A spike generator mechanism model simulates utricular afferents response to sinusoidal vibrations

Using a model of spike generator mechanism (SGM) with a variable threshold we simulate the responses of utricular afferents to sinusoidal vibrations. It reproduces the phase locking characteristics (bifurcations diagrams) and the stimulus frequency firing rate relationships of different types of utricular afferents. We estimate the model parameters selecting the values which best fit the experimental results and we compare them with those from basic mechanisms involved in utricular codification.     

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.     

The topology of phase response curves induced by single and paired stimuli in spontaneously oscillating chick heart cell aggregates.

The topological properties of the phase resetting of biological oscillators by an isolated stimulus delivered at various phases of the cycle depend on whether the stimulus is "weak" or "strong." When multiple stimuli are delivered to the oscillator, the response to stimulation also depends on the time between the stimuli, and the rate at which the oscillator returns to an underlying limit cycle attractor. If the time between two consecutive "weak" stimuli is sufficiently short, the effects produced by the pair of stimuli may be characteristic of a single "strong" stimulus. These results are demonstrated in a model experimental system, spontaneously beating aggregates of cells derived from embryonic chick heart, and are illustrated by consideration of a simple theoretical model of nonlinear oscillators, the Poincaré oscillator.     

Photobehavior of Halobacterium halobium: sinusoidal stimulation and a suppression effect of responses to flashes

Sequences of reversals recorded by single-cell observation of Halobacterium halobium are analyzed. Autocorrelation functions of spontaneous and stimulated reversals are computed; the results show that the only periodicity present in our data is that of the stimulus. Several different patterns of light stimuli were used. Responses to repetitive linear ramps of different slopes and to sinusoidal lights with different mean values and/or modulation depths are reported, showing that the modulation depth is the stimulus parameter most effective in eliciting photoresponses. Responses to more complex stimuli obtained by superimposing flashes to sinusoidal stimuli are also reported; a suppression effect depending on the phase of the sinusoidal stimulation is shown in responses to complex stimuli. A model which accounts for this effect is proposed.     

Time coding in the midbrain of mormyrid electric fish. II. Stimulus selectivity in the nucleus exterolateralis pars posterior

The anterior and posterior exterolateral nuclei (ELa and ELp) of the mormyrid midbrain are thought to play a critical role in the temporal analysis of the electric discharge waveforms of other individuals. The peripheral electroreceptors receiving electric organ discharges (EODs) of other fish project through the brainstem to ELa via a rapid conducting pathway. EODs, composed of brief, but stereotyped waveforms are encoded as a temporal pattern of spikes. From previous work, we know that phase locking is precise in ELa. Here it is shown that evoked potentials recorded from ELp show a similar high degree of phase locking, although the evoked potentials last much longer. Single-unit recordings in ELp reveal two distinct populations of neurons in ELp: type I cells are responsive to voltage step functions, and not tuned for stimulus duration; type II cells are tuned to a specific range of stimulus durations. Type II cells are less responsive than type I cells, tend to respond with bursts of action potentials rather than with single spikes, have a longer latency, show weaker time locking to stimuli, and are more sensitive to stimulus polarity and amplitude. The stimulus selectivity of type II cells may arise from convergence of type I cell inputs. Despite the loss of rapid conduction between ELa and ELp, analysis of temporal features of waveforms evidently continues in ELp, perhaps through a system of labeled lines. Accepted: 25 June 1997     

Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord

The segmental locomotor network in the lamprey spinal cord was simulated on a computer using a connectionist-type neural network. The cells of the network were identical except for their excitatory levels and their synaptic connections. The synaptic connections used were based on previous experimental work. It was demonstrated that the connectivity of the circuit is capable of generating oscillatory activity with the appropriate phase relations among the cells. Intersegmental coordination was explored by coupling two identical segmental networks using only the cells of the network. Each of the possible couplings of a bilateral pair of cells in one oscillator with a bilateral pair of cells in the other oscillator produced stable phase locking of the two oscillators. The degree of phase difference was dependent upon synaptic weight, and the operating range of synaptic weights varied among the pairs of connections. The coupling was tested using several criteria from experimental work on the lamprey spinal cord. Coupling schemes involving several pairs of connecting cells were found which 1) achieved steadystate phase locking within a single cycle, 2) exhibited constant phase differences over a wide range of cycle periods, and 3) maintained stable phase locking in spite of large differences in the intrinsic frequencies of the two oscillators. It is concluded that the synaptic connectivity plays a large role in producing oscillations in this network and that it is not necessary to postulate a separate set of coordinating neurons between oscillators in order to achieve appropriate phase coupling.     

