Frequency modulation of large oscillatory neural networks

Dynamical systems which generate periodic signals are of interest as models of biological central pattern generators and in a number of robotic applications. A basic functionality that is required in both biological modelling and robotics is frequency modulation. This leads to the question of whether there are generic mechanisms to control the frequency of neural oscillators. Here we describe why this objective is of a different nature, and more difficult to achieve, than modulating other oscillation characteristics (like amplitude, offset, signal shape). We propose a generic way to solve this task which makes use of a simple linear controller. It rests on the insight that there is a bidirectional dependency between the frequency of an oscillation and geometric properties of the neural oscillator’s phase portrait. By controlling the geometry of the neural state orbits, it is possible to control the frequency on the condition that the state space can be shaped such that it can be pushed easily to any frequency.     

Atrial reflexes during high frequency oscillatory ventilation

High frequency oscillatory ventilation (HFOV) is a new method of artificial ventilation which has been advocated for use in critically ill individuals. It alters the discharge in pulmonary stretch receptors (SAR) from a phasic to a continuous pattern. Since some cardiovascular neurones in the medulla are influenced by the discharge from SAR, experiments were undertaken to determine whether the reflexes from the left atrial (volume) receptors (LAR) were influenced by HFOV. The reflex increases in heart rate and urine flow which result from activation of the (LAR) were examined during both intermittent positive pressure ventilation (IPPV) and HFOV. In five dogs, the increase in heart rate was 23.9 +/- 4.3 and 24.5 +/- 5.4 beats/min during IPPV and HFOV, respectively. In six dogs the response of an increase in urine flow was examined and this response also was not altered by HFOV. It is concluded that the integrity of these reflexes was unaffected by HFOV in the anesthetized dog model.     

A method of nonlinear analysis in the frequency domain.

A method is developed for the analysis of nonlinear biological systems based on an input temporal signal that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grafting, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.     

Cellular-based modeling of oscillatory dynamics in brain networks

Oscillatory, population activities have long been known to occur in our brains during different behavioral states. We know that many different cell types exist and that they contribute in distinct ways to the generation of these activities. I review recent papers that involve cellular-based models of brain networks, most of which include theta, gamma and sharp wave-ripple activities. To help organize the modeling work, I present it from a perspective of three different types of cellular-based modeling: 'Generic', 'Biophysical' and 'Linking'. Cellular-based modeling is taken to encompass the four features of experiment, model development, theory/analyses, and model usage/computation. The three modeling types are shown to include these features and interactions in different ways.     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

Local and global cycles in an acarine predator-prey system: a frequency domain analysis

Techniques of time series analysis are applied to the dynamics of the phytophagous miteTetranychus urticae Koch and its predatorTyphlodromus occidentalis Nesbitt in six experimental mini-orchards, sampled weekly during two years (van de Klashorst et al., 1992). Autocovariance and crosscovariance functions characterize local and global behaviour in the time domain. Spectral density function and cross amplitude spectrum provide important information of the system's behaviour in the frequency domain. Because of a strikingly different behaviour, the total record was cut into two distinct periods. During the first period, all local systems oscillate with a frequency of four cycles per year and all in phase, resulting in a strongly periodical global behaviour at a high mean level. Since the mean local power spectra coincide with the global power spectrum over a wide range of frequencies, it is concluded that the total system of six orchards is homogeneous. During the second period, all local power spectra are mutually different, more or less smoothed with no apparent peak pointing to a periodical component. The resulting global power spectrum is almost flat at a low mean level. The system is heterogeneous with a quasi-stable global behaviour.From the cross-amplitude spectrum it became clear that the dynamics of the two species within the orchards remained strongly coupled over a wide range of frequencies.Since the experimental circumstances had not been intentionally changed, the origin of the drastic change in behaviour could not be identified. If high rates of dispersal have been the synchronizer during the first period, it is not clear why asynchrony suddenly occured in the second period.A comparison of the overall record with the results of Nachman's (1987) stochastic simulation model suggests that the change could possibly be of stochastic origin.     

Normocapnic high frequency oscillatory hyperventilation increases oxygenation in pigs

High frequency oscillatory ventilation (HFOV), contrary to conventional ventilation, enables a safe increase in tidal volume (V(T)) without endangering alveoli by volutrauma or barotrauma. The aim of the study is to introduce the concept of normocapnic high frequency oscillatory hyperventilation and to assess its effect upon oxygen gain under experimental conditions. Laboratory pigs (n = 9) were investigated under total intravenous anesthesia in three phases. Phase 1: Initial volume controlled HFOV period. Phase 2: Hyperventilation--V(T) was increased by (46 +/- 12) % when compared to normocapnic V(T) during phase 1. All other ventilatory parameters were unchanged. A significant increase in PaO(2) (by 3.75 +/- 0.52 kPa, p < 0.001) and decrease in PaCO(2) (by -2.05 +/- 0.31 kPa, p < 0.001) were obtained. Phase 3: Normocapnia during hyperventilation was achieved by an iterative increase in the CO(2) fraction in the inspiratory gas by a CO(2) admixture. All ventilatory parameters were unchanged. A significant increase in PaO(2) (by 3.79 +/- 0.73 kPa, p < 0.001), similar to that which was observed in phase 2, was preserved in phase 3 whereas normocapnia was fully re-established. The concept of high frequency normocapnic hyperventilation offers a lung protective strategy that significantly improves oxygenation whilst preserving normocapnia.     

