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1.  State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data 
PLoS Computational Biology  2012;8(3):e1002385.
Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.
Author Summary
Nearly half a century ago, the Canadian psychologist D. O. Hebb postulated the formation of assemblies of tightly connected cells in cortical recurrent networks because of changes in synaptic weight (Hebb's learning rule) by repetitive sensory stimulation of the network. Consequently, the activation of such an assembly for processing sensory or behavioral information is likely to be expressed by precisely coordinated spiking activities of the participating neurons. However, the available analysis techniques for multiple parallel neural spike data do not allow us to reveal the detailed structure of transiently active assemblies as indicated by their dynamical pairwise and higher-order spike correlations. Here, we construct a state-space model of dynamic spike interactions, and present a recursive Bayesian method that makes it possible to trace multiple neurons exhibiting such precisely coordinated spiking activities in a time-varying manner. We also formulate a hypothesis test of the underlying dynamic spike correlation, which enables us to detect the assemblies activated in association with behavioral events. Therefore, the proposed method can serve as a useful tool to test Hebb's cell assembly hypothesis.
doi:10.1371/journal.pcbi.1002385
PMCID: PMC3297562  PMID: 22412358
2.  The Local Field Potential Reflects Surplus Spike Synchrony 
Cerebral Cortex (New York, NY)  2011;21(12):2681-2695.
While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP.
doi:10.1093/cercor/bhr040
PMCID: PMC3209854  PMID: 21508303
motor cortex; oscillation; population signals; synchrony
3.  Neuronal Functional Connection Graphs among Multiple Areas of the Rat Somatosensory System during Spontaneous and Evoked Activities 
PLoS Computational Biology  2013;9(6):e1003104.
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However, the functional microscopic level, where the nodes of a network are represented by single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connection graphs exhibit small-world organization, it is not known whether and how these maps, potentially distributed in multiple brain regions, change across different conditions, such as spontaneous and stimulus-evoked activities. We addressed these questions by analyzing the data from simultaneous multi-array extracellular recordings in three brain regions of rats, diversely involved in somatosensory information processing: the ventropostero-lateral thalamic nuclei, the primary somatosensory cortex and the centro-median thalamic nuclei. From both spike and Local Field Potential (LFP) recordings, we estimated the functional connection graphs by using the Normalized Compression Similarity for spikes and the Phase Synchrony for LFPs. Then, by using graph-theoretical statistics, we characterized the functional topology both during spontaneous activity and sensory stimulation. Our main results show that: (i) spikes and LFPs show SWN organization during spontaneous activity; (ii) after stimulation onset, while substantial functional graph reconfigurations occur both in spike and LFPs, small-worldness is nonetheless preserved; (iii) the stimulus triggers a significant increase of inter-area LFP connections without modifying the topology of intra-area functional connections. Finally, investigating computationally the functional substrate that supports the observed phenomena, we found that (iv) the fundamental concept of cell assemblies, transient groups of activating neurons, can be described by small-world networks. Our results suggest that activity of neurons from multiple areas of the rat somatosensory system contributes to the integration of local computations arisen in distributed functional cell assemblies according to the principles of SWNs.
Author Summary
Cell assemblies (sequences of neuronal activations), seem to represent a functional unit of information processing. However, it remains unclear how groups of neurons may organize their activity during information processing, working as a sole functional unit. One prominent principle in complex network theory is covered by small-world networks, in which each node is easily reachable by each other and organized in highly dense clusters. Small-world networks have been already observed on large scales in human and primate brain areas while their presence at the neuronal level remains unclear. The aim of this work was to investigate the possibility that functional, related neural populations, encompassing multiple brain regions, could be organized in small-world networks. We investigated the coherent neuronal activity among multiple rat brain regions involved in somatosensory information processing. We found that the recorded neuronal populations represented small-world networks and that these topologies were maintained during stimulations. Furthermore, by using simulations to explore the hidden substrates supporting the observed topological features, we inferred that small-world networks represent a plausible topology for cell assemblies. This work suggests that the coherent activity of neurons from multiple brain areas promotes the integration of local computations, the functional principle of small-world networks.
