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1.  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
2.  Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia 
PLoS ONE  2012;7(12):e51530.
Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson's disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson's disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson's disease.
doi:10.1371/journal.pone.0051530
PMCID: PMC3526636  PMID: 23284707
3.  Intermittent neural synchronization in Parkinson’s disease 
Nonlinear dynamics  2011;68(3):329-346.
Motor symptoms of Parkinson’s disease are related to the excessive synchronized oscillatory activity in the beta frequency band (around 20Hz) in the basal ganglia and other parts of the brain. This review explores the dynamics and potential mechanisms of these oscillations employing ideas and methods from nonlinear dynamics. We present extensive experimental documentation of the relevance of synchronized oscillations to motor behavior in Parkinson’s disease, and we discuss the intermittent character of this synchronization. The reader is introduced to novel time-series analysis techniques aimed at the detection of the fine temporal structure of intermittent phase locking observed in the brains of parkinsonian patients. Modeling studies of brain networks are reviewed, which may describe the observed intermittent synchrony, and we discuss what these studies reveal about brain dynamics in Parkinson’s disease. The parkinsonian brain appears to exist on the boundary between phase-locked and nonsynchronous dynamics. Such a situation may be beneficial in the healthy state, as it may allow for easy formation and dissociation of transient patterns of synchronous activity which are required for normal motor behavior. Dopaminergic degeneration in Parkinson’s disease may shift the brain networks closer to this boundary, which would still permit some motor behavior while accounting for the associated motor deficits. Understanding the mechanisms of the intermittent synchrony in Parkinson’s disease is also important for biomedical engineering since efficient control strategies for suppression of pathological synchrony through deep brain stimulation require knowledge of the dynamics of the processes subjected to control.
doi:10.1007/s11071-011-0223-z
PMCID: PMC3347643  PMID: 22582010
Intermittency; phase locking; phase synchronization; basal ganglia; subthalamic nucleus; neuronal modeling
4.  Asynchronous response of coupled pacemaker neurons 
Physical review letters  2009;102(6):068102.
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock spike-to-spike for strong mutual coupling. But the shared input can desynchronize the locked spike-pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.
PMCID: PMC2679421  PMID: 19257636
5.  The neuromagnetic response to spoken sentences: Co-modulation of theta band amplitude and phase 
NeuroImage  2012;60(4):2118-2127.
Speech elicits a phase-locked response in the auditory cortex that is dominated by theta (3–7 Hz) frequencies when observed via magnetoencephalography (MEG). This phase-locked response is potentially explained as new phase-locked activity superimposed on the ongoing theta oscillation or, alternatively, as phase-resetting of the ongoing oscillation. The conventional method used to distinguish between the two hypotheses is the comparison of post- to prestimulus amplitude for the phase-locked frequency across a set of trials. In theory, increased amplitude indicates the presence of additive activity, while unchanged amplitude points to phase-resetting. However, this interpretation may not be valid if the amplitude of ongoing background activity also changes following the stimulus. In this study, we employ a new approach that circumvents this problem. Specifically, we utilize a fine-grained time–frequency analysis of MEG channel data to examine the co-modulation of amplitude change and phase coherence in the post-stimulus theta-band response. If the phase-locked response is attributable solely to phase-resetting of the ongoing theta oscillation, then amplitude and phase coherence should be uncorrelated. In contrast, additive activity should produce a positive correlation. We find significant positive correlation not only during the onset response but also throughout the response period. In fact, transient increases in phase coherence are accompanied by transient increases in amplitude in accordance with a “signal plus background” model of the evoked response. The results support the hypothesis that the theta-band phase-locked response to attended speech observed using MEG is dominated by additive phase-locked activity.
doi:10.1016/j.neuroimage.2012.02.028
PMCID: PMC3593735  PMID: 22374481
Auditory; Speech; MEG; Evoked; Phase; Amplitude
6.  Ethanol reduces the phase locking of neural activity in human and rodent brain 
Brain research  2012;1450:67-79.
