Coupled oscillators for modeling and analysis of EEG/MEG oscillations.

This study presents three EEG/MEG applications in which the modeling of oscillatory signal components offers complementary analysis and an improved explanation of the underlying generator structures. Coupled oscillator networks were used for modeling. Parameters of the corresponding ordinary coupled differential equation (ODE) system are identified using EEG/MEG data and the resulting solution yields the modeled signals. This model-related analysis strategy provides information about the coupling quantity and quality between signal components (example 1, neonatal EEG during quiet sleep), allows identification of the possible contribution of hidden generator structures (example 2, 600-Hz MEG oscillations in somatosensory evoked magnetic fields), and can explain complex signal characteristics such as amplitude-frequency coupling and frequency entrainment (example 3, EEG burst patterns in sedated patients).     

Universality in the brain while listening to music.

The human brain, which is one of the most complex organic systems, involves billions of interacting physiological and chemical processes that give rise to experimentally observed neuroelectrical activity, which is called an electroencephalogram (EEG). The presence of non-stationarity and intermittency render standard available methods unsuitable for detecting hidden dynamical patterns in the EEG. In this paper, a method that is suitable for non-stationary signals and preserving the phase characteristics and that combines wavelet and Hilbert transforms was applied to multivariate EEG signals from human subjects at rest as well as in different cognitive states: listening to music, listening to text and performing spatial imagination. It was found that, if suitably rescaled, the gamma band EEG over distributed brain areas while listening to music can be described by a universal and homogeneous scaling, whereas this homogeneity in scale is reduced at resting conditions and also during listening to text and performing spatial imagination. The degree of universality is characterized by a Kullback-Leibler divergence measure. By statistical surrogate analysis, nonlinear phase interaction was found to play an important role in exhibiting universality among multiple cortical regions.     

Selecting EEG components using time series analysis in brain death diagnosis

In diagnosis of brain death for human organ transplant, EEG (electroencephalogram) must be flat to conclude the patient’s brain death but it has been reported that the flat EEG test is sometimes difficult due to artifacts such as the contamination from the power supply and ECG (electrocardiogram, the signal from the heartbeat). ICA (independent component analysis) is an effective signal processing method that can separate such artifacts from the EEG signals. Applying ICA to EEG channels, we obtain several separated components among which some correspond to the brain activities while others contain artifacts. This paper aims at automatic selection of the separated components based on time series analysis. In the flat EEG test in brain death diagnosis, such automatic component selection is helpful.     

A Molecular Network That Produces Spontaneous Oscillations in Excitable Cells of Dictyostelium

A network of interacting proteins has been found that can account for the spontaneous oscillations in adenylyl cyclase activity that are observed in homogenous populations of Dictyostelium cells 4 h after the initiation of development. Previous biochemical assays have shown that when extracellular adenosine 3′,5′-cyclic monophosphate (cAMP) binds to the surface receptor CAR1, adenylyl cyclase and the MAP kinase ERK2 are transiently activated. A rise in the internal concentration of cAMP activates protein kinase A such that it inhibits ERK2 and leads to a loss-of-ligand binding by CAR1. ERK2 phosphorylates the cAMP phosphodiesterase REG A that reduces the internal concentration of cAMP. A secreted phosphodiesterase reduces external cAMP concentrations between pulses. Numerical solutions to a series of nonlinear differential equations describing these activities faithfully account for the observed periodic changes in cAMP. The activity of each of the components is necessary for the network to generate oscillatory behavior; however, the model is robust in that 25-fold changes in the kinetic constants linking the activities have only minor effects on the predicted frequency. Moreover, constant high levels of external cAMP lead to attenuation, whereas a brief pulse of cAMP can advance or delay the phase such that interacting cells become entrained.     

Power and phase properties of oscillatory neural responses in the presence of background activity

Natural sensory inputs, such as speech and music, are often rhythmic. Recent studies have consistently demonstrated that these rhythmic stimuli cause the phase of oscillatory, i.e. rhythmic, neural activity, recorded as local field potential (LFP), electroencephalography (EEG) or magnetoencephalography (MEG), to synchronize with the stimulus. This phase synchronization, when not accompanied by any increase of response power, has been hypothesized to be the result of phase resetting of ongoing, spontaneous, neural oscillations measurable by LFP, EEG, or MEG. In this article, however, we argue that this same phenomenon can be easily explained without any phase resetting, and where the stimulus-synchronized activity is generated independently of background neural oscillations. It is demonstrated with a simple (but general) stochastic model that, purely due to statistical properties, phase synchronization, as measured by ‘inter-trial phase coherence’, is much more sensitive to stimulus-synchronized neural activity than is power. These results question the usefulness of analyzing the power and phase of stimulus-synchronized activity as separate and complementary measures; particularly in the case of attempting to demonstrate whether stimulus-synchronized neural activity is generated by phase resetting of ongoing neural oscillations.     

