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1.  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
2.  Estimating the contribution of assembly activity to cortical dynamics from spike and population measures 
The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.
doi:10.1007/s10827-010-0241-8
PMCID: PMC2978895  PMID: 20480218
LFP; Synchrony; Oscillations; Network dynamics; Motor cortex
3.  A novel, jitter-based method for detecting and measuring spike synchrony and quantifying temporal firing precision 
Background
Precise spike synchrony, at the millisecond or even sub-millisecond time scale, has been reported in different brain areas, but its neurobiological meaning and its underlying mechanisms remain unknown or controversial. Studying these questions is complicated by the lack of a validated, well-normalized and robust index for quantifying synchrony. Previously used measures of synchrony are often improperly normalized and thereby are not comparable between different experimental conditions, are sensitive to variations in firing rate or to the firing rate differential between the two neurons, and/or rely on untenable assumptions of firing rate stationarity and Poisson statistics. I describe here a novel measure, the Jitter-Based Synchrony Index (JBSI), that overcomes these issues.
Results and discussion
The JBSI method is based on the introduction of virtual spike jitter. While previous implementations of the jitter method used it only to detect synchrony, the JBSI method also quantifies synchrony. Previous implementations of the jitter method used computationally intensive Monte Carlo simulations to generate surrogate spike trains, whereas the JBSI is computed analytically. The JBSI method does not assume any specific firing model, and does not require that the spike trains be locked to a repeating external stimulus. The JBSI can assume values from 1 (maximal possible synchrony) to −1 (minimal possible synchrony) and is therefore properly normalized. Using simulated Poisson spike trains with introduced controlled spike coincidences, I demonstrate that the JBSI is a linear measure of the spike coincidence rate, is independent of the mean firing frequency or the firing frequency differential between the two neurons, and is not sensitive to co-modulations in the firing rates of the two neurons. In contrast, several commonly used synchrony indices fail under one or more of these scenarios. I also demonstrate how the JBSI can be used to estimate the spike timing precision in the system.
Conclusions
The JBSI is a conceptually simple and computationally efficient method that can be used to compute the statistical significance of firing synchrony, to quantify synchrony as a well-normalized index, and to estimate the degree of temporal precision in the system.
doi:10.1186/2042-1001-2-5
PMCID: PMC3423071  PMID: 22551243
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.
doi:10.1371/journal.pcbi.1000551
PMCID: PMC2760751  PMID: 19876377
5.  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
6.  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.
doi:10.1371/journal.pcbi.1002176
PMCID: PMC3188510  PMID: 21998568
7.  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
8.  Inhibitory synchrony as a mechanism for attentional gain modulation☆ 
Journal of physiology, Paris  2005;98(4-6):296-314.
Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30–50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron’s firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f–I) curves. For a large number of inhibitory inputs (~50), the f–I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity—the model neuron responded to weaker inputs I. For a small number (~10), the f–I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response—the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.
doi:10.1016/j.jphysparis.2005.09.002
PMCID: PMC2872773  PMID: 16274973
Selective attention; Synchrony; Noise; Gamma oscillation; Gain modulation; Computer model
9.  Context Matters: The Illusive Simplicity of Macaque V1 Receptive Fields 
PLoS ONE  2012;7(7):e39699.
Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron’s own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R2 as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R2∼5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.
doi:10.1371/journal.pone.0039699
PMCID: PMC3389039  PMID: 22802940
10.  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
11.  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
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.  Predicting Spike Occurrence and Neuronal Responsiveness from LFPs in Primary Somatosensory Cortex 
PLoS ONE  2012;7(5):e35850.
Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.