How the neuromolecular actions of ethanol translate to its observed intoxicating effects remains poorly understood. Synchrony of phase (phase locking) of event-related oscillations (EROs) within and between different brain areas has been suggested to reflect communication exchange between neural networks and as such may be a sensitive and translational measure of ethanol’s effects. Using a similar auditory event-related potential paradigm in both rats and humans we investigated the phase variability of EROs collected from 38 young men who had participated in an ethanol/placebo challenge protocol, and 46 adult male rats given intraperitoneal injections of ethanol/saline. Phase locking was significantly higher in the delta frequencies in humans than in rats. Phase locking was also higher for the rare (target) tone than the frequent (non-target) tone in both species. Significant reductions in phase locking to the rare (target) tone in the delta, theta, alpha, beta and gamma frequencies, within and between brain sites, was found at one hour following ethanol as compared to placebo/saline administration in both rats and humans. Reductions in phase locking in the alpha frequencies in the parietal cortex were found to be correlated with blood ethanol concentrations. These findings are consistent with the hypothesis that ethanol’s intoxicating actions in the brain include reducing synchrony within and between neuronal networks, perhaps by increasing the level of noise in key neuromolecular interactions.
doi:10.1016/j.brainres.2012.02.039
PMCID: PMC3503530  PMID: 22410292
EEG; ERO; ERP; phase locking index; ethanol; time series analysis
7.  Maximal variability of phase synchrony in cortical networks with neuronal avalanches 
The Journal of Neuroscience  2012;32(3):1061-1072.
Ongoing interactions among cortical neurons often manifest as network-level synchrony. Understanding the spatiotemporal dynamics of such spontaneous synchrony is important because it may 1) influence network response to input, 2) shape activity-dependent microcircuit structure, and 3) reveal fundamental network properties, such as an imbalance of excitation (E) and inhibition (I). Here we delineate the spatiotemporal character of spontaneous synchrony in rat cortex slice cultures and a computational model over a range of different E-I conditions including disfacilitated (antagonized AMPA, NMDA receptors), unperturbed, and disinhibited (antagonized GABAA receptors). Local field potential was recorded with multi-electrode arrays during spontaneous burst activity. Synchrony among neuronal groups was quantified based on phase-locking among recording sites. As network excitability was increased from low to high, we discovered three phenomena at an intermediate excitability level: 1) onset of synchrony, 2) maximized variability of synchrony, and 3) neuronal avalanches. Our computational model predicted that these three features occur when the network operates near a unique balanced E-I condition called ‘criticality’. These results were invariant to changes in the measurement spatial extent, spatial resolution, and frequency bands. Our findings indicate that moderate average synchrony, which is required to avoid pathology, occurs over a limited range of E-I conditions and emerges together with maximally variable synchrony. If variable synchrony is detrimental to cortical function, this is a cost paid for moderate average synchrony. However, if variable synchrony is beneficial, then by operating near criticality the cortex may doubly benefit from moderate mean and maximized variability of synchrony.
doi:10.1523/JNEUROSCI.2771-11.2012
PMCID: PMC3319677  PMID: 22262904
multi-site electrode recording; synchrony; phase synchrony; entropy; neuronal avalanches; neural excitability; critical phenomena
8.  Variety of Alternative Stable Phase-Locking in Networks of Electrically Coupled Relaxation Oscillators 
PLoS ONE  2014;9(2):e86572.
We studied the dynamics of a large-scale model network comprised of oscillating electrically coupled neurons. Cells are modeled as relaxation oscillators with short duty cycle, so they can be considered either as models of pacemaker cells, spiking cells with fast regenerative and slow recovery variables or firing rate models of excitatory cells with synaptic depression or cellular adaptation.
It was already shown that electrically coupled relaxation oscillators exhibit not only synchrony but also anti-phase behavior if electrical coupling is weak. We show that a much wider spectrum of spatiotemporal patterns of activity can emerge in a network of electrically coupled cells as a result of switching from synchrony, produced by short external signals of different spatial profiles. The variety of patterns increases with decreasing rate of neuronal firing (or duty cycle) and with decreasing strength of electrical coupling. We study also the effect of network topology - from all-to-all – to pure ring connectivity, where only the closest neighbors are coupled.
We show that the ring topology promotes anti-phase behavior as compared to all-to-all coupling. It also gives rise to a hierarchical organization of activity: during each of the main phases of a given pattern cells fire in a particular sequence determined by the local connectivity. We have analyzed the behavior of the network using geometric phase plane methods and we give heuristic explanations of our findings.
