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.     

A phase response curve for circannual rhythm in the varied carpet beetle <Emphasis Type="Italic">Anthrenus verbasci</Emphasis>

We know that entrainment, a stable phase relationship with an environmental cycle, must be established for a biological clock to function properly. Phase response curves (PRCs), which are plots of phase shifts that result as a function of the phase of a stimulus, have been created to examine the mode of entrainment. In circadian rhythms, single-light pulse PRCs have been obtained by giving a light pulse to various phases of a free-running rhythm under continuous darkness. This successfully explains the entrainment to light-dark cycles. Some organisms show circannual rhythms. In some of these, changes in photoperiod entrain the circannual rhythms. However, no single-pulse PRCs have been created. Here we show the PRC to a long-day pulse superimposed for 4 weeks over constant short days in the circannual pupation rhythm in the varied carpet beetle Anthrenus verbasci. Because the shape of that PRC closely resembles that of the Type 0 PRC with large phase shifts in circadian rhythms, we suggest that an oscillator having a common feature in the phase response with the circadian clock, produces a circannual rhythm.     

Probing the circadian pacemaker of a mouse using two light pulses

In two separate sets of experiments, the phases of the locomotor activity rhythm of the nocturnal field mouse Mus booduga were probed using two light pulses (LPs). In the first set of experiments, the circadian pacemaker underlying the locomotor activity rhythm was perturbed at circadian time 14 (CT 14) using a resetting light pulse LP1 of 1000 lux intensity and 15 min duration. The phases of the resetting pacemaker were then probed at all even CTs between CT 16 and CT 14 using a PRC probing light pulse LP2 of equal strength. The "LP2 PRC" thus obtained was then compared with the single light pulse PRC in terms of the area under delay (D) and advance (A) zones of the PRCs. The time course and waveform of the two LP PRCs suggest that the LP2 PRC resembled the single LP PRC, displaced by 2 h toward the right. The LP1 PRC had smaller D compared to the single LP PRC (p = 0.007), whereas both the PRCs had A of equal magnitude (p = 0.23). This suggests that the pacemaker phase shifts rapidly after LP perturbations. In the second set of experiments, the LP1 was administered at CT 14. The phase of the pacemaker was then perturbed on day 1 (next cycle after LP1) either 2 h after activity onset (at ca. CT 14 of the transient cycle) or 8 h after activity onset (at ca. CT 20 of the transient cycle) using an LP2 of equal strength. It was observed that the steady-state phase shifts evoked by positioning an LP2, 2 h after activity onset, were positively correlated with the phase shifts observed on day 1. The steady-state phase shifts observed, when the LP2 was positioned, 8 h after activity onset, were negatively correlated with the phase shifts observed on day 1. These results suggest that the transient cycles do not mirror the state of the pacemaker oscillator.     

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.     

延髓腹外侧Boetzinger复合体呼吸时相转换效应的研究

The effects of electrical stimulation of B?tzinger complex (Bot.C) on respiratory rhythm were investigated in 40 urethane anesthetized adult rabbits. The results were as follows. (1) A short train stimulation delivered in the early inspiratory phase produced a transient inhibition of phrenic discharge. The stimulus, when delivered in the mid or late inspiratory phase, could cause a premature termination of the inspiratory phase ("inspiratory off-switch") and a switching to the expiratory phase, which was accompanied with the reduced duration of the consecutive expiratory phase. There was a negative linear correlation between the threshold intensity of inspiratory off-switching and delivery time of stimulation. (2) A short train stimulation delivery in the expiratory phase elicited a transient phrenic discharge. The discharge in the late expiratory phase was followed by a premature onset inspiration. This effect was also dependent on the strength and delivery time of the stimulus. The results suggest that the Bot.C is involved in the central control of respiratory phase-switching.     

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.     

Effects of temperature and temperature-steps on circadian locomotor rhythmicity in the blow fly Calliphora vicina

The free-running period (in darkness) of the locomotor activity rhythm in adult blow flies (Calliphora vicina) was temperature-compensated between 15 and 25 degrees C, showing Q(10) values between 0.98 and 1.04. Single steps-up (20 to 25 degrees C) or steps-down (20 to 15 degrees C) in temperature caused stable phase shifts of the activity rhythm, giving rise to temperature-step phase response curves (PRCs) with both advances and delays. Phase advances, however, were dominant for steps-up, and phase delays for steps-down; the two PRCs were almost "mirror images" of each other. Following protocols introduced by Zimmerman et al. [(1968) Temperature compensation of the circadian oscillation in Drosophila pseudoobscura and its entrainment by temperature cycles, Journal of Insect Physiology, 14, 669-684] for the rhythm of pupal eclosion in Drosophila pseudoobscura, the steps-up and steps-down PRCs for C. vicina were used to compute a theoretical PRC for a 6 h low temperature pulse, and from this a theoretical steady-state phase relationship of the locomotor activity rhythm to a train of such pulses making up a temperature cycle (18 h at 20 degrees and 6 h at 15 degrees C).     