doi:10.1371/journal.pcbi.1003104
PMCID: PMC3681651  PMID: 23785273
4.  From neurons to circuits: linear estimation of local field potentials 
Extracellular physiological recordings are typically separated into two frequency bands: local field potentials (LFPs, a circuit property) and spiking multi-unit activity (MUA). There has been increased interest in LFPs due to their correlation with fMRI measurements and the possibility of studying local processing and neuronal synchrony. To further understand the biophysical origin of LFPs, we asked whether it is possible to estimate their time course based on the spiking activity from the same or nearby electrodes. We used Signal Estimation Theory to show that a linear filter operation on the activity of one/few neurons can explain a significant fraction of the LFP time course in the macaque primary visual cortex. The linear filter used to estimate the LFPs had a stereotypical shape characterized by a sharp downstroke at negative time lags and a slower positive upstroke for positve time lags. The filter was similar across neocortical regions and behavioral conditions including spontaneous activity and visual stimulation. The estimations had a spatial resolution of ~1 mm and a temporal resolution of ~200 ms. By considering a causal filter, we observed a temporal asymmetry such that the positive time lags in the filter contributed more to the LFP estimation than negative time lags. Additionally, we showed that spikes occurring within ~10 ms of spikes from nearby neurons yielded better estimation accuracies than nonsynchronous spikes. In sum, our results suggest that at least some circuit-level local properties of the field potentials can be predicted from the activity of one or a few neurons.
doi:10.1523/JNEUROSCI.2390-09.2009
PMCID: PMC2924964  PMID: 19889990
local field potentials; neuronal circuits; signal estimation theory; spike trains; computational neuroscience; biophysical models
5.  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.
Aim:
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.
Methods:
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).
Results:
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).
Conclusion:
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.
doi:10.1038/aps.2012.180
PMCID: PMC4002786  PMID: 23474704
medial septum diagonal band of Broca; theta oscillations; spike; LFP; nicotinic acetylcholine receptor; nicotine; dihydro-β-erythroidine; brain slice; electrophysiology
6.  RESPONSE PROPERTIES OF LOCAL FIELD POTENTIALS AND NEIGHBORING SINGLE NEURONS IN AWAKE PRIMARY VISUAL CORTEX 
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.
doi:10.1523/JNEUROSCI.0429-12.2012
PMCID: PMC3436073  PMID: 22895722
LFP; area V1; striate cortex; orientation selectivity; visual cortex; receptive field
7.  Improved measures of phase-coupling between spikes and the Local Field Potential 
An important tool to study rhythmic neuronal synchronization is provided by relating spiking activity to the Local Field Potential (LFP). Two types of interdependent spike-LFP measures exist. The first approach is to directly quantify the consistency of single spike-LFP phases across spikes, referred to here as point-field phase synchronization measures. We show that conventional point-field phase synchronization measures are sensitive not only to the consistency of spike-LFP phases, but are also affected by statistical dependencies between spike-LFP phases, caused by e.g. non-Poissonian history-effects within spike trains such as bursting and refractoriness. To solve this problem, we develop a new pairwise measure that is not biased by the number of spikes and not affected by statistical dependencies between spike-LFP phases. The second approach is to quantify, similar to EEG-EEG coherence, the consistency of the relative phase between spike train and LFP signals across trials instead of across spikes, referred to here as spike train to field phase synchronization measures. We demonstrate an analytical relationship between point-field and spike train to field phase synchronization measures. Based on this relationship, we prove that the spike train to field pairwise phase consistency (PPC), a quantity closely related to the squared spike-field coherence, is a monotonically increasing function of the number of spikes per trial. This derived relationship is exact and analytic, and takes a linear form for weak phase-coupling. To solve this problem, we introduce a corrected version of the spike train to field PPC that is independent of the number of spikes per trial. Finally, we address the problem that dependencies between spike-LFP phase and the number of spikes per trial can cause spike-LFP phase synchronization measures to be biased by the number of trials. We show how to modify the developed point-field and spike train to field phase synchronization measures in order to make them unbiased by the number of trials.
doi:10.1007/s10827-011-0374-4
PMCID: PMC3394239  PMID: 22187161
Spike-triggered average; Spike-field locking; Spike-LFP; Phase locking; Spike-field coherence; Phase-synchronization
8.  Cross-correlation of instantaneous amplitudes of field potential oscillations: a straightforward method to estimate the directionality and lag between brain areas 
Journal of neuroscience methods  2010;191(2):191-200.
