Representation of Time-Varying Stimuli by a Network Exhibiting Oscillations on a Faster Time Scale

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp.     

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.     

A mathematical model of spontaneous calcium(II) oscillations in astrocytes

Astrocytes exhibit oscillations and waves of Ca²⁺ ions within their cytosol and it appears that this behavior helps facilitate the astrocyte's interaction with its environment, including its neighboring neurons. Often changes in the oscillatory behavior are initiated by an external stimulus such as glutamate, recently however, it has been observed that oscillations are also initiated spontaneously. We propose here a mathematical model of how spontaneous Ca²⁺ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment.     

Synchronization of electrically induced calcium firings in self-assembled cardiac cells

We study the adaptive changes of a population of cells responding to external stimulus. Two-dimensionally distributed cardiac cells were homogeneously subjected to periodic electrical stimulus and intracellular calcium concentration ([Ca(2+)](i)) changes were simultaneously observed. In the absence of stimulation, coupled cells in monolayer formed groups of several cells oscillating in similar phase, while isolated cells showed irregular periodicity. In both systems, [Ca(2+)](i) oscillations were modulated by periodic stimulation, and ascending degrees of synchronization among [Ca(2+)](i) oscillations were shown as stimulation intensity increased. In a population of coupled cells, the cells act like a single robust oscillator. These results are evaluated using statistical calculations, comparing the response manner of isolated cells.     

Latency correlates with period in a model for signal-induced Ca2+ oscillations based on Ca2(+)-induced Ca2+ release.

Oscillations in cytosolic Ca2+ develop in a variety of cells after an induction phase, called latency, the duration of which depends on the magnitude of external stimulation. Experiments in hepatocytes indicate that the period and latency of Ca2+ oscillations both decrease as the level of the stimulus increases. We analyze the correlation between period and latency in a model recently proposed for signal-induced Ca2+ oscillations. We show that the linear relationship between period and latency observed in the experiments arises naturally in this model as a result of the mechanism of Ca2(+)-induced Ca2+ release on which it is based.     

Phase reset affects auditory-visual simultaneity judgment

We continuously receive the external information from multiple sensors simultaneously. The brain must judge a source event of these sensory informations and integrate them. It is thought that judging the simultaneity of such multisensory stimuli is an important cue when we discriminate whether the stimuli are derived from one event or not. Although previous studies have investigated the correspondence between an auditory-visual (AV) simultaneity perceptions and the neural responses, there are still few studies of this. Electrophysiological studies have reported that ongoing oscillations in human cortex affect perception. Especially, the phase resetting of ongoing oscillations has been examined as it plays an important role in multisensory integration. The aim of this study was to investigate the relationship of phase resetting for the judgment of AV simultaneity judgement tasks. The subjects were successively presented with auditory and visual stimuli with intervals that were controlled as SOA_50% and they were asked to report whether they perceived them simultaneously or not. We investigated the effects of the phase of ongoing oscillations on simultaneity judgments with AV stimuli with SOAs in which the detection rate of asynchrony was 50 %. It was found that phase resetting at the beta frequency band in the brain area that related to the modality of the following stimulus occurred after preceding stimulus onset only when the subjects perceived AV stimuli as simultaneous. This result suggested that beta phase resetting occurred in areas that are related to the subsequent stimulus, supporting perception multisensory stimuli as simultaneous.     

Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release.

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.     

Stimulus-dependent oscillations and evoked potentials in chinchilla auditory cortex

Besides the intensity and frequency of an auditory stimulus, the length of time that precedes the stimulation is an important factor that determines the magnitude of early evoked neural responses in the auditory cortex. Here we used chinchillas to demonstrate that the length of the silent period before the presentation of an auditory stimulus is a critical factor that modifies late oscillatory responses in the auditory cortex. We used tetrodes to record local-field potential (LFP) signals from the left auditory cortex of ten animals while they were stimulated with clicks, tones or noise bursts delivered at different rates and intensity levels. We found that the incidence of oscillatory activity in the auditory cortex of anesthetized chinchillas is dependent on the period of silence before stimulation and on the intensity of the auditory stimulus. In 62.5% of the recordings sites we found stimulus-related oscillations at around 8-20 Hz. Stimulus-induced oscillations were largest and consistent when stimuli were preceded by 5 s of silence and they were absent when preceded by less than 500 ms of silence. These results demonstrate that the period of silence preceding the stimulus presentation and the stimulus intensity are critical factors for the presence of these oscillations.     