Methods of Measuring Phase Shifts: Why I Continue to Use an Aschoff Type II Procedure Despite the Skepticism of Referees

Figure 1 shows the test procedure used in many experiments from this laboratory on nonphotic clock resetting. The animal, a hamster, is in an LD cycle until the day when the stimulus is given. Very close to the time the stimulus is introduced the lights are turned off and remain off until the end of the test, usually just a few days later. This is a modification of Aschoff's (1) type II method for determining phase shifts and phase response curves (PRCs).     

Methods of Measuring Phase Shifts: Why I Continue to Use an Aschoff Type II Procedure Despite the Skepticism of Referees

Figure 1 shows the test procedure used in many experiments from this laboratory on nonphotic clock resetting. The animal, a hamster, is in an LD cycle until the day when the stimulus is given. Very close to the time the stimulus is introduced the lights are turned off and remain off until the end of the test, usually just a few days later. This is a modification of Aschoff's (1) type II method for determining phase shifts and phase response curves (PRCs).     

Modeling circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators: phase shifts and phase response curves

Circadian rhythm generation in the suprachiasmatic nucleus was modeled by locally coupled self-sustained oscillators. The model is composed of 10,000 oscillators, arranged in a square array. Coupling between oscillators and standard deviation of (randomly determined) intrinsic oscillator periods were varied. A stable overall rhythm emerged. The model behavior was investigated for phase shifts of a 24-h zeitgeber cycle. Prolongation of either the dark or the light phase resulted in a lengthening of the period, whereas shortening of the dark or the light phase shortened the period. The model's response to shifts in the light-dark cycle was dependent only on the extent of the shift and was insensitive to changes in parameters. Phase response curves (PRC) and amplitude response curves were determined for single and triple 5-h light pulses (1000 lux). Single pulses lead to type 1 PRCs with larger phase shifts for weak coupling. Triple pulses generally evoked type 1 PRCs with the exception of weak coupling, where a type 0 PRC was observed.     

Revised limit cycle oscillator model of human circadian pacemaker

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.     

Phase resetting of the respiratory cycle before and after unilateral pontine lesion in cat.

The pontine respiratory group (PRG) facilitates the mechanism for terminating the inspiratory phase but may influence other phases in the respiratory cycle as well. We determined the effects of PRG lesions on the response of the respiratory cycle to superior laryngeal nerve stimulation delivered in each phase of the cycle in decerebrate, vagotomized, paralyzed, and ventilated cats (n = 6). We measured the duration of inspiration (TI) and expiration (TE) for three breaths before and in the perturbed breath and TI for three breaths after the perturbation. The delay to next inspiration was plotted against the phase at which the stimulus was delivered. Before lesioning, premature inspiratory termination was followed by phase-dependent shortening of TE. After lesioning, premature inspiratory termination did not systematically change the following TE. Breath-by-breath variability (measured 50 breaths) increased and stimulus after-effects (prolonged TI in the subsequent cycle) were augmented following lesions. These data indicate that the PRG plays an important role in the control of TE after perturbation and in the stability of the respiratory central pattern generator.     

Die rhythmogenese der atmung beschrieben mit hilfe des Lotka-Volterra-modells: Experimente und simulation

The aim of the present study was to simulate respiratory responses to vagal stimulation using theLotka-Volterra model, a system of two simultaneous non-linear differential equations. The experiments were carried out on vagotomized, artificially ventilated rabbits. Low-threshold, fast-conducting vagal afferent fibres were stimulated with relatively high frequencies (100–200 cps) at various stages of the respiratory cycle. The phrenic activity was recorded in order to analyze the latency and duration of exspiratory reactions with regard to the time relation between stimulatory and respiratory phase. The onset of the stimulatory phase was progressively delayed with regard to the onset of the inspiratory or expiratory phase, stimulation ceasing at the onset of the ensuing respiratory cycle. Real-time simulation was carried out on a hybrid computer. The vagal stimulation was imitated by altering the values of one of the system parameters. The onset of parameter changes was progressively delayed with regard to the onset of the inspiratory or expiratory phase of the model, and the parameters were reset to the initial values as soon as the following respiratory phase began. Comparison of experimental and model data revealed satisfactory agreement between the time-dependent system properties of both respiratory centre and model. The results are discussed with regard to the central nervous processes underlying the genesis of respiratory rhythm. Further light is also thrown on the central processing of afferent vagal input subserving inspiratory inhibitory reactions.

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Ausgeführt mit Unterstützung durch den Schweizerischen Nationalfonds, Kredit Nr. 3.9050.72 und die Hartmann-Müller-Stiftung     

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.     

