Phase resetting of embryonic chick atrial heart cell aggregates. Experiment and theory.

The influence of brief duration current pulses on the spontaneous electrical activity of embryonic chick atrial heart cell aggregates was investigated experimentally and theoretically. A pulse could either delay or advance the time of the action potential subsequent to the pulse depending upon the time in the control cycle at which it was applied. The perturbed cycle length throughout the transition from delay to advance was a continuous function of the time of the pulse for small pulse amplitudes, but was discontinuous for larger pulse amplitudes. Similar results were obtained using a model of the ionic currents which underlie spontaneous activity in these preparations. The primary ion current components which contribute to phase resetting are the fast inward sodium ion current, INa, and the primary, potassium ion repolarization current, IX1. The origin of the discontinuity in phase resetting of the model can be elucidated by a detailed examination of the current-voltage trajectories in the region of the phase response curve where the discontinuity occurs.     

Phase resetting and phase singularity of an insect circannual oscillator

In circadian rhythms, the shape of the phase response curves (PRCs) depends on the strength of the resetting stimulus. Weak stimuli produce Type 1 PRCs with small phase shifts and a continuous transition between phase delays and advances, whereas strong stimuli produce Type 0 PRCs with large phase shifts and a distinct break point at the transition between delays and advances. A stimulus of an intermediate strength applied close to the break point in a Type 0 PRC sometimes produces arrhythmicity. A PRC for the circannual rhythm was obtained in pupation of the varied carpet beetle, Anthrenus verbasci, by superimposing a 4-week long-day pulse (a series of long days for 4 weeks) over constant short days. The shape of this PRC closely resembles that of the Type 0 PRC. The present study shows that the PRC to 2-week long-day pulses was Type 1, and that a 4-week long-day pulse administered close to the PRC’s break point induced arrhythmicity in pupation. It is, therefore, suggested that circadian and circannual oscillators share the same mode in phase resetting to the stimuli.     

Effects of unsignaled delays of reinforcement on fixed-interval schedule performance

Key pecking of pigeons was maintained by a fixed-interval (FI) 61-s schedule. The effects of resetting and nonresetting unsignaled delays of reinforcement then were examined. The resetting delay was programmed as a differential-reinforcement-of-other-behavior schedule, and the nonresetting delay as a fixed-time schedule. Three delay durations (0.5, 1 and 10 s) were examined. Overall response rates were decreased by one and 10-s delays and increased by 0.5-s delays. Response patterns changed from positively accelerated to more linear when resetting or nonresetting 10-s delays were imposed, but remained predominantly positively accelerated when resetting and nonresetting 0.5- and 1-s delays were in effect. In general, temporal control, as measured by quarter-life values, changed less than overall response rates when delays of reinforcement were in effect. The response patterns controlled by FI schedules are more resilient to the nominally disruptive effects of delays of reinforcement than are corresponding overall response rates.     

Melatonin rhythm observed throughout a three-cycle bright-light stimulus designed to reset the human circadian pacemaker.

