PRC Bisection Tests

This communication presents a new method for evaluating phase response curves (PRCs). A PRC describes the phase shifts produced in an oscillator by stimuli applied at different initial phase‐states of that oscillator. In the PRC bisection tests, we repeatedly cut in half the circular distribution of the initial phase‐states of the oscillator when stimuli are given. Empirically, we locate that optimal diameter which best bisects the circular distribution of phase responses into arcs of relative phase advance and phase delay. We compute a D score reflecting the success of the best bisection. The null hypothesis of a random distribution of phase responses by initial phase is tested with a Monte Carlo procedure, which computes D_r scores from random combinations of phase shifts with initial phases, thus determining the probability, given the null hypothesis, that the observed D score was from a random distribution. The bisection procedure can be extended to examine whether stronger phase shifts are produced in one phase response curve than in contrasting curves. Also, the bisection procedure yields an estimate of the inflection point of the phase response curve. A method is given to estimate the power of the PRC bisection test.     

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.     

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.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Effect of light intensity on the phase and period response curves in the nocturnal field mouse Mus booduga

The effect of light intensity on the phase response curve (PRC) and the period response curve (τRC) of the nocturnal field mouse Mus booduga was studied. PRCs and τRCs were constructed by exposing animals free-running in constant darkness (DD), to fluorescent light pulses (LPs) of 100 lux and 1000 lux intensities for 15min duration. The waveform of the PRCs and τRCs evoked by high light intensity (1000 lux) stimuli was significantly different compared to those constructed using low light intensity (100 lux). Moreover, a weak but significant correlation was observed between phase shifts and period changes when light stimuli of 1000 lux intensity were used; however, the phase shifts and period changes in the 100 lux PRC and τRC were not correlated. This suggests that the intensity of light stimuli affects both phase and period responses in the locomotor activity rhythm of the nocturnal field mouse M. booduga. These results indicate that complex mechanisms are involved in entrainment of circadian clocks, even in nocturnal rodents, in which PRC, τRC, and dose responses play a significant role.     

Effect of Light Intensity on the Phase and Period Response Curves in the Nocturnal Field Mouse Mus booduga

The effect of light intensity on the phase response curve (PRC) and the period response curve (τRC) of the nocturnal field mouse Mus booduga was studied. PRCs and τRCs were constructed by exposing animals free-running in constant darkness (DD), to fluorescent light pulses (LPs) of 100 lux and 1000 lux intensities for 15min duration. The waveform of the PRCs and τRCs evoked by high light intensity (1000 lux) stimuli was significantly different compared to those constructed using low light intensity (100 lux). Moreover, a weak but significant correlation was observed between phase shifts and period changes when light stimuli of 1000 lux intensity were used; however, the phase shifts and period changes in the 100 lux PRC and τRC were not correlated. This suggests that the intensity of light stimuli affects both phase and period responses in the locomotor activity rhythm of the nocturnal field mouse M. booduga. These results indicate that complex mechanisms are involved in entrainment of circadian clocks, even in nocturnal rodents, in which PRC, τRC, and dose responses play a significant role.     

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.     

Circadian phase shifting induced by clonidine injections in Syrian hamsters

Abstract

The mammalian circadian pacemaker can be phase shifted by photic, pharmacological, and behaviorally‐derived stimuli. The phase‐response curves (PRCs) characterizing these diverse stimuli may comprise two distinct families; a photic PRC typified by the response to brief light pulses, and a non‐photic PRC, typified by the response to dark pulses and to behavioral activation. The present study examined the phase shifting effects of acute systemic treatment with the alpha2‐adrenoceptor agonist, clonidine, in Syrian hamsters. Clonidine injections (0.25 mg/kg, ip) delivered during subjective night mimicked the phase shifting effects of light pulses in animals housed in both constant darkness (DD) and constant red light (RR), but similar effects were not seen in saline‐treated controls. Both clonidine and saline injections resulted in phase advances during subjective day, but only in RR‐housed animals. Clonidine‐induced phase shifting was dose‐dependent, but rather high doses were required to induce phase shifts. Pretreatment with the selective noradrenergic neurotoxin, DSP‐4, blocked clonidine‐induced phase shifting. These results suggest that clonidine acts at presynaptic alpha2‐adrenergic autoreceptors to disinhibit spontaneous and/or evoked activity in the photic entrainment pathway.     