Human cortical traveling waves: dynamical properties and correlations with responses

The spatiotemporal behavior of human EEG oscillations is investigated. Traveling waves in the alpha and theta ranges are found to be common in both prestimulus and poststimulus EEG activity. The dynamical properties of these waves, including their speeds, directions, and durations, are systematically characterized for the first time, and the results show that there are significant changes of prestimulus spontaneous waves in the presence of an external stimulus. Furthermore, the functional relevance of these waves is examined by studying how they are correlated with reaction times on a single trial basis; prestimulus alpha waves traveling in the frontal-to-occipital direction are found to be most correlated to reaction speeds. These findings suggest that propagating waves of brain oscillations might be involved in mediating long-range interactions between widely distributed parts of human cortex.     

Smooth muscle stiffness variation due to external longitudinal oscillations

This research focuses on an in vitro investigation of the stiffness changes of contracted airway smooth muscles (ASM) subjected to external longitudinal oscillations. ASM tissues were dissected from excised pig tracheas and stimulated by a chemical stimulus (acetylcholine, 10(-3) M) to produce maximum contractions. The tissues were then systematically excited with external oscillations. Various frequencies, amplitudes and durations were used in the experiments to determine stiffness changes in response to these variations. Force changes were recorded to reflect the muscle stiffness changes. Two stiffness definitions were used to quantify the results, dynamic stiffness to reflect variations during oscillation and static stiffness to reflect the net effect of oscillation. Under isometric contractions, these two stiffnesses were determined before, during and after oscillations. Incorporating an empirical stiffness equation, a two-dimensional finite element model (FEM) was developed to generalize the tissue responses to oscillation. The main outcomes from this work are: the dynamic stiffness has the tendency to decrease as the frequency and/or amplitude of external oscillation increases; the static stiffness has the tendency of decreasing with an increase in the frequency and/or amplitude of excitation until it reaches almost a constant value for frequencies at and above 25 Hz. The difference in the behavior of the dynamic and static stiffness changes may be attributed to the effect of elasticity and mass inertia that are involved in the dynamic motion. The findings of this research are in agreement with the hypothesis that oscillations exert a direct action on the contractile processes by causing an increased rate of actin-myosin detachments.     

Investigations on emergent spatio-temporal neural response characteristics in a small network model

Although the functional role synchronous oscillations may play has been investigated in depth, the underlying processes and spatio-temporal aspects that establish the synchrony are still not thoroughly understood. Experimental studies suggest the existence of two types of activity: stimulus locked and stimulus induced. While stimulus-locked oscillations are systematically dependent on the stimulus (they are phase-locked to stimulus transients), stimulus-induced activity patterns (occurring in the γ-frequency range) show no such phase-locking. We propose a unifying approach which employs very generic connection structures. The above-mentioned two types of activity patterns with different temporal properties are observed as an emergent feature of the network structure. Our model demonstrates that stimulus-locked and stimulus-induced activity patterns are two distinct states of the same system. A transition from one state to the other is observed, and the influence of structural network parameters (e.g. connections strengths) on this behavior and its dependence on stimulus situations is investigated. Received: 13 July 1999 / Accepted in revised form: 26 May 2000     

Sound Asleep: Processing and Retention of Slow Oscillation Phase-Targeted Stimuli

The sleeping brain retains some residual information processing capacity. Although direct evidence is scarce, a substantial literature suggests the phase of slow oscillations during deep sleep to be an important determinant for stimulus processing. Here, we introduce an algorithm for predicting slow oscillations in real-time. Using this approach to present stimuli directed at both oscillatory up and down states, we show neural stimulus processing depends importantly on the slow oscillation phase. During ensuing wakefulness, however, we did not observe differential brain or behavioral responses to these stimulus categories, suggesting no enduring memories were formed. We speculate that while simpler forms of learning may occur during sleep, neocortically based memories are not readily established during deep sleep.     

Cytosolic calcium oscillators

Many cells display oscillations in intracellular calcium resulting from the periodic release of calcium from intracellular reservoirs. Frequencies are varied, but most oscillations have periods ranging from 5 to 60 s. For any given cell, frequency can vary depending on external conditions, particularly the concentration of natural stimuli or calcium. This cytosolic calcium oscillator is particularly sensitive to those stimuli (neurotransmitters, hormones, growth factors) that hydrolyze phosphoinositides to give diacylglycerol and inositol 1,4,5-trisphosphate (Ins1,4,5P3). The ability of Ins1,4,5P3 to mobilize intracellular calcium is a significant feature of many of the proposed models that are used to explain oscillatory activity. Receptor-controlled oscillator models propose that there are complex feedback mechanisms that generate oscillations in the level of Ins1,4,5P3. Second messenger-controlled oscillator models demonstrate that the oscillator is a component of the calcium reservoir, which is induced to release calcium by a constant input of either Ins1,4,5P3 or calcium itself. In the latter case, the process of calcium-induced calcium release might be the basis of oscillatory activity in many cell types. The function of calcium oscillations is still unknown. Because oscillator frequency can vary with agonist concentration, calcium transients might be part of a frequency-encoded signaling system. When an external stimulus arrives at the cell surface the information is translated into a train of calcium spikes, i.e., the signal is digitized. Certain cells may then convey information by varying the frequency of this digital signal.     

