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1.  Different Origins of Gamma Rhythm and High-Gamma Activity in Macaque Visual Cortex 
PLoS Biology  2011;9(4):e1000610.
High-gamma (80–200 Hz) activity can be dissociated from gamma rhythms in the monkey cortex, and appears largely to reflect spiking activity in the vicinity of the electrode.
During cognitive tasks electrical activity in the brain shows changes in power in specific frequency ranges, such as the alpha (8–12 Hz) or gamma (30–80 Hz) bands, as well as in a broad range above ∼80 Hz, called the high-gamma band. The role or significance of this broadband high-gamma activity is unclear. One hypothesis states that high-gamma oscillations serve just like gamma oscillations, operating at a higher frequency and consequently at a faster timescale. Another hypothesis states that high-gamma power is related to spiking activity. Because gamma power and spiking activity tend to co-vary during most stimulus manipulations (such as contrast modulations) or cognitive tasks (such as attentional modulation), it is difficult to dissociate these two hypotheses. We studied the relationship between high-gamma power, gamma rhythm, and spiking activity in the primary visual cortex (V1) of awake monkeys while varying the stimulus size, which increased the gamma power but decreased the firing rate, permitting a dissociation. We found that gamma power became anti-correlated with the high-gamma power, suggesting that the two phenomena are distinct and have different origins. On the other hand, high-gamma power remained tightly correlated with spiking activity under a wide range of stimulus manipulations. We studied this relationship using a signal processing technique called Matching Pursuit and found that action potentials are associated with sharp transients in the LFP with broadband power, which is visible at frequencies as low as ∼50 Hz. These results distinguish broadband high-gamma activity from gamma rhythms as an easily obtained and reliable electrophysiological index of neuronal firing near the microelectrode. Further, they highlight the importance of making a careful dissociation between gamma rhythms and spike-related transients that could be incorrectly decomposed as rhythms using traditional signal processing methods.
Author Summary
Electrical activity in the brain often shows oscillations at distinct frequencies, such as the alpha (8–12 Hz) or gamma (30–80 Hz) bands, which have been linked with distinct cognitive states. In addition, changes in power are seen in a broad range above ∼80 Hz, called the “high-gamma” band. High-gamma power could arise either from sustained oscillations (similar to gamma rhythms but operating at higher frequencies) or from brief bursts of power associated with spikes generated near the electrode (“spike bleed-through”). It is difficult to dissociate these two hypotheses because gamma oscillations and spiking are correlated during most stimulus or cognitive manipulations. Further, most signal processing techniques decompose any signal into a set of oscillatory functions, making it difficult to represent any transient power fluctuations that occur at the time of spikes. We address the first issue by using a stimulus manipulation for which gamma oscillations and spiking activity are anti-correlated, permitting dissociation. To address the second issue, we use a signal processing technique called Matching Pursuit, which is well suited to capture transient activity. We show that gamma and high-gamma power become anti-correlated, suggesting different biophysical origins. Spikes and high-gamma power, however, remain tightly correlated. Broadband high-gamma activity could therefore be an easily obtained and reliable electrophysiological index of neuronal firing in the vicinity of an electrode.
PMCID: PMC3075230  PMID: 21532743
2.  Effects of nicotine stimulation on spikes, theta frequency oscillations, and spike-theta oscillation relationship in rat medial septum diagonal band Broca slices 
Acta Pharmacologica Sinica  2013;34(4):464-472.
Spiking activities and neuronal network oscillations in the theta frequency range have been found in many cortical areas during information processing. The aim of this study is to determine whether nicotinic acetylcholine receptors (nAChRs) mediate neuronal network activity in rat medial septum diagonal band Broca (MSDB) slices.
Extracellular field potentials were recorded in the slices using an Axoprobe 1A amplifier. Data analysis was performed off-line. Spike sorting and local field potential (LFP) analyses were performed using Spike2 software. The role of spiking activity in the generation of LFP oscillations in the slices was determined by analyzing the phase-time relationship between the spikes and LFP oscillations. Circular statistic analysis based on the Rayleigh test was used to determine the significance of phase relationships between the spikes and LFP oscillations. The timing relationship was examined by quantifying the spike-field coherence (SFC).
Application of nicotine (250 nmol/L) induced prominent LFP oscillations in the theta frequency band and both small- and large-amplitude population spiking activity in the slices. These spikes were phase-locked to theta oscillations at specific phases. The Rayleigh test showed a statistically significant relationship in phase-locking between the spikes and theta oscillations. Larger changes in the SFC were observed for large-amplitude spikes, indicating an accurate timing relationship between this type of spike and LFP oscillations. The nicotine-induced spiking activity (large-amplitude population spikes) was suppressed by the nAChR antagonist dihydro-β-erythroidine (0.3 μmol/L).
The results demonstrate that large-amplitude spikes are phase-locked to theta oscillations and have a high spike-timing accuracy, which are likely a main contributor to the theta oscillations generated in MSDB during nicotine receptor activation.