Light flashes of different durations (0.063-3.33 msec) phase shift the circadian flight activity of a bat

The phase-response curve (PRC) for the circadian rhythm in the flight activity of a cave-dwelling bat, Hipposideros speoris, constructed with 0.063-msec light flashes, reported here is the first of its kind for any circadian system and is unlike any other phase-response curves constructed for other nocturnal animals. The phase responding with maximal advances (90 degrees) and the phase responding with maximal delays (0 degree) of this PRC were exposed to light flashes of systematically varying durations from 0.083 to 3.33-msec. For 0 degree phase, the flashes of 0.063-3.33 msec effected delay phase shifts of comparable magnitude. For 90 degrees phase, the flashes of 0.063-1.0 msec effected advance phase shifts, whereas 3.33-msec flashes effected unmistakable delay phase shifts with advancing transients. Phase shifts evoked with such light flashes are further compared with phase shifts evoked with pulses of longer durations (15 min to 2.8 hr) for H. speoris.     

Period responses to Zeitgeber signals stabilize circadian clocks during entrainment

Circadian clocks with characteristic period (τ) can be entrained to light/dark (LD) cycles by means of (i) phase shifts which are due to D/L “dawn” and/or L/D “dusk” transitions, (ii) period changes associated with long-term light exposure, or (iii) by combinations of the above possibilities. Based on stability analysis of a model circadian clock it was predicted that nocturnal burrowing mammals would benefit less from period responses than their diurnal counterparts. The model further predicted that maximal stability of circadian clock is reached when the clock slightly changes both its phase and period in response to light stimuli. Analyses of empirical phase response curve (PRC) and period response curve (τRC) of some diurnal and nocturnal mammals revealed that PRCs of both diurnal and nocturnal mammals have similar waveform while τRCs of nocturnal mammals are of smaller amplitude than those of diurnal mammals. The shape of the τRC also changes with age and with increasing strength of light stimuli. During erratic fluctuations in light intensity under different weather conditions, the stability of phase of entrainment of circadian clocks appears to be achieved by an interplay between phase and period responses and the strength of light stimuli.     

Melatonin enhances the sensitivity of circadian pacemakers to light in the nocturnal field mouse Mus booduga

The effect of exogenous melatonin (1 mg/kg) on light pulse (LP) induced phase shifts of the circadian locomotor activity rhythm was studied in the nocturnal field mouse Mus booduga. Three phase response curves (PRCs: LP, control, and experimental) were constructed to study the effect of co-administration of light and melatonin at various circadian times (CTs). The LP PRC was constructed by exposing animals free-running in constant darkness (DD) to LPs of 100-lux intensity and 15-min duration, at various CTs. The control and experimental PRCs were constructed by using a single injection of either 50% DMSO or melatonin (1 mg/kg dissolved in 50% DMSO), respectively, administered 5 min before LPs, to animals free-running in DD. A single dose of melatonin significantly modified the waveform of the LP PRC. The experimental PRC had significantly larger areas under advance and delay regions of the PRC compared to the control PRC. This was also confirmed when the phase shifts obtained at various CTs were compared between the three PRCs. The phase delays at three phases (CT12, CT14, and CT16) of the experimental PRCs were significantly greater than those of the control and the LP PRCs. Based on these results we conclude that phase shifting effects of melatonin and light add up to produce larger responses.     

Phase response curves for social entrainment

Summary Phase shifts in free-running activity rhythms of male golden hamsters,Mesocricetus auratus, often occur when they establish a new territory and home after a cage change. Similar shifts also often occur after pairs of animals interact with each other for half an hour. When these events take place during the middle of the hamsters' subjective day, they produce phase advances: when late in the subjective night, they produce phase delays. Repeated social interactions at the same time of day can entrain activity rhythms in a way consistent with the shape of the phase response curves. Not all individuals become entrained, as is predictable from the modest amplitude of the phase response curve. The effects of social interactions and of other disturbances may be mediated through an oscillator phased by general arousal. The present findings have implications for the interpretation of drug-induced changes in biological rhythms.     

Circadian Phase Shifting Associated with Routine Cage Maintenance: A Retrospective Analysis

Stimuli that evoke behavioral activation can phase-shift free-running circadian activity rhythms in Syrian hamsters. Activation-induced phase shifting is characterized by a phase-response curve (PRC) that is dissimilar to the PRC for photic phase shifting, and recent studies indicate that complex interactions may occur between photic and non-photic phase shifting. Since animals in the laboratory may be exposed to both photic and behaviorally activating stimulation during routine cage maintenance procedures, we performed a retrospective analysis of possible phase shifts associated with cage cleaning in individually housed hamsters maintained in either constant darkness (DD) or dim red light (RR) during the course of an ongoing study of drug-induced phase shifting. All cage cleanings were conducted under RR and were separated from drug treatments by at least one week. The results indicated that both photic and non-photic phase shifts could be induced by routine cage maintenance procedures, depending on the circadian timing of the procedure, on lighting conditions, and on the degree of evoked activity.     