Human gamma oscillations during slow wave sleep

Neocortical local field potentials have shown that gamma oscillations occur spontaneously during slow-wave sleep (SWS). At the macroscopic EEG level in the human brain, no evidences were reported so far. In this study, by using simultaneous scalp and intracranial EEG recordings in 20 epileptic subjects, we examined gamma oscillations in cerebral cortex during SWS. We report that gamma oscillations in low (30-50 Hz) and high (60-120 Hz) frequency bands recurrently emerged in all investigated regions and their amplitudes coincided with specific phases of the cortical slow wave. In most of the cases, multiple oscillatory bursts in different frequency bands from 30 to 120 Hz were correlated with positive peaks of scalp slow waves ("IN-phase" pattern), confirming previous animal findings. In addition, we report another gamma pattern that appears preferentially during the negative phase of the slow wave ("ANTI-phase" pattern). This new pattern presented dominant peaks in the high gamma range and was preferentially expressed in the temporal cortex. Finally, we found that the spatial coherence between cortical sites exhibiting gamma activities was local and fell off quickly when computed between distant sites. Overall, these results provide the first human evidences that gamma oscillations can be observed in macroscopic EEG recordings during sleep. They support the concept that these high-frequency activities might be associated with phasic increases of neural activity during slow oscillations. Such patterned activity in the sleeping brain could play a role in off-line processing of cortical networks.     

Positive Feedback Promotes Oscillations in Negative Feedback Loops

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.     

Influence of time delay and channel blocking on multiple coherence resonance in Hodgkin-Huxley neuron networks

Toxins such as tetraethylammonium (TEA) and tetrodotoxin (TTX) may reduce the number of working potassium and sodium ion channels by poisoning and making them blocked, respectively. In this paper, we study how channel blocking (CB) affects the time delay-induced multiple coherence resonance (MCR), i.e., a phenomenon that the spiking of neuronal networks intermittently reaches the most ordered state, in stochastic Hodgkin-Huxley neuron networks. It is found that potassium and sodium CB have distinct effects. For potassium CB, the MCR occurs more frequently as the CB develops, but for sodium CB the MCR is badly impaired and only the first coherence resonance (CR) holds and, consequently, the MCR evolves into a single CR as sodium CB develops. We found for sodium CB the spiking becomes disordered at larger delay lengths, which may be the reason for the destruction of the MCR. The underlying mechanism is briefly discussed in terms of distinct effects of potassium and sodium CB on the spiking activity. These results show that potassium CB can increase the frequency of MCR with time delay, but sodium CB may suppress and even destroy the delay-induced MCR. These findings may help to understand the joint effects of CB and time delay on the spiking coherence of neuronal networks.     

Non-zero mean alpha oscillations revealed with computational model and empirical data

Ongoing oscillations and evoked responses are two main types of neuronal activity obtained with diverse electrophysiological recordings (EEG/MEG/iEEG/LFP). Although typically studied separately, they might in fact be closely related. One possibility to unite them is to demonstrate that neuronal oscillations have non-zero mean which predicts that stimulus- or task-triggered amplitude modulation of oscillations can contribute to the generation of evoked responses. We validated this mechanism using computational modelling and analysis of a large EEG data set. With a biophysical model, we indeed demonstrated that intracellular currents in the neuron are asymmetric and, consequently, the mean of alpha oscillations is non-zero. To understand the effect that neuronal currents exert on oscillatory mean, we varied several biophysical and morphological properties of neurons in the network, such as voltage-gated channel densities, length of dendrites, and intensity of incoming stimuli. For a very large range of model parameters, we observed evidence for non-zero mean of oscillations. Complimentary, we analysed empirical rest EEG recordings of 90 participants (50 young, 40 elderly) and, with spatio-spectral decomposition, detected at least one spatially-filtred oscillatory component of non-zero mean alpha oscillations in 93% of participants. In order to explain a complex relationship between the dynamics of amplitude-envelope and corresponding baseline shifts, we performed additional simulations with simple oscillators coupled with different time delays. We demonstrated that the extent of spatial synchronisation may obscure macroscopic estimation of alpha rhythm modulation while leaving baseline shifts unchanged. Overall, our results predict that amplitude modulation of neural oscillations should at least partially explain the generation of evoked responses. Therefore, inference about changes in evoked responses with respect to cognitive conditions, age or neuropathologies should be constructed while taking into account oscillatory neuronal dynamics.     