PMCID: PMC4002786  PMID: 23474704
medial septum diagonal band of Broca; theta oscillations; spike; LFP; nicotinic acetylcholine receptor; nicotine; dihydro-β-erythroidine; brain slice; electrophysiology
3.  Synchronous Chaos and Broad Band Gamma Rhythm in a Minimal Multi-Layer Model of Primary Visual Cortex 
PLoS Computational Biology  2011;7(10):e1002176.
Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity. However, analysis of Local Field Potentials (LFPs) across different experiments reveals considerable diversity in the degree of oscillatory behavior of this induced activity. Contrast-dependent power enhancements can indeed occur over a broad band in the gamma frequency range and spectral peaks may not arise at all. Furthermore, even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. We show that the strength of the inter-layer coupling crucially affects this spatiotemporal structure. We predict that layer VI inactivation should induce global changes in the spectral properties of induced LFPs, reflecting their slower temporal decorrelation in the absence of inter-layer feedback. Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.
Author Summary
Visual stimulation elicits neuronal responses in visual cortex. When the contrast of the used stimuli increases, the power of this induced activity is boosted over a broad frequency range (30–100 Hz), called the “gamma band.” It would be tempting to hypothesize that this phenomenon is due to the emergence of oscillations in which many neurons fire collectively in a rhythmic way. However, previous models trying to explain contrast-related power enhancements using synchronous oscillations failed to reproduce the observed spectra because they originated unrealistically sharp spectral peaks. The aim of our study is to reconcile synchronous oscillations with broad-band power spectra. We argue here that, thanks to the interaction between neuronal populations at different depths in the cortical tissue, the induced oscillatory responses are synchronous, but, at the same time, chaotic. The chaotic nature of the dynamics makes it possible to have broad-band power spectra together with synchrony. Our modeling study allows us formulating qualitative experimental predictions that provide a potential test for our theory. We predict that if the interactions between cortical layers are suppressed, for instance by inactivating neurons in deep layers, the induced responses might become more regular and narrow isolated peaks might develop in their power spectra.
PMCID: PMC3188510  PMID: 21998568
4.  Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb 
PLoS Computational Biology  2009;5(10):e1000551.
Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.
Author Summary
Olfactory function relies on a chain of neural relays that extends from the periphery to the central nervous system and implies neural activity with various timescales. A central question in neuroscience is how information is encoded by the neural activity. In the mammalian olfactory bulb, local neural activity oscillations in the 40–80 Hz range (gamma) may influence the timing of individual neuron activities such that olfactory information may be encoded in this way. In this study, we first characterize in vivo the detailed activity of individual neurons relative to the oscillation and find that, depending on their state, neurons can exhibit periodic activity patterns. We also find, at least qualitatively, a relation between this activity and a particular odor. This is reminiscent of general physical phenomena—the entrainment by an oscillation—and to verify this hypothesis, in a second phase, we build a biologically realistic model mimicking these in vivo conditions. Our model confirms quantitatively this hypothesis and reveals that entrainment is maximal in the gamma range. Taken together, our results suggest that the neuronal activity may be specifically formatted in time during the gamma oscillation in such a way that it could, at this stage, encode the odor.
PMCID: PMC2760751  PMID: 19876377
5.  Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons 
PLoS Computational Biology  2008;4(12):e1000239.
Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.
Author Summary
The brain displays rhythmic activity in almost all areas and over a wide range of frequencies and amplitudes. However, the role of these rhythms in the processing of sensory information is still unclear. To study the interplay between visual stimuli and ongoing oscillations in the brain, we developed a model of a local circuit of the visual cortex. We injected into the network the signal recorded in the thalamus of an anesthetized monkey watching a movie, to mimic the effect of a naturalistic stimulus arriving at the visual cortex. Our results are in striking agreement with recordings from the visual cortex. Furthermore, through manipulations of the signal and information analysis, we found that two specific frequency bands of the neurons' activity are used to encode independent stimuli features. These results describe how sensory stimuli can modulate frequency and amplitude of ongoing neural activity and how these modulations can be used to convey sensory information through the different layers of the brain.
PMCID: PMC2585056  PMID: 19079571
6.  Gamma Oscillations in the Auditory Cortex of Awake Rats 
Numerous reports of human electrophysiology have demonstrated gamma (30–150 Hz) frequency oscillations in the auditory cortex during listening. However, only a small number of studies in non-human animals have provided evidence for gamma oscillations during listening. In this report, multi-site recordings from primary auditory cortex (A1) were carried out using a 16-channel microelectrode array in awake rats as they passively listened to tones. We addressed two fundamental questions: 1) Is passive listening associated with an increase in gamma oscillation in A1?; if so, 2) Are A1 gamma oscillations during passive listening coherent within local networks and/or over long distances? All sites within A1 showed a short-latency burst of activity in the low-gamma (30–70 Hz) and high-gamma (90–150 Hz) bands in the local field potential (LFP). Additionally, 53% of sites within A1 also showed longer-latency bursts of gamma oscillation that occurred episodically for up to 350 ms after tone onset, but these varied both in latency and occurrence across trials. There was significant coherence in the low-gamma band between spike activity and the LFP recorded with the same electrode. However, neither LFPs nor the spike activity between sites spaced at least 300 μm apart showed coherent activity in the gamma band. The experiments demonstrated that gamma oscillations are present, but not uniformly expressed, throughout A1 during passive listening and that there is strong local coherence in the spatiotemporal organization of gamma activity.