How to Achieve Fast Entrainment? The Timescale to Synchronization

Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker.     

Analysis of functional brain connections for positive–negative emotions using phase locking value

In this study, we investigate the brain networks during positive and negative emotions for different types of stimulus (audio only, video only and audio + video) in \(\alpha , \beta\), and \(\gamma\) bands in terms of phase locking value, a nonlinear method to study functional connectivity. Results show notable hemispheric lateralization as phase synchronization values between channels are significant and high in right hemisphere for all emotions. Left frontal electrodes are also found to have control over emotion in terms of functional connectivity. Besides significant inter-hemisphere phase locking values are observed between left and right frontal regions, specifically between left anterior frontal and right mid-frontal, inferior-frontal and anterior frontal regions; and also between left and right mid frontal regions. ANOVA analysis for stimulus types show that stimulus types are not separable for emotions having high valence. PLV values are significantly different only for negative emotions or neutral emotions between audio only/video only and audio only/audio + video stimuli. Finding no significant difference between video only and audio + video stimuli is interesting and might be interpreted as that video content is the most effective part of a stimulus.     

Phase resetting and fixed-delay stimulation of a simple model of respiratory rhythm generation.

In a previous study (Lewis et al., 1990), the response of the respiratory rhythm to a perturbing stimulus was investigated using two different stimulus protocols: phase resetting and fixed-delay stimulation. The first protocol consists of measuring the effects of perturbing an oscillator at different phases of the cycle on the duration of the perturbed cycle. The resulting phase response curves (PRCs) can be used to characterize the properties of the oscillator (Winfree, 1980). A second protocol, fixed-delay stimulation, involves perturbing an oscillator at a fixed latency from the onset of the cycle, repeated every n-th cycle. If a single stimulus produces an effect that lasts longer than a single cycle, complicated responses can be expected from fixed-delay stimulation (Lewis et al., 1987). A simple three-phase model for respiratory rhythm generation based on a hypothesis by Richter and coworkers (1982, 1983, 1986) was investigated in the context of these experimental studies. Phase resetting and fixed-delay stimulation protocols were simulated in the model. PRCs of the model resemble those obtained experimentally: a phase-dependent prolongation or shortening of the inspiratory phase depending on the stimulus magnitude, and a slight prolongation of the expiratory phase. Stimuli delivered to the model repetitively during successive inspiratory periods at a fixed-delay produced various combinations of shortened and prolonged cycles, similar to those observed in the experiments. However, the marked increases in cycle duration observed in the experiments during, as well as after, stimulation were not evident in the model. These comparisons suggest that (1) PRCs may not be an adequate way to evaluate certain models of rhythmogenesis, and (2) to improve the present simplified formulation of the three-phase model of the respiratory oscillator, time-varying stimulus dependent effects should be incorporated.     

Theoretical computation of phase locking in embryonic atrial heart cell aggregates

The effects of periodic stimulation of spontaneously beating aggregates of chick atrial heart cells are considered. Provided the effects of a single stimulus do not change the properties of the oscillation, and that the oscillation is re-established rapidly following a stimulus, this system can be modeled by one-dimensional finite difference equations. These equations employ experimentally generated phase resetting data that describe the effects of a single isolated stimulus at different phases of the oscillation. A complete analysis of the predicted dynamics is given over a broad range of stimulation frequencies and amplitudes. Prominent features of the dynamics include phase locking, bistability, chaos, and disappearance of Arnold tongues at large stimulation amplitudes. The fine details of the bifurcations are sensitive to properties of the phase resetting curves, and consequently, the observed bifurcations are not expected to be "universal" for larger stimulation amplitudes. Experimental traces show many correspondences with theoretical computations.     

心肌振荡模型的非线性动力学研究

通过计算机对心肌振荡模型的研究,得到它在单刺激下的相角转移曲线.用相角转移曲线研究了振子在不同周期刺激下表现出来的锁相、分叉及混沌现象,进而对某些常见的心律失常产生的机制进行了讨论.     

