Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry

In subjects suffering from early onset strabismus, signals conveyed by the two eyes are not perceived simultaneously but in alternation. We exploited this phenomenon of interocular suppression to investigate the neuronal correlate of binocular rivalry in primary visual cortex of awake strabismic cats. Monocularly presented stimuli that were readily perceived by the animal evoked synchronized discharges with an oscillatory patterning in the γ-frequency range. Upon dichoptic stimulation, neurons responding to the stimulus that continued to be perceived increased the synchronicity and the regularity of their oscillatory patterning while the reverse was true for neurons responding to the stimulus that was no longer perceived. These differential changes were not associated with modifications of discharge rate, suggesting that at early stages of visual processing the degree of synchronicity rather than the amplitude of responses determines which signals are perceived and control behavioral responses.

Titration of chaos with added noise

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.

Intracortical and corticothalamic coherency of fast spontaneous oscillations.

We report that fast (mainly 30- to 40-Hz) coherent electric field oscillations appear spontaneously during brain activation, as expressed by electroencephalogram (EEG) rhythms, and they outlast the stimulation of mesopontine cholinergic nuclei in acutely prepared cats. The fast oscillations also appear during the sleep-like EEG patterns of ketamine/xylazine anesthesia, but they are selectively suppressed during the prolonged phase of the slow (<1-Hz) sleep oscillation that is associated with hyperpolarization of cortical neurons. The fast (30- to 40-Hz) rhythms are synchronized intracortically within vertical columns, among closely located cortical foci, and through reciprocal corticothalamic networks. The fast oscillations do not reverse throughout the depth of the cortex. This aspect stands in contrast with the conventional depth profile of evoked potentials and slow sleep oscillations that display opposite polarity at the surface and midlayers. Current-source-density analyses reveal that the fast oscillations are associated with alternating microsinks and microsources across the cortex, while the evoked potentials and the slow oscillation display a massive current sink in midlayers, confined by two sources in superficial and deep layers. The synchronization of fast rhythms and their high amplitudes indicate that the term "EEG desynchronization," used to designate brain-aroused states, is incorrect and should be replaced with the original term, "EEG activation" [Moruzzi, G. & Magoun, H.W. (1949) Electroencephalogr. Clin. Neurophysiol. 1, 455-473].

Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

Recurrent excitatory postsynaptic potentials induced by synchronized fast cortical oscillations

Gamma frequency (about 20–70 Hz) oscillations occur during novel sensory stimulation, with tight synchrony over distances of at least 7 mm. Synchronization in the visual system has been proposed to reflect coactivation of different parts of the visual field by a single spatially extended object. We have shown that intracortical mechanisms, including spike doublet firing by interneurons, can account for tight long-range synchrony. Here we show that synchronous gamma oscillations in two sites also can cause long-lasting (>1 hr) potentiation of recurrent excitatory synapses. Synchronous oscillations lasting >400 ms in hippocampal area CA1 are associated with an increase in both excitatory postsynaptic potential (EPSP) amplitude and action potential afterhyperpolarization size. The resulting EPSPs stabilize and synchronize a prolonged beta frequency (about 10–25 Hz) oscillation. The changes in EPSP size are not expressed during non-oscillatory behavior but reappear during subsequent gamma-oscillatory events. We propose that oscillation-induced EPSPs serve as a substrate for memory, whose expression either enhances or blocks synchronization of spatially separated sites. This phenomenon thus provides a dynamical mechanism for storage and retrieval of stimulus-specific neuronal assemblies.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Synchronization between prefrontal and posterior association cortex during human working memory

We measured coherence between the electroencephalogram at different scalp sites while human subjects performed delayed response tasks. The tasks required the retention of either verbalizable strings of characters or abstract line drawings. In both types of tasks, a significant enhancement in coherence in the θ range (4–7 Hz) was found between prefrontal and posterior electrodes during 4-s retention intervals. During 6-s perception intervals, far fewer increases in θ coherence were found. Also in other frequency bands, coherence increased; however, the patterns of enhancement made a relevance for working memory processes seem unlikely. Our results suggest that working memory involves synchronization between prefrontal and posterior association cortex by phase-locked, low frequency (4–7 Hz) brain activity.

Gamma rhythms and beta rhythms have different synchronization properties

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12–29 Hz) have a different dynamical structure than that of gamma (30–70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures.

Information about movement direction obtained from synchronous activity of motor cortical neurons

Although neuronal synchronization has been shown to exist in primary motor cortex (MI), very little is known about its possible contribution to coding of movement. By using cross-correlation techniques from multi-neuron recordings in MI, we observed that activity of neurons commonly synchronized around the time of movement initiation. For some cell pairs, synchrony varied with direction in a manner not readily predicted by the firing of either neuron. Information theoretic analysis demonstrated quantitatively that synchrony provides information about movement direction beyond that expected by simple rate changes. Thus, MI neurons are not simply independent encoders of movement parameters but rather engage in mutual interactions that could potentially provide an additional coding dimension in cortex.

Experimentally determined chaotic phase synchronization in a neuronal system

Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that rapidly can transform into robustly determined multicellular coherence.

Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Dynamic Localization of the Swe1 Regulator Hsl7 During the Saccharomyces cerevisiae Cell Cycle

In Saccharomyces cerevisiae, entry into mitosis requires activation of the cyclin-dependent kinase Cdc28 in its cyclin B (Clb)-associated form. Clb-bound Cdc28 is susceptible to inhibitory tyrosine phosphorylation by Swe1 protein kinase. Swe1 is itself negatively regulated by Hsl1, a Nim1-related protein kinase, and by Hsl7, a presumptive protein-arginine methyltransferase. In vivo all three proteins localize to the bud neck in a septin-dependent manner, consistent with our previous proposal that formation of Hsl1-Hsl7-Swe1 complexes constitutes a checkpoint that monitors septin assembly. We show here that Hsl7 is phosphorylated by Hsl1 in immune-complex kinase assays and can physically associate in vitro with either Hsl1 or Swe1 in the absence of any other yeast proteins. With the use of both the two-hybrid method and in vitro binding assays, we found that Hsl7 contains distinct binding sites for Hsl1 and Swe1. A differential interaction trap approach was used to isolate four single-site substitution mutations in Hsl7, which cluster within a discrete region of its N-terminal domain, that are specifically defective in binding Hsl1. When expressed in hsl7Δ cells, each of these Hsl7 point mutants is unable to localize at the bud neck and cannot mediate down-regulation of Swe1, but retains other functions of Hsl7, including oligomerization and association with Swe1. GFP-fusions of these Hsl1-binding defective Hsl7 proteins localize as a bright perinuclear dot, but never localize to the bud neck; likewise, in hsl1Δ cells, a GFP-fusion to wild-type Hsl7 or native Hsl7 localizes to this dot. Cell synchronization studies showed that, normally, Hsl7 localizes to the dot, but only in cells in the G1 phase of the cell cycle. Immunofluorescence analysis and immunoelectron microscopy established that the dot corresponds to the outer plaque of the spindle pole body (SPB). These data demonstrate that association between Hsl1 and Hsl7 at the bud neck is required to alleviate Swe1-imposed G2-M delay. Hsl7 localization at the SPB during G1 may play some additional role in fine-tuning the coordination between nuclear and cortical events before mitosis.