PMCID: PMC3914729  PMID: 21059115
oscillations; sensory processing; auditory system; Rattus norvegicus
7.  Whisker barrel cortex delta oscillations and gamma power in the awake mouse are linked to respiration 
Nature Communications  2014;5:3572.
Current evidence suggests that delta oscillations (0.5–4 Hz) in the brain are generated by intrinsic network mechanisms involving cortical and thalamic circuits. Here we report that delta band oscillation in spike and local field potential (LFP) activity in the whisker barrel cortex of awake mice is phase locked to respiration. Furthermore, LFP oscillations in the gamma frequency band (30–80 Hz) are amplitude modulated in phase with the respiratory rhythm. Removal of the olfactory bulb eliminates respiration-locked delta oscillations and delta-gamma phase-amplitude coupling. Our findings thus suggest respiration-locked olfactory bulb activity as a main driving force behind delta oscillations and gamma power modulation in the whisker barrel cortex in the awake state.
Oscillatory neuronal activity in the mammalian neocortex is implicated in cognitive processes but its generation is poorly understood. In this study, the authors show that delta band oscillatory activity in mice phase-locks with respiratory activity and that this is mediated by activity in the olfactory bulb.
PMCID: PMC3988824  PMID: 24686563
8.  Influence of spiking activity on cortical local field potentials 
The Journal of Physiology  2013;591(Pt 21):5291-5303.
The intra-cortical local field potential (LFP) reflects a variety of electrophysiological processes including synaptic inputs to neurons and their spiking activity. It is still a common assumption that removing high frequencies, often above 300 Hz, is sufficient to exclude spiking activity from LFP activity prior to analysis. Conclusions based on such supposedly spike-free LFPs can result in false interpretations of neurophysiological processes and erroneous correlations between LFPs and behaviour or spiking activity. Such findings might simply arise from spike contamination rather than from genuine changes in synaptic input activity. Although the subject of recent studies, the extent of LFP contamination by spikes is unclear, and the fundamental problem remains. Using spikes recorded in the motor cortex of the awake monkey, we investigated how different factors, including spike amplitude, duration and firing rate, together with the noise statistic, can determine the extent to which spikes contaminate intra-cortical LFPs. We demonstrate that such contamination is realistic for LFPs with a frequency down to ∼10 Hz. For LFP activity below ∼10 Hz, such as movement-related potential, contamination is theoretically possible but unlikely in real situations. Importantly, LFP frequencies up to the (high-) gamma band can remain unaffected. This study shows that spike–LFP crosstalk in intra-cortical recordings should be assessed for each individual dataset to ensure that conclusions based on LFP analysis are valid. To this end, we introduce a method to detect and to visualise spike contamination, and provide a systematic guide to assess spike contamination of intra-cortical LFPs.
PMCID: PMC3936368  PMID: 23981719
9.  Influence of spiking activity on cortical local field potentials 
The Journal of Physiology  2013;591(21):5291-5303.
The intra-cortical local field potential (LFP) reflects a variety of electrophysiological processes including synaptic inputs to neurons and their spiking activity. It is still a common assumption that removing high frequencies, often above 300 Hz, is sufficient to exclude spiking activity from LFP activity prior to analysis. Conclusions based on such supposedly spike-free LFPs can result in false interpretations of neurophysiological processes and erroneous correlations between LFPs and behaviour or spiking activity. Such findings might simply arise from spike contamination rather than from genuine changes in synaptic input activity. Although the subject of recent studies, the extent of LFP contamination by spikes is unclear, and the fundamental problem remains. Using spikes recorded in the motor cortex of the awake monkey, we investigated how different factors, including spike amplitude, duration and firing rate, together with the noise statistic, can determine the extent to which spikes contaminate intra-cortical LFPs. We demonstrate that such contamination is realistic for LFPs with a frequency down to ∼10 Hz. For LFP activity below ∼10 Hz, such as movement-related potential, contamination is theoretically possible but unlikely in real situations. Importantly, LFP frequencies up to the (high-) gamma band can remain unaffected. This study shows that spike–LFP crosstalk in intra-cortical recordings should be assessed for each individual dataset to ensure that conclusions based on LFP analysis are valid. To this end, we introduce a method to detect and to visualise spike contamination, and provide a systematic guide to assess spike contamination of intra-cortical LFPs.
PMCID: PMC3936368  PMID: 23981719
10.  Gamma Oscillations in Human Primary Somatosensory Cortex Reflect Pain Perception  
PLoS Biology  2007;5(5):e133.
