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Nonstationarity in epileptic EEG and implications for neural dynamics.

In this paper, we use a recently developed method to analyze the nonstationarity in time series from intracranial depth and subdural recordings of patients with temporal lobe epilepsy. We show that the nonstationarity in the signal can be accounted for by the variation of a single parameter. We then show that the various dominant nonlinear waveforms observed in different electrodes can be explained by a simple stochastic model in which the mesoscopic collection of neurons, whose potential the electrodes measure, can be on one of two states. The nonstationarity observed in our analysis is a consequence of a time-dependent transition probability between these two states. In general, this transition probability increases as a seizure is approached. The model that we propose incorporates this bistability. We find good agreement between real data and simulated data generated by our model. We understand that this mesoscopic bistability may be associated with the existence of excitation waves traversing the brain in these patients.

Electroencephalography↗

Fractal and complexity measures of heart rate variability.

Heart rate variability has been analyzed conventionally with time and frequency domain methods, which measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of heart rate dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear heart rate dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional heart rate variability indexes. In particular, the short-term fractal scaling exponent measured by the detrended fluctuation analysis method has predicted fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of heart rate dynamics, that describes the complexity of RR interval behavior, has provided information on the vulnerability to atrial fibrillation. Many other nonlinear indexes, e.g., Lyapunov exponent and correlation dimensions, also give information on the characteristics of heart rate dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of heart rate behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.

Animals↗

Chaos in blood pressure control.

A number of control mechanisms are comprised within blood pressure regulation, ranging from events on the cellular level up to circulating hormones. Despite their vast number, blood pressure fluctuations occur preferably within a certain range (under physiological conditions). A specific class of dynamic systems has been extensively studied over the past several years: nonlinear coupled systems, which often reveal a characteristic form of motion termed "chaos". The system is restricted to a certain range in phase space, but the motion is never periodic. The attractor the system moves on has a non-integer dimension. What all chaotic systems have in common is their sensitive dependence on initial conditions. The question arises as to whether blood pressure regulation can be explained by such models. Many efforts have been made to characterise heart rate variability and EEG dynamics by parameters of chaos theory (e.g., fractal dimensions and Lyapunov exponents). These method were successfully applied to dynamics observed in single organs, but very few studies have dealt with blood pressure dynamics. This mini-review first gives an overview on the history of blood pressure dynamics and the methods suitable to characterise the dynamics by means of tools derived from the field of nonlinear dynamics. Then applications to systemic blood pressure are discussed. After a short survey on heart rate variability, which is indirectly reflected in blood pressure variability, some dynamic aspects of resistance vessels are given. Intriguingly, systemic blood pressure reveals a change in fractal dimensions and Lyapunov exponents, when the major short-term control mechanism--the arterial baroreflex--is disrupted. Indeed it seems that cardiovascular time series can be described by tools from nonlinear dynamics [66]. These methods allow a novel description of some important aspects of biological systems. Both the linear and the nonlinear tools complement each other and can be useful in characterising the stability and complexity of blood pressure control.

Animals↗

Negative feedback regulation is responsible for the non-linear modulation of photosynthetic activity in plants and cyanobacteria exposed to a dynamic light environment.

Photosynthetic organisms exposed to a dynamic light environment exhibit complex transients of photosynthetic activities that are strongly dependent on the temporal pattern of the incident irradiance. In a harmonically modulated light of intensity I approximately const.+sin(omegat), chlorophyll fluorescence response consists of a steady-state component, a component modulated with the angular frequency of the irradiance omega and several upper harmonic components (2omega, 3omega and higher). Our earlier reverse engineering analysis suggests that the non-linear response can be caused by a negative feedback regulation of photosynthesis. Here, we present experimental evidence that the negative feedback regulation of the energetic coupling between phycobilisome and Photosystem II (PSII) in the cyanobacterium Synechocystis sp. PCC6803 indeed results in the appearance of upper harmonic modes in the chlorophyll fluorescence emission. Dynamic changes in the coupling of the phycobilisome to PSII are not accompanied by corresponding antiparallel changes in the Photosystem I (PSI) excitation, suggesting a regulation limited to PSII. Strong upper harmonic modes were also found in the kinetics of the non-photochemical quenching (NPQ) of chlorophyll fluorescence, of the P700 redox state and of the CO(2) assimilation in tobacco (Nicotiana tabaccum) exposed to harmonically modulated light. They are ascribed to negative feedback regulation of the reactions of the Calvin-Benson cycle limiting the photosynthetic electron transport. We propose that the observed non-linear response of photosynthesis may also be relevant in a natural light environment that is modulated, e.g., by ocean waves, moving canopy or by varying cloud cover. Under controlled laboratory conditions, the non-linear photosynthetic response provides a new insight into dynamics of the regulatory processes.