Formulas for intrinsic noise evaluation in oscillatory genetic networks

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.     

Fluorescence lifetime heterogeneity resolution in the frequency domain by lifetime moments analysis

Fluorescence lifetime imaging microscopy presents a powerful tool in biology and biophysics because it allows the investigation of the local environment of a fluorochrome in living cells in a quantitative manner. Furthermore, imaging F?rster-type resonance energy transfer (FRET) by fluorescence lifetime imaging microscopy enables protein-protein interactions and intermolecular distances to be mapped under physiological conditions. Quantitative and precise data analysis methods are required to access the richness of information that is contained in FRET data on biological samples. Lifetime detection in the frequency-domain yields two lifetime estimations. The lifetime moments analysis (LiMA) provides a quantitative measure of the lifetime distribution broadness by exploiting the analytical relationship between the phase- and demodulation-lifetime estimations and relating them to the weighted average and variance of the lifetime distribution. The LiMA theoretical framework is validated by comparison with global analysis and by applying it to a constrained two-component FRET system using simulations and experiments. Furthermore, a novel LIMA-based error analysis and a more intuitive formalism for global analysis are presented. Finally, a new method to resolve a FRET system is proposed and experimentally applied to the investigation of protein-protein interactions.     

Time-course analysis of cyanobacterium transcriptome: detecting oscillatory genes

The microarray technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining these data one can identify the dynamics of the gene expression time series. The detection of genes that are periodically expressed is an important step that allows us to study the regulatory mechanisms associated with the circadian cycle. The problem of finding periodicity in biological time series poses many challenges. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, outliers and unevenly sampled time points. Consequently, the method for finding periodicity should preferably be robust against such anomalies in the data. In this paper, we propose a general and robust procedure for identifying genes with a periodic signature at a given significance level. This identification method is based on autoregressive models and the information theory. By using simulated data we show that the suggested method is capable of identifying rhythmic profiles even in the presence of noise and when the number of data points is small. By recourse of our analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis.     

Decomposing neural synchrony: toward an explanation for near-zero phase-lag in cortical oscillatory networks

Background

Synchronized oscillation in cortical networks has been suggested as a mechanism for diverse functions ranging from perceptual binding to memory formation to sensorimotor integration. Concomitant with synchronization is the occurrence of near-zero phase-lag often observed between network components. Recent theories have considered the importance of this phenomenon in establishing an effective communication framework among neuronal ensembles.

Methodology/Principal Findings

Two factors, among possibly others, can be hypothesized to contribute to the near-zero phase-lag relationship: (1) positively correlated common input with no significant relative time delay and (2) bidirectional interaction. Thus far, no empirical test of these hypotheses has been possible for lack of means to tease apart the specific causes underlying the observed synchrony. In this work simulation examples were first used to illustrate the ideas. A quantitative method that decomposes the statistical interdependence between two cortical areas into a feed-forward, a feed-back and a common-input component was then introduced and applied to test the hypotheses on multichannel local field potential recordings from two behaving monkeys.

Conclusion/Significance

The near-zero phase-lag phenomenon is important in the study of large-scale oscillatory networks. A rigorous mathematical theorem is used for the first time to empirically examine the factors that contribute to this phenomenon. Given the critical role that oscillatory activity is likely to play in the regulation of biological processes at all levels, the significance of the proposed method may extend beyond systems neuroscience, the level at which the present analysis is conceived and performed.     

The squared distance approach to frequency domain time‐resolved fluorescence analysis

A frequency‐domain (FD) analysis of fluorescence lifetime (FLT) is a unique and rapid method for cellular and intracellular classifications that can serve for medical diagnostics purposes. Nevertheless, its data analysis process demands nonlinear fitting algorithms that may distort the resolution of the FLT data and hence diminish the classification ability of the method. This research suggests a sample classification technique that is unaffected by the analysis process as it is based on the squared distance (D²) between the raw frequency response data (FRD). In addition, it presents the theory behind this technique and its validation in two simulated data sets of six groups with similar widely and closely spaced FLT data as well as in experimental data of 43 samples from bacterial and viral infected and non‐infected patients. In the two simulated tests, the classification accuracy was above 95% for all six groups. In the experimental data, the classification of 41 out of 43 samples matched earlier report and 29 out of 31 agreed with preliminary physician diagnosis. The D² approach has the potential to promote FD‐time resolved fluorescence measurements as a medical diagnostic technique with high specifity and high sensitivity for many of today's conventional diagnostic procedures.      