Successful behavior requires selection and preferred processing of relevant sensory information. The cortical representation of relevant sensory information has been related to neuronal oscillations in the gamma frequency band. Pain is of invariably high behavioral relevance and, thus, nociceptive stimuli receive preferred processing. Here, by using magnetoencephalography, we show that selective nociceptive stimuli induce gamma oscillations between 60 and 95 Hz in primary somatosensory cortex. Amplitudes of pain-induced gamma oscillations vary with objective stimulus intensity and subjective pain intensity. However, around pain threshold, perceived stimuli yielded stronger gamma oscillations than unperceived stimuli of equal stimulus intensity. These results show that pain induces gamma oscillations in primary somatosensory cortex that are particularly related to the subjective perception of pain. Our findings support the hypothesis that gamma oscillations are related to the internal representation of behaviorally relevant stimuli that should receive preferred processing.
Author Summary
Pain is a highly subjective sensation of inherent behavioral importance and is therefore expected to receive enhanced processing in relevant brain regions. We show that painful stimuli induce high-frequency oscillations in the electrical activity of the human primary somatosensory cortex. Amplitudes of these pain-induced gamma oscillations were more closely related to the subjective perception of pain than to the objective stimulus attributes. They correlated with participants' ratings of pain and were stronger for laser stimuli that caused pain, compared with the same stimuli when no pain was perceived. These findings indicate that gamma oscillations may represent an important mechanism for processing behaviorally relevant sensory information.
Magnetoencephalography reveals that gamma oscillations in the somatosensory cortex correlate with the subjective rating of pain and are stronger for laser stimuli that cause pain, compared with the same stimuli when no pain is perceived.
PMCID: PMC1854914  PMID: 17456008
11.  Representation of Time-Varying Stimuli by a Network Exhibiting Oscillations on a Faster Time Scale 
PLoS Computational Biology  2009;5(5):e1000370.
Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp.
Author Summary
Sensory processing of time-varying stimuli, such as speech, is associated with high-frequency oscillatory cortical activity, the functional significance of which is still unknown. One possibility is that the oscillations are part of a stimulus-encoding mechanism. Here, we investigate a computational model of such a mechanism, a spiking neuronal network whose intrinsic oscillations interact with external input (waveforms simulating short speech segments in a single acoustic frequency band) to encode stimuli that extend over a time interval longer than the oscillation's period. The network implements a temporally sparse encoding, whose robustness to time warping and neuronal noise we quantify. To our knowledge, this study is the first to demonstrate that a biophysically plausible model of oscillations occurring in the processing of auditory input may generate a representation of signals that span multiple oscillation cycles.
PMCID: PMC2671161  PMID: 19412531
12.  State-Dependent Spike and Local Field Synchronization between Motor Cortex and Substantia Nigra in Hemiparkinsonian Rats 
Excessive beta frequency oscillatory and synchronized activity has been reported in the basal ganglia of Parkinsonian patients and animal models of the disease. To gain insight into processes underlying this activity, this study explores relationships between oscillatory activity in motor cortex and basal ganglia output in behaving rats after dopamine cell lesion. During inattentive rest, seven days after lesion, increases in motor cortex-substantia nigra pars reticulata (SNpr) coherence emerged in the 8–25 Hz range, with significant increases in local field potential (LFP) power in SNpr but not motor cortex. In contrast, during treadmill walking, marked increases in both motor cortex and SNpr LFP power, as well as coherence, emerged in the 25–40 Hz band with a peak frequency at 30–35 Hz. Spike-triggered waveform averages showed that 77% of SNpr neurons, 77% of putative cortical interneurons and 44% of putative pyramidal neurons were significantly phase-locked to the increased cortical LFP activity in the 25–40 Hz range. Although the mean lag between cortical and SNpr LFPs fluctuated around zero, SNpr neurons phase-locked to cortical LFP oscillations fired, on average, 17 ms after synchronized spiking in motor cortex. High coherence between LFP oscillations in cortex and SNpr supports the view that cortical activity facilitates entrainment and synchronization of activity in basal ganglia after loss of dopamine. However, the dramatic increases in cortical power and relative timing of phase-locked spiking in these areas suggest that additional processes help shape the frequency-specific tuning of the basal ganglia-thalamocortical network during ongoing motor activity.
