The Origin of Extracellular Fields and Currents — EEG, Ecog, LFP and Spikes

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The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes

György Buzsáki1,2,3, Costas A. Anastassiou4 and Christof Koch4,5 Abstract | Neuronal activity in the brain gives rise to transmembrane currents that can be measured in the extracellular medium. Although the major contributor of the extracellular signal is the synaptic transmembrane current, other sources — including Na+ and Ca2+ spikes, ionic fluxes through voltage- and ligand-gated channels, and intrinsic membrane oscillations — can substantially shape the extracellular field. High-density recordings of field activity in animals and subdural grid recordings in humans, combined with recently developed data processing tools and computational modelling, can provide insight into the cooperative behaviour of neurons, their average synaptic input and their spiking output, and can increase our understanding of how these processes contribute to the extracellular signal.

Electric current contributions from all active cellular Recent advances in microelectrode technology processes within a volume of brain tissue superimpose using silicon-based polytrodes offer new possibilities at a given location in the extracellular medium and for estimating input–output transfer functions in vivo,

generate a potential, Ve (a scalar measured in Volts), and high-density recordings of electric and magnetic with respect to a reference potential. The difference in fields of the brain now provide unprecedented spatial

Ve between two locations gives rise to an electric field coverage and resolution of the elementary processes (a vector whose amplitude is measured in Volts per involved in generating the extracellular field. In 1Center for Molecular and distance) that is defined as the negative spatial gradient addition, novel time-resolved spectral methods provide Behavioural Neuroscience, of Ve. Electric fields can be monitored by extracellularly insights into the functional meaning of the information- Rutgers, The State University placed electrodes with submillisecond time resolution rich high-frequency bands of the V signal3,4. These of New Jersey, e 197 University Avenue, and can be used to interpret many facets of neuronal new developments have led to a more in-depth Newark, New Jersey 07102, communication and computation (FIG. 1). A major understanding not only of the relationship between USA. advantage of extracellular field recording techniques is network activity and cognitive behaviour5 but also of 2New York University that, in contrast to several other methods used for the the pathomechanisms in brain diseases6. Neuroscience Institute, New York University Langone investigation of network activity, the biophysics related Several excellent but somewhat dated reviews Medical Center, New York, to these measurements are well understood. This has discuss various aspects of extracellular signals in the – New York 10016, USA. enabled the development of reliable and quantitative brain2,7 25. Here we provide an overview of our present 3Center for Neural Science, mathematical models to elucidate how transmembrane understanding of the mechanisms that underlie New York University, New currents give rise to the recorded electric potential. the generation of extracellular currents and fields. York, New York 10003, USA. 4Division of Biology, Historically, Ve has been referred to as the electro- Although all nervous structures generate extracellular California Institute of encephalogram (EEG) when recorded from the scalp, fields, our focus is the mammalian cerebral cortex, Technology, 1200 East as the electrocorticogram (ECoG) when recorded by as most of our quantitative knowledge is the result of California Boulevard, subdural grid electrodes on the cortical surface, and studies in cortex. Pasadena, California 91125, USA. as the local field potential (LFP; also known as micro-, 1 5Allen Institute for Brain depth or intracranial EEG ) when recorded by a small- Contributors to extracellular fields Science, 551 North 34th size electrode in the brain (BOX 1; FIG. 1). The term ‘local Any excitable membrane — whether it is a spine, Street, Seattle, Washington field potential’ (meaning an electric potential (Ve)), is dendrite, soma, axon or axon terminal — and any 98103, USA. a regrettable malapropism, but we continue to use the type of transmembrane current contributes to the Correspondence to G.B. e-mail: gyorgy.buzsaki@ term LFP because it is familiar to most neuroscientists. extracellular field. The field is the superposition of nyumc.org The magnetic field induced by the same activity is all ionic processes, from fast action potentials to the doi:10.1038/nrn3241 referred to as the magnetoencephalogram (MEG)2. slowest fluctuations in glia. All currents in the brain

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a b superimpose at any given point in space to yield Ve

V at that location. Thus, any transmembrane current, Cz µ Depth irrespective of its origin, leads to an intracellular as

150 (LFP) SM well as an extracellular (that is, LFP) voltage deflection.

V µ The characteristics of the LFP waveform, such as the

800 amplitude and frequency, depend on the proportional Grid EC contribution of the multiple sources and various (ECoG) properties of the brain tissue. The larger the distance Strip of the recording electrode from the current source, the (ECoG) HC less informative the measured LFP becomes about the events occurring at the location(s) of the source(s). This Strip is mainly owing to the fact that the V amplitude scales (ECoG) Am e with the inverse of the distance r between the source Fz Scalp and the recording site, and to the inclusion of other EEG O2 (interfering) signals (leading to ‘spatial averaging’). In 1 s 1 s addition to the magnitude and sign of the individual c current sources, and their spatial density, the temporal 1000 100 coordination of the respective current sources (that

500 V) is, their synchrony) shapes the extracellular field. µ Thus, extracellular currents can emerge from multiple 0 0 sources, and these are described below. iEEG ( MEG (fT) –500 –100 –1000 1 s Synaptic activity. In physiological situations, synaptic activity is often the most important source of extracellular current flow. The idea that synaptic d I LFP surface currents contribute to the LFP stems from the II recognition that extracellular currents from many individual compartments must overlap in time to induce III a measurable signal, and such overlap is most easily LFP depth achieved for relatively slow events, such as synaptic 7,10,23 IV Intracellular currents . The dendrites and soma of a neuron form a tree-like structure with an electrically conducting V interior that is surrounded by a relatively insulating