Our results show that complex spatiotemporal activity patterns can emerge due to the action of stochastic or sensory stimuli in neural networks without chemical synapses, where each cell is equally coupled to others via gap junctions. This suggests that in developing nervous systems where only electrical coupling is present such a mechanism can lead to the establishment of proto-networks generating premature multiphase oscillations whereas the subsequent emergence of chemical synapses would later stabilize generated patterns.
doi:10.1371/journal.pone.0086572
PMCID: PMC3919711  PMID: 24520321
9.  A Phase-Locked Loop Model of the Response of the Postural Control System to Periodic Platform Motion 
A phase-locked loop (PLL) model of the response of the postural control system to periodic platform motion is proposed. The PLL model is based on the hypothesis that quiet standing (QS) postural sway can be characterized as a weak sinusoidal oscillation corrupted with noise. Because the signal to noise ratio is quite low, the characteristics of the QS oscillator are not measured directly from the QS sway, instead they are inferred from the response of the oscillator to periodic motion of the platform. When a sinusoidal stimulus is applied, the QS oscillator changes speed as needed until its frequency matches that of the platform, thus achieving phase lock in a manner consistent with a PLL control mechanism. The PLL model is highly effective in representing the frequency, amplitude, and phase shift of the sinusoidal component of the phase-locked response over a range of platform frequencies and amplitudes. Qualitative analysis of the PLL control mechanism indicates that there is a finite range of frequencies over which phase lock is possible, and that the size of this capture range decreases with decreasing platform amplitude. The PLL model was tested experimentally using nine healthy subjects and the results reveal good agreement with a mean phase shift error of 13.7° and a mean amplitude error of 0.8 mm.
doi:10.1109/TNSRE.2010.2047593
PMCID: PMC2913702  PMID: 20378479
Mathematical model; phase-locked loop; postural control
10.  Fast Computations in Cortical Ensembles Require Rapid Initiation of Action Potentials 
The abilities of neuronal populations to encode rapidly varying stimuli and respond quickly to abrupt input changes are crucial for basic neuronal computations, such as coincidence detection, grouping by synchrony, and spike-timing-dependent plasticity, as well as for the processing speed of neuronal networks. Theoretical analyses have linked these abilities to the fast-onset dynamics of action potentials (APs). Using a combination of whole-cell recordings from rat neocortical neurons and computer simulations, we provide the first experimental evidence for this conjecture and prove its validity for the case of distal AP initiation in the axon initial segment (AIS), typical for cortical neurons. Neocortical neurons with fast-onset APs in the soma can phase-lock their population firing to signal frequencies up to ~300 – 400 Hz and respond within 1–2 ms to subtle changes of input current. The ability to encode high frequencies and response speed were dramatically reduced when AP onset was slowed by experimental manipulations or was intrinsically slow due to immature AP generation mechanisms. Multicompartment conductance-based models reproducing the initiation of spikes in the AIS could encode high frequencies only if AP onset was fast at the initiation site (e.g., attributable to cooperative gating of a fraction of sodium channels) but not when fast onset of somatic AP was produced solely by backpropagation. We conclude that fast-onset dynamics is a genuine property of cortical AP generators. It enables fast computations in cortical circuits that are rich in recurrent connections both within each region and across the hierarchy of areas.
doi:10.1523/JNEUROSCI.0771-12.2013
PMCID: PMC3964617  PMID: 23392659
11.  Identification of highly synchronized subnetworks from gene expression data 
BMC Bioinformatics  2013;14(Suppl 9):S5.
Background
There has been a growing interest in identifying context-specific active protein-protein interaction (PPI) subnetworks through integration of PPI and time course gene expression data. However the interaction dynamics during the biological process under study has not been sufficiently considered previously.
Methods
Here we propose a topology-phase locking (TopoPL) based scoring metric for identifying active PPI subnetworks from time series expression data. First the temporal coordination in gene expression changes is evaluated through phase locking analysis; The results are subsequently integrated with PPI to define an activity score for each PPI subnetwork, based on individual member expression, as well topological characteristics of the PPI network and of the expression temporal coordination network; Lastly, the subnetworks with the top scores in the whole PPI network are identified through simulated annealing search.