Exposure to light and darkness can rapidly induce phase shifts of the human circadian pacemaker. A type 0 phase response curve (PRC) to light that has been reported for humans was based on circadian phase data collected from constant routines performed before and after a three-cycle light stimulus, but resetting data observed throughout the entire resetting protocol have not been previously reported. Pineal melatonin secretion is governed by the hypothalamic circadian pacemaker via a well-defined neural pathway and is reportedly less subject to the masking effects of sleep and activity than body temperature. The authors reasoned that observation of the melatonin rhythm throughout the three-cycle light resetting trials could provide daily phase-resetting information, allowing a dynamic view of the resetting response of the circadian pacemaker to light. Subjects (n = 12) living in otherwise dim light (approximately 10-15 lux) were exposed to a noncritical stimulus of three cycles of bright light (approximately 9500 lux for 5 h per day) timed to phase advance or phase delay the human circadian pacemaker; control subjects (n = 11) were scheduled to the same protocols but exposed to three 5-h darkness cycles instead of light. Subjects underwent initial and final constant routine phase assessments; hourly melatonin samples and body temperature data were collected throughout the protocol. Average daily phase shifts of 1 to 3 h were observed in 11 of 12 subjects receiving the bright light, supporting predictions obtained using Kronauer's phase-amplitude model of the resetting response of the human circadian pacemaker. The melatonin rhythm in the 12th subject progressively attenuated in amplitude throughout the resetting trial, becoming undetectable for >32 hours preceding an abrupt reappearance of the rhythm at a shifted phase with a recovered amplitude. The data from control subjects who remained in dim lighting and darkness delayed on average -0.2 h per day, consistent with the daily delay expected due to the longer than 24-h intrinsic period of the human circadian pacemaker. Both temperature and melatonin rhythms shifted by equivalent amounts in both bright light-treated and control subjects (R = 0.968; p<0.0001; n = 23). Observation of the melatonin rhythm throughout a three-cycle resetting trial has provided a dynamic view of the daily phase-resetting response of the human circadian pacemaker. Taken together with the observation of strong type 0 resetting in humans in response to the same three-cycle stimulus applied at a critical phase, these data confirm the importance of considering both phase and amplitude when describing the resetting of the human circadian pacemaker by light.     

Circadian phase resetting in response to light-dark and dark-light transitions

Phase shifting of circadian systems by light has been attributed both to parametric effects on angular velocity elicited by a tonic response to the luminance level and to nonparametric instantaneous shifts induced by a phasic response to the dark-light (D>L) and light-dark (L>D) transitions. Claims of nonparametric responses are partly based on "step-PRCs," that is, phase response curves derived from such transitions. Step-PRCs in nocturnal mammals show mostly delays after lights-on and advances after lights-off, and therefore appear incompatible with phase delays generated by light around dusk and advances by light around dawn. We have pursued this paradox with 2 experimental protocols in mice. We first use the classic step-PRC protocol on wheel running activity, using the center of gravity as a phase marker to minimize the masking effects of light. The experiment was done for 3 different light intensities (1, 10, and 100 lux). D>L transitions evoke mostly delays and L>D transitions show no clear tendency to either delay or advance. Overall there is little or no circadian modulation. A 2nd protocol aimed to avoid the problem of masking by assessing phase before and after the light stimuli, both in DD. Light stimuli consisted of either a slow light intensity increase over 48 h followed by abruptly switching off the light, or an abrupt switch on followed by a slow decrease toward total darkness during 48 h. If the abrupt transitions were responsible for phase shifting, we expected large differences between the 2 stimuli. Both light stimuli yielded similar PRCs characterized by delays only with circadian modulation. The results can be adequately explained by a model in which all PRCs evoked by steps result in fact from tonic responses to the light following a step-up or preceding a step-down. In this model only the response reduction of tonic velocity change after the 1st hour is taken into account. The data obtained in both experiments are thus compatible with tonic velocity responses. Contrary to standard interpretation of step-PRCs, nonparametric responses to the transitions are unlikely since they would predict delays in response to lights-off, advances in response to lights-on, while the opposite was found. Although such responses cannot be fully excluded, parsimony does not require invocation of a role for transitions, since all the data can readily be explained by tonic velocity (parametric) effects, which must exist because of the dependence of tau on light intensity.     

Phase resetting of the rhythmic activity of embryonic heart cell aggregates. Experiment and theory.