20 mV membrane, with hundreds to tens of thousands of VI synapses located along it. Neurotransmitters acting on Figure 1 | Extracellular traces using different recording methods are synaptic AMPA and NMDA receptors mediate excitatory + 2+ fundamentally similar. a | Simultaneous recordings fromNature three Reviewsdepth electrodes | Neuroscience (two currents, involving Na or Ca ions, respectively, selected sites each) in the left amygdala and hippocampus (measuring the local field which flow inwardly at the synapse. This influx of cations from the extracellular into the intracellular cortex (measuring the electrocorticogram (ECoG); two four-contact strips placed under space gives rise to a local extracellular sink. To achieve the inferior temporal surface (measuring the ECoG); an eight-contact strip placed effective electroneutrality within the time constants of over the left orbitofrontal surface (measuring the ECoG); and scalp electroencephalo- relevance for systems neuroscience, the extracellular graphy (EEG) over both hemispheres (selected sites are the Fz and O2) in a patient with sink needs to be ‘balanced’ by an extracellular source, drug-resistant epilepsy. The amplitude signals are larger and the higher-frequency that is, an opposing ionic flux from the intracellular to patterns have greater resolution at the intracerebral (LFP) and ECoG sites compared to scalp EEG. b | A 6 s epoch of slow waves recorded by scalp EEG (Cz, red), and LFP (blue) the extracellular space, along the neuron; this flux is recorded by depth electrodes placed in the deep layers of the supplementary motor area termed passive current or return current. Depending on (SM) and entorhinal cortex (EC), hippocampus (HC) and amygdala (Am). Also shown are the location of the sink current(s) and its distance from multiple-unit activity (green) and spikes of isolated neurons (black ticks). c | Simultaneously the source current(s), a dipole or a higher-order n-pole recorded magnetoencephalogram (MEG; black) and anterior hippocampus depth EEG is formed (FIG. 2a). The contribution of a monopole to (red) from a patient with drug-resistant epilepsy. Note the similar theta oscillations Ve scales as 1/r, whereas the contribution of a dipole recorded by the depth electrode and the trace calculated by the MEG, without any phase decays faster, as 1/r2; this steeper decay is due to the two delay. d | Simultaneously recorded LFP traces from the superficial (‘surface’) and deep opposing charges that comprise the dipole cancelling (‘depth’) layers of the motor cortex in an anaesthetized cat and an intracellular trace each other out to first order. from a layer 5 pyramidal neuron. Note the alternation of hyperpolarization and Notably, GABA subtype A (GABA ) receptor- depolarization (slow oscillation) of the layer 5 neuron and the corresponding changes in A mediated inhibitory currents are typically assumed the LFP. The positive waves in the deep layer (close to the recorded neuron) are also – known as delta waves. iEEG, intracranial EEG. Part a courtesy of G. Worrell, Mayo Clinic, to add very little to the extracellular field as the Cl Minneapolis, Minnesota, USA, and S. Makeig, University of California at San Diego, USA. equilibrium potential is close to the resting membrane 26,27 Part b is reproduced, with permission, from REF. 157 © (2011) Cell Press. Part c courtesy of potential . However, in actively spiking neurons the S. S. Dalal, University of Konstanz, Germany, and J.-P. Lachaux and L. Garnero, Université membrane is depolarized, and therefore inhibitory (and de Paris, France. Part d is reproduced, with permission, from REF. 158 © (1995) Society often hyperpolarizing) currents can generate substantial for Neuroscience. transmembrane currents28–30 (FIG. 2b,c).

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Fast action potentials. Fast (Na+) action potentials gen- the extracellular medium27. Although Na+ spikes gener- (FIG. 2d) erate the strongest currents across the neuronal mem- ate large-amplitude Ve deflections near the soma , brane and can be detected as ‘unit’ or ‘spike’ activity in until recently they were thought not to contribute substantially to the traditionally considered LFP band (<100 Hz) or to the scalp-recorded EEG10,16, because Box 1 | Recordings methods of extracellular events the strongest fields they generate are of short duration (<2 ms) and nearby neurons rarely fire synchronously Electroencephalography in such short time windows under physiological con- Electroencephalography (EEG) is one of the oldest and most widely used methods for ditions31. However, synchronous action potentials from the investigation of the electric activity of the brain10,16. The scalp electroencephalogram, recorded by a single electrode, is a spatiotemporally smoothed version of the local many neurons can contribute substantially to high- field potential (LFP), integrated over an area of 10 cm2 or more. Under most conditions, it frequency components of the LFP. Therefore, with has little discernible relationship with the firing patterns of the contributing individual appropriate methods, valuable information can be neurons16, and this is largely due to the distorting and attenuating effects of the soft and extracted from the LFP about the temporal structure of hard tissues between the current source and the recording electrode. The recently spiking neuronal populations (see below). introduced ‘high-density’ EEG recordings, in combination with source-modelling that can account for the gyri and sulci (as inferred from structural MRI imaging) of the Calcium spikes. Other non-synaptic events that can 16,146,147 subject, have substantially improved the spatial resolution of EEG . contribute prominently to the extracellular field are Magnetoencephalography the long-lasting (10–100 ms) Ca2+-mediated spikes32. Magnetoencephalography (MEG) uses superconducting quantum interference devices Because voltage-dependent regenerative Ca2+ spikes are (SQUIDs) to measure tiny magnetic fields outside the skull (typically in the 10–1,000 fT often triggered by NMDA receptor-mediated excitatory 2 range) from currents generated by the neurons . Because MEG is non-invasive and has a postsynaptic potentials (EPSPs)33–36, separating 2, it has them from EPSPs in extracellular recordings is not become a popular method for monitoring neuronal activity in the human brain. An advantage of MEG is that magnetic signals are much less dependent on the straightforward. A potential differentiating factor is that, 2+ conductivity of the extracellular space than EEG. The scaling properties (that is, the in contrast to EPSPs, Ca spikes can actively propagate frequency versus power relationship) of EEG and MEG often show differences, typically within the cell and can therefore generate fields across in the higher-frequency bands. These differences may be partly explained by the the laminar boundaries of afferent inputs. Ca2+ spikes capacitive properties of the extracellular medium (such as skin and scalp muscles) that can also be triggered by back-propagating somatic distort the EEG signal but not the MEG signal148. action potentials37, in which case they are independent Electrocorticography of synaptic activity. Because dendritic Ca2+ spikes are Electrocorticography (ECoG) is becoming an increasingly popular tool for studying large (10–50 mV) and long lasting37–39, their share in the various cortical phenomena in clinical settings149. It uses subdural platinum–iridium or measured extracellular events can be substantial under stainless steel electrodes to record electric activity directly from the surface of the certain circumstances (FIG. 3). Unfortunately, very little cerebral cortex, thereby bypassing the signal-distorting skull and intermediate tissue. is known about Ca2+ spikes in vivo40. The spatial resolution of the recorded electric field can be substantially improved (<5 mm2)102 by using flexible, closely spaced subdural grid or strip electrodes (FIG. 1). Intrinsic currents and resonances. Ih currents and Local field potential I currents are prominent examples of intrinsic, EEG, MEG and ECoG mainly sample electrical activity that occurs in the superficial T voltage-dependent membrane responses39. layers of the cortex. Electrical events at deeper locations can be explored by inserting metal or glass electrodes, or silicon probes into the brain to record the LFP (also known Although synaptically induced voltage changes are a prerequisite for the activation of voltage-dependent contains both action potentials and other membrane potential-derived fluctuations in a hyperpolarization-activated cyclic nucleotide (HCN)- gated and T-type calcium channels, the large membrane studying cortical electrogenesis. Many observation points, with short distances and extracellular currents that these channels generate between the recording sites and with minimal impact on brain tissue, are needed to are not synaptic events. These and other voltage- achieve high spatial resolution. In principle, the spiking activity of nearly all or at least a gated currents contribute to intrinsic resonance and representative fraction of the neuron population in a small volume can be monitored oscillation of the membrane potential. Several neuron with a sufficiently large density of recording sites. Additional clues about the types possess resonant properties; that is, they respond intracellular dynamics can be deduced from the waveform changes of the 99,150 more effectively to inputs of a particular frequency extracellular action potentials . Progress in this field has been accelerated by the 39 availability of micro-machined silicon-based probes with ever-increasing numbers of range . When intracellular depolarization is sufficiently recording sites,151,152. strong, the resonant property of the membrane can give way to a self-sustained oscillation of the voltage. Voltage-sensitive dye imaging Voltage changes can also be detected by membrane-bound voltage-sensitive dyes or Voltage-dependent resonance and oscillations at theta by genetically expressed voltage-sensitive proteins. Using the voltage-sensitive frequency have been described in principal neurons of 39,41–44 dye imaging (VSDI) method, the membrane voltage changes of neurons in a region of several cortical regions . By contrast, perisomatic interest can be detected optically, using a high-resolution fast-speed digital camera, at inhibitory interneurons have a preferred resonance in the peak excitation wavelength of the dye. A major advantage of VSDI is that it directly the gamma frequency (30–90 Hz) range45,46. Because resonance is both voltage- and frequency-dependent39,41, potential. A second advantage is that the provenance of the signal can be identified if a its impact on the magnitude of the extracellular field can known promoter is used to express the voltage-sensitive protein. Limitations are vary in a complex manner. To contribute substantially to 156 inherent in all optical probe-based methods , and for VSDI these include interference the LFP, resonant membrane potential fluctuations must with the physiological functions of the cell membrane, photoxicity, a low occur synchronously in nearby neurons, a feature that signal-to-noise ratio and the fact that it can only measure surface events. most often occurs in inhibitory interneurons.