PMCID: PMC3423905  PMID: 22674263
Parkinson’s disease; basal ganglia; substantia nigra pars reticulata; beta frequency; local field potentials; gait; motor cortex; dopamine; 6-hydroxydopamine
13.  Cross-frequency interaction of the eye-movement related LFP signals in V1 of freely viewing monkeys 
Recent studies have emphasized the functional role of neuronal activity underlying oscillatory local field potential (LFP) signals during visual processing in natural conditions. While functionally relevant components in multiple frequency bands have been reported, little is known about whether and how these components interact with each other across the dominant frequency bands. We examined this phenomenon in LFP signals obtained from the primary visual cortex of monkeys performing voluntary saccadic eye movements (EMs) on still images of natural-scenes. We identified saccade-related changes in respect to power and phase in four dominant frequency bands: delta-theta (2–4 Hz), alpha-beta (10–13 Hz), low-gamma (20–40 Hz), and high-gamma (>100 Hz). The phase of the delta-theta band component is found to be entrained to the rhythm of the repetitive saccades, while an increment in the power of the alpha-beta and low-gamma bands were locked to the onset of saccades. The degree of the power modulation in these frequency bands is positively correlated with the degree of the phase-locking of the delta-theta oscillations to EMs. These results suggest the presence of cross-frequency interactions in the form of phase-amplitude coupling (PAC) between slow (delta-theta) and faster (alpha-beta and low gamma) oscillations. As shown previously, spikes evoked by visual fixations during free viewing are phase-locked to the fast oscillations. Thus, signals of different types and at different temporal scales are nested to each other during natural viewing. Such cross-frequency interaction may provide a general mechanism to coordinate sensory processing on a fast time scale and motor behavior on a slower time scale during active sensing.
PMCID: PMC3572441  PMID: 23420631
local field potential; oscillation; saccade; natural vision; cross-frequency coupling
14.  Input-Dependent Frequency Modulation of Cortical Gamma Oscillations Shapes Spatial Synchronization and Enables Phase Coding 
PLoS Computational Biology  2015;11(2):e1004072.
Fine-scale temporal organization of cortical activity in the gamma range (∼25–80Hz) may play a significant role in information processing, for example by neural grouping (‘binding’) and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.
Author Summary
Almost 350 years ago the physicist and polymath Christiaan Huygens first observed the synchronization between two pendulum clocks attached to a common support. Since then synchronization has been recognized as a universal phenomenon from astronomy to biology. The phase-locking (synchrony) and the phase-relation between the two pendulums are determined by two principal forces: the synchronization force exerted over the connection and the tendency to desynchronize due to frequency (speed) differences. We propose that gamma synchronization (25–80Hz) among oscillating cortical neurons in the brain can be understood according to the same principles—like a field of many connected pendula—with the critical addition that input changes the frequency of gamma oscillations, as shown by recent experimental studies. It has been assumed that input-dependent changes in oscillation frequency are detrimental for a meaningful role of gamma synchronization in neural processing. To the contrary, our theoretical analysis demonstrates that because input can change the frequency of the oscillation, phase-locking and phase-relations among neurons relate systematically to input. By analogy, it is because a local push to a pendulum will change its frequency, that resulting changes in phase-locking and phase-relation among the pendula can be used to derive the external force applied.
PMCID: PMC4334551  PMID: 25679780
15.  Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution 
Understanding the sources of variability in single-neuron spiking responses is an important open problem for the theory of neural coding. This variability is thought to result primarily from spontaneous collective dynamics in neuronal networks. Here, we investigate how well collective dynamics reflected in motor cortex local field potentials (LFPs) can account for spiking variability during motor behavior. Neural activity was recorded via microelectrode arrays implanted in ventral and dorsal premotor and primary motor cortices of non-human primates performing naturalistic 3-D reaching and grasping actions. Point process models were used to quantify how well LFP features accounted for spiking variability not explained by the measured 3-D reach and grasp kinematics. LFP features included the instantaneous magnitude, phase and analytic-signal components of narrow band-pass filtered (δ,θ,α,β) LFPs, and analytic signal and amplitude envelope features in higher-frequency bands. Multiband LFP features predicted single-neuron spiking (1ms resolution) with substantial accuracy as assessed via ROC analysis. Notably, however, models including both LFP and kinematics features displayed marginal improvement over kinematics-only models. Furthermore, the small predictive information added by LFP features to kinematic models was redundant to information available in fast-timescale (<100 ms) spiking history. Overall, information in multiband LFP features, although predictive of single-neuron spiking during movement execution, was redundant to information available in movement parameters and spiking history. Our findings suggest that, during movement execution, collective dynamics reflected in motor cortex LFPs primarily relate to sensorimotor processes directly controlling movement output, adding little explanatory power to variability not accounted by movement parameters.
PMCID: PMC4475911  PMID: 26157365
neural dynamics; neural point processes; generalized linear models; local field potentials; neural variability
Recordings from local field potentials (LFPs) are becoming increasingly common in research and clinical applications, however, we still have a poor understanding of how LFP stimulus selectivity originates from the combined activity of single neurons. Here, we systematically compared the stimulus selectivity of LFP and neighboring single unit activity (SUA) recorded in area V1 of awake primates. We demonstrate that LFP and SUA have similar stimulus preferences for orientation, direction of motion, contrast, size, temporal frequency and even spatial phase. However, the average SUA had 50 times better signal to noise, 20% higher contrast sensitivity, 45% higher direction selectivity and 15% more tuning depth than the average LFP. Low LFP frequencies (< 30 Hz) were most strongly correlated with the spiking frequencies of neurons with non-linear spatial summation and poor orientation/direction selectivity that were located near cortical current sinks (negative LFPs). In contrast, LFP gamma frequencies (> 30 Hz) were correlated with a more diverse group of neurons located near cortical sources (positive LFPs). In summary, our results indicate that low- and high-frequency LFP pools signals from V1 neurons with similar stimulus preferences but different response properties and cortical depths.