Results
Application of TopoPL to simulated data and to the yeast cell cycle data showed that it can more sensitively identify biologically meaningful subnetworks than the method that only utilizes the static PPI topology, or the additive scoring method. Using TopoPL we identified a core subnetwork with 49 genes important to yeast cell cycle. Interestingly, this core contains a protein complex known to be related to arrangement of ribosome subunits that exhibit extremely high gene expression synchronization.
Conclusions
Inclusion of interaction dynamics is important to the identification of relevant gene networks.
doi:10.1186/1471-2105-14-S9-S5
PMCID: PMC3698028  PMID: 23901792
12.  Neural Correlates of True and False Memory in Mild Cognitive Impairment 
PLoS ONE  2012;7(10):e48357.
The goal of this research was to investigate the changes in neural processing in mild cognitive impairment. We measured phase synchrony, amplitudes, and event-related potentials in veridical and false memory to determine whether these differed in participants with mild cognitive impairment compared with typical, age-matched controls. Empirical mode decomposition phase locking analysis was used to assess synchrony, which is the first time this analysis technique has been applied in a complex cognitive task such as memory processing. The technique allowed assessment of changes in frontal and parietal cortex connectivity over time during a memory task, without a priori selection of frequency ranges, which has been shown previously to influence synchrony detection. Phase synchrony differed significantly in its timing and degree between participant groups in the theta and alpha frequency ranges. Timing differences suggested greater dependence on gist memory in the presence of mild cognitive impairment. The group with mild cognitive impairment had significantly more frontal theta phase locking than the controls in the absence of a significant behavioural difference in the task, providing new evidence for compensatory processing in the former group. Both groups showed greater frontal phase locking during false than true memory, suggesting increased searching when no actual memory trace was found. Significant inter-group differences in frontal alpha phase locking provided support for a role for lower and upper alpha oscillations in memory processing. Finally, fronto-parietal interaction was significantly reduced in the group with mild cognitive impairment, supporting the notion that mild cognitive impairment could represent an early stage in Alzheimer’s disease, which has been described as a ‘disconnection syndrome’.
doi:10.1371/journal.pone.0048357
PMCID: PMC3485202  PMID: 23118992
13.  Connectivity in the Yeast Cell Cycle Transcription Network: Inferences from Neural Networks 
PLoS Computational Biology  2006;2(12):e169.
A current challenge is to develop computational approaches to infer gene network regulatory relationships based on multiple types of large-scale functional genomic data. We find that single-layer feed-forward artificial neural network (ANN) models can effectively discover gene network structure by integrating global in vivo protein:DNA interaction data (ChIP/Array) with genome-wide microarray RNA data. We test this on the yeast cell cycle transcription network, which is composed of several hundred genes with phase-specific RNA outputs. These ANNs were robust to noise in data and to a variety of perturbations. They reliably identified and ranked 10 of 12 known major cell cycle factors at the top of a set of 204, based on a sum-of-squared weights metric. Comparative analysis of motif occurrences among multiple yeast species independently confirmed relationships inferred from ANN weights analysis. ANN models can capitalize on properties of biological gene networks that other kinds of models do not. ANNs naturally take advantage of patterns of absence, as well as presence, of factor binding associated with specific expression output; they are easily subjected to in silico “mutation” to uncover biological redundancies; and they can use the full range of factor binding values. A prominent feature of cell cycle ANNs suggested an analogous property might exist in the biological network. This postulated that “network-local discrimination” occurs when regulatory connections (here between MBF and target genes) are explicitly disfavored in one network module (G2), relative to others and to the class of genes outside the mitotic network. If correct, this predicts that MBF motifs will be significantly depleted from the discriminated class and that the discrimination will persist through evolution. Analysis of distantly related Schizosaccharomyces pombe confirmed this, suggesting that network-local discrimination is real and complements well-known enrichment of MBF sites in G1 class genes.