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a d Sink µV By convention, a site on the Membrane potential 100 10 1 0.1 neuronal membrane where 100 positive charges enter the 1 nA neuron. 10–1 Electroneutrality The phenomenon that, owing 10–2 to charge conservation, at any 0.1 µV given point in time the total 10–3 charge entering and leaving the Normalized power cell across all of its membrane 10–4 equals zero. 100 101 102 103 Frequency (Hz) Sources Locations along the neuronal b c membrane where positive 400

600 m) charge flows out of the neuron. µ 300 SLM 10 µV For negative charge, the m

–70.0 200 µ location of sinks and sources is 400 SR 100 inverted. 100

Vm 0

Count SP Return current 200 –100 –70.5 SO A loop current that flows in the

–200 V Distance from SP ( Distance from opposite direction to an active 40 mV –0.4 0.0 0.4 0.8 5 ms

0 50 sink or source. –30 –15 0 15 30 ms Amplitude (normalized) Dipole Figure 2 | Excitatory and inhibitory postsynaptic currents are the most ubiquitous contributors to V . An ideal electric dipole is Nature Reviews | Neurosciencee defined by two charges of a | Computer-simulated local field potential (LFP) traces (left panel; grey) in response to an excitatory synaptic current opposite polarity with infinitely input (a sink, shown by the blue circle) injected into the distal apical dendrite of a purely passive layer 5 pyramidal model small separation, such that the neuron. The waveform of the injected current is illustrated in the box. Red and blue contour lines correspond to positive product of the charge times the and negative values for the LFP amplitude, respectively. The calculated double logarithmic power spectra of the distance r separating them transmembrane potential are also shown (right panel), following injection of current into the apical dendrite near the remains finite. The electric injection site (blue trace), mid-apical dendrite (green trace) and soma (orange trace). Note that high-frequency activity potential of a dipole falls off decreases with the distance from the active synaptic site (that is, the sink). b | A monosynaptic inhibitory connection 2 as 1/r . between a putative layer 3 entorhinal cortical interneuron (red circle) and intracellularly recorded pyramidal cell (blue triangle). Below it, a cross-correlogram between the spikes of the reference interneuron (at time 0, red line) and the Equilibrium potential The voltage difference between pyramidal cell and, superimposed on it, the spike-triggered average of the membrane potential (Vm) of the pyramidal cell intracellular and extracellular (in blue). Note the small, short-latency hyperpolarization (the dip) superimposed on the rising phase of the intracellular space of a neuron when the net theta oscillation and the corresponding decreased spike discharge of the pyramidal cell. c | Inhibition-induced LFPs. LFPs ionic flux across the membrane were generated in the vicinity of a pyramidal neuron (bottom cell) by intracellularly induced action potentials in a nearby equals zero. basket cell (top cell), and were recorded extracellularly at six sites in multiple layers of the hippocampus. The mean LFP amplitude at each site is shown by the blue squares. Example LFP traces (blue) from six sites and the action potential of the I currents h basket cell (red trace) are shown on the right. Note that the largest positive response by inhibition-induced Currents flowing through hyperpolarization occurs near the soma. d | Extracellular contribution of an action potential (‘spike’) to the LFP in the hyperpolarization deinactivated vicinity of the spiking pyramidal cell. The magnitude of the spike is normalized. The peak-to-peak voltage range is cyclic nucleotide-gated channels. indicated by the colour of the traces. Note that the spike amplitude decreases rapidly with distance from the soma, without a change in polarity within the pyramidal layer (the approximate area of which is shown by the box), in contrast to IT currents Low-threshold the quadrupole (that is, reversed polarity signals both above and below the pyramidal layers) formed along the (hyperpolarization-induced) somatodendritic axis. The distance-dependence of the spike amplitude within the pyramidal layer is shown (bottom left transient Ca2+ currents, which panel) with voltages drawn to scale, using the same colour identity as the traces in the boxed area in d. The same traces are often lead to burst firing. shown normalized to the negative peak (bottom right panel). Note the widening of the spike with distance from the soma, owing to greater contributions from dendritic currents and intrinsic filtering of high-frequency currents by the cell Resonance membrane. SLM, stratum lacunosum moleculare; SO, stratum oriens; SP, stratum pyramidale; SR, stratum radiatum. Part a A property of the neuronal is reproduced, with permission, from REF. 83 (2010) Springer. Part b is reproduced, with permission, from REF. 137 membrane to respond to some © © input frequencies more (2010) Society for Neuroscience. Part c is reproduced from REF. 29 © (2009) Macmillan Publishers Ltd. All rights reserved. strongly than others. At the Part d courtesy of E. W. Schomburg, California Institute of Technology, USA. resonant frequency, even weak periodic driving can produce large-amplitude oscillations. Spike afterhyperpolarizations and ‘down’ states. afterhyperpolarizations (AHPs) can be as large (and last Elevation of the intracellular concentration of a certain as long as) synaptic events, AHPs also contribute to the Silicon probes 48 Multiple-site recording ion may trigger influx of other ions through activation of extracellular field , particularly when bursting of nearby electrodes for high spatial ligand-gated channels, and this will in turn contribute to neurons occurs in a temporally coordinated fashion: for density monitoring of the 49 Ve. For example, bursts of fast spikes and associated den- example, following hippocampal sharp-wave events . extracellular field. The dritic Ca2+ spikes are often followed by hyperpolarization In the intact brain, responses to unexpected stimuli or recordings sites can record Ve 2+ along one, two or even three of the membrane, owing to activation of a Ca -mediated movement initiation are often associated with relatively + 47 orthogonal axes. increase of K conductance in the somatic region . long-lasting (0.5–2 s) LFP shifts, which might be medi- As the amplitude and duration of such burst-induced ated by synchronized AHPs. This slow LFP is often

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A Extra Ba referred to as Bereitschaftspotential50, readiness potential 51