Adaptation, Physiological↗

A systems approach to appraisal mechanisms in emotion.

While artificial neural networks are regularly employed in modeling the perception of facial and vocal emotion expression as well as in automatic expression decoding by artificial agents, this approach is yet to be extended to the modeling of emotion elicitation and differentiation. In part, this may be due to the dominance of discrete and dimensional emotion models, which have not encouraged computational modeling. This situation has changed with the advent of appraisal theories of emotion and a number of attempts to develop rule-based models can be found in the literature. However, most of these models operate at a high level of conceptual abstraction and rarely include the underlying neural architecture. In this contribution, an appraisal-based emotion theory, the Component Process Model (CPM), is described that seems particularly suited to modeling with the help of artificial neural network approaches. This is due to its high degree of specificity in postulating underlying mechanisms including efferent physiological and behavioral manifestations as well as to the possibility of linking the theoretical assumptions to underlying neural architectures and dynamic processes. This paper provides a brief overview of the model, suggests constraints imposed by neural circuits, and provides examples on how the temporal unfolding of emotion can be conceptualized and experimentally tested. In addition, it is shown that the specific characteristics of emotion episodes can be profitably explored with the help of non-linear dynamic systems theory.

Animals↗

EEG predictability: adequacy of non-linear forecasting methods.

The predictive properties of EEG segments were analyzed. The sample included alpha, delta as well as spike and wave EEG activity recordings. Most of these segments are better described with non-linear autoregressive models, and a non-linear forecasting algorithm is routinely required. In terms of their predictive properties, segments can be divided into unpredictable, predictable and very predictable, these three groups being similarly represented among the alpha activity EEG segments. In EEG segments with alpha activity, poor predictability is associated with poor organization of the rhythmic pattern. Concerning dynamic properties, it was found that cyclic skeletons were highly represented among the very predictable segments, which reflect a contribution of the deterministic component of the autoregressive model to the predictability of the segments. Notable contributions of the noise component may explain the properties of unpredictable segments. These results point to a great diversity of predictive patterns among EEG recordings. Other factors besides the existence of chaotic dynamics must be regarded.

Algorithms↗

Interdependencies in the spontaneous EEG while listening to music.

We studied the patterns of interdependency between different brain regions during the performance of higher cognitive functions. Our goal was to check the existence in these patterns of both task-related differences (e.g. listening to music vs. rest) and training-related differences (musicians vs. non-musicians). For this purpose, a non-linear measure, called similarity index (S.I.), was used to detect asymmetric interdependencies between different brain regions by means of EEG signals. Relatively active and passive regions of the brain were found where the degree of activity was represented by excited degrees of freedom. The S.I. obtained during listening to different kinds of music was compared statistically with the S.I. with eyes closed, and significant changes (P< or = 0.05) were entered into schematic brain maps. A topographical representation of the S.I. yielded differences in the interdependency while performing different cognitive tasks. The results demonstrate the occurrence of task-related differences in both groups of subjects. Furthermore, subjects with musical training possessed significantly higher degrees of interdependencies than such without musical training while listening to music but not to text. We conclude that the new measure can be successfully applied for studying the dynamical co-operation between cortical areas during higher cognitive functioning.

Adult↗

Oscillatory dynamics protect enzymes and possibly cells against toxic substances.

We have used the oscillating peroxidase-oxidase (PO) reaction as a model system to study how oscillatory dynamics may affect the influence of toxic reaction intermediates on enzyme stability. In the peroxidase-oxidase reaction reactive intermediates, such as hydrogen peroxide, superoxide, and hydroxyl radical are formed. Such intermediates inactivate many cellular macromolecules such as proteins and nucleic acids. These reaction intermediates also react with peroxidase itself to form an inactive enzyme. The fact that the PO reaction shows bistability between an oscillatory and a steady state gives us a unique possibility to compare such inactivation when the system is in one of these two states. We show that inactivation of peroxidase is slower when the system is in an oscillatory state, and using numerical simulations we provide evidence that oscillatory dynamics lower the average concentration of the reactive intermediates.

Cells↗

Dynamics of bound states of same-chirality spiral waves.