Synopsis
A current challenge is to develop computational approaches to infer gene network regulatory relationships by integrating multiple types of large-scale functional genomic data. This paper shows that simple artificial neural networks (ANNs) employed in a new way do this very well. The ANN models are well-suited to capitalize on natural properties of gene networks in ways that many previous methods do not. Resulting gene network connections inferred between transcription factors and RNA output patterns are robust to noise in large-scale input datasets and to differences in RNA clustering class inputs. This was shown by using the yeast cell cycle gene network as a test case. The cycle has multiple classes of oscillatory RNAs, and Hart, Mjolsness, and Wold show that the ANNs identify key connections that associate genes from each cell cycle phase group with known and candidate regulators. Comparative analysis of network connectivity across multiple genomes showed strong conservation of basic factor-to-output relationships, although at the greatest evolutionary distances the specific target genes have mainly changed identity.
doi:10.1371/journal.pcbi.0020169
PMCID: PMC1761652  PMID: 17194216
14.  Connectivity in the Yeast Cell Cycle Transcription Network: Inferences from Neural Networks 
PLoS Computational Biology  2006;2(12):e169.
A current challenge is to develop computational approaches to infer gene network regulatory relationships based on multiple types of large-scale functional genomic data. We find that single-layer feed-forward artificial neural network (ANN) models can effectively discover gene network structure by integrating global in vivo protein:DNA interaction data (ChIP/Array) with genome-wide microarray RNA data. We test this on the yeast cell cycle transcription network, which is composed of several hundred genes with phase-specific RNA outputs. These ANNs were robust to noise in data and to a variety of perturbations. They reliably identified and ranked 10 of 12 known major cell cycle factors at the top of a set of 204, based on a sum-of-squared weights metric. Comparative analysis of motif occurrences among multiple yeast species independently confirmed relationships inferred from ANN weights analysis. ANN models can capitalize on properties of biological gene networks that other kinds of models do not. ANNs naturally take advantage of patterns of absence, as well as presence, of factor binding associated with specific expression output; they are easily subjected to in silico “mutation” to uncover biological redundancies; and they can use the full range of factor binding values. A prominent feature of cell cycle ANNs suggested an analogous property might exist in the biological network. This postulated that “network-local discrimination” occurs when regulatory connections (here between MBF and target genes) are explicitly disfavored in one network module (G2), relative to others and to the class of genes outside the mitotic network. If correct, this predicts that MBF motifs will be significantly depleted from the discriminated class and that the discrimination will persist through evolution. Analysis of distantly related Schizosaccharomyces pombe confirmed this, suggesting that network-local discrimination is real and complements well-known enrichment of MBF sites in G1 class genes.
Synopsis
A current challenge is to develop computational approaches to infer gene network regulatory relationships by integrating multiple types of large-scale functional genomic data. This paper shows that simple artificial neural networks (ANNs) employed in a new way do this very well. The ANN models are well-suited to capitalize on natural properties of gene networks in ways that many previous methods do not. Resulting gene network connections inferred between transcription factors and RNA output patterns are robust to noise in large-scale input datasets and to differences in RNA clustering class inputs. This was shown by using the yeast cell cycle gene network as a test case. The cycle has multiple classes of oscillatory RNAs, and Hart, Mjolsness, and Wold show that the ANNs identify key connections that associate genes from each cell cycle phase group with known and candidate regulators. Comparative analysis of network connectivity across multiple genomes showed strong conservation of basic factor-to-output relationships, although at the greatest evolutionary distances the specific target genes have mainly changed identity.
doi:10.1371/journal.pcbi.0020169
PMCID: PMC1761652  PMID: 17194216
15.  Nested synchrony—a novel cross-scale interaction among neuronal oscillations 
Neuronal interactions form the basis for our brain function, and oscillations and synchrony are the principal candidates for mediating them in the cortical networks. Phase synchrony, where oscillatory neuronal ensembles directly synchronize their phases, enables precise integration between separated brain regions. However, it is unclear how neuronal interactions are dynamically coordinated in space and over time. Cross-scale effects have been proposed to be responsible for linking levels of processing hierarchy and to regulate neuronal dynamics. Most notably, nested oscillations, where the phase of a neuronal oscillation modulates the amplitude of a faster one, may locally integrate neuronal activities in distinct frequency bands. Yet, hierarchical control of inter-areal synchrony could provide a more comprehensive view to the dynamical structure of oscillatory interdependencies in the human brain. In this study, the notion of nested oscillations is extended to a cross-frequency and inter-areal model of oscillatory interactions. In this model, the phase of a slower oscillation modulates inter-areal synchrony in a higher frequency band. This would allow cross-scale integration of global interactions and, thus, offers a mechanism for binding distributed neuronal activities. We show that inter-areal phase synchrony can be modulated by the phase of a slower neuronal oscillation using magnetoencephalography (MEG). This effect is the most pronounced at frequencies below 35 Hz. Importantly, changes in oscillation amplitudes did not explain the findings. We expect that the novel cross-frequency interaction could offer new ways to understand the flexible but accurate dynamic organization of ongoing neuronal oscillations and synchrony.