0.2 mV or contingent negative variation . Bb 50 mV During non-rapid eye movement (non-REM) sleep, 50 ms the membrane potential of cortical neurons periodically 2 s shifts (0.5–1.5 Hz) between a hyperpolarized ‘down’ Bc state and a more depolarized ‘up’ (that is, spiking) state52 (FIGS 1d,3D). At least part of the cessation of spiking during the down states can be explained by –50 mV Intra Bd AHPs of the synchronously bursting pyramidal cells –70 mV in the up state48,53. The temporally coordinated silent down state of nearby neurons is associated with a Cover-glass C Vdend positive Ve in infragranular layers and a negative Ve Agar 1.0 ECoG Pia in the supragranular layers (these down states are also 1 48,54–56 10 mV known as delta waves ). Various mechanisms Vdend 2/3 0.5 contribute to these state transitions, including a 4 gradual decrease in extracellular Ca2+ concentration 5 ∆ F/F ECoG spike amplitude (mV) 0.0 and a corresponding decrease in synaptic transmission, 50% 0 25 50 10 ms 53,57 Slow potential inactivation of Ih channels , and other network amplitude (mV) effects52. As the largest-amplitude up–down shifts of D E the membrane voltage occur in large layer 5 pyramidal D1 D2 D3 D4 neurons53,58, it has been suggested that the large voltage 473 nm; 140 µW shifts in the somata of the synchronously active–silent neurons induce the formation of an extracellular dipole between deep (infragranular) and superficial (supragranular) layers48,58. Neither interneurons nor the thalamocortical inputs are active during the down state, 593 nm; 220 µW so that the down state (characterized by delta waves) is a 10 ms disfacilitatory, non-synaptic event that can be mimicked 100 ms 200 µV by synchronous hyperpolarization of nearby pyramidal Figure 3 | Non-synaptic contributions to the LFP. Ca2+ spikes, disfacilitation and neurons (FIG. 3E). disinhibition contribute to the local field potential (LFP). A | Voltage-dependence of a theta-frequency oscillation in a hippocampal pyramidal cell dendrite . A continuous Gap junctions and neuron–glia interactions. Direct recording of extracellular (extra) and intradendritic (intra) activity in a hippocampal CA1 electric communication between neurons through pyramidal cell is shown. The holding potential was manually shifted to progressively more gap junctions (also known as electrical ‘synapses’)59–61 depolarized levels by intradendritic current injection. The recording electrode contained 49,62,63 QX-314 to block Na+ spikes. Note the large increase in the amplitude of the intradendritic can enhance neuronal synchrony . Although gap theta oscillation upon depolarization. Arrows, putative high-threshold Ca2+ spikes junctions allow ionic movement across neurons and, phase-locked to the LFP theta oscillation. Ba | Dendritic Ca2+ spikes (shown by an arrow) therefore, do not involve any extracellular current flow, have a large amplitude and are long-lasting . Bb–Bd | The response of a CA1 pyramidal they can affect neuronal excitability and contribute cell to ventral hippocampal commissural stimulation (vertical arrows) paired with dendritic indirectly to the extracellular field. depolarization. Such inhibition can delay (Bb), prevent (Bc) or abort (Bd) the dendritic Ca2+ Membrane potential changes in non-neuronal cells, spike. LFPs recorded from a nearby electrode in the pyramidal layer show the timing and such as glia, may also give rise to V . Recent studies on 2+ e magnitude of the stimulation (lower traces in Bb–Bd). Note that the number of Na spikes neuron–glia interactions have indicated that the glial 2+ remains approximately the same, irrespective of the presence or absence of the Ca spike. syncytium may contribute to slow and infraslow (<0.1 Hz) C | Whisker stimulation-evoked dendritic Ca2+ spikes correlate with surface cortical LFP field patterns1,64,65. These slow LFPs may arise from glia, changes. The setup for recording the electrocorticogram (ECoG), intradendritic potential 66–68 2+ glia–neuron interactions or from vascular events . (Vdend) and Ca fluorescence is shown in the left panel. The relationship between the intradendritic potential amplitude (horizontal arrows) and simultaneously measured Ca2+ F/F) is shown in the middle panel. The ECoG response as a function of the Ca2+ spike Ephaptic effects. Neurons are surrounded by a (‘slow potential’) amplitude is shown in the right panel. D | ‘Down’ states in cortical conducting medium — the extracellular space — pyramidal cells during sleep produce extracellular LFP ‘delta’ waves. Shown are and can therefore ‘sense’ the electric gradients they simultaneously recorded LFP (top) and unit activity (bottom) at three layer 5 intracortical generate during neuronal processing. In fact, the effect of gradients brought about by synchronous down states (shaded areas), reflected as positive waves (delta waves) in the LFP, can be population activity along cable-like dendrites can either strongly localized (in D2 and D3) or more widespread (in D1 and D4). E | Generation be mimicked by appropriate intracellular current of extracellular potentials by depolarization or hyperpolarization of a limited number of injections69,70. This raises the question of whether the CA1 neurons that express both channelrhodopsin 2 (ChR2) and halorhodopsin, in response to blue (top) and yellow (bottom) light . Note the depolarization-induced negative spatiotemporal field fluctuations in the brain are merely LFP (top) and the hyperpolarization-induced positive LFP (bottom) in the pyramidal layer. an epiphenomenon of coordinated cellular activity or Part A is reproduced, with permission, from REF. 159 ©B is reproduced, whether they also have a functional ‘feedback’ (or even with permission, from REF. 160 © (1996) National Academy of Sciences. Part C is amplification) role by affecting the discharge properties reproduced from REF. 161 © (1999) Macmillan Publishers Ltd. All rights reserved. Part D is of neurons71. That is, do they serve any function for reproduced, with permission, from REF. 56 © (2005) Cambridge Journals. Part E courtesy of the organism or are they like the heartbeat, a useful E. Stark, New York University, Langone Medical Center, USA. diagnostic epiphenomenon? Given the resistivity of