Injection of a current pulse of brief duration into an aggregate of spontaneously beating chick embryonic heart cells resets the phase of the activity by either advancing or delaying the time of occurrence of the spontaneous beat subsequent to current injection. This effect depends upon the polarity, amplitude, and duration of the current pulse, as well as on the time of injection of the pulse. The transition from prolongation to shortening of the interbeat interval appears experimentally to be discontinuous for some stimulus conditions. These observations are analyzed by numerical investigation of a model of the ionic currents that underlie spontaneous activity in these preparations. The model consists of: Ix, which underlies the repolarization phase of the action potential, IK2, a time-dependent potassium ion pacemaker current, Ibg, a background or time-independent current, and INa, an inward sodium ion current that underlies the upstroke of the action potential. The steady state amplitude of the sum of these currents is an N-shaped function of potential. Slight shifts in the position of this current-voltage relation along the current axis can produce either one, two, or three intersections with the voltage axis. The number of these equilibrium points and the voltage dependence of INa contribute to apparent discontinuities of phase resetting. A current-voltage relation with three equilibrium points has a saddle point in the pacemaker voltage range. Certain combinations of current-pulse parameters and timing of injection can shift the state point near this saddle point and lead to an interbeat interval that is unbounded . Activation of INa is steeply voltage dependent. This results in apparently discontinuous phase resetting behavior for sufficiently large pulse amplitudes regardless of the number of equilibrium points. However, phase resetting is fundamentally a continuous function of the time of pulse injection for these conditions. These results demonstrate the ionic basis of phase resetting and provide a framework for topological analysis of this phenomenon in chick embryonic heart cell aggregates.     

Transition Between Advance and Delay Responses to Eastbound Transmeridian Flights

In response to eastbound transmeridian flights, which result in zeitgeber phase advance shifts, adaptation of the circadian system to the new time zone by phase delays and advances are observed. The delay response to an advance zeitgeber shift has been called an antidromic response. For the shift at which the transition from an advance to an antidromic response occurs, the term critical shift is introduced.

For the study of critical shifts, a flight experiment across nine time zones and numerical simulations of a van der Pol equation have been evaluated. The interest is focussed on the determination of a range for critical abrupt shifts. An abrupt shift means that the ensemble of zeitgebers including geophysical zeitgebers and the rest-activity cycle is shifted immediately in the new time zone. The range of critical advance shifts has been estimated to reach from + 7 to + 10 hr. In the literature, results were reported which would imply a much wider range. The discussion of these observations shows that the actual shifts were presumably not abrupt in the quoted experiments.

The consequences of critical shifts for jet lag symptoms are investigated. If reduced circadian amplitudes and long times taken for the resynchronization contribute to the feeling of jet lag, the symptoms will be worst for shifts close to the critical one, as numerical simulations revealed. Manipulations of such shifts with the aim to alleviate jet lag are discussed.     

MPer1 and mper2 are essential for normal resetting of the circadian clock

Mammalian Per1 and Per2 genes are involved in the mechanism of the circadian clock and are inducible by light. A light pulse can evoke a change in the onset of wheel-running activity in mice by shifting the onset of activity to earlier times (phase advance) or later times (phase delays) thereby advancing or delaying the clock (clock resetting). To assess the role of mouse Per (mPer) genes in circadian clock resetting, mice carrying mutant mPer1 or mPer2 genes were tested for responses to a light pulse at ZT 14 and ZT 22, respectively. The authors found that mPer1 mutants did not advance and mPer2 mutants did not delay the clock. They conclude that the mammalian Per genes are not only light-responsive components of the circadian oscillator but also are involved in resetting of the circadian clock.     

Photic and nonphotic circadian phase resetting in a diurnal primate, the common marmoset

Despite the considerable literature on circadian entrainment, there is little information on this subject in diurnal mammals. Contributing to this lack of understanding is the problem of separating photic from nonphotic (behavioral) phase-resetting events in diurnal species. In the present study, photic phase resetting was obtained in diurnal common marmosets held under constant dim light (DimDim; <0.5 lx) by using a 20-s pulse of bright light to minimize time available for behavioral arousal. This stimulus elicited phase advances at circadian time (CT) 18-22 and phase delays at CT9-12. Daily presentation of these 20-s pulses produced entrainment with a phase angle of approximately 11 h (0 h = activity onset). Nonphotic phase resetting was obtained under DimDim with the use of a 1-h-induced activity pulse, consisting of intermittent cage agitation and water sprinkling, delivered in total darkness to minimize photic effects. This stimulus caused phase delays at CT20-24, and entrainment to a scheduled daily regimen of these pulses occurred with a phase angle of approximately 0 h. These results indicate that photic and nonphotic phase-response curves (PRCs) of marmosets are similar to those of nocturnal rodents and that nonphotic PRCs are keyed to the phase of the suprachiasmatic nucleus pacemaker, not to the phase of the activity-rest cycle.     