Researchers performing multi-site recordings are often interested in identifying the directionality of functional connectivity and estimating lags between sites. Current techniques for determining directionality require spike trains or involve multivariate autoregressive modeling. However, it is often difficult to sample large numbers of spikes from multiple areas simultaneously, and modeling can be sensitive to noise. A simple, model-independent method to estimate directionality and lag using local field potentials (LFPs) would be of general interest. Here we describe such a method using the cross-correlation of the instantaneous amplitudes of filtered LFPs. The method involves four steps. First, LFPs are band-pass filtered; second, the instantaneous amplitude of the filtered signals is calculated; third, these amplitudes are cross-correlated and the lag at which the cross-correlation peak occurs is determined; fourth, the distribution of lags obtained is tested to determine if it differs from zero. This method was applied to LFPs recorded from the ventral hippocampus and the medial prefrontal cortex in awake behaving mice. The results demonstrate that the hippocampus leads the mPFC, in good agreement with the time lag calculated from the phase locking of mPFC spikes to vHPC LFP oscillations in the same dataset. We also compare the amplitude cross-correlation method to partial directed coherence, a commonly used multivariate autoregressive model-dependent method, and find that the former is more robust to the effects of noise. These data suggest that the cross-correlation of instantaneous amplitude of filtered LFPs is a valid method to study the direction of flow of information across brain areas.
doi:10.1016/j.jneumeth.2010.06.019
PMCID: PMC2924932  PMID: 20600317
cross-correlation; theta oscillations; medial prefrontal cortex; ventral hippocampus; local field potential; multi-site recording; directionality
9.  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.
doi:10.1113/jphysiol.2013.258228
PMCID: PMC3936368  PMID: 23981719
10.  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.
doi:10.1113/jphysiol.2013.258228
PMCID: PMC3936368  PMID: 23981719
11.  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.
doi:10.1523/JNEUROSCI.4567-13.2014
PMCID: PMC4107409  PMID: 25057195
collective dynamics; conditional inference; epilepsy; maximum entropy
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.
doi:10.1523/JNEUROSCI.0943-12.2012
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.  Detailed Characterization of Local Field Potential Oscillations and Their Relationship to Spike Timing in the Antennal Lobe of the Moth Manduca sexta 
The transient oscillatory model of odor identity encoding seeks to explain how odorants with spatially overlapped patterns of input into primary olfactory networks can be discriminated. This model provides several testable predictions about the distributed nature of network oscillations and how they control spike timing. To test these predictions, 16 channel electrode arrays were placed within the antennal lobe (AL) of the moth Manduca sexta. Unitary spiking and multi site local field potential (LFP) recordings were made during spontaneous activity and in response to repeated presentations of an odor panel. We quantified oscillatory frequency, cross correlations between LFP recording sites, and spike–LFP phase relationships. We show that odor-driven AL oscillations in Manduca are frequency modulating (FM) from ∼100 to 30 Hz; this was odorant and stimulus duration dependent. FM oscillatory responses were localized to one or two recording sites suggesting a localized (perhaps glomerular) not distributed source. LFP cross correlations further demonstrated that only a small (r < 0.05) distributed and oscillatory component was present. Cross spectral density analysis demonstrated the frequency of these weakly distributed oscillations was state dependent (spontaneous activity = 25–55 Hz; odor-driven = 55–85 Hz). Surprisingly, vector strength analysis indicated that unitary phase locking of spikes to the LFP was strongest during spontaneous activity and dropped significantly during responses. Application of bicuculline, a GABAA receptor antagonist, significantly lowered the frequency content of odor-driven distributed oscillatory activity. Bicuculline significantly reduced spike phase locking generally, but the ubiquitous pattern of increased phase locking during spontaneous activity persisted. Collectively, these results indicate that oscillations perform poorly as a stimulus-mediated spike synchronizing mechanism for Manduca and hence are incongruent with the transient oscillatory model.