Temporal dynamics of natural enemy–pest interactions in a changing environment

Agroecosystems contain complex networks of interacting organisms and these interaction webs are structured by the relative timing of key biological and ecological events. Recent intensification of land management and global changes in climate threaten to desynchronize the temporal structure of interaction webs and disrupt the provisioning of ecosystem services, such as biological control by natural enemies. It is therefore critical to recognize the central role of temporal dynamics in driving predator–prey interactions in agroecosystems. Specifically, ecological dynamics in crop fields routinely behave as periodic oscillations, or cycles. Familiar examples include phenological cycles, diel activity rhythms, and crop-management cycles. The relative timing and the degree of overlap among ecological cycles determine the nature and magnitude of the ecological interactions among organisms, and ultimately determine whether ecosystem services, such as biological control, can be provided. Additionally, the ecological dynamics in many cropping systems are characterized by a pattern of frequent disturbances due to management actions such as harvest, sowing and pesticide applications. These disturbance cycles cause agroecosystems to be dominated by dispersal and repopulation dynamics. However, they also serve as selective filters that regulate which animals can persist in agroecosystems over larger temporal scales. Here, we review key concepts and examples from the literature on temporal dynamics in ecological systems, and provide a framework to guide biological control strategies for sustainable pest management in a changing world.     

Discovering implicit protein–protein interactions in the <Emphasis Type="Italic">Cell Cycle</Emphasis> using bioinformatics approaches

The cell division control protein (Cdc2) kinase is a catalytic subunit of a protein kinase complex, called the M phase promoting factor, which induces entry into mitosis and is universal among eukaryotes. This protein is believed to play a major role in cell division and control. The lives of biological cells are controlled by proteins interacting in metabolic and signaling pathways, in complexes that replicate genes and regulate gene activity, and in the assembly of the cytoskeletal infrastructure. Our knowledge of protein–protein (P–P) interactions has been accumulated from biochemical and genetic experiments, including the widely used yeast two-hybrid test. In this paper we examine if P–P interactions in regenerating tissues and cells of the anuran Xenopus laevis can be discovered from biomedical literature using computational and literature mining techniques. Using literature mining techniques, we have identified a set of implicitly interacting proteins in regenerating tissues and cells of Xenopus laevis that may interact with Cdc2 to control cell division. Genome sequence based bioinformatics tools were then applied to validate a set of proteins that appear to interact with the Cdc2 protein. Pathway analysis of these proteins suggests that Myc proteins function as the regulator of M phase initiation by controlling expression of the Akt1 molecule that ultimately inhibits the Cdc2-cyclin B complex in cells. P–P interactions that are implicitly appearing in literature can be effectively discovered using literature mining techniques. By applying evolutionary principles on the P–P interacting pairs, it is possible to quantitatively analyze the significance of the associations with biological relevance. The developed BioMap system allows discovering implicit P–P interactions from large quantity of biomedical literature data. The unique similarities and differences observed within the interacting proteins can lead to the development of the new hypotheses that can be used to design further laboratory experiments.     

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.     

Association between individual EEG characteristics and the level of intelligence

The aim of this study was to investigate the relationship between individual electroencephalogram (EEG) characteristics in the resting state and the level of nonverbal intelligence. The study involved 77 students of Demidov Yaroslavl State University. Analysis of the relationship between IQ and spectral parameters of EEG theta, alpha, and two subbands of beta oscillations revealed that the amplitude and power of alphaband EEG oscillations and low frequency beta-band EEG oscillations were positively correlated with the performance in the nonverbal intelligence test. The variety of brain periodic regimes was assessed using the correlation dimension (CD) of EEG. The correlation dimension can be used to quantify the degree of complexity of the nonlinear dynamical system. It was found that the value of the EEG correlation dimension was positively associated with the level of intelligence. The periodicity of the EEG signal was studied using autocorrelation analysis. It was shown that the autocorrelogram duration was negatively associated with IQ and the autocorrelogram amplitude was positively associated with IQ. A regression equation for predicting the level of nonverbal intelligence based on the power of theta- and beta-band oscillations, alpha-band oscillation indexes, and the amplitude and autocorrelation characteristics of the EEG signal was obtained.     