Efficacy of a single sequence of intermittent bright light pulses for delaying circadian phase in humans

It has been shown in animal studies that exposure to brief pulses of bright light can phase shift the circadian pacemaker and that the resetting action of light is most efficient during the first minutes of light exposure. In humans, multiple consecutive days of exposure to brief bright light pulses have been shown to phase shift the circadian pacemaker. The aim of the present study was to determine whether a single sequence of brief bright light pulses administered during the early biological night would phase delay the human circadian pacemaker. Twenty-one healthy young subjects underwent a 6.5-h light exposure session in one of three randomly assigned conditions: 1) continuous bright light of approximately 9,500 lux, 2) intermittent bright light (six 15-min bright light pulses of approximately 9,500 lux separated by 60 min of very dim light of <1 lux), and 3) continuous very dim light of <1 lux. Twenty subjects were included in the analysis. Core body temperature (CBT) and melatonin were used as phase markers of the circadian pacemaker. Phase delays of CBT and melatonin rhythms in response to intermittent bright light pulses were comparable to those measured after continuous bright light exposure, even though the total exposure to the intermittent bright light represented only 23% of the 6.5-h continuous exposure. These results demonstrate that a single sequence of intermittent bright light pulses can phase delay the human circadian pacemaker and show that intermittent pulses have a greater resetting efficacy on a per minute basis than does continuous exposure.     

Conditioning and time representation in long short-term memory networks

Dopaminergic models based on the temporal-difference learning algorithm usually do not differentiate trace from delay conditioning. Instead, they use a fixed temporal representation of elapsed time since conditioned stimulus onset. Recently, a new model was proposed in which timing is learned within a long short-term memory (LSTM) artificial neural network representing the cerebral cortex (Rivest et al. in J Comput Neurosci 28(1):107–130, 2010). In this paper, that model’s ability to reproduce and explain relevant data, as well as its ability to make interesting new predictions, are evaluated. The model reveals a strikingly different temporal representation between trace and delay conditioning since trace conditioning requires working memory to remember the past conditioned stimulus while delay conditioning does not. On the other hand, the model predicts no important difference in DA responses between those two conditions when trained on one conditioning paradigm and tested on the other. The model predicts that in trace conditioning, animal timing starts with the conditioned stimulus offset as opposed to its onset. In classical conditioning, it predicts that if the conditioned stimulus does not disappear after the reward, the animal may expect a second reward. Finally, the last simulation reveals that the buildup of activity of some units in the networks can adapt to new delays by adjusting their rate of integration. Most importantly, the paper shows that it is possible, with the proposed architecture, to acquire discharge patterns similar to those observed in dopaminergic neurons and in the cerebral cortex on those tasks simply by minimizing a predictive cost function.     

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.     