doi:10.3389/fneng.2011.00012
PMCID: PMC3200547  PMID: 22046161
olfaction; odor coding; oscillations; synchrony; GABAA; olfactory bulb; antennal lobe
14.  Predicting stimulus-locked single unit spiking from cortical local field potentials 
The rapidly increasing use of the local field potential (LFP) has motivated research to better understand its relation to the gold standard of neural activity, single unit (SU) spiking. We addressed this in an in vivo, awake, restrained mouse auditory cortical electrophysiology preparation by asking whether the LFP could actually be used to predict stimulus-evoked SU spiking. Implementing a Bayesian algorithm to predict the likelihood of spiking on a trial by trial basis from different representations of the despiked LFP signal, we were able to predict, with high quality and fine temporal resolution (2 ms), the time course of a SU's excitatory or inhibitory firing rate response to natural species-specific vocalizations. Our best predictions were achieved by representing the LFP by its wide-band Hilbert phase signal, and approximating the statistical structure of this signal at different time points as independent. Our results show that each SU's action potential has a unique relationship with the LFP that can be reliably used to predict the occurrence of spikes. This “signature” interaction can reflect both pre- and post-spike neural activity that is intrinsic to the local circuit rather than just dictated by the stimulus. Finally, the time course of this “signature” may be most faithful when the full bandwidth of the LFP, rather than specific narrow-band components, is used for representation.
doi:10.1007/s10827-010-0221-z
PMCID: PMC2935517  PMID: 20143142
LFP; Spike prediction; Auditory cortex; Gamma band; Theta band; Beta band; Oscillation; Bayesian algorithm; A1; Evoked potentials; Electroencephalography; EEG; Hilbert transform; Single cortical cells; Phase; Despiking
15.  Mapping the spatio-temporal structure of motor cortical LFP and spiking activities during reach-to-grasp movements 
Grasping an object involves shaping the hand and fingers in relation to the object’s physical properties. Following object contact, it also requires a fine adjustment of grasp forces for secure manipulation. Earlier studies suggest that the control of hand shaping and grasp force involve partially segregated motor cortical networks. However, it is still unclear how information originating from these networks is processed and integrated. We addressed this issue by analyzing massively parallel signals from population measures (local field potentials, LFPs) and single neuron spiking activities recorded simultaneously during a delayed reach-to-grasp task, by using a 100-electrode array chronically implanted in monkey motor cortex. Motor cortical LFPs exhibit a large multi-component movement-related potential (MRP) around movement onset. Here, we show that the peak amplitude of each MRP component and its latency with respect to movement onset vary along the cortical surface covered by the array. Using a comparative mapping approach, we suggest that the spatio-temporal structure of the MRP reflects the complex physical properties of the reach-to-grasp movement. In addition, we explored how the spatio-temporal structure of the MRP relates to two other measures of neuronal activity: the temporal profile of single neuron spiking activity at each electrode site and the somatosensory receptive field properties of single neuron activities. We observe that the spatial representations of LFP and spiking activities overlap extensively and relate to the spatial distribution of proximal and distal representations of the upper limb. Altogether, these data show that, in motor cortex, a precise spatio-temporal pattern of activation is involved for the control of reach-to-grasp movements and provide some new insight about the functional organization of motor cortex during reaching and object manipulation.
doi:10.3389/fncir.2013.00048
PMCID: PMC3608913  PMID: 23543888
cortical map; high-density recordings; monkey motor cortex; spiking activity; LFP
16.  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.
doi:10.1371/journal.pcbi.1000551
PMCID: PMC2760751  PMID: 19876377
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.