doi:10.3389/fphys.2012.00384
PMCID: PMC3458414  PMID: 23055985
neuronal oscillations; magnetoencephalography; nested oscillations; oscillation synchrony
16.  Oscillations and hippocampal–prefrontal synchrony 
Current opinion in neurobiology  2011;21(3):467-474.
The hippocampus, a structure required for many types of memory, connects to the medial prefrontal cortex, an area that helps direct neuronal information streams during intentional behaviors. Increasing evidence suggests that oscillations regulate communication between these two regions. Theta rhythms may facilitate hippocampal inputs to the medial prefrontal cortex during mnemonic tasks and may also integrate series of functionally relevant gamma-mediated cell assemblies in the medial prefrontal cortex. During slow-wave sleep, temporal coordination of hippocampal sharp wave-ripples and medial prefrontal cortex spindles may be an important component of the process by which memories become hippocampus-independent. Studies using rodent models indicate that oscillatory phase-locking is disturbed in schizophrenia, emphasizing the need for more studies of oscillatory synchrony in the hippocampal–prefrontal network.
doi:10.1016/j.conb.2011.04.006
PMCID: PMC3578407  PMID: 21571522
17.  Auditory steady state responses in a schizophrenia rat model probed by excitatory/inhibitory receptor manipulation 
Alterations in neural synchrony and oscillations may contribute to the pathophysiology of schizophrenia and reflect aberrations in cortical glutamatergic and GABAergic neurotransmission. We tested the effects of a GABA agonist and a NMDA antagonist on auditory steady state responses (ASSRs) in awake rats with neonatal ventral hippocampal lesions (NVHLs) as a neurodevelopmental model of schizophrenia. NVHL vs. SHAM lesioned rats were injected with saline then either ketamine (NMDA antagonist) or muscimol (GABAA agonist). Time-frequency analyses examined alterations in phase locking (consistency) across trials and changes in total power (magnitude). ASSRs were compared at 5 stimulation frequencies (10, 20, 30, 40, and 50 Hz). In SHAM rats, phase locking and power generally increased with stimulation frequency. Both ketamine and muscimol also increased phase locking and power in SHAM rats, but mostly in the 20 to 40 Hz range. NVHL and ketamine altered the frequency dependence of phase locking, while only ketamine changed power frequency dependence. Muscimol affected power, but not phase locking, in the NVHL rats. NVHL and ketamine models of schizophrenia produce similar independent effects on ASSR, potentially representing similar forms of cortical network/glutamatergic dysfunction, albeit the effects of ketamine were more robust. Muscimol produced NVHL-dependent reductions in ASSR measures, suggesting that cortical networks in this model are intolerant to post-synaptic GABAergic stimulation. These findings suggest the utility of combining lesion, pharmacological, and ASSR approaches in understanding neural mechanisms underlying disturbed synchrony in schizophrenia.
doi:10.1016/j.ijpsycho.2012.04.002
PMCID: PMC3443327  PMID: 22504207
ASSRs; GABA; NMDA; NVHL; schizophrenia; synchronization
18.  Phase Locking Asymmetries at Flexor-Extensor Transitions during Fictive Locomotion 
PLoS ONE  2013;8(5):e64421.
The motor output for walking is produced by a network of neurons termed the spinal central pattern generator (CPG) for locomotion. The basic building block of this CPG is a half-center oscillator composed of two mutually inhibitory sets of interneurons, each controlling one of the two dominant phases of locomotion: flexion and extension. To investigate symmetry between the two components of this oscillator, we analyzed the statistics of natural variation in timing during fictive locomotion induced by stimulation of the midbrain locomotor region in the cat. As a complement to previously published analysis of these data focused on burst and cycle durations, we present a new analysis examining the strength of phase locking at the transitions between flexion and extension. Across our sample of nerve pairs, phase locking at the transition from extension to flexion (E to F) is stronger than at the transition from flexion to extension (F to E). This pattern did not reverse when considering bouts of fictive locomotion that were flexor vs. extensor dominated, demonstrating that asymmetric locking at the transitions between phases is dissociable from which phase dominates cycle duration. We also find that the strength of phase locking is correlated with the mean latency between burst offset and burst onset. These results are interpreted in the context of a hypothesis where network inhibition and intrinsic oscillatory mechanisms make distinct contributions to flexor-extensor alternation in half-center networks.
doi:10.1371/journal.pone.0064421
PMCID: PMC3660298  PMID: 23700475
19.  Cross-frequency phase coupling of brain rhythms during the orienting response 
Brain research  2008;1232:163-172.
