly, and consequently also participate in fast rhythmogenesis (Stacey et al., 2009).

FIELD EFFECTS AND COMPUTATIONS IN SINGLE NEURONS
While the aforementioned studies provide preliminary evidence that fi eld effects infl uence network dynamics in the hippocampus and neocortex, evidence for a computational role in these structures is lacking. In this context the example of the Mauthner cell may be instructive. There integration of fi eld effect inhibition with chemical and electrotonic excitation defi nes the threshold of activation and consequently the performance of the corresponding C-start behavior. Whether or not fi eld effects play a similar role for the diverse computations performed by single hippocampal and neocortical neurons is unknown.
The infl uence of fi eld effects on spike timing in single neurons has been described (Radman et al., 2007;Anastassiou et al., 2010) and underlies the described network effect in Figure 5 (Fujisawa et al., 2004). When an intracellular current ramp is applied to CA1 pyramidal neurons in the presence of a DC fi eld or an AC fi eld in the gamma frequency band the spikes produced by the ramp are advanced or delayed by the applied fi eld (Radman et al., 2007). Similarly, spatially inhomogenous theta and sharp wave fi elds, derived from in vivo experimental data, were found to infl uence excitability and infl uence spike timing in simulated cortical pyramidal neurons, particularly in the apical dendrites (Anastassiou et al., 2010). Whether such effects are also important in by a similar mechanism and may also involve slow shifts in the transmembrane potential via fi eld effect interactions (Grenier et al., 2003).
The sharp wave-ripple complex described in area CA1 of the hippocampus (O'Keefe and Nadel, 1978) may involve fi eld effect interactions as well (Buzsaki et al., 1992). First, the synaptic currents generated on the apical dendrites of pyramidal neurons by Schaffer collateral activation during the sharp wave could infl uence the timing of dendritic spikes in neighboring neurons (Anastassiou et al., 2010). Second, the pooled currents that contribute to the high-frequency ripple, thought to be generated by perisomatic GABAergic synapses (Buzsaki et al., 1992;Ylinen et al., 1995;Klausberger et al., 2003Klausberger et al., , 2004, or in part by gap junctions (Draguhn et al., 1998;Traub and Bibbig, 2000;Maier et al., 2002;Nimmrich et al., 2005;Roopun et al., 2010), could promote neuronal discharges during the trough of the ripple oscillation (Buzsaki et al., 1992;Ylinen et al., 1995;Chrobak and Buzsaki, 1996) via fi eld effect interactions (Bikson et al., 2003;Foffani et al., 2007;Jiruska et al., 2010). In support of this hypothesis, hippocampal slices from epileptic rats with a lower tissue resistivity at the somatic layer of area CA3 due to sclerosis exhibit smaller amplitude fi eld effects and abnormal high-frequency ripples (Foffani et al., 2007). The frequency of the ripple is thought to increase because of a desynchronization between individual cell activation and the network oscillation.
If in fact field effects do mediate the sharp wave-ripple complex they may be involved in determining the pattern of pyramidal cell activation that is transferred to entrorhinal cortex (Chrobak and Buzsaki, 1996) and neocortex (Siapas and Wilson, 1998;Sirota et al., 2003;Girardeau et al., 2009;Wierzynski et al., 2009). It is unclear if this interaction could be computationally advantageous as opposed to a form of crosstalk, since the functional topographical organization of the hippocampus is still not entirely established (Jung et al., 1994;Redish et al., 2001;Maurer et al., 2005;Kjelstrup et al., 2008;Lubenov and Siapas, 2009  tors (Liebetanz et al., 2002;Nitsche et al., 2003;Siebner et al., 2004), although this conclusion has been contested (Ardolino et al., 2005). Also, tDCs induced plasticity has been attributed to the involvement of catecholamines , acetylcholine (Kuo et al., 2007), and alterations of excitatory-inhibitory balance (Stagg et al., 2009). Studying transcranial electrical stimulation may provide insights to the functional roles of fi eld effects in neural circuits (Ozen et al., 2009), since fi elds similar in strength to those that occur endogenously infl uence memory encoding (Kirov et al., 2009), consolidation (Marshall et al., 2006), and perception (Kanai et al., 2008). For example, a slow AC fi eld <1 Hz applied during non-REM sleep was shown to increase cortical slow oscillations and slow spindle activity and enhance retention in a declarative memory task in humans (Marshall et al., 2006). The mechanism that underlies this impressive result was investigated in an in vivo rat model (Ozen et al., 2009). Application of a similar transcranial 1 Hz signal could entrain spiking in neocortical neurons. Unexpectedly, the degree of entrainment was dependent on the intrinsic oscillatory state of the animal, as correlated with the stage of the sleep/wakefulness cycle. Entrainment was also observed in regions of cortex distant from the stimulating electrode, i.e., where the electric fi eld amplitude was minimal. Therefore, network interactions act to amplify a fi eld effect not only in vitro, but also in vivo, which may explain why transcranial application of weak fi elds can perhaps infl uence plasticity and induce dramatic and long lasting behavioral effects.