Directionality of phase locking in auditory nerve fibers of the leopard frog Rana pipiens pipiens

Summary A dorsal approach to the eighth nerve and free-field stimulation were used to investigate the effect of sound direction and intensity on phase locking in auditory nerve fibers of the leopard frog Rana pipiens pipiens.Tuning curves of 75 auditory neurons were analyzed (Fig. 2). Amphibian papillar neurons, but not basilar papillar neurons, exhibit significant phase locking to short tone bursts at the characteristic frequency (CF), the degree of phase locking (vector strength) decreasing with the neuron's CF (Figs. 3, 4 and 10E). Vector strength increases with sound pressure level to saturate about 20 dB above threshold, while the preferred firing phase is only slightly affected (Figs. 5 and 6).In contrast, sound direction hardly affects vector strength (Figs. 7, 8, 9A and 10A and C), but has a strong influence on the preferred firing phase (Figs. 7, 8, 9B and C, 10B and D): With respect to anterior tone presentation there are phase lags for ipsilateral and phase leads for posterior and contralateral presentation. Phase differences between both ears show a sinusoidal or cardioid/ovoidal directional characteristic; maximum differences are found with antero-lateral tone presentation (Fig. 11). The directionality of phase locking decreases with the neuron's CF (Fig. 10F) and only slightly changes with sound pressure level (Fig. 12). Thus, phase locking of amphibian papilla neurons can potentially provide intensity-independent information for sound localization.Abbreviations SPL sound pressure level - FTC frequency threshold curve - CF characteristic frequency - TF test frequency - VS vector strength - AP amphibian papilla - BP basilar papilla     

Phase plane description of crayfish swimmeret oscillator

Crayfish swimmeret system shows rhythmic, coordinated behavior when the command fibers are stimulated chronically by electrical pulses, and the oscillating frequency becomes faster with increasing stimulus frequency. This behavior is organized by the distributed neural oscillators in the abdominal ganglia. We investigated the dynamics of the neural oscillators which are controlled by command fibers. Phase resetting experiment technique was used for this purpose; a temporary cessation of commanding pulses, which was regarded as suppressive perturbation for the neural oscillator, was applied to the chronically stimulated oscillator, and phase transition curves (PTCs) were measured. For the short cessation of command pulses, type 1 PTCs were obtained. With increasing cessation length, the PTC shifted downward, and finally changed into type 0. We also measured PTCs for temporarily increased stimulus frequency, which was an excitatory perturbation for the neural oscillator and increased the frequency of the oscillation transiently. For the short excitatory perturbation, the PTCs were also type 1 and shifted upward. PTCs changed their shapes from type 1 into type 0, as increasing the perturbation length. These shapes of the PTCs contain important information about the properties of the neural oscillator. Analyzing these PTCs, we present a phase plane diagram which describes the character of the command control of the neural oscillator.     

Automatic classification of interference patterns in driven event series: application to single sympathetic neuron discharge forced by mechanical ventilation

This study proposes a method for the automatic classification of nonlinear interactions between a strictly periodical event series modelling the activity of an exogenous oscillator working at a fixed and well-known rate and an event series modelling the activity of a self-sustained oscillator forced by the exogenous one. The method is based on a combination of several well-known tools (probability density function of the cyclic relative phase, probability density function of the count of forced events per forcing cycle, conditional entropy of the cyclic relative phase sequence and a surrogate data approach). Classification is reached via a sequence of easily applicable decision rules, thus rendering classification virtually user-independent and fully reproducible. The method classifies four types of dynamics: full uncoupling, quasiperiodicity, phase locking and aperiodicity. In the case of phase locking, the coupling ratio (i.e. n:m) and the strength of the coupling are calculated. The method, validated on simulations of simple and complex phase-locking dynamics corrupted by different levels of noise, is applied to data derived from one anesthetized and artificially ventilated rat to classify the nonlinear interactions between mechanical ventilation and: (1) the discharges of two (contemporaneously recorded) single postganglionic sympathetic neurons innervating the caudal ventral artery in the tail and (2) arterial blood pressure. Under central apnea, the activity of the underlying sympathetic oscillators is perturbed by means of five different lung inflation rates (0.58, 0.64, 0.76, 0.95, 1.99 Hz). While ventilation and arterial pressure are fully uncoupled, ventilation is capable of phase locking sympathetic discharges, thus producing 40% of phase-locked patterns (one case of 2:5, 1:1, 3:2 and 2:2) and 40% of aperiodic dynamics. In the case of phase-locked patterns, the coupling strength is low, thus demonstrating that this pattern is sliding. Non-stationary interactions are observed in 20% of cases. The two discharges behave differently, suggesting the presence of a population of sympathetic oscillators working at different frequencies.     