PMCID: PMC3436073  PMID: 22895722
LFP; area V1; striate cortex; orientation selectivity; visual cortex; receptive field
17.  Stimulus-induced dissociation of neuronal firing rates and local field potential gamma power and its relationship to the blood oxygen level-dependent signal in macaque primary visual cortex 
The European Journal of Neuroscience  2011;34(11):1857-1870.
The functional magnetic resonance imaging (fMRI) blood oxygenation level-dependent (BOLD) signal is regularly used to assign neuronal activity to cognitive function. Recent analyses have shown that the local field potential (LFP) gamma power is a better predictor of the fMRI BOLD signal than spiking activity. However, LFP gamma power and spiking activity are usually correlated, clouding the analysis of the neural basis of the BOLD signal. We show that changes in LFP gamma power and spiking activity in the primary visual cortex (V1) of the awake primate can be dissociated by using grating and plaid pattern stimuli, which differentially engage surround suppression and cross-orientation inhibition/facilitation within and between cortical columns. Grating presentation yielded substantial V1 LFP gamma frequency oscillations and significant multi-unit activity. Plaid pattern presentation significantly reduced the LFP gamma power while increasing population multi-unit activity. The fMRI BOLD activity followed the LFP gamma power changes, not the multi-unit activity. Inference of neuronal activity from the fMRI BOLD signal thus requires detailed a priori knowledge of how different stimuli or tasks activate the cortical network.
PMCID: PMC3274700  PMID: 22081989
BOLD; cross-orientation inhibition; fMRI; LFP; spiking; V1
18.  The Laminar Cortex Model: A New Continuum Cortex Model Incorporating Laminar Architecture 
PLoS Computational Biology  2012;8(10):e1002733.
Local field potentials (LFPs) are widely used to study the function of local networks in the brain. They are also closely correlated with the blood-oxygen-level-dependent signal, the predominant contrast mechanism in functional magnetic resonance imaging. We developed a new laminar cortex model (LCM) to simulate the amplitude and frequency of LFPs. Our model combines the laminar architecture of the cerebral cortex and multiple continuum models to simulate the collective activity of cortical neurons. The five cortical layers (layer I, II/III, IV, V, and VI) are simulated as separate continuum models between which there are synaptic connections. The LCM was used to simulate the dynamics of the visual cortex under different conditions of visual stimulation. LFPs are reported for two kinds of visual stimulation: general visual stimulation and intermittent light stimulation. The power spectra of LFPs were calculated and compared with existing empirical data. The LCM was able to produce spontaneous LFPs exhibiting frequency-inverse (1/ƒ) power spectrum behaviour. Laminar profiles of current source density showed similarities to experimental data. General stimulation enhanced the oscillation of LFPs corresponding to gamma frequencies. During simulated intermittent light stimulation, the LCM captured the fundamental as well as high order harmonics as previously reported. The power spectrum expected with a reduction in layer IV neurons, often observed with focal cortical dysplasias associated with epilepsy was also simulated.
Author Summary
Local field potentials (LFPs) are low-frequency fluctuations of the electric fields produced by the brain. They have been widely studied to understand brain function and activity. LFPs reflect the activity of neurons within a few square millimeters of the cerebral cortex, an area containing more than 10,000 neurons. To avoid the complexity of simulating such a large number of individual neurons, the continuum cortex model was devised to simulate the collective activity of groups of neurons generating cortical LFPs. However, the continuum cortex model assumes that the cortex is two-dimensional and does not take into account the laminar architecture of the cerebral cortex. We developed a three-dimensional laminar cortex model (LCM) by combining laminar architecture with the continuum cortex model. This expansion enables the LCM to simulate the detailed three-dimensional distribution of the LFP within the cortex. We used the LCM to simulate LFPs within the visual cortex under different conditions of visual stimulation. The LCM reproduced the key features of LFPs observed in electrophysiological experiments. We conclude that the LCM is a potentially useful tool to investigate the underlying mechanism of LFPs.
PMCID: PMC3475685  PMID: 23093925
19.  Beta Oscillation Dynamics in Extrastriate Cortex after Removal of Primary Visual Cortex 
The Journal of Neuroscience  2014;34(35):11857-11864.