CONCLUSION
Over a decade's worth of progress in the study of the functional role of fi eld effects in the nervous system supports the conclusion that such interactions should be considered when discerning the biophysical basis of network dynamics and computation. However, prudence is required in assigning functionality to biophysical mechanisms in neural systems, especially since fi eld effects are diffi cult to experimentally defi ne and antagonize. Experiments that will overcome these boundaries and offer more defi nitive evidence must simultaneously record intracellularly and extracellularly in vivo (Grenier et al., 2003;Harvey et al., 2009) to determine the actual transmembrane potential, simulate or partially negate fi eld effects in this setting with electrical stimulation (Weiss et al., 2008), and implement computer simulations to confi rm the experimental data (Mori et al., 2008;Anastassiou et al., 2010). The pace of research in this area is sure to accelerate, given the interest in clinical applications, and it is likely that in the decade to come functional fi eld effect interactions will become increasingly recognized in diverse brain structures. ACKNOWLEDGMENTS S. A. Weiss and D. S. Faber would like to acknowledge Dr. Flavio Frohlich, for his comments on this manuscript and related work, and Drs. Michael Bennett, Jose Luis Péna, and Alberto Pereda for input during the evolution of this work. a computational context in single neurons depends on the strength of the fi eld, the pattern of the synaptic activity, and the nature of the computation in question.
One potential computational mechanism that could involve fi eld effect interactions is spike-phase coding. This involves converting the excitatory drive in individual neurons in to a phase value relative to the LFP (O' Keefe and Recce, 1993;Hopfi eld, 1995;Fries et al., 2007;Jacobs et al., 2007;Huxter et al., 2008;Montemurro et al., 2008;Pastalkova et al., 2008;Kayser et al., 2009). This conversion is thought to occur because such neurons receive phasic synaptic activity in addition to the primary excitatory drive. If fi eld effects also participated in spike-phase encoding by providing feedback between the phasic LFP and individual neurons it would be advantageous since the amplitude of polarization resulting from a fi eld effect is independent of membrane potential (Faber and Korn, 1989) and fi eld effects could provide a common oscillatory reference frame. It is unclear however if fi elds with amplitudes suffi cient to subserve this role indeed occur during sensory processing or behavior, and it seems unlikely to be the case for spike-phase encoding for hippocampal place cells (Harvey et al., 2009).
If fi eld effects do indeed participate in computations in single neurons, an important consideration is how such effects are regulated. The onset (Fries et al., 2007;Buzsaki, 2002) and offset (Poulet and Petersen, 2008) of oscillations in the LFP accompany sensory processing and behavior and could also signify the regulation of the corresponding fi eld effect. These events, as well as the strength, temporal and spatial characteristics of a fi eld, are determined by network parameters such as synchronicity (Klausberger et al., 2003;Klausburger and Somogyi, 2008), and the balance of excitation and inhibition within a network (Atallah and Scanziani, 2009).

FIELD EFFECTS AND TRANSCRANIAL ELECTRICAL STIMULATION-INVESTIGATIONAL TOOL AND PROMISING NEW THERAPEUTIC MODALITY
Understanding fi eld effects in the CNS may also have important clinical applications. Strong fi elds produced by surgically implanted electrodes positioned in the hippocampi, may be able to entrain seizures (Richardson et al., 2003;Sunderam et al., 2009), while weak DC and AC fi elds produced by the transcranial application of current have been shown to have a wide variety of effects that are potentially useful therapeutically (Wasserman, 2008).
In the case of transcranial DC stimulation (tDCs), it was well established, by Purpura and McMurtry (1965) for one, that applying anodal DC to the cortical surface increases neuronal activity and paroxysmal events, whereas cathodal stimulation reduces neuronal activity (Figure 2A). The effect appears to be primarily mediated by fi eld interactions with voltage sensitive cation channels on the neuron (Chan et al., 1988;Lopez et al., 1991;Liebetanz et al., 2002). It has also been speculated that effects that outlast the stimulation (Reis et al., 2009) may be mediated by modulation of NMDA recep-