doi:10.1111/j.1460-9568.2011.07877.x
PMCID: PMC3274700  PMID: 22081989
BOLD; cross-orientation inhibition; fMRI; LFP; spiking; V1
18.  Decoupling Action Potential Bias from Cortical Local Field Potentials 
Neurophysiologists have recently become interested in studying neuronal population activity through local field potential (LFP) recordings during experiments that also record the activity of single neurons. This experimental approach differs from early LFP studies because it uses high impendence electrodes that can also isolate single neuron activity. A possible complication for such studies is that the synaptic potentials and action potentials of the small subset of isolated neurons may contribute disproportionately to the LFP signal, biasing activity in the larger nearby neuronal population to appear synchronous and cotuned with these neurons. To address this problem, we used linear filtering techniques to remove features correlated with spike events from LFP recordings. This filtering procedure can be applied for well-isolated single units or multiunit activity. We illustrate the effects of this correction in simulation and on spike data recorded from primary auditory cortex. We find that local spiking activity can explain a significant portion of LFP power at most recording sites and demonstrate that removing the spike-correlated component can affect measurements of auditory tuning of the LFP.
doi:10.1155/2010/393019
PMCID: PMC2821772  PMID: 20169096
19.  Local field potentials indicate network state and account for neuronal response variability 
Multineuronal recordings have revealed that neurons in primary visual cortex (V1) exhibit coordinated fluctuations of spiking activity in the absence and in the presence of visual stimulation. From the perspective of understanding a single cell’s spiking activity relative to a behavior or stimulus, these network flutuations are typically considered to be noise. We show that these events are highly correlated with another commonly recorded signal, the local field potential (LFP), and are also likely related to global network state phenomena which have been observed in a number of neural systems. Moreover, we show that attributing a component of cell firing to these network fluctuations via explicit modeling of the LFP improves the recovery of cell properties. This suggests that the impact of network fluctuations may be estimated using the LFP, and that a portion of this network activity is unrelated to the stimulus and instead reflects ongoing cortical activity. Thus, the LFP acts as an easily accessible bridge between the network state and the spiking activity.
doi:10.1007/s10827-009-0208-9
PMCID: PMC3604740  PMID: 20094906
Local field potential; correlation; network state; spontaneous activity; multielectrode array; decoding; population coding
20.  Interactions between Stimulus Dynamics and Network Activity in the Representation of Natural Auditory Scenes 
The efficient cortical encoding of natural scenes is essential for guiding adaptive behavior. As natural scenes and network activity in cortical circuits share similar temporal scales, it is necessary to understand how the temporal structure of natural scenes influences network dynamics in cortical circuits and thereby spiking output. We examined the relationship between the structure of natural acoustic scenes and its impact on network activity (as indexed by the LFP) and spiking responses in macaque primary auditory cortex. Natural auditory scenes led to a change in the power of the LFP in the 2 – 9 Hz and 16 – 30 Hz frequency ranges relative to the ongoing activity. In contrast, ongoing rhythmic activity in the 9 – 16 Hz range was largely unaffected by the natural scene. Phase coherence analysis showed that scene-related changes in LFP power were at least partially due to the locking of the LFP and spiking activity to the temporal structure in the scene— with locking extending up to 25 Hz for some scenes and cortical sites. Consistent with a distributed place and temporal representation, a key predictor of phase locking and power changes was the overlap between the spectral selectivity of a cortical site and the spectral structure of the scene. Finally, during the processing of natural acoustic scenes, spikes were locked to LFP phase at frequencies up to 30 Hz. These results are consistent with an idea that the cortical representation of natural scenes emerges from an interaction between network activity and stimulus dynamics.
doi:10.1523/JNEUROSCI.3174-10.2010
PMCID: PMC3005258  PMID: 20962214
Natural Scenes; LFP; Phase locking; Spike-field coherence
21.  Timing of Single-Neuron and Local Field Potential Responses in the Human Medial Temporal Lobe 
Current Biology  2014;24(3):299-304.
Summary
The relationship between the firing of single cells and local field potentials (LFPs) has received increasing attention, with studies in animals [1–11] and humans [12–14]. Recordings in the human medial temporal lobe (MTL) have demonstrated the existence of neurons with selective and invariant responses [15], with a relatively late but precise response onset around 300 ms after stimulus presentation [16–18] and firing only upon conscious recognition of the stimulus [19]. This represents a much later onset than expected from direct projections from inferotemporal cortex [16, 18]. The neural mechanisms underlying this onset remain unclear. To address this issue, we performed a joint analysis of single-cell and LFP responses during a visual recognition task. Single-neuron responses were preceded by a global LFP deflection in the theta range. In addition, there was a local and stimulus-specific increase in the single-trial gamma power. These LFP responses correlated with conscious recognition. The timing of the neurons’ firing was phase locked to these LFP responses. We propose that whereas the gamma phase locking reflects the activation of local networks encoding particular recognized stimuli, the theta phase locking reflects a global activation that provides a temporal window for processing consciously perceived stimuli in the MTL.