We describe the dynamics of bound states of same-chirality spirals in a generic numerical model of an excitable medium. For each bound state, we analyze its tip trajectory patterns and determine its characteristic frequencies. We report two previously unidentified bound states: for spiral pairs, a state that exhibits alternating cycles of small and large distances between collisions (A2); for triplets, the first example of a meandering bound state (M3). In parameter space, A2 lies in between the previously described oscillating pairs (O2) and master-slave pairs (MS). We present numerical evidence that the transition O2-->A2 occurs via a supercritical period-doubling bifurcation, while the transition A2-->MS occurs via a symmetry breaking secondary Hopf bifurcation. A classification of all regimes according to dynamical systems theory exposes the wealth of phenomena exhibited by multiarmed spiral waves.

Models, Theoretical↗

Responses of neurons of the cat central cervical nucleus to natural neck and vestibular stimulation.

1. The central cervical nucleus (CCN) is known to receive neck and vestibular input and to project to the contralateral cerebellum and vestibular nuclei. To investigate the processing of neck and vestibular input by cells in the CCN, we studied their responses to sinusoidal neck rotation and to whole-body tilt in vertical planes in decerebrate, paralyzed cats. CCN neurons were identified by antidromic stimulation with electrodes placed in or near the contralateral restiform body. 2. For every neuron, we first identified the preferred direction of neck rotation (response vector orientation), then studied the neuron's dynamics with rotations in a plane close to this direction at 0.05-1 Hz. 3. Responses of CCN neurons to neck rotation resembled those of previously studied neck spindle primary afferents in terms of their dynamics and nonlinear responses to stimuli of differing amplitudes. They also resembled the neck responses of Deiters' neurons studied in similar preparations. 4. The activity of two-thirds of CCN neurons also was modulated by natural vestibular stimulation. Orientation and dynamics of vestibular responses were characterized in the same way as neck responses. Labyrinthine input originated predominantly from the contralateral vertical canals, and there was no evidence of otolith input. Neck and vestibular inputs were always antagonistic, but the gain of the vestibular response was lower than that of the neck response at all frequencies studied. 5. The quantitative aspects of the interaction between neck and vestibular inputs can be expected to vary with the type of preparation and with stimulus parameters, and its functional significance remains to be investigated.

Afferent Pathways↗

Mathematical modeling of intracellular signaling pathways.

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems.

Animals↗

Statistical mechanics beyond the Hopfield model: solvable problems in neural network theory.

We present four 'case study' examples of solvable problems in the theory of recurrent neural networks, which are relevant to our understanding of information processing in the brain, but which are also interesting from a purely statistical mechanical point of view, even at the level of simple models (which helps in stimulating interdisciplinary work). The examples concern issues in network dynamics, network connectivity, spike timing and synaptic plasticity.

Action Potentials↗

[The study of the mixing layer by the point image method].

The properties of the mixing layer in dynamic systems were studied by the example of a mathematical model of the cubic image type. Its role in the generation of information and the evolution of its significance was shown. At the moment of generation, information is of zero significance, and this significance then increases. A criterion of efficiency was proposed, and the optimum moment of making a decision in creative work was determined. It was shown that the increase in the variability of the parameters of a living system upon entry into the mixing layer and its decrease upon exit can serve as objective indicators of the transition of the system from one dynamic regime (attractor) to another.

Algorithms↗

[The chaos theory in parasitology].

Fundamental ideas of the chaotic non-linear dynamical systems and their application in parasitology (e.g. Cephalomyvia populations, Trichomronas vaginalis invasions, Homo-Plasmodium systems) are discussed.

Algorithms↗

Dynamics of peak dispersion in capillary zone electrophoresis including wall adsorption I. Theoretical model and results of simulation.

A mathematical model is described for the simulation of peak profiles in capillary zone electrophoresis taking wall adsorption into account. It is based on such physico-chemical relations as mass balance equations, sorption rate equations and appropriate boundary conditions. The numerical solution of the model is carried out, allowing the depiction of the concentration profile of the sample in the capillary as a result of the dynamics of the processes involved, which depend on a number of input parameters: rate constants, adsorption isotherms, column dimensions, field strength etc. Four cases are discussed in detail, namely those with either slow or fast adsorption kinetics and linear or nonlinear isotherms.

Adsorption↗

mfERG response dynamics of the aging retina.