Efficient parametric analysis of the chemical master equation through model order reduction

ABSTRACT: BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. RESULTS: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.     

The effects of time delays in a phosphorylation-dephosphorylation pathway

Complex signaling cascades involve many interlocked positive and negative feedback loops which have inherent delays. Modeling these complex cascades often requires a large number of variables and parameters. Delay differential equation models have been helpful in describing inherent time lags and also in reducing the number of governing equations. However the consequences of model reduction via delay differential equations have not been fully explored. In this paper we systematically examine the effect of delays in a complex network of phosphorylation-dephosphorylation cycles (described by Gonze and Goldbeter, J. Theor. Biol., 210, (2001) 167-186), which commonly occur in many biochemical pathways. By introducing delays in the positive and negative regulatory interactions, we show that a delay differential model can indeed reduce the number of cycles actually required to describe the phosphorylation-dephosphorylation pathway. In addition, we find some of the unique properties of the network and a quantitative measure of the minimum number of delay variables required to model the network. These results can be extended for modeling complex signalling cascades.     

A new method of breaking down the electroencephalogram into a system of oscillations that allows for the analysis of EEG phenomena of different durations

With the purpose of levelling the restrictions appearing at the EEG correlative-spectral analysis, particularly of short (1-2 sec) realizations, as a result of Fourier transform, a new algorithm is elaborated of decomposition and analysis of bioelectrical activity. The created algorithm of complete EEG reduction to the list of oscillations singled out has been tested by a corresponding program. It provides for the measurement of parameters of concrete characteristics of the curve, and the adequacy of decomposition is ascertained by the exact restoration from the list of oscillations of the initial EEG. The method shows good sensitivity to the revealing of transient EEG phenomena and also regional specificity of the cortical bioelectrical activity.     

Transcranial electrical currents to probe EEG brain rhythms and memory consolidation during sleep in humans

Previously the application of a weak electric anodal current oscillating with a frequency of the sleep slow oscillation (～0.75 Hz) during non-rapid eye movement sleep (NonREM) sleep boosted endogenous slow oscillation activity and enhanced sleep-associated memory consolidation. The slow oscillations occurring during NonREM sleep and theta oscillations present during REM sleep have been considered of critical relevance for memory formation. Here transcranial direct current stimulation (tDCS) oscillating at 5 Hz, i.e., within the theta frequency range (theta-tDCS) is applied during NonREM and REM sleep. Theta-tDCS during NonREM sleep produced a global decrease in slow oscillatory activity conjoint with a local reduction of frontal slow EEG spindle power (8-12 Hz) and a decrement in consolidation of declarative memory, underlining the relevance of these cortical oscillations for sleep-dependent memory consolidation. In contrast, during REM sleep theta-tDCS appears to increase global gamma (25-45 Hz) activity, indicating a clear brain state-dependency of theta-tDCS. More generally, results demonstrate the suitability of oscillating-tDCS as a tool to analyze functions of endogenous EEG rhythms and underlying endogenous electric fields as well as the interactions between EEG rhythms of different frequencies.     

Multimodal functional network connectivity: an EEG-fMRI fusion in network space

EEG and fMRI recordings measure the functional activity of multiple coherent networks distributed in the cerebral cortex. Identifying network interaction from the complementary neuroelectric and hemodynamic signals may help to explain the complex relationships between different brain regions. In this paper, multimodal functional network connectivity (mFNC) is proposed for the fusion of EEG and fMRI in network space. First, functional networks (FNs) are extracted using spatial independent component analysis (ICA) in each modality separately. Then the interactions among FNs in each modality are explored by Granger causality analysis (GCA). Finally, fMRI FNs are matched to EEG FNs in the spatial domain using network-based source imaging (NESOI). Investigations of both synthetic and real data demonstrate that mFNC has the potential to reveal the underlying neural networks of each modality separately and in their combination. With mFNC, comprehensive relationships among FNs might be unveiled for the deep exploration of neural activities and metabolic responses in a specific task or neurological state.