Highlights
•Global theta LFP increases immediately precede MTL single-cell responses•Gamma power reflects activations of local networks encoding specific stimuli•The timing of the neurons’ firing is phase locked to LFP responses•LFP responses give a temporal window for processing consciously perceived stimuli
Rey et al. show that, in human medial temporal lobe (MTL), single-cell responses triggered by consciously perceived stimuli are locked to global theta and local gamma LFP responses; the latter reflects local activations, but the former shortly precedes the spike responses and may provide a window for stimulus processing in the MTL.
doi:10.1016/j.cub.2013.12.004
PMCID: PMC3963414  PMID: 24462002
22.  Comparison of LFP-Based and Spike-Based Spectro-Temporal Receptive Fields and Cross-Correlation in Cat Primary Auditory Cortex 
PLoS ONE  2011;6(5):e20046.
Multi-electrode array recordings of spike and local field potential (LFP) activity were made from primary auditory cortex of 12 normal hearing, ketamine-anesthetized cats. We evaluated 259 spectro-temporal receptive fields (STRFs) and 492 frequency-tuning curves (FTCs) based on LFPs and spikes simultaneously recorded on the same electrode. We compared their characteristic frequency (CF) gradients and their cross-correlation distances. The CF gradient for spike-based FTCs was about twice that for 2–40 Hz-filtered LFP-based FTCs, indicating greatly reduced frequency selectivity for LFPs. We also present comparisons for LFPs band-pass filtered between 4–8 Hz, 8–16 Hz and 16–40 Hz, with spike-based STRFs, on the basis of their marginal frequency distributions. We find on average a significantly larger correlation between the spike based marginal frequency distributions and those based on the 16–40 Hz filtered LFP, compared to those based on the 4–8 Hz, 8–16 Hz and 2–40 Hz filtered LFP. This suggests greater frequency specificity for the 16–40 Hz LFPs compared to those of lower frequency content. For spontaneous LFP and spike activity we evaluated 1373 pair correlations for pairs with >200 spikes in 900 s per electrode. Peak correlation-coefficient space constants were similar for the 2–40 Hz filtered LFP (5.5 mm) and the 16–40 Hz LFP (7.4 mm), whereas for spike-pair correlations it was about half that, at 3.2 mm. Comparing spike-pairs with 2–40 Hz (and 16–40 Hz) LFP-pair correlations showed that about 16% (9%) of the variance in the spike-pair correlations could be explained from LFP-pair correlations recorded on the same electrodes within the same electrode array. This larger correlation distance combined with the reduced CF gradient and much broader frequency selectivity suggests that LFPs are not a substitute for spike activity in primary auditory cortex.
doi:10.1371/journal.pone.0020046
PMCID: PMC3100317  PMID: 21625385
23.  Sustained increase of spontaneous input and spike transfer in the CA3-CA1 pathway following long-term potentiation in vivo 
Long-term potentiation (LTP) is commonly used to study synaptic plasticity but the associated changes in the spontaneous activity of individual neurons or the computational properties of neural networks in vivo remain largely unclear. The multisynaptic origin of spontaneous spikes makes it difficult to estimate the impact of a particular potentiated input. Accordingly, we adopted an approach that isolates pathway-specific postsynaptic activity from raw local field potentials (LFPs) in the rat hippocampus in order to study the effects of LTP on ongoing spike transfer between cell pairs in the CA3-CA1 pathway. CA1 Schaffer-specific LFPs elicited by spontaneous clustered firing of CA3 pyramidal cells involved a regular succession of elementary micro-field-EPSPs (gamma-frequency) that fired spikes in CA1 units. LTP increased the amplitude but not the frequency of these ongoing excitatory quanta. Also, the proportion of Schaffer-driven spikes in both CA1 pyramidal cells and interneurons increased in a cell-specific manner only in previously connected CA3-CA1 cell pairs, i.e., when the CA3 pyramidal cell had shown pre-LTP significant correlation with firing of a CA1 unit and potentiated spike-triggered average (STA) of Schaffer LFPs following LTP. Moreover, LTP produced subtle reorganization of presynaptic CA3 cell assemblies. These findings show effective enhancement of pathway-specific ongoing activity which leads to increased spike transfer in potentiated segments of a network. They indicate that plastic phenomena induced by external protocols may intensify spontaneous information flow across specific channels as proposed in transsynaptic propagation of plasticity and synfire chain hypotheses that may be the substrate for different types of memory involving multiple brain structures.