doi:10.1371/journal.pone.0035850
PMCID: PMC3346760  PMID: 22586452
14.  Spike-Timing Dependent Plasticity and Feed-Forward Input Oscillations Produce Precise and Invariant Spike Phase-Locking 
In the hippocampus and the neocortex, the coupling between local field potential (LFP) oscillations and the spiking of single neurons can be highly precise, across neuronal populations and cell types. Spike phase (i.e., the spike time with respect to a reference oscillation) is known to carry reliable information, both with phase-locking behavior and with more complex phase relationships, such as phase precession. How this precision is achieved by neuronal populations, whose membrane properties and total input may be quite heterogeneous, is nevertheless unknown. In this note, we investigate a simple mechanism for learning precise LFP-to-spike coupling in feed-forward networks – the reliable, periodic modulation of presynaptic firing rates during oscillations, coupled with spike-timing dependent plasticity. When oscillations are within the biological range (2–150 Hz), firing rates of the inputs change on a timescale highly relevant to spike-timing dependent plasticity (STDP). Through analytic and computational methods, we find points of stable phase-locking for a neuron with plastic input synapses. These points correspond to precise phase-locking behavior in the feed-forward network. The location of these points depends on the oscillation frequency of the inputs, the STDP time constants, and the balance of potentiation and de-potentiation in the STDP rule. For a given input oscillation, the balance of potentiation and de-potentiation in the STDP rule is the critical parameter that determines the phase at which an output neuron will learn to spike. These findings are robust to changes in intrinsic post-synaptic properties. Finally, we discuss implications of this mechanism for stable learning of spike-timing in the hippocampus.
doi:10.3389/fncom.2011.00045
PMCID: PMC3216007  PMID: 22110429
spike-timing dependent plasticity; oscillations; phase-locking; stable learning; stability of neuronal plasticity; place fields
15.  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
16.  Computing with Neural Synchrony 
PLoS Computational Biology  2012;8(6):e1002561.
Neurons communicate primarily with spikes, but most theories of neural computation are based on firing rates. Yet, many experimental observations suggest that the temporal coordination of spikes plays a role in sensory processing. Among potential spike-based codes, synchrony appears as a good candidate because neural firing and plasticity are sensitive to fine input correlations. However, it is unclear what role synchrony may play in neural computation, and what functional advantage it may provide. With a theoretical approach, I show that the computational interest of neural synchrony appears when neurons have heterogeneous properties. In this context, the relationship between stimuli and neural synchrony is captured by the concept of synchrony receptive field, the set of stimuli which induce synchronous responses in a group of neurons. In a heterogeneous neural population, it appears that synchrony patterns represent structure or sensory invariants in stimuli, which can then be detected by postsynaptic neurons. The required neural circuitry can spontaneously emerge with spike-timing-dependent plasticity. Using examples in different sensory modalities, I show that this allows simple neural circuits to extract relevant information from realistic sensory stimuli, for example to identify a fluctuating odor in the presence of distractors. This theory of synchrony-based computation shows that relative spike timing may indeed have computational relevance, and suggests new types of neural network models for sensory processing with appealing computational properties.
Author Summary
How does the brain compute? Traditional theories of neural computation describe the operating function of neurons in terms of average firing rates, with the timing of spikes bearing little information. However, numerous studies have shown that spike timing can convey information and that neurons are highly sensitive to synchrony in their inputs. Here I propose a simple spike-based computational framework, based on the idea that stimulus-induced synchrony can be used to extract sensory invariants (for example, the location of a sound source), which is a difficult task for classical neural networks. It relies on the simple remark that a series of repeated coincidences is in itself an invariant. Many aspects of perception rely on extracting invariant features, such as the spatial location of a time-varying sound, the identity of an odor with fluctuating intensity, the pitch of a musical note. I demonstrate that simple synchrony-based neuron models can extract these useful features, by using spiking models in several sensory modalities.
doi:10.1371/journal.pcbi.1002561
PMCID: PMC3375225  PMID: 22719243
17.  Saccade-Related Modulations of Neuronal Excitability Support Synchrony of Visually Elicited Spikes 
Cerebral Cortex (New York, NY)  2011;21(11):2482-2497.
During natural vision, primates perform frequent saccadic eye movements, allowing only a narrow time window for processing the visual information at each location. Individual neurons may contribute only with a few spikes to the visual processing during each fixation, suggesting precise spike timing as a relevant mechanism for information processing. We recently found in V1 of monkeys freely viewing natural images, that fixation-related spike synchronization occurs at the early phase of the rate response after fixation-onset, suggesting a specific role of the first response spikes in V1. Here, we show that there are strong local field potential (LFP) modulations locked to the onset of saccades, which continue into the successive fixation periods. Visually induced spikes, in particular the first spikes after the onset of a fixation, are locked to a specific epoch of the LFP modulation. We suggest that the modulation of neural excitability, which is reflected by the saccade-related LFP changes, serves as a corollary signal enabling precise timing of spikes in V1 and thereby providing a mechanism for spike synchronization.