A critical function of the brain’s orienting response is to evaluate novel environmental events in order to prepare for potential behavioral action. Here, measures of synchronization (power, coherence) and nonlinear cross-frequency phase coupling (m:n phase locking measured with bicoherence and cross-bicoherence) were computed on 62-channel electroencephalographic (EEG) data during a paradigm in which unexpected, highly-deviant, novel sounds were randomly intermixed with frequent standard and infrequent target tones. Low frequency resolution analyses showed no significant changes in phase coupling for any stimulus type, though significant changes in power and synchrony did occur. High frequency resolution analyses, on the other hand, showed significant differences in phase coupling, but only for novel sounds compared to standard tones. Novel sounds elicited increased power and coherence in the delta band together with m:n phase locking (bicoherence) of delta:theta (1:3) and delta:alpha (1:4) rhythms in widespread fronto-central, right parietal, temporal, and occipital regions. Cross-bicoherence revealed that globally synchronized delta oscillations were phase coupled to theta oscillations in central regions and to alpha oscillations in right parietal and posterior regions. These results suggest that globally synchronized low frequency oscillations with phase coupling to more localized higher frequency oscillations provide a neural mechanism for the orienting response.
doi:10.1016/j.brainres.2008.07.030
PMCID: PMC2578845  PMID: 18675795
Bicoherence; cross-frequency coupling; orienting response; novelty; P3; coherence
20.  Neural Dynamics in Parkinsonian Brain: The Boundary Between Synchronized and Nonsynchronized Dynamics 
Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from parkinsonian patients. We show that the experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine. Comparison of the experimental and modeling data suggest that brain activity in Parkinson’s disease resides in the large boundary region between synchronized and nonsynchronized dynamics. Being on the edge of synchrony may allow for easy formation of transient neuronal assemblies.
PMCID: PMC3100589  PMID: 21599224
21.  Directed Cortical Information Flow during Human Object Recognition: Analyzing Induced EEG Gamma-Band Responses in Brain's Source Space 
PLoS ONE  2007;2(8):e684.
The increase of induced gamma-band responses (iGBRs; oscillations >30 Hz) elicited by familiar (meaningful) objects is well established in electroencephalogram (EEG) research. This frequency-specific change at distinct locations is thought to indicate the dynamic formation of local neuronal assemblies during the activation of cortical object representations. As analytically power increase is just a property of a single location, phase-synchrony was introduced to investigate the formation of large-scale networks between spatially distant brain sites. However, classical phase-synchrony reveals symmetric, pair-wise correlations and is not suited to uncover the directionality of interactions. Here, we investigated the neural mechanism of visual object processing by means of directional coupling analysis going beyond recording sites, but rather assessing the directionality of oscillatory interactions between brain areas directly. This study is the first to identify the directionality of oscillatory brain interactions in source space during human object recognition and suggests that familiar, but not unfamiliar, objects engage widespread reciprocal information flow. Directionality of cortical information-flow was calculated based upon an established Granger-Causality coupling-measure (partial-directed coherence; PDC) using autoregressive modeling. To enable comparison with previous coupling studies lacking directional information, phase-locking analysis was applied, using wavelet-based signal decompositions. Both, autoregressive modeling and wavelet analysis, revealed an augmentation of iGBRs during the presentation of familiar objects relative to unfamiliar controls, which was localized to inferior-temporal, superior-parietal and frontal brain areas by means of distributed source reconstruction. The multivariate analysis of PDC evaluated each possible direction of brain interaction and revealed widespread reciprocal information-transfer during familiar object processing. In contrast, unfamiliar objects entailed a sparse number of only unidirectional connections converging to parietal areas. Considering the directionality of brain interactions, the current results might indicate that successful activation of object representations is realized through reciprocal (feed-forward and feed-backward) information-transfer of oscillatory connections between distant, functionally specific brain areas.
doi:10.1371/journal.pone.0000684
PMCID: PMC1925146  PMID: 17668062
22.  Computational synchronization of microarray data with application to Plasmodium falciparum 
Proteome Science  2012;10(Suppl 1):S10.