doi:10.3389/fncir.2012.00071
PMCID: PMC3464490  PMID: 23060752
synaptic plasticity; local field potentials; long-term potentiation; independent component analysis; synfire chain; spontaneous activity; neuronal circuits
24.  Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons 
PLoS Computational Biology  2012;8(4):e1002478.
The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.
Author Summary
Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.
doi:10.1371/journal.pcbi.1002478
PMCID: PMC3325187  PMID: 22511861
25.  Temporal Correlation Mechanisms and Their Role in Feature Selection: A Single-Unit Study in Primate Somatosensory Cortex 
PLoS Biology  2014;12(11):e1002004.
How neurons pay attention Top-down selective attention mediates feature selection by reducing the noise correlations in neural populations and enhancing the synchronized activity across subpopulations that encode the relevant features of sensory stimuli.
Studies in vision show that attention enhances the firing rates of cells when it is directed towards their preferred stimulus feature. However, it is unknown whether other sensory systems employ this mechanism to mediate feature selection within their modalities. Moreover, whether feature-based attention modulates the correlated activity of a population is unclear. Indeed, temporal correlation codes such as spike-synchrony and spike-count correlations (rsc) are believed to play a role in stimulus selection by increasing the signal and reducing the noise in a population, respectively. Here, we investigate (1) whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature, (2) the interplay between spike-synchrony and rsc during feature selection, and (3) whether feature attention effects are common across the visual and tactile systems. Single-unit recordings were made in secondary somatosensory cortex of three non-human primates while animals engaged in tactile feature (orientation and frequency) and visual discrimination tasks. We found that both firing rate and spike-synchrony between neurons with similar feature selectivity were enhanced when attention was directed towards their preferred feature. However, attention effects on spike-synchrony were twice as large as those on firing rate, and had a tighter relationship with behavioral performance. Further, we observed increased rsc when attention was directed towards the visual modality (i.e., away from touch). These data suggest that similar feature selection mechanisms are employed in vision and touch, and that temporal correlation codes such as spike-synchrony play a role in mediating feature selection. We posit that feature-based selection operates by implementing multiple mechanisms that reduce the overall noise levels in the neural population and synchronize activity across subpopulations that encode the relevant features of sensory stimuli.
Author Summary
Attention can select stimuli in space based on the stimulus features most relevant for a task. Attention effects have been linked to several important phenomena such as modulations in neuronal spiking rate (i.e., the average number of spikes per unit time) and spike-spike synchrony between neurons. Attention has also been associated with spike count correlations, a measure that is thought to reflect correlated noise in the population of neurons. Here, we studied whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature. Simultaneous single-unit recordings were obtained from multiple neurons in secondary somatosensory cortex in non-human primates performing feature-attention tasks. Both firing rate and spike-synchrony were enhanced when attention was directed towards the preferred feature of cells. However, attention effects on spike-synchrony had a tighter relationship with behavior. Further, attention decreased spike-count correlations when it was directed towards the receptive field of cells. Our data indicate that temporal correlation codes play a role in mediating feature selection, and are consistent with a feature-based selection model that operates by reducing the overall noise in a population and synchronizing activity across subpopulations that encode the relevant features of sensory stimuli.
doi:10.1371/journal.pbio.1002004
PMCID: PMC4244037  PMID: 25423284

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