Desynchronization of brain rhythms with soft phase-resetting techniques

 Composite stimulation techniques are presented here which are based on a soft (i.e., slow and mild) reset. They effectively desynchronize a cluster of globally coupled phase oscillators in the presence of noise. A composite stimulus contains two qualitatively different stimuli. The first stimulus is either a periodic pulse train or a smooth, sinusoidal periodic stimulus with an entraining frequency close to the cluster's natural frequency. In the course of several periods of the entrainment, the cluster's dynamics is reset (restarted), independently of its initial dynamic state. The second stimulus, a single pulse, is administered with a fixed delay after the first stimulus in order to desynchronize the cluster by hitting it in a vulnerable state. The incoherent state is unstable, and thus the desynchronized cluster starts to resynchronize. Nevertheless, resynchronization can effectively be blocked by repeatedly delivering the same composite stimulus. Previously designed stimulation techniques essentially rely on a hard (i.e., abrupt) reset. With the composite stimulation techniques based on a soft reset, an effective desynchronization can be achieved even if strong, quickly resetting stimuli are not available or not tolerated. Accordingly, the soft methods are very promising for applications in biology and medicine requiring mild stimulation. In particular, it can be applied to effectively maintain incoherency in a population of oscillatory neurons which try to synchronize their firing. Accordingly, it is explained how to use the soft techniques for (i) an improved, milder, and demand-controlled deep brain stimulation for patients with Parkinson's disease or essential tremor, and for (ii) selectively blocking gamma activity in order to manipulate visual binding. Received: 3 July 2001 / Accepted in revised form: 7 February 2002     

Phase resetting analysis of high potassium epileptiform activity in CA3 region of the rat hippocampus

The theory of phase resetting can reveal important information about the dynamic behavior of a periodic system when a single brief stimulus is applied to that system at the appropriate time. Phase resetting studies have revealed the existence in some biological systems of a vulnerable stimulus window generating desynchronization and suppression of the activity. The objective of this study was to test the hypothesis that a "singular" stimulus could annihilate this activity. Perfusion with the high-K solution produced synchronous, quasi-periodic population bursts with inter-burst interval of ~0.8-1.5 seconds. A single 0.1 ms duration anodic pulse of programmable delay and magnitude was applied to the somatic layer of the CA3 pyramidal cells. Three types of phase-resetting behavior were observed: (1) Weak resetting with little or no effect on the timing of the subsequent burst, (2) Strong resetting where the applied current pulse delayed the next event by one time period, (3) Singular behavior where the applied pulse partially or completely suppressed the subsequent bursting. The singular stimulus parameter window, however, was very narrow making it difficult to generate the singular behavior reliably. Nevertheless, the results indicate that singularities exist for high potassium neural activity and that a well timed pulse applied with the right amplitude can suppress this activity. This study suggests that phase resetting of a population of neurons is possible for quasi-periodic interictal activity and similar techniques could be applied to the control of epileptic seizures.     

Phase resetting in a model of cardiac Purkinje fiber.

The phase-resetting response of a model of spontaneously active cardiac Purkinje fiber is investigated. The effect on the interbeat interval of injecting a 20-ms duration depolarizing current pulse is studied as a function of the phase in the cycle at which the pulse is delivered. At low current amplitudes, a triphasic response is recorded as the pulse is advanced through the cycle. At intermediate current amplitudes, the response becomes quinquephasic, due to the presence of supernormal excitability. At high current amplitudes, a triphasic response is seen once more. At low stimulus amplitudes, type 1 phase resetting occurs; at medium amplitudes, a type could not be ascribed to the phase resetting because of the presence of effectively all-or-none depolarization; at high amplitudes, type 0 phase resetting occurs. The modeling results closely correspond with published experimental data; in particular type 1 and type 0 phase resetting are seen. Implications for the induction of ventricular arrhythmias are considered.     

Short conduction delays cause inhibition rather than excitation to favor synchrony in hybrid neuronal networks of the entorhinal cortex

How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity.     

Dynamic resetting of the human circadian pacemaker by intermittent bright light

In humans, experimental studies of circadian resetting typically have been limited to lengthy episodes of exposure to continuous bright light. To evaluate the time course of the human endogenous circadian pacemaker's resetting response to brief episodes of intermittent bright light, we studied 16 subjects assigned to one of two intermittent lighting conditions in which the subjects were presented with intermittent episodes of bright-light exposure at 25- or 90-min intervals. The effective duration of bright-light exposure was 31% or 63% compared with a continuous 5-h bright-light stimulus. Exposure to intermittent bright light elicited almost as great a resetting response compared with 5 h of continuous bright light. We conclude that exposure to intermittent bright light produces robust phase shifts of the endogenous circadian pacemaker. Furthermore, these results demonstrate that humans, like other species, exhibit an enhanced sensitivity to the initial minutes of bright-light exposure.     