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the extracellular medium in the mammalian brain explains why the amplitude of the LFP decreases from and the highly transient nature of spikes, it is unlikely rat to cat, and from cat to primate86,87. Another reason that spikes from individual neurons greatly affect the why brain size affects the magnitude of the extracellular excitability of nearby neurons through ephaptic coupling. current is that mammals with smaller brains have smaller However, the situation is very different when many pyramidal neurons, which are therefore more densely neurons are simultaneously active, as such synchrony packed compared to mammals with larger brains88, can generate strong spatial gradients in the extracellular leading to a smaller conductivity σ. Indeed, all LFP voltage. Experiments have shown that small-amplitude, patterns have larger amplitude in the mouse brain than slow-frequency application of extracranial currents in the rat brain89. (trans-cranial electrical stimulation) has a detectable Another important geometric factor that affects effect on neuronal activity72 and cognitive function73; the magnitude of the extracellular current flow is the the small but effective voltage gradients brought about highly folded nature of the cortex in higher mammals10. in brain tissue by such external fields are comparable to When the cortical sheet bends to form a gyrus, the the voltage gradients produced by population patterns apical dendrites are pushed closer to each other on in vivo under physiological conditions70,74–76. Ephaptic the concave side, and current density becomes higher coupling has been shown to affect population activity compared to when the apical dendrites occupy the during hypersynchronous epileptic discharges77,78. convex side of the curve16. The influence of tissue Furthermore, ephaptic feedback may enhance spike– curving on the LFP is particularly striking in the dentate field coherence and bias the preferred spiking phases gyrus–hippocampus–subiculum axis, where concave with respect to the LFP also under physiological and convex bends alternate90. In subcortical structures, conditions75,76,79–81; for example, during hippocampal spatial regularity of neurons and afferents is much less sharp waves or theta waves70,76,77. prominent. Nevertheless, afferent fibres from one source may have some asymmetric distribution on spherically Neuronal geometry and architecture symmetric neurons (for example, cortical afferents to All neuron types contribute to the extracellular field, the medium spiny neurons of the striatum91), whose but their relative contribution depends in part on the temporally synchronous activity can generate spatially shape of the cell. Pyramidal cells are the most populous distinct sinks and sources. cell type. They have long, thick apical dendrites that can generate strong dipoles along the somatodendritic Temporal scaling properties axis. Such dipoles give rise to an open field, as there is Geometric factors alone cannot fully explain the considerable spatial separation of the active sink (or magnitude of the extracellular current. For example, Ephaptic coupling The effect of the extracellular the source) from the return currents. This induces the cerebellum is a perfectly ordered structure with field on the transmembrane substantial ionic flow in the extracellular medium stratified inputs and a single layer of giant Purkinje potential of a neuron. (FIG. 2). Therefore, neurons that generate open fields, neurons, but it generates very small extracellular such as pyramidal cells, make a sizeable contribution fields92. This is because cerebellar computation is Open field When the sink (or the source) is to the extracellular field. By contrast, spherically mainly local and therefore does not require the substantially spatially symmetric neurons — such as thalamocortical cells cooperation of large numbers of neurons. However, separated from the return — that emanate dendrites of relatively equal size in all when synchrony is imposed on the cerebellar cortex currents of the dipole. directions, can give rise to a closed field82. However, a from the outside, large-amplitude LFP signals can strictly closed field only occurs when several dendrites emerge from cerebellar circuits93. Thus, in addition to Closed field When the sink (or the source) is are simultaneously activated. As this is rarely the case, cytoarchitecture, a second critical factor in determining minimally spatially separated depolarization of a single dendrite generates a small the magnitude of the extracellular current is the from the return currents of the dipole even in spherically symmetric cells83. temporally synchronous fluctuations of the membrane dipole. Assuming a homogeneous medium, the two most potential in large neuronal aggregates. Synchrony,

Power law (of LFP) important determinants of the extracellular field strength which is often brought about through network The power law of LFP describes are the spatial alignment of neurons and the temporal oscillations, explains why different brain states are a relationship between the synchrony (discussed in the next section) of the dipole associated with dramatically different magnitudes of amplitude of the extracellular moments they generate13,22,84. In cytoarchitecturally LFP9–14. A consistent quantitative feature of the LFP is signal and its temporal regular structures, such as the cortex, the apical dendrites that the magnitude of LFP power (that is, the square of frequency. A descending straight line on the log–log plot of pyramidal neurons lie parallel to each other and the the Fourier amplitude) is inversely related to temporal n (power versus frequency) afferent inputs run perpendicular to the dendritic frequency f, that is, there is 1/f scaling with n = 1–2 would be an indication of a axis. This geometry is ideal for the superposition (the exact value of n depends on various factors)94,95. power law that scales as 1/fn. of synchronously active dipoles and is the primary These features have given rise to much speculation

Low-pass frequency filtering reason why LFPs are largest in cortex. In the rodent regarding the relationship between network features A process by which the hippocampus, the somata of pyramidal cells occupy only of the brain and the extracellular signal (see below), frequency components of a a few rows. By contrast, in the human hippocampus the although a strict power law behaviour of the LFP is still signal beyond a cutoff cell bodies are vertically shifted relative to each other being debated94,96–98. frequency are increasingly and form a wider somatic layer85. As a result, the source The 1/fn scaling of the LFP power can be primarily attenuated, typically owing to low-pass frequency filtering a serial capacitance (for currents from the soma flow in the opposite direction attributed to the property 83,99,100 example, the bi-lipid to the sink currents from the dendrites of neighbouring of dendrites . Simulations have shown that in membrane). neurons, effectively cancelling each other. This partly layer 5 pyramidal neurons (FIG. 2a) the effect of a

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high-frequency local input (100 Hz) to the distal The role of volume conduction in Ve dendrite can be detected extracellularly near the The electric field specifies the forces acting upon a distal dendritic segment, whereas the signal is charged particle. The field is defined at every point attenuated approximately 100-fold near the soma. of space from which one can measure a force ‘felt’ by Slower signals (for example, 1 Hz) are attenuated much an electric charge, and it can be transmitted through less. The low-pass filtering effect of a purely passive volume (for example, through brain tissue); a neuron depends on the distance between the soma and phenomenon known as volume conduction. The origin the location of the input, and on the membrane time of the volume-conducted field is the return currents of constant27. This suggests that dendritic morphology the dipoles18,22,83. The extent of volume conduction is an important factor in frequency filtering and depends on the intricate relationships between the that pyramidal cells, with their long dendrites, are current dipole and the features of the conductive particularly effective low-pass filters. However, as the medium84,112. Consequently, some LFP patterns can electrotonic length and input resistance of neurons can be recorded far away from the source, whereas others be effectively altered by synaptically induced excitatory remain relatively local. The most robust demonstration and inhibitory conductance changes26,101, the frequency of the importance and extent of volume conduction is filtering performance of neurons depends not only on that return currents from active dipoles in brain tissue the geometric characteristics of the neurons but also can be measured on the scalp by electric recording on their physiological state. Another frequently cited methods (BOX 1). cause of high-frequency attenuation of the LFP is the Assuming that conductivity in the brain is purely 96,102 ohmic capacitive nature of the extracellular medium itself , , the Ve induced by a current dipole depends on although the capacitive and inductive properties of the the magnitude and location of the current source, and brain tissue remain a subject of debate16,24,103. on the conductivity of the extracellular medium. In turn, Network mechanisms also contribute to the 1/fn conductivity in the medium depends on the degree of feature of the power spectrum. In a brief time window, isotropy and homogeneity of the medium and is there- only a limited number of neurons can be recruited in fore a function of a number of factors, including the a given volume, whereas in longer time windows the geometry of the extracellular space. The relationship current source density activity of many more neurons can contribute to the LFP, between Ve and the (CSD) J (meas- therefore generating larger amplitude LFP at slower ured in A m–2) at a particular point of brain tissue is frequencies. This frequency dependence is also given by Maxwell’s equations of electromagnetism, that reflected in the phase coherence–distance relationship, in their simplified form (that is, when the magnetic con- → → with lower-frequency signals having higher coherence tributions can be neglected) dictate ∇(σ Ve) = –∇ J , compared to high-frequency signals. Provided that where σ→ (amplitude measured in S m–1) is the extracel- neuronal recruitment occurs within the time constant lular conductivity tensor. The properties of σ→ crucially of an integrating mechanism (for example, NMDA or affect the waveform and functionality of the spatiotem-

GABAB receptors have a slow time constant, whereas poral Ve deflections. Assuming that the extracellular