Analysis of entrainment of respiratory rhythm by somatic afferent stimulation in cats using phase response curves

To elucidate how peripheral somatic afferents synchronize the respiratory rhythm to the exercise rhythm, the phrenic nerve activity in the vagotomized, paralyzed, and artificially ventilated cats anesthetized with chloralose-urethane was recorded during electrical stimulation of the superficial radial nerve afferents. At first, a single pulse train was given at various times of the respiratory cycle to obtain a phase-response curve (PRC). The stimulation given at mid to late expiration produced a phase advance, but the stimulation during inspiration produced no measurable phase shifts in most animals (8/10). The maximum phase advance changed depending on the stimulus intensity. The stronger the stimulus intensity, the greater became the maximum phase advance. Repetitive somatic afferent stimulation produced 1:1 entrainment of the respiratory frequency to the repetitive stimulation. Theoretical predictions on the stable entrainment phase and on the entrainment frequency range from the obtained PRC were close to the experimental results. The present study demonstrated the presence of a neuronal circuit synchronizing the respiratory rhythm to the periodic somatic afferents and the manner of how such entrainment occurs.     

Circadian phototransduction: phase resetting and frequency of the circadian clock of Gonyaulax cells in red light

Constant red light (RR) influences the Gonyaulax clock in several ways: (1) Phase resetting by white or blue light pulses is stronger under background RR than in constant white light (WW); (2) frequency of the rhythm is less in RR than in WW; and (3) the amplitude of the spontaneous flashing rhythm is greater in RR than in WW. The phase response curve (PRC) to 4-hr white or blue light pulses is of high amplitude (Type 0) for cells in RR, but is of lower amplitude (Type 1) for cells in WW. In all cases, the PRC is highly asymmetrical: The magnitude of advance phase resetting is far higher than that of delay resetting. Consistent with this PRC, Gonyaulax cells in RR (free-running period greater than 24 hr) will entrain to T cycles of between 21 and 26.5 hr. The bioluminescence rhythms exhibit "masking" by blue light pulses while entrained to these T cycles. The fluence response of phase resetting to light-pulse intensity is not linear or logarithmic--rather, it is discontinuous. This feature is consistent with a limit cycle interpretation of Type 0 resetting of circadian clocks. Light pulses that cause large phase shifts also shorten the subsequent free-running period. The phase angle difference between the clock and the previous LD cycle is within 2 hr of the same phase between 16 degrees C and 25 degrees C, as determined from the light PRCs at various temperatures. Several drugs that inhibit mitochondria and/or electron transport will partially inhibit the phase shift by light.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

Existence and stability criteria for phase-locked modes in ring neural networks based on the spike time resetting curve method

We developed a systematic and consistent mathematical approach to predicting 1:1 phase-locked modes in ring neural networks of spiking neurons based on the open loop spike time resetting curve (STRC) and its almost equivalent counterpart—the phase resetting curve (PRC). The open loop STRCs/PRCs were obtained by injecting into an isolated model neuron a triangular shaped time-dependent stimulus current closely resembling an actual synaptic input. Among other advantages, the STRC eliminates the confusion regarding the undefined phase for stimuli driving the neuron outside of the unperturbed limit cycle. We derived both open loop PRC and STRC-based existence and stability criteria for 1:1 phase-locked modes developed in ring networks of spiking neurons. Our predictions were in good agreement with the closed loop numerical simulations. Intuitive graphical methods for predicting phase-locked modes were also developed both for half-centers and for larger ring networks.     

Respiratory resetting induced by spinal cord stimulation in the cat

Electrical stimulation (50-150 microA, 0.5-ms duration, 3-300 Hz) was performed within three different regions (lateral, ventrolateral, and ventral) of the C2-C3 spinal cord of decerebrate, vagotomized, paralyzed, and artificially ventilated cats. Spinal cord stimulation sites were located by inserting monopolar or bipolar stimulating electrodes either at the dorsolateral sulcus or at least 1 mm medial or lateral to the sulcus. With stimulation at each site, alterations in respiratory rhythm, orthodromic phrenic nerve responses, and antidromic activation of medullary respiratory-modulated neurons were examined. Phrenic nerve responses to cervical spinal cord stimulation consisted of an early excitation (2-4 ms) and/or a late excitation (4-8 ms). Stimulation of the lateral region evoked the greatest amplitude early response and stimulation of the ventrolateral region produced the greatest late excitation. All three stimulus sites elicited antidromic activation of some respiratory-modulated neurons in the dorsal (DRG) and ventral respiratory groups (VRG). The lateral region was the least effective resetting site, and it had the highest incidence of antidromic activation of both DRG and VRG neurons. The ventrolateral region of the cervical spinal cord was the most effective resetting site, but it had the lowest incidence of antidromic activation of DRG respiratory-modulated neurons. In addition, resetting responses were observed with spinal cord stimulation at similar sites in the thoracic and lumbar spinal cord regions thought to be devoid of inspiratory bulbospinal axons.(ABSTRACT TRUNCATED AT 250 WORDS)