doi:10.1093/cercor/bhr020
PMCID: PMC3183421  PMID: 21459839
free viewing; local field potential; phase locking; primary visual cortex; spike synchrony
18.  Network rhythms influence the relationship between spike-triggered local field potential and functional connectivity 
Characterizing the functional connectivity between neurons is key for understanding brain function. We recorded spikes and local field potentials (LFP) from multi-electrode arrays implanted in monkey visual cortex to test the hypotheses that spikes generated outward traveling LFP waves and the strength of functional connectivity depended on stimulus contrast, as described recently. These hypotheses were proposed based on the observation that the latency of the peak negativity of the spike-triggered LFP average (STA) increased with distance between the spike and LFP electrodes, and the magnitude of the STA negativity and the distance over which it was observed decreased with increasing stimulus contrast. Detailed analysis of the shape of the STA, however, revealed contributions from two distinct sources – a transient negativity in the LFP locked to the spike (∼0 ms) that attenuated rapidly with distance, and a low frequency rhythm with peak negativity ∼25 ms after the spike that attenuated slowly with distance. The overall negative peak of the LFP, which combined both these components, shifted from ∼0 to ∼25 ms going from electrodes near the spike to electrodes far from the spike, giving an impression of a traveling wave, although the shift was fully explained by changing contributions from the two fixed components. The low frequency rhythm was attenuated during stimulus presentations, decreasing the overall magnitude of the STA. These results highlight the importance of accounting for the network activity while using STAs to determine functional connectivity.
doi:10.1523/JNEUROSCI.1856-11.2011
PMCID: PMC3488382  PMID: 21880928
19.  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
20.  Rapid Changes in Thalamic Firing Synchrony During Repetitive Whisker Stimulation 
Thalamic firing synchrony is thought to ensure selective transmission of relevant sensory information to the recipient cortical neurons by rendering them more responsive to temporally correlated input spikes. However, direct evidence for a synchrony code in the thalamus is limited. Here, we directly measure thalamic firing synchrony and its stimulus-induced modulation over time, using simultaneous single unit recordings from individual thalamic barreloids in the rat somatosensory whisker/barrel system. Employing whisker deflections varying in velocity or frequency and a cross-correlation approach, we find systematic changes in both time-course and strength of thalamic firing synchrony as a function of stimulus parameters and sensory adaptation. Synchrony develops faster and is greater with higher velocity deflections. Greater firing synchrony reflects stimulus-dependent increases in instantaneous firing rates, greater spike time precision relative to stimulus onset as well as common input that likely arises from divergent trigeminothalamic and corticothalamic neurons. With adaptation, synchrony decreases and takes longer to develop but is more dependent on the cells’ common inputs. Rapid, sharp increases in thalamic synchrony mirroring quick increases in whisker velocity occur also during ongoing random, high-frequency whisker vibrations. Together, results demonstrate millisecond by millisecond changes in thalamic near-synchronous firing during complex patterns of ongoing vibrissa movements that may ensure transmission of preferred sensory information in local thalamocortical circuits during whisking and active touch.
doi:10.1523/JNEUROSCI.1586-08.2008
PMCID: PMC2617717  PMID: 18971458
thalamocortical; firing synchrony; somatosensory; barreloid; barrel cortex; whiskers
21.  The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics 
PLoS Computational Biology  2009;5(9):e1000493.
The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.
Author Summary
A central issue in biology is how local processes yield global consequences. This is especially relevant for neurons since these spatially extended cells process local synaptic inputs to generate global action potential output. The dendritic tree of a neuron, which receives most of the inputs, expresses ion channels that can generate nonlinear dynamics. A prominent phenomenon resulting from such ion channels are voltage oscillations. The distribution of the active membrane channels throughout the cell is often highly non-uniform. This can turn the dendritic tree into a network of sparsely spaced local oscillators. Here we analyze whether local dendritic oscillators can produce cell-wide voltage oscillations. Our mathematical theory shows that indeed even when the dendritic oscillators are weakly coupled, they lock their phases and give global oscillations. We show how the biophysical properties of the dendrites determine the global locking and how it can be controlled by synaptic inputs. As a consequence of global locking, even individual synaptic inputs can affect the timing of action potentials. In fact, dendrites locking in synchrony can lead to sustained firing of the cell. We show that dendritic trees can be bistable, with dendrites locking in either synchrony or asynchrony, which may provide a novel mechanism for single cell-based memory.
doi:10.1371/journal.pcbi.1000493
PMCID: PMC2725317  PMID: 19730677
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.  Task-Dependent Changes in Cross-Level Coupling between Single Neurons and Oscillatory Activity in Multiscale Networks 
PLoS Computational Biology  2012;8(12):e1002809.