The local field potential (LFP) in visual cortex is typically characterized by the following spectral pattern: before the onset of a visual stimulus, low-frequency oscillations (beta, 12–20 Hz) dominate, whereas during the presentation of a stimulus these oscillations diminish and are replaced by fluctuations at higher frequencies (gamma, >30 Hz). The origin of beta oscillations in vivo remains unclear, as is the basis of their suppression during visual stimulation. Here we investigate the contribution of ascending input from primary visual cortex (V1) to beta oscillation dynamics in extrastriate visual area V4 of behaving monkeys. We recorded LFP activity in V4 before and after resecting a portion of V1. After the surgery, the visually induced gamma LFP activity in the lesion projection zone of V4 was markedly reduced, consistent with previously reported spiking responses (Schmid et al., 2013). In the beta LFP range, the lesion had minimal effect on the normal pattern of spontaneous oscillations. However, the lesion led to a surprising and permanent reversal of the normal beta suppression during visual stimulation, with visual stimuli eliciting beta magnitude increases up to 50%, particularly in response to moving stimuli. This reversed beta activity pattern was specific to stimulus locations affected by the V1 lesion. Our results shed light on the mechanisms of beta activity in extrastriate visual cortex: The preserved spontaneous oscillations point to a generation mechanism independent of the geniculostriate pathway, whereas the positive beta responses support the contribution of visual information to V4 via direct thalamo-extrastriate projections.
PMCID: PMC4145181  PMID: 25164679
blindsight; cortex; monkey; neurophysiology; oscillation; V4
20.  Speech Rhythms and Multiplexed Oscillatory Sensory Coding in the Human Brain 
PLoS Biology  2013;11(12):e1001752.
A neuroimaging study reveals how coupled brain oscillations at different frequencies align with quasi-rhythmic features of continuous speech such as prosody, syllables, and phonemes.
Cortical oscillations are likely candidates for segmentation and coding of continuous speech. Here, we monitored continuous speech processing with magnetoencephalography (MEG) to unravel the principles of speech segmentation and coding. We demonstrate that speech entrains the phase of low-frequency (delta, theta) and the amplitude of high-frequency (gamma) oscillations in the auditory cortex. Phase entrainment is stronger in the right and amplitude entrainment is stronger in the left auditory cortex. Furthermore, edges in the speech envelope phase reset auditory cortex oscillations thereby enhancing their entrainment to speech. This mechanism adapts to the changing physical features of the speech envelope and enables efficient, stimulus-specific speech sampling. Finally, we show that within the auditory cortex, coupling between delta, theta, and gamma oscillations increases following speech edges. Importantly, all couplings (i.e., brain-speech and also within the cortex) attenuate for backward-presented speech, suggesting top-down control. We conclude that segmentation and coding of speech relies on a nested hierarchy of entrained cortical oscillations.
Author Summary
Continuous speech is organized into a nested hierarchy of quasi-rhythmic components (prosody, syllables, phonemes) with different time scales. Interestingly, neural activity in the human auditory cortex shows rhythmic modulations with frequencies that match these speech rhythms. Here, we use magnetoencephalography and information theory to study brain oscillations in participants as they process continuous speech. We show that auditory brain oscillations at different frequencies align with the rhythmic structure of speech. This alignment is more precise when participants listen to intelligible rather than unintelligible speech. The onset of speech resets brain oscillations and improves their alignment to speech rhythms; it also improves the alignment between the different frequencies of nested brain oscillations in the auditory cortex. Since these brain oscillations reflect rhythmic changes in neural excitability, they are strong candidates for mediating the segmentation of continuous speech at different time scales corresponding to key speech components such as syllables and phonemes.
PMCID: PMC3876971  PMID: 24391472
21.  Searching for Autocoherence in the Cortical Network with a Time-Frequency Analysis of the Local Field Potential 
Gamma-band peaks in the power spectrum of local field potentials (LFP) are found in multiple brain regions. It has been theorized that gamma oscillations may serve as a ’clock’ signal for the purposes of precise temporal encoding of information and ’binding’ of stimulus features across regions of the brain. Neurons in model networks may exhibit periodic spike firing or synchronized membrane potentials that give rise to a gamma-band oscillation that could operate as a ’clock’. The phase of the oscillation in such models is conserved over the length of the stimulus. We define these types of oscillations to be autocoherent. We investigated the hypothesis that autocoherent oscillations are the basis of the experimentally observed gamma-band peaks: the autocoherent oscillator (ACO) hypothesis. To test the ACO hypothesis, we developed a new analysis technique to analyze the autocoherence of a time-varying signal. This analysis used the continuous Gabor transform to examine the time evolution of the phase of each frequency component in the power spectrum. Using this analysis method, we formulated a statistical test to compare the ACO hypothesis with measurements of the LFP in macaque primary visual cortex, V1. The experimental data were not consistent with the ACO hypothesis. Gamma-band activity recorded in V1 did not have the properties of a ’clock’ signal during visual stimulation. We propose instead that the source of the gamma-band spectral peak is the resonant V1 network driven by random inputs.