Inositol trisphosphate and calcium oscillations

InsP3 has two important functions in generating Ca2+ oscillations. It releases Ca2+ from the internal store and it can contribute to Ca2+ entry. A hypothesis has been developed to describe a mechanism for Ca2+ oscillations with particular emphasis on the way agonist concentration regulates oscillator frequency. The main idea is that the InsP3 receptors are sensitized to release Ca2+ periodically by cyclical fluctuations of Ca2+ within the lumen of the endoplasmic reticulum. Each time a pulse of Ca2+ is released, the luminal level of Ca2+ declines and has to be replenished before the InsP3 receptors are resensitized to deliver the next pulse of Ca2+. It is this loading of the internal store that explains why frequency is sensitive to external Ca2+ and may also account for how variations in agonist concentration are translated into changes in oscillation frequency. Variations in agonist-induced entry of external Ca2+, which can occur through different mechanisms, determine the variable rates of store loading responsible for adjusting the sensitivity of the InsP3 receptors to produce the periodic pulses of Ca2+. The Ca2+ oscillator is an effective analogue-to-digital converter in that variations in the concentration of the external stimulus are translated into a change in oscillator frequency.     

Hippocampal State-Dependent Behavioral Reflex to an Identical Sensory Input in Rats

We examined the local field potential of the hippocampus to monitor brain states during a conditional discrimination task, in order to elucidate the relationship between ongoing brain states and a conditioned motor reflex. Five 10-week-old Wistar/ST male rats underwent a serial feature positive conditional discrimination task in eyeblink conditioning using a preceding light stimulus as a conditional cue for reinforced trials. In this task, a 2-s light stimulus signaled that the following 350-ms tone (conditioned stimulus) was reinforced with a co-terminating 100-ms periorbital electrical shock. The interval between the end of conditional cue and the onset of the conditioned stimulus was 4±1 s. The conditioned stimulus was not reinforced when the light was not presented. Animals successfully utilized the light stimulus as a conditional cue to drive differential responses to the identical conditioned stimulus. We found that presentation of the conditional cue elicited hippocampal theta oscillations, which persisted during the interval of conditional cue and the conditioned stimulus. Moreover, expression of the conditioned response to the tone (conditioned stimulus) was correlated with the appearance of theta oscillations immediately before the conditioned stimulus. These data support hippocampal involvement in the network underlying a conditional discrimination task in eyeblink conditioning. They also suggest that the preceding hippocampal activity can determine information processing of the tone stimulus in the cerebellum and its associated circuits.     

Dyslexic adults can learn from repeated stimulus presentation but have difficulties in excluding external noise

We examined whether the characteristic impairments of dyslexia are due to a deficit in excluding external noise or a deficit in taking advantage of repeated stimulus presentation. We compared non-impaired adults and adults with poor reading performance on a visual letter detection task that varied two aspects: the presence or absence of background visual noise, and a small or large stimulus set. There was no interaction between group and stimulus set size, indicating that the poor readers took advantage of repeated stimulus presentation as well as the non-impaired readers. The poor readers had higher thresholds than non-impaired readers in the presence of high external noise, but not in the absence of external noise. The results support the hypothesis that an external noise exclusion deficit, not a perceptual anchoring deficit, impairs reading for adults.     

A class of parametrically excited calcium oscillation detectors.

Intracellular Ca2+ oscillations are often a response to external signals such as hormones. Changes in the external signal can alter the frequency, amplitude, or form of the oscillations suggesting that information is encoded in the pattern of Ca2+ oscillations. How might a cell decode this signal? We show that an excitable system whose kinetic parameters are modulated by the Ca2+ concentration can function as a Ca2+ oscillation detector. Such systems have the following properties: (1) They are more sensitive to an oscillatory than to a steady Ca2+ signal. (2) Their response is largely independent of the signal amplitude. (3) They can extract information from a noisy signal. (4) Unlike other frequency sensitive detectors, they have a flat frequency response. These properties make a Ca(2+)-sensitive excitable system nearly ideal for detecting and decoding Ca2+ oscillations. We suggest that Ca2+ oscillations, in concert with these detectors, can act as cellular timekeepers to coordinate related biochemical reactions and enhance their overall efficiency.     

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.