PURPOSE: To determine age-related changes in retinal response dynamics derived from multifocal electroretinograms (mfERGs). METHODS: MfERG data were obtained from 70 subjects with normal phakic eyes, age 9 to 80 years. Whereas the first- and higher-order kernels resulting from the mfERG contain detailed information regarding the nonlinear response dynamics of the retina, they do not lend themselves directly to an easy and intuitive interpretation. To achieve a better appreciation of fast adaptive mechanisms and their changes with aging, regional averages of the kernel series were translated at different retinal eccentricities (0 degrees -5 degrees, 5 degrees -15 degrees, and 15 degrees -25 degrees ) into responses generated in different contexts. Specifically, the effect of aging on responses to stimuli presented in isolation was compared with the effect on responses adapted by preceding stimuli ("forward" effect). The interference of the immediately following stimuli with the response generation ("backward effect") was also considered. RESULTS: Age-related changes were found in the isolated flash response as well as in the backward and forward interactions between consecutive flash responses. Larger fractional changes with age were found in response density than in implicit time, and the rate of change with age was larger for responses to isolated flashes than for responses adapted by preceding flashes. CONCLUSIONS: Senescent changes in the isolated flash response and in consecutive flash interactions derived from the binary kernel series indicate an aging process at an early stage in the visual system. Mechanisms of retinal adaptation may partially compensate for age-related reductions in the isolated flash response.

Adaptation, Ocular↗

Changes in actin and myosin structural dynamics due to their weak and strong interactions.

Figure 3 summarizes the effects of actomyosin binding on the internal and global dynamics of either protein, as discussed in this chapter. These effects depend primarily on the strength of the interaction; which in turn depends on the state of the nucleotide at the myosin active site. When either no nucleotide or ADP is bound, the interaction is strong and the effect on each protein is maximal. When the nucleotide is ATP or ADP.Pi, or the equivalent nonhydrolyzable analogs, the interaction is weak and the effect on molecular dynamics of each protein is minimal. The weaker effects in weak-binding states are not simply the reflection of lower occupancy of binding sites--the molecular models in Fig. 3 illustrate the effects of the formation of the ternary complex, after correction for the free actin and myosin in the system. Thus EPR on myosin (Berger and Thomas 1991; Thomas et al. 1995) and pyrene fluorescence studies on actin (Geeves 1991) have shown that the formation of a ternary complex has a negligible effect on the internal dynamics of both [figure: see text] proteins (left side of Fig. 3, white arrows). As shown by both EPR (Baker et al. 1998; Roopnarine et al. 1998) and phosphorescence (Ramachandran and Thomas 1999), both domains of myosin are dynamically disordered in weak-binding states, and this is essentially unaffected by the formation of the ternary complex (left side of Fig. 3, indicated by disordered myosin domains). The only substantial effect of the formation of the weak interaction that has been reported is the EPR-detected (Ostap and Thomas 1991) restriction of the global dynamics of actin upon weak myosin binding (left column of Fig. 3, gray arrow). The effects of strong actomyosin formation are much more dramatic. While substantial rotational dynamics, both internal and global, exist in both myosin and actin in the presence of ADP or the absence of nucleotides, spin label EPR, pyrene fluorescence, and phosphorescence all show dramatic restrictions in these motions upon formation of the strong ternary complex (right column of Fig. 3). One implication of this is that the weak-to-strong transition is accompanied by a disorder-to-order transition in both actin and myosin, and this is itself an excellent candidate for the structural change that produces force (Thomas et al. 1995). Another clear implication is that the crystal structures obtained for isolated myosin and actin are not likely to be reliable representations of structures that exist in ternary complexes of these proteins (Rayment et al. 1993a and 1993b; Dominguez et al. 1998; Houdusse et al. 1999). This is clearly true of the strong-binding states, since the spectroscopic studies indicate consistently that substantial changes occur in both proteins upon strong complex formation. For the weak complexes, the problem is not that complex formation induces large structural changes, but that the structures themselves are dynamically disordered. This is probably why so many different structures have been obtained for myosin S1 with nucleotides bound--each crystal is selecting one of the many different substates represented by the dynamic ensemble. Finally, there is the problem that the structures of actomyosin complexes are probably influenced strongly by their mechanical coupling to muscle protein lattice (Baker at al. 2000). Thus, even if co-crystals of actin and myosin are obtained in the future, an accurate description of the structural changes involved in force generation will require further experiments using site-directed spectroscopic probes of both actin and myosin, in order to detect the structural dynamics of these ternary complexes under physiological conditions.

Actins↗

The effects of attention and handedness on coordination dynamics in a bimanual Fitts' law task.

Two experiments were conducted to investigate the effects of attention and handedness on bimanual coordination in the context of a dynamical model of coordinated movements. Participants performed a bimanual, rhythmic Fitts' law task in which the relative amount of attention directed to each task was manipulated by the relative difficulty associated with the pair of targets that each hand tapped. In both experiments, participants tended to lead with their preferred hand. The effects of attention, though, were mixed, which suggested that there was a combined effect of an attentional asymmetry and an asymmetry in the hands' uncoupled frequency, both of which are captured in the dynamical model.

Adult↗