AMPA or GABAA receptors have a fast time constant), milieu can be satisfactorily described by a purely homo-

the amplitude of low-frequency LFP components will geneous and isotropic ohmic conductivity σ, Ve is gov- 2 be larger than the amplitude of high-frequency LFP erned by Laplace’s equation ∇ Ve = 0, with the boundary

components. Finally, the different network oscillations condition along a cable-like source described by σ Ve = J generated in the cerebral cortex show a hierarchical (with J as the transmembrane current density). For a relationship5,104,105, often expressed by cross-frequency single point source in an unbounded isotropic volume 106–111 Phase–amplitude coupling coupling between the various rhythms . As the conductor, the solution is Ve = I/4πσr, in which I (unit, The power of a faster phase of the slower oscillations modulates the power A) is the current amplitude of the point source and r oscillation is phase-modulated of higher-frequency events (a phenomenon known as (unit, m) is the distance from the source to the measure- by a slower oscillation. phase–amplitude coupling), the duration of the faster ment. Multiple current sinks and sources then combine Ohmic events is limited by the ‘allowable’ phase of the slower linearly by the superposition principle. Conceptually, Electrical current flow through event. In summary, multiple mechanisms can contribute the point-source equation is key to computing the a purely resistive milieu. The to the 1/fn power scaling. extracellular potential in response to any transmem- extracellular cytoplasm is Although the phenomenological 1/fn relationship brane current. It also follows that the transmembrane primarily ohmic in the 1–10,000 kHz frequency may capture various statistical aspects of brain dynamics voltage, often used in intracellular versus extracellular range. at longer timescales, it should be emphasized that comparisons, is a relatively poor estimator of the LFP, most neuronal computation takes place in short time whereas the transmembrane current is a more reliable Current source density windows (from tens to hundreds of milliseconds). estimator99. The above calculations assume that the (CSD). The current source density reflects the rate of The spectral properties of such short time windows extracellular medium is homogeneous and isotropic current flow in a given direction strongly deviate from the scale-free frequency–power (that is, a constant σ). Measurements of the extracellular through the unit surface (unit, distribution and are often dominated by oscillations or medium in the relevant frequency range (<10 kHz) have A m–2) or volume (unit, A m–3). sensory input-triggered ‘evoked’ or ‘induced’ events. not yet fully resolved this issue, with some experiments These stimulus-driven, transient LFP events are the concluding that the extracellular medium is anisotropic Anisotropic 24,113 Ansiotropic tissue can conduct physiologically relevant time windows from which one and homogeneous , and others suggesting that it is 68,103,114 electricity in a direction- aims to infer neuronal computation from the mean field strongly anisotropic, inhomogeneous and may dependent manner. behaviour of neuronal populations13. even possess capacitive features91,96,97.

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Striking examples of volume-conducted events have extracellular space) and sinks (that is, cations flowing been described in hemispherectomized patients over into the cell) that give rise to the LFP, the concept of the missing hemisphere115. Furthermore, auditory- CSD is useful. CSD is a quantity that represents the evoked brain stem responses recorded over the scalp volume density of the net current entering or leaving are a clinically used diagnostic tool that is based on the extracellular space113,121. Consider a distant current volume conduction116. Volume conduction clearly source relative to three linearly and equally spaced poses problems for the interpretation of the functional recording sites in a homogenous volume (FIG. 4). Each meaning of the relationship between signals recorded electrode will measure some contribution to the field from different brain locations. For example, two nearby from the distant source, and the voltage difference dipoles with different orientations can produce volume- between the middle and side electrodes will be small. conducted fields at distant sites. When the coherence As a consequence, the difference between the ‘voltage between signals recorded at these distant sites increases differences per distance’ (that is, the second spatial –2 (for example, as a function of behaviour), this may derivative of Ve, a vector with units of V m ) between be falsely interpreted to reflect some ‘dynamic’ or the middle and side electrodes is small; an indication ‘functional coupling’ between the circuits residing at that the field can be attributed to a distant source. By the sites of the recording electrodes, even though the contrast, if the three electrodes span the location of coherence increase was brought about by the temporal the current-generating synapse or neuron group, the shifts between the two close dipoles117. For these reasons, voltage at the three recording sites will be unequal verification of the local nature of the signal always and the difference magnitude of this derivative will be requires the demonstration of a correlation between the large; an indication of the local origin of the current. LFP and local neuronal firing. The current flow between two recording sites can be calculated from the voltage difference and resistivity The inverse problem of LFP using Ohm’s law, provided that information about Extracellular signals provide information about the conductance (which is inversely proportional to the collective behaviour of aggregates of neurons, resistivity) of the tissue is available (0.15–0.35 Ω m particularly with regard to the temporal scales of their in brain tissue68,103,113). The conductance is a factor of activity. However, the same macroscopic extracellular both conductivity and the specific geometry of volume. signal can be generated by diverse cellular events. Using high-density recording probes to monitor the Thus, a seemingly similar theta oscillation in the LFP, it is possible to precisely determine the maximum hippocampus and neocortex may be brought about CSD and therefore the exact location of the current by different elementary mechanisms. A common sink (or source). obstacle in interpreting the ‘mean field signal’ is the ‘inverse problem’16,118. The inverse problem arises Interpreting current density. Unfortunately, it is not when attempting to infer the microscopic variables possible to conclude using CSD measurement alone from the macroscopic ones — in this case, inferring whether, for example, an outward current close to the characteristics of the primary current dipoles the cell body layer is due to active inhibitory synaptic from the spatiotemporal profile of the volume- currents or reflects the passive return current of active conducted field. The inverse problem is commonly excitatory currents impinging along the dendritic arbor. dealt with by first solving the ‘forward problem’ — The missing information may be obtained by selectively deriving macroscopic variables from their elementary, stimulating the various anatomically identified inputs causal constituents — and then using the established to the recorded circuit (FIG. 4). This process helps to relationships between microscopic and macroscopic attribute the sinks (and sources) to the known sources variables to gain insight into the microscopic events of synaptic inputs106,122. In addition to anatomical from the macroscopic patterns. The first step in this knowledge, simultaneous intracellular recordings from process is to identify the contribution of the suspected representative neurons within the population responsible synaptic and non-synaptic mechanisms of the LFP by for the generation of the LFP may be required. correlating the macroscopic events (that is, the LFP) Alternatively, it is possible to record extracellularly from and the microscopic events119,120,122. The second step is identified pyramidal cells and inhibitory interneurons to experimentally recreate the LFP from its primary in the same volume of tissue and use the spike–field constituents, such as synaptic currents and the spiking correlations to determine whether, for example, a local patterns of various neuron types. The technical current is an active hyperpolarizing current or a passive means required to create such LFP patterns are now return current from a more distant depolarizing event. available (FIG. 3E). Alternatively, synthetic mean fields Unfortunately, ambiguity may still remain if the sinks can be generated in network models of neurons in and sources are generated by a non-synaptic mechanism which events in the different domains of the neurons rather than by a synaptic mechanism. are timed on the basis of experimentally observed Somatic hyperpolarization brought about by temporal patterns. the activity of perisomatic basket neurons44,123 also generates a voltage gradient between the soma Localizing the current sinks and sources: CSD analysis. and dendrites (inhibitory dipole; FIGS 2b,c,4a,b). As In deciphering the location of the current sources (that dendritic excitation and somatic inhibition result in is, cations flowing from the intracellular space to the the same direction of current flow, the excitatory and

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a b Recordings close to source CSD close to source o

r Recordings far from source CSD far from source

hf 0.5 mV 150 mV mm–2 100 ms 100 ms

c d o p

r CA1 Source

hf Sink CA3

2 mV 100 ms Figure 4 | Identifying current sources. a | A current source–sink dipole, embedded in a homogeneousNature Reviews and |isotropic Neuroscience conductive medium, that is induced by barrage-like inhibitory input (shown by the red symbol) impinging on the perisomatic region. Lines show the iso-potentials (red, positive; blue, negative). A triplet of linearly and equally spaced recording electrodes (shown in yellow) is located near the soma (top), that is, close to the current source, and another is located far from

the current source. b | Ve traces (left panels) measured at the three equally spaced locations relative to an ideal infinite (reference) site. The middle trace in the top panel is from the electrode positioned closest to the soma. The voltage contribution induced by the active dipole decays in the medium as the inverse square of the distance (compare with FIG. 2a).