Background
Microarrays are widely used to investigate the blood stage of Plasmodium falciparum infection. Starting with synchronized cells, gene expression levels are continually measured over the 48-hour intra-erythrocytic cycle (IDC). However, the cell population gradually loses synchrony during the experiment. As a result, the microarray measurements are blurred. In this paper, we propose a generalized deconvolution approach to reconstruct the intrinsic expression pattern, and apply it to P. falciparum IDC microarray data.
Methods
We develop a statistical model for the decay of synchrony among cells, and reconstruct the expression pattern through statistical inference. The proposed method can handle microarray measurements with noise and missing data. The original gene expression patterns become more apparent in the reconstructed profiles, making it easier to analyze and interpret the data. We hypothesize that reconstructed gene expression patterns represent better temporally resolved expression profiles that can be probabilistically modeled to match changes in expression level to IDC transitions. In particular, we identify transcriptionally regulated protein kinases putatively involved in regulating the P. falciparum IDC.
Results
By analyzing publicly available microarray data sets for the P. falciparum IDC, protein kinases are ranked in terms of their likelihood to be involved in regulating transitions between the ring, trophozoite and schizont developmental stages of the P. falciparum IDC. In our theoretical framework, a few protein kinases have high probability rankings, and could potentially be involved in regulating these developmental transitions.
Conclusions
This study proposes a new methodology for extracting intrinsic expression patterns from microarray data. By applying this method to P. falciparum microarray data, several protein kinases are predicted to play a significant role in the P. falciparum IDC. Earlier experiments have indeed confirmed that several of these kinases are involved in this process. Overall, these results indicate that further functional analysis of these additional putative protein kinases may reveal new insights into how the P. falciparum IDC is regulated.
doi:10.1186/1477-5956-10-S1-S10
PMCID: PMC3380736  PMID: 22759568
23.  Spike-Timing Precision and Neuronal Synchrony Are Enhanced by an Interaction between Synaptic Inhibition and Membrane Oscillations in the Amygdala 
PLoS ONE  2012;7(4):e35320.
The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (∼2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ∼300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ∼130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.
doi:10.1371/journal.pone.0035320
PMCID: PMC3338510  PMID: 22563382
24.  Minimal Size of Cell Assemblies Coordinated by Gamma Oscillations 
PLoS Computational Biology  2012;8(2):e1002362.
In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25–100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.
Author Summary
Gamma-frequency (25–100 Hz) oscillations in the brain often arise as a result of an interaction between excitatory and inhibitory cell populations. For this mechanism to work, the interaction must be sufficiently strong, and connectivity and external drives to participating neurons must be sufficiently homogeneous. As the interactions become weaker, either because the neuronal ensembles become smaller or because synapses weaken, the rhythms deteriorate, and eventually break down. This fact, by itself, is not surprising, but details of how the breakdown occurs are subtle. In particular, our analysis leads to the conclusion that in realistically heterogeneous networks, gamma rhythms must arise quickly, within a small number of oscillation periods, if they arise at all. Our findings suggest explanations for recent experimental findings concerning the minimal spatial extent of stimuli eliciting gamma oscillations in the primary visual cortex, the modulation of gamma oscillations in the primary visual cortex by attention, as well as our own experimental results, reported here, concerning the minimal light intensity below which optogenetic drive to pyramidal cells in a kainate-activated hippocampal slice results in disruption of an ongoing gamma oscillation. Our analysis leads to experimentally testable predictions about the behavior of the excitatory and inhibitory cells in these experiments.
doi:10.1371/journal.pcbi.1002362
PMCID: PMC3276541  PMID: 22346741
25.  Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus 
The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed.
doi:10.3389/fnsys.2013.00111
PMCID: PMC3863724  PMID: 24379763
absence status; delta oscillation; absence seizure; spike-wave discharge; phase-locking; thalamo-cortical system

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