Hypertonicity triggers RhoA-dependent assembly of myosin-containing striated polygonal actin networks in endothelial cells

Electrical slow waves determine the timing and force of peristaltic contractions in the stomach. Slow waves originate from a dominant pacemaker in the orad corpus and propagate actively around and down the stomach to the pylorus. The mechanism of slow-wave propagation is controversial. We tested whether Ca(2+) entry via a voltage-dependent, dihydropyridine-resistant Ca(2+) conductance is necessary for active propagation in canine gastric antral muscles. Muscle strips cut parallel to the circular muscle were studied with intracellular electrophysiological techniques using a partitioned-chamber apparatus. Slow-wave upstroke velocity and plateau amplitude decreased from the greater to the lesser curvature, and this corresponded to a decrease in the density of interstitial cells of Cajal in the lesser curvature. Slow-wave propagation velocity between electrodes impaling cells in two regions of muscle and slow-wave upstroke and plateau were measured in response to experimental conditions that reduce the driving force for Ca(2+) entry or block voltage-dependent Ca(2+) currents. Nicardipine (0.1-1 microM) did not affect slow-wave upstroke or propagation velocities. Upstroke velocity, amplitude, and propagation velocity were reduced in a concentration-dependent manner by Ni(2+) (1-100 microM), mibefradil (10-30 microM), and reduced extracellular Ca(2+) (0.5-1.5 mM). Depolarization (by 10-15 mM K(+)) or hyperpolarization (10 microM pinacidil) also reduced upstroke and propagation velocities. The higher concentrations (or lowest Ca(2+)) of these drugs and ionic conditions tested blocked slow-wave propagation. Treatment with cyclopiazonic acid to empty Ca(2+) stores did not affect propagation. These experiments show that voltage-dependent Ca(2+) entry is obligatory for the upstroke phase of slow waves and active propagation.     

Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays

Time delay is an inevitable factor in neural networks due to the finite propagation velocity and switching speed. Neural system may lose its stability even for very small delay. In this paper, a two-neural network system with the different types of delays involved in self- and neighbor- connection has been investigated. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the multiple delays can lead the system dynamic behavior to exhibit stability switches. The delay-dependent stability regions are illustrated in the delay-parameter plane, followed which the double Hopf bifurcation points can be obtained from the intersection points of the first and second Hopf bifurcation, i.e., the corresponding characteristic equation has two pairs of imaginary eigenvalues. Taking the delays as the bifurcation parameters, the classification and bifurcation sets are obtained in terms of the central manifold reduction and normal form method. The dynamical behavior of system may exhibit the quasi-periodic solutions due to the Neimark- Sacker bifurcation. Finally, numerical simulations are made to verify the theoretical results.     

A vestibulo-ocular reflex with no head movement

Eye movements were produced in an elasmobranch preparation by electrical stimulation of the horizontal canal ampullary nerves. A pseudorandom binary sequence of stimulus pulse trains was delivered bilaterally. Eye position during this stimulus was cross-correlated with the stimulus pattern to obtain a linear model of the response. Sums of exponential functions were fitted to the crosscorrelogram data to estimate time-constants and transfer functions. The data was examined in the frequency domain by using Fourier transformation.The response is accurately described by a second order linear filter, which is essentially a low pass filter with a cutoff at 0.22 Hz. This nearly two octaves below the cutoff frequency of the eye motor plant, which has been estimated by the same method. Our data shows that there is no central phase compensation or prediction which might offset the substantial delay in eye motor plant response. We hypothesise that the necessary phase compensation may be achieved by driving the vestibulo-ocular reflex with sensory neurons having a phase advance at high frequency.