Phase-locked responses in the Limulus lateral eye. Theoretical and experimental investigation.

The 1:1 phase locking of the neural discharge to sinusoidally modulated stimuli was investigated both theoretically and experimentally. On the theoretical side, a neural encoder model, the self-inhibited leaky integrator, was considered, and the phase of the locked impulse was computed for each frequency in the locking range by imposing the condition that the "leaky integral" u(t) of the driving signal should reach the threshold for the first time one stimulus period after the preceding impulse. As u(t) can be a nonmonotonic function, this approach leads to results that sometimes differ from those reported in the literature. It turns out that the phase excursion is often much smaller than the values of about 180 degrees predicted from previous analysis. Moreover, our analysis shows a peculiar effect; the phase locking frequency range narrows when the input modulation depth increases. The theoretical predictions are then compared with phase-locked discharge patterns recorded from visual cells of the Limulus lateral eye, stimulated by sinusoidally modulated light or depolarizing current. The phases of the locked spikes at each of a number of modulation frequencies have been measured. The predictions offered by the model fit the experimental data, although there are some difficulties in determining the effective driving signal.     

Stimulus Phase Locking of Cortical Oscillation for Auditory Stream Segregation in Rats

The phase of cortical oscillations contains rich information and is valuable for encoding sound stimuli. Here we hypothesized that oscillatory phase modulation, instead of amplitude modulation, is a neural correlate of auditory streaming. Our behavioral evaluation provided compelling evidences for the first time that rats are able to organize auditory stream. Local field potentials (LFPs) were investigated in the cortical layer IV or deeper in the primary auditory cortex of anesthetized rats. In response to ABA- sequences with different inter-tone intervals and frequency differences, neurometric functions were characterized with phase locking as well as the band-specific amplitude evoked by test tones. Our results demonstrated that under large frequency differences and short inter-tone intervals, the neurometric function based on stimulus phase locking in higher frequency bands, particularly the gamma band, could better describe van Noorden’s perceptual boundary than the LFP amplitude. Furthermore, the gamma-band neurometric function showed a build-up-like effect within around 3 seconds from sequence onset. These findings suggest that phase locking and amplitude have different roles in neural computation, and support our hypothesis that temporal modulation of cortical oscillations should be considered to be neurophysiological mechanisms of auditory streaming, in addition to forward suppression, tonotopic separation, and multi-second adaptation.     

On the complex dynamics of intracellular ganglion cell light responses in the cat retina

We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights, and compared the response dynamics with a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a smooth generator (G) potential and corresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus-dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties. We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator, and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might carry information.To the memory of Prof. Otto-Joachim Grusser     

New roles for DIF? Effects on early development in Dictyostelium

The DIFs are unusual, chlorinated molecules which induce stalk cell differentiation during the later, multicellular phase of Dictyostelium development. Here we provide evidence that one or more DIFs have a role during early development, when small amounts are known to be made. Initial indications came from an optical technique which detects changes in shape or cohesion of cells in suspension (Gerisch and Hess, PNAS 71, 2118, 1974). After a period of optical inactivity at the start of development, cell suspensions normally produce spontaneous spike-shaped light-scattering oscillations synchronised by oscillations in extracellular cAMP levels, followed by sinusoidal oscillations where the synchroniser is not known. DIFs 1 and 2 produce optical responses from cells at all these early stages of development. The phase of both spiked and sinusoidal oscillations can be shifted, indicating an effect on the oscillator in each case. We find further: (1) cAMP oscillations and cAMP relay during spiked oscillations are transiently inhibited by DIF-1. (2) DIF-1 causes a transient decrease in cellular cGMP levels in cells taken before oscillations commence and likewise inhibits the cGMP response to a cAMP stimulus in cells taken later in development. Cytoskeletal organization and hence cell shape might be affected by DIF-1 by this indirect route. (3) The effects of DIF-1 are transient, even though it is essentially stable in the cell suspension. Cells somehow adapt to DIF-1. (4) The effects are chemically specific: DIF-1 and DIF-2 are active at 10(-7) to 10(-8) M, with DIF-2 being the more active, whereas related compounds have little or no activity at 10(-6) M. These results indicate that cells are responsive to DIFs 1 and 2 from the start of development and suggest a wider role for the DIFs. This role might involve effects on cAMP signalling and on intracellular second messengers.