Use of frequency domain analysis of skin conductance for evaluation of mental workload

A specially designed mental task was performed by 16 subjects for frequency domain analysis of skin conductance (SC) to evaluate mental workload. The task was to memorize target letters, detect them within a 4 x 4 alphabet arrangement, and answer whether the number of targets contained in the arrangement corresponded to a randomly displayed number. As the number of target letters increased, the score for the card-sort NASA Task Load Index (CSTLX) and task performance increased significantly. The traditional parameter for the number of transient wave forms of SC response (SCR) and the height of its wave did not show any significant effect of task difficulty. In addition, SCRs were subjected to Fourier transformation and integration of the spectrum from 0.03 to 0.5 Hz. This frequency domain analysis enabled detection of small differences in mental workload that could not be detected by traditional amplitude domain analysis. Frequency-based analysis enables easy processing of physiological signals and is very effective in evaluating mental stress using SC recorded under actual environmental conditions such as the driving of a vehicle.     

Uncovering interactions in the frequency domain

Oscillatory activity plays a critical role in regulating biological processes at levels ranging from subcellular, cellular, and network to the whole organism, and often involves a large number of interacting elements. We shed light on this issue by introducing a novel approach called partial Granger causality to reliably reveal interaction patterns in multivariate data with exogenous inputs and latent variables in the frequency domain. The method is extensively tested with toy models, and successfully applied to experimental datasets, including (1) gene microarray data of HeLa cell cycle; (2) in vivo multi-electrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of a sheep; and (3) in vivo LFPs recorded from distributed sites in the right hemisphere of a macaque monkey.     

Interaction and domain networks of yeast

Data of currently available protein-protein interaction sets and protein domain sets of yeast are used to set up protein and domain interaction and domain sequence networks. All of them are far from being random or regular networks. In fact, they turn out to be sparse and locally well clustered indicating so-called scale-free and partially small-world topology. These subtle topologies display considerable indirect properties which are measured with a newly introduced transitivity coefficient. Fairly small sets of highly connected proteins and domains shape the topologies of the underlying networks, emphasizing a kind of backbone the nets are based on. The biological nature of these particular nodes is further investigated. Since highly connected proteins and domains accumulated a significant higher number of links by their important involvement in certain cellular aspects, their mutational effect on the cell is considered by a perturbation analysis. In comparison to domains of yeast, what factors force domains to accumulate links to other domains in protein sequences of higher eukaryotes are investigated.     

Evolutionary cores of domain co-occurrence networks

Background  

The modeling of complex systems, as disparate as the World Wide Web and the cellular metabolism, as networks has recently uncovered a set of generic organizing principles: Most of these systems are scale-free while at the same time modular, resulting in a hierarchical architecture. The structure of the protein domain network, where individual domains correspond to nodes and their co-occurrences in a protein are interpreted as links, also falls into this category, suggesting that domains involved in the maintenance of increasingly developed, multicellular organisms accumulate links. Here, we take the next step by studying link based properties of the protein domain co-occurrence networks of the eukaryotes S. cerevisiae, C. elegans, D. melanogaster, M. musculus and H. sapiens.     

Functional coherence in domain interaction networks

MOTIVATION: Extracting functional information from protein-protein interactions (PPI) poses significant challenges arising from the noisy, incomplete, generic and static nature of data obtained from high-throughput screening. Typical proteins are composed of multiple domains, often regarded as their primary functional and structural units. Motivated by these considerations, domain-domain interactions (DDI) for network-based analyses have received significant recent attention. This article performs a formal comparative investigation of the relationship between functional coherence and topological proximity in PPI and DDI networks. Our investigation provides the necessary basis for continued and focused investigation of DDIs as abstractions for functional characterization and modularization of networks. RESULTS: We investigate the problem of assessing the functional coherence of two biomolecules (or segments thereof) in a formal framework. We establish essential attributes of admissible measures of functional coherence, and demonstrate that existing, well-accepted measures are ill-suited to comparative analyses involving different entities (i.e. domains versus proteins). We propose a statistically motivated functional similarity measure that takes into account functional specificity as well as the distribution of functional attributes across entity groups to assess functional similarity in a statistically meaningful and biologically interpretable manner. Results on diverse data, including high-throughput and computationally predicted PPIs, as well as structural and computationally inferred DDIs for different organisms show that: (i) the relationship between functional similarity and network proximity is captured in a much more (biologically) intuitive manner by our measure, compared to existing measures and (ii) network proximity and functional similarity are significantly more correlated in DDI networks than in PPI networks, and that structurally determined DDIs provide better functional relevance as compared to computationally inferred DDIs.     

Scale-free behavior in protein domain networks

Several technical, social, and biological networks were recently found to demonstrate scale-free and small-world behavior instead of random graph characteristics. In this work, the topology of protein domain networks generated with data from the ProDom, Pfam, and Prosite domain databases was studied. It was found that these networks exhibited small-world and scale-free topologies with a high degree of local clustering accompanied by a few long-distance connections. Moreover, these observations apply not only to the complete databases, but also to the domain distributions in proteomes of different organisms. The extent of connectivity among domains reflects the evolutionary complexity of the organisms considered.