The current source density (CSD) traces (right panels) are calculated from the voltage traces. Although dipole-induced Ve can be measured far from the source, CSD is spatially confined and can therefore help to identify the anatomical location of the dipole. c | Simultaneous recordings from 96 sites (six shanks (represented by columns in the figure) with 16 recording sites each (LFP traces shown in grey)) in a behaving rat. Simultaneously recorded evoked field responses in the CA1–dentate gyrus axis of the rat hippocampus (black lines show the outline of the layers) in response to electrical stimulation of entorhinal afferents are shown. Such trisynaptic activation of CA1 pyramidal cells is reflected as negative LFP (and sink, blue) in the apical dendritic layer (stratum radiatum, r). The black rectangle indicates missing channels. d | A CSD map of average spontaneously occurring sharp waves. Note the nearly identical distribution of sinks and sources in CA1 during the evoked responses and sharp waves, supporting the idea that sharp waves reflect CA3-induced depolarization of the apical dendrites of CA1 neurons. Selective activation of known afferents thus can be used to ‘calibrate’ the locations of sinks and sources, and relate them to the CSD distribution of spontaneously occurring LFP events. hf, stratum lacunosum-moleculare; o, stratum oriens; p, pyramidal layer. Parts c and d courtesy of J. Csicsvari, Institute of Science and Technology, Austria, and D. Sullivan, New York University, Langone Medical Center, USA.

inhibitory return currents will superimpose in the measured correlation between LFP and spiking activity extracellular space, resulting in large-amplitude LFPs. can vary substantially even within a small volume. Although strong somatic inhibition can enhance the Such variable coupling between LFP and unit firing magnitude of the LFP, it may at the same time ‘veto’ the may be one of the sources of the controversy regarding occurrence of action potentials in pyramidal cells. This the contribution of LFP versus spikes to the functional complex relationship is the reason why large-amplitude MRI (blood oxygen level-dependent (BOLD)) signal extracellular current flow may be associated with because often there is a strong correlation between strong spiking, moderate spiking or no spike output LFP power in the gamma-frequency band and spiking at all from the pyramidal neurons. As a result, the activity23,124.

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a b No interneurons No pyramidal cells 1 200 No spikes 15 14 12 10 10 0.5 100 5 8 6

0 (dB) Power 4 Frequency (Hz) Frequency

Power decrease (%) decrease Power 2 Firing rate (normalized) Firing rate 0 0 –5 0 0 200 400 0 200 400 0 200 400 0 200 400 100 600 Time (ms) Time (ms) Frequency (Hz)

Figure 5 | Spike contribution to the LFP. a | Average multiunit recording of the visual cortex of a monkey during Nature Reviews | Neuroscience time–frequency–power difference plots demonstrating the difference between baseline power (in dB) and power in and synchrony of units after stimulus onset. The arrow indicates sustained gamma frequency oscillation. b | The effect of local field potential (LFP) ‘de-spiking’ on spectral power. The figure shows the percentage change of power at different frequencies after de-spiking the LFP. Thick lines indicate the frequencies at which there was a significant difference between the original LFP power and the power of the LFP after removing interneuron spikes (No interneurons), pyramidal cell spikes (No pyramidal cells) or all spikes (No spikes). Part a is reproduced from REF. 162. Part b is reproduced, with permission, from REF. 111 © (2012) Society for Neuroscience.

The CSD method described above is, in principle, bands135,136 (FIG. 5). However, when spike AHPs are applicable to any other a priori identified rhythmic also considered, the contribution of action potentials or transient LFP event. However, it is important may be substantial in the lower-frequency range as to emphasize that conventional one-dimensional well, even in the absence of synaptic transmission119. (typically along the somatodendritic axis) estimation Thus, increased power in the higher-frequency bands of CSD is possible only in a situation in which the can be regarded as an index of spiking synchrony. LFP varies little in the lateral direction, that is, within Third, high-frequency power has a restricted spatial the same layer. The assumption is often not satisfied component: it increases in layers with a high density when the layers curve. In this case, two-dimensional of cell bodies111,137 and axon terminals. Fourth, high- estimation of the CSD, using equally spaced high- frequency power, which largely reflects spiking activity, density electrodes in both vertical and horizontal co-varies with LFP components that emanate from directions, is required113,125. Further complications arise postsynaptic potentials and other non-spike-related when several dipoles are involved in the generation membrane voltage fluctuations18,22,23,86,98,100–112,133,136. of LFP patterns, particularly when these dipoles are Fifth, the high-frequency power can be phase-locked temporally disparate, as is the case in the generation to lower-frequency oscillations; this occurs because it is of most cortical patterns48,126,127. Nevertheless, the largely the phase-locked spiking neurons that generate above strategies have been successfully used in the the rhythmic extracellular currents22,23,86,111,112,133,136. identification of evoked and spontaneous LFP patterns Last, the high-frequency power of extracellular in multiple brain regions121,122,128,129. The ever-increasing LFP provides indirect access to the spike outputs of density of recording sites on silicon-based recording neurons4,111,124,138. Together, these aspects show that probes130 in combination with optogenetic tools131 will spike ‘contamination’ of the LFP should be regarded help us to disentangle the contribution of multiple as good news, in that high-frequency LFP power dipoles. can provide a ‘proxy’ for the assessment of neuronal outputs. The ‘mesoscopic’ information provided by Spike contribution to the LFP the high-frequency band of the LFP is therefore an As noted above, any transmembrane current important link between the macroscopic-level EEG contributes to the LFP, including currents that are and the microscopic-level spiking activity of neuronal generated by action potentials. The action potential assemblies. includes not only the ‘spike’ itself but also spike- induced AHPs, which have durations and magnitudes Conclusions and future directions that vary for different neuron types and that can change Electric currents from all excitable membranes as a function of brain state132. The spike contribution contribute to the extracellular voltage. These currents to the LFP has important implications. First, increased emerge mainly from synaptic activity but often with spiking generates a broad-frequency spectrum with a substantial contributions from Ca2+ spikes and other power distribution that depends on the composition of voltage-dependent intrinsic events, as well as from the active cell types95,98,111,133,134. Second, both increased action potentials and spike afterpotentials. The two spike frequency and synchrony increase spectral most important factors contributing to the LFP are power, particularly in the higher-frequency (>100 Hz) the cellular-synaptic architectural organization of