Understanding the principles governing the dynamic coordination of functional brain networks remains an important unmet goal within neuroscience. How do distributed ensembles of neurons transiently coordinate their activity across a variety of spatial and temporal scales? While a complete mechanistic account of this process remains elusive, evidence suggests that neuronal oscillations may play a key role in this process, with different rhythms influencing both local computation and long-range communication. To investigate this question, we recorded multiple single unit and local field potential (LFP) activity from microelectrode arrays implanted bilaterally in macaque motor areas. Monkeys performed a delayed center-out reach task either manually using their natural arm (Manual Control, MC) or under direct neural control through a brain-machine interface (Brain Control, BC). In accord with prior work, we found that the spiking activity of individual neurons is coupled to multiple aspects of the ongoing motor beta rhythm (10–45 Hz) during both MC and BC, with neurons exhibiting a diversity of coupling preferences. However, here we show that for identified single neurons, this beta-to-rate mapping can change in a reversible and task-dependent way. For example, as beta power increases, a given neuron may increase spiking during MC but decrease spiking during BC, or exhibit a reversible shift in the preferred phase of firing. The within-task stability of coupling, combined with the reversible cross-task changes in coupling, suggest that task-dependent changes in the beta-to-rate mapping play a role in the transient functional reorganization of neural ensembles. We characterize the range of task-dependent changes in the mapping from beta amplitude, phase, and inter-hemispheric phase differences to the spike rates of an ensemble of simultaneously-recorded neurons, and discuss the potential implications that dynamic remapping from oscillatory activity to spike rate and timing may hold for models of computation and communication in distributed functional brain networks.
Author Summary
How is the functional role of a particular neuron established within an ensemble? The concept of a neural tuning curve – the mapping from input variables such as movement direction to output firing rate – has proven useful in investigating neural function. However, prior work shows that tuning curves are not fixed but may be remapped as a function of task demands – presumably via high-level mechanisms of cognitive control. How is this accomplished? Brain rhythms may play a causal role in this process, but the coupling of single cells to network activity remains poorly understood. We investigated the coupling between rhythmic beta activity and spiking as macaques performed two different tasks. This coupling can be described in terms of a function that maps oscillatory amplitude and phase to instantaneous spike rate. Similarly to direction tuning, this “internal” tuning curve also exhibits task-dependent changes. We characterize these changes across a large ensemble of simultaneously-recorded cells, and consider some of the neuro-computational implications presented by cross-level coupling between single cells and large-scale networks. In particular, relative to the slow time-scale of behavior, the observed beta-to-rate mappings may prove useful for modulating winner-take-all dynamics on intermediate time-scales and relative spike timing on fast time-scales.
doi:10.1371/journal.pcbi.1002809
PMCID: PMC3527280  PMID: 23284276
24.  Attention Reduces Stimulus-Driven Gamma Frequency Oscillations and Spike Field Coherence in V1 
Neuron  2010;66(1-2):114-125.
Summary
Rhythmic activity of neuronal ensembles has been proposed to play an important role in cognitive functions such as attention, perception, and memory. Here we investigate whether rhythmic activity in V1 of the macaque monkey (macaca mulatta) is affected by top-down visual attention. We measured the local field potential (LFP) and V1 spiking activity while monkeys performed an attention-demanding detection task. We show that gamma oscillations were strongly modulated by the stimulus and by attention. Stimuli that engaged inhibitory mechanisms induced the largest gamma LFP oscillations and the largest spike field coherence. Directing attention toward a visual stimulus at the receptive field of the recorded neurons decreased LFP gamma power and gamma spike field coherence. This decrease could reflect an attention-mediated reduction of surround inhibition. Changes in synchrony in V1 would thus be a byproduct of reduced inhibitory drive, rather than a mechanism that directly aids perceptual processing.
Highlights
► Gamma synchronization in V1 depends on activation of normalization mechanisms ► Attention reduces strength of LFP gamma synchronization in V1 ► Attention reduces spike field coherence in V1 ► Increased gamma spike field coherence in is not a universal mechanism of attention
doi:10.1016/j.neuron.2010.03.013
PMCID: PMC2923752  PMID: 20399733
SYSNEURO
25.  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

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