PMCID: PMC2897248  PMID: 20237274
Visual Cortex; Local Field Potential; extracellular; V1; time-frequency analysis; data analysis
22.  Mechanisms for Phase Shifting in Cortical Networks and their Role in Communication through Coherence 
In the primate visual cortex, the phase of spikes relative to oscillations in the local field potential (LFP) in the gamma frequency range (30–80 Hz) can be shifted by stimulus features such as orientation and thus the phase may carry information about stimulus identity. According to the principle of communication through coherence (CTC), the relative LFP phase between the LFPs in the sending and receiving circuits affects the effectiveness of the transmission. CTC predicts that phase shifting can be used for stimulus selection. We review and investigate phase shifting in models of periodically driven single neurons and compare it with phase shifting in models of cortical networks. In a single neuron, as the driving current is increased, the spike phase varies systematically while the firing rate remains constant. In a network model of reciprocally connected excitatory (E) and inhibitory (I) cells phase shifting occurs in response to both injection of constant depolarizing currents and to brief pulses to I cells. These simple models provide an account for phase-shifting observed experimentally and suggest a mechanism for implementing CTC. We discuss how this hypothesis can be tested experimentally using optogenetic techniques.
PMCID: PMC2987601  PMID: 21103013
attention; gamma oscillations; synchrony; phase shifting; phase locking
23.  Neural correlates of high-gamma oscillations (60–200 Hz) in macaque local field potentials and their potential implications in electrocorticography 
Recent studies using electrocorticographic (ECoG) recordings in humans have shown that functional activation of cortex is associated with an increase in power in the high-gamma frequency range (∼60–200 Hz). Here we investigate the neural correlates of this high-gamma activity in local field potential (LFP). Single units and LFP were recorded with microelectrodes from the hand region of macaque SII cortex while vibrotactile stimuli of varying intensities were presented to the hand. We found that high-gamma power in the LFP was strongly correlated with the average firing rate recorded by the microelectrodes, both temporally and on a trial-by-trial basis. In comparison, the correlation between firing rate and low-gamma power (40–80 Hz) was much smaller. In order to explore the potential effects of neuronal firing on ECoG, we developed a model to estimate ECoG power generated by different firing patterns of the underlying cortical population and studied how ECoG power varies with changes in firing rate versus the degree of synchronous firing between neurons in the population. Both an increase in firing rate and neuronal synchrony increased high-gamma power in the simulated ECoG data. However, ECoG high-gamma activity was much more sensitive to increases in neuronal synchrony than firing rate.
PMCID: PMC2715840  PMID: 18987189
Secondary somatosensory cortex; gamma; high-gamma; local field potential; ECoG; synchrony
24.  Neuronal Ensemble Synchrony during Human Focal Seizures 
The Journal of Neuroscience  2014;34(30):9927-9944.
Seizures are classically characterized as the expression of hypersynchronous neural activity, yet the true degree of synchrony in neuronal spiking (action potentials) during human seizures remains a fundamental question. We quantified the temporal precision of spike synchrony in ensembles of neocortical neurons during seizures in people with pharmacologically intractable epilepsy. Two seizure types were analyzed: those characterized by sustained gamma (∼40–60 Hz) local field potential (LFP) oscillations or by spike-wave complexes (SWCs; ∼3 Hz). Fine (<10 ms) temporal synchrony was rarely present during gamma-band seizures, where neuronal spiking remained highly irregular and asynchronous. In SWC seizures, phase locking of neuronal spiking to the SWC spike phase induced synchrony at a coarse 50–100 ms level. In addition, transient fine synchrony occurred primarily during the initial ∼20 ms period of the SWC spike phase and varied across subjects and seizures. Sporadic coherence events between neuronal population spike counts and LFPs were observed during SWC seizures in high (∼80 Hz) gamma-band and during high-frequency oscillations (∼130 Hz). Maximum entropy models of the joint neuronal spiking probability, constrained only on single neurons' nonstationary coarse spiking rates and local network activation, explained most of the fine synchrony in both seizure types. Our findings indicate that fine neuronal ensemble synchrony occurs mostly during SWC, not gamma-band, seizures, and primarily during the initial phase of SWC spikes. Furthermore, these fine synchrony events result mostly from transient increases in overall neuronal network spiking rates, rather than changes in precise spiking correlations between specific pairs of neurons.
PMCID: PMC4107409  PMID: 25057195
collective dynamics; conditional inference; epilepsy; maximum entropy
25.  Local Field Potentials in the Gustatory Cortex Carry Taste Information 
The Journal of Neuroscience  2014;34(26):8778-8787.
It has been recently shown that local field potentials (LFPs) from the auditory and visual cortices carry information about sensory stimuli, but whether this is a universal property of sensory cortices remains to be determined. Moreover, little is known about the temporal dynamics of sensory information contained in LFPs following stimulus onset. Here we investigated the time course of the amount of stimulus information in LFPs and spikes from the gustatory cortex of awake rats subjected to tastants and water delivery on the tongue. We found that the phase and amplitude of multiple LFP frequencies carry information about stimuli, which have specific time courses after stimulus delivery. The information carried by LFP phase and amplitude was independent within frequency bands, since the joint information exhibited neither synergy nor redundancy. Tastant information in LFPs was also independent and had a different time course from the information carried by spikes. These findings support the hypothesis that the brain uses different frequency channels to dynamically code for multiple features of a stimulus.
PMCID: PMC4069356  PMID: 24966378

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