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Theta SPW-R

ori ori CA1 pyr CA1 pyr * * rad rad

Im Im mol mol gc gc

CA3 CA3 hil hil

Figure 6 | Spikes are embedded in unique synapsembles and spatially distributed LFP. Spike-triggered averages of the local field potential (LFP) in the hippocampus during exploration (left panel) and sleep (right panel). During Nature Reviews | Neuroscience exploration, spikes were sampled while the rat ran on a linear track for a water reward; during sleep, spikes were sampled during sharp wave-ripples (SPW-R). Recordings were made by an eight-shank (300 m intershank distance), 256-site silicon prove (32 recording sites on each shank, linerarly spaced 50 m apart). The LFP was smoothed both within and across shanks. The LFP was triggered by the spikes of a fast-firing putative interneuron in CA1 stratum oriens (ori; shown by a star). Both panels show a 100 s snapshot of the LFP map at the time of the spike occurrence. Note that during exploration (left panel), the spike is associated with synaptic activity (negative wave, hot colours) mainly in the stratum lacunosum-moleculare (lm; shown by an arrow) and the dentate molecular layer (mol), indicating entorhinal cortex activation. During sleep (right panel), activity arises in CA3 and invades the CA1 stratum radiatum (rad; shown by an arrow). We propose that such LFP ‘snapshots’ reflect unique constellations of cell assemblies responsible for the discharge of the neuron. The LFP map changes characteristically with time (see Supplementary information S1 and S2 (movies)). We suggest that the time-evolving constellation of the LFP map or vector reflects a unique distribution of postsynaptic potentials (that is, synapsembles139) brought about by the evolving spike assemblies within and upstream of the hippocampus. Sufficiently high-density LFP recordings can therefore be informative of the evolving cell assemblies that

the network and synchrony of the current sources. steps are required to reveal the spiking content of The extracellular potential can be reconstructed from the LFP patterns. In the intact brain, spiking neurons simultaneous monitoring of several current source are embedded in interconnected networks and may generators across the neuronal membrane, provided be influenced by the local electric field through that sufficient details are known about the contributing ephaptic effects. Therefore, the output spikes of sources and the extracellular milieu. This forward the cell assemblies within and across networks are reconstruction is theoretically possible because the transformed into spatially distributed transmembrane 139 physical processes underlying the generation of Ve are events through synaptic activity (‘synapsembles’) . Of mostly understood. The forward reconstruction of the course, these transmembane events are responsible for LFP is accelerated by advancements in microelectrode the LFP. We suggest that as the composition of spiking technology and other new methods, and developments assemblies varies over time, the spike patterns induce in computational modelling. Reconstruction of the unique patterns of LFPs, which vary from moment to LFP signal from the measured current sources and moment (for example, from one gamma cycle to the sinks can, in turn, provide insights into resolving next). Recording the LFP from a sufficiently large and the inverse problem, that is, the deduction of the representative neuronal volume with sufficiently high microscopic processes from the macroscopic LFP spatial density may therefore provide access to the measurements. time-evolving synaptic currents brought about by the A practically important application of the forward– spiking assemblies (FIG. 6; Supplementary information inverse relationship would be the reconstruction of cell S1 and S2 (movies)). Such synapsembles139, reflected assembly sequences from the constellation of the LFP. indirectly by the LFP vectors, can be as informative Cell assemblies can be defined as a temporal coalition about the encoded information as the spiking cell of neurons — typically within gamma cycles — the assemblies themselves140–142. In support of this idea, it collective action of which can lead to the discharge of has been shown that during cognitive tasks, the spatial a downstream ‘reader’ neuron139. Such assemblies (or distribution of spectral power varies in a task-relevant ‘neural letters’) are organized into assembly sequences manner98,134,143–145. We foresee that the spatially resolved, (or ‘neural words’) by the slower rhythms. Although wide-band LFP signal, which contains information the temporal organization of neuronal dynamics about both afferent patterns and assembly outputs, may can be effectively inferred from the cross-frequency turn out to be the most useful signal for understanding coupling of the various brain rhythms, additional neuronal computations11,13,135.

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153. Siegel, M. S. & Isacoff, E. Y. A genetically encoded dependent phase-precession of action potentials. Scientific Thinking and the Human Frontiers Science Program optical probe of membrane voltage. Neuron 19, Hippocampus 8, 244–261 (1998). (grant RGP0032/2011). Parts of this Review were written 735–741 (1997). 160. Buzsáki, G., Penttonen, M., Nádasdy, Z. & Bragin, A. while G.B. was a visiting scholar at the Interdisciplinary 154. Grinvald, A. & Hildesheim, R. VSDI: a new era in Pattern and inhibition-dependent invasion of Center for Neural Computation, Hebrew University, functional imaging of cortical dynamics. Nature Rev. pyramidal cell dendrites by fast spikes in the Jerusalem (2007) and at the Zukunftskolleg Program, Neurosci. 5, 874–885 (2004). hippocampus in vivo. Proc. Natl Acad. Sci. USA 93, University of Konstanz, Germany (2011). We thank G. 155. Akemann, W., Mutoh, H., Perron, A., Rossier, J. & 9921–9925 (1996). Einevoll, E. Schomburg and J. Taxidis for their comments on Knopfel, T. Imaging brain electric signals with 161. Helmchen, F., Svoboda, K., Denk, W. & Tank, D. W. the manuscript. genetically targeted voltage-sensitive fluorescent In vivo dendritic calcium dynamics in deep-layer proteins. Nature Methods 7, 643–649 (2010). cortical pyramidal neurons. Nature Neurosci. 2, Competing interests statement 156. Denk, W. et al. Anatomical and functional imaging of 989–996 (1999). The authors declare no competing financial interests. neurons using 2-photon laser-scanning microscopy. 162. Ray, S. & Maunsell, J. H. R. Different origins of gamma J. Neurosci. Methods 54, 151–162 (1994). rhythm and high-gamma activity in macaque visual FURTHER INFORMATION 157. Nir, Y. et al. Regional slow waves and spindles in cortex. PLoS Biol. 9, e1000610 (2011). György Buzsáki’s homepage: http://www.med.nyu.edu/ human sleep. Neuron 70, 153–169 (2011). buzsakilab/ 158. Contreras D. & Steriade M. Cellular basis of EEG slow Acknowledgements Christof Koch’s homepage: http://www.klab.caltech.edu rhythms: a study of dynamic corticothalamic The authors are supported by the National Institutes of relationships. J. Neurosci. 51, 604–622 (1995). Health (grants NS34994, MH54671 and NS074015), the SUPPLEMENTARY INFORMATION 159. Kamondi, A., Acsády, L., Wang, X. J. & Buzsáki, G. Swiss National Science Foundation (grant PA00P3_131470), See online article: S1 (movie) | S2 (movie) Theta oscillations in somata and dendrites of the G. Harold and Leila Y. Mathers Charitable Foundation, the ALL LINKS ARE ACTIVE IN THE ONLINE PDF hippocampal pyramidal cells in vivo: activity- US–Israel Binational Foundation, the Global Institute for

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