Circadian Phase Shifting Associated with Routine Cage Maintenance: A Retrospective Analysis

Stimuli that evoke behavioral activation can phase-shift free-running circadian activity rhythms in Syrian hamsters. Activation-induced phase shifting is characterized by a phase-response curve (PRC) that is dissimilar to the PRC for photic phase shifting, and recent studies indicate that complex interactions may occur between photic and non-photic phase shifting. Since animals in the laboratory may be exposed to both photic and behaviorally activating stimulation during routine cage maintenance procedures, we performed a retrospective analysis of possible phase shifts associated with cage cleaning in individually housed hamsters maintained in either constant darkness (DD) or dim red light (RR) during the course of an ongoing study of drug-induced phase shifting. All cage cleanings were conducted under RR and were separated from drug treatments by at least one week. The results indicated that both photic and non-photic phase shifts could be induced by routine cage maintenance procedures, depending on the circadian timing of the procedure, on lighting conditions, and on the degree of evoked activity.     

Phase and period responses to short light pulses in a wild diurnal rodent,Funambulus pennanti

Photic phase response curves (PRCs) have been extensively studied in many laboratory-bred diurnal and nocturnal rodents. However, comparatively fewer studies have addressed the effects of photic cues on wild diurnal mammals. Hence, we studied the effects of short durations of light pulses on the circadian systems of the diurnal Indian Palm squirrel, Funambulus pennanti. Adult males entrained to a light–dark cycle (12?h–12?h) were transferred to constant darkness (DD). Free-running animals were exposed to brief light pulses (250 lux) of 15?min, 3 circadian hours (CT) apart (CT 0, 3, 6, 9, 12, 15, 18 and 21). Phase shifts evoked at different phases were plotted against CT and a PRC was constructed. F. pennanti exhibited phase-dependent phase shifts at all the CTs studied, and the PRC obtained was of type 1 at the intensity of light used. Phase advances were evoked during the early subjective day and late subjective night, while phase delays occurred during the late subjective day and early subjective night, with maximum phase delay at CT 15 (?2.04?±?0.23?h), and maximum phase advance at CT 21 (1.88?±?0.31?h). No dead zone was seen at this resolution. The free-running period of the rhythm was concurrently lengthened (deceleration) during the late subjective day and early subjective night, while period shortening (acceleration) occurred during the late subjective night. The maximum deceleration was noticed at CT 15 (?0.40?±?0.09?h) and the maximum acceleration at CT 21 (0.39?±?0.07?h). A significant positive correlation exists between the phase shifts and the period changes (r?=?0.684, p?=?0.001). The shapes of both the PRC and period response curve (τRC) qualitatively resemble each other. This suggests that the palm squirrel’s circadian system is entrained both by phase and period responses to light. Thus, F. pennanti exhibits robust clock-resetting in response to light pulses.     

Serotonin phase-shifts the circadian rhythm of locomotor activity in the cockroach

Serotonin, a putative neurotransmitter in insects, was found to cause consistent phase shifts of the circadian rhythm of locomotor activity of the cockroach Leucophaea maderae when administered during the early subjective night as a series of 4-microliters pulses (one every 15 min) for either 3 or 6 hr. Six-hour treatments with dopamine also caused significant phase shifts during the early subjective night, but 3-hr treatments with dopamine had no phase-shifting effect. Other substances tested in early subjective night (norepinephrine, octopamine, gamma-aminobutyric acid, glutamate, carbachol, histamine, tryptophan, tryptamine, N-acetyl serotonin, or 5-hydroxyindole-3-acetic acid) did not consistently cause phase shifts. The phase-shifting effect of serotonin was found to be phase-dependent. The phase response curve (PRC) for serotonin treatments was different from the PRC for light. Like light, serotonin caused phase delays in the late subjective day and early subjective night, but serotonin did not phase-shift rhythms when tested at phases where light causes phase advances.     

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.     

Critical pulses of anisomycin drive the circadian oscillator inGonyaulax towards its singularity

Summary Dose and phase response curves for phase shifting the circadian oscillator in the dinoflagellateGonyaulax polyedra were measured with pulses of the antibiotic anisomycin (an inhibitor of protein synthesis on 80 S ribosomes), using the bioluminescent glow rhythm as the assay. The three dimensional surface of final phase, initial phase, and concentration was found to be a right handed helix, with the axis at a critical initial phase near circadian time 12 h, and critical concentration near 0.2 micromolar anisomycin (for 1 h pulses). The normally rhythmic glow of populations ofGonyaulax was significantly disrupted by pulses with these critical parameters, and in many instances appeared nearly arrhythmic.With increasing drug concentration, phase response curves appear to move bodily to earlier phases, and no saturation is evident in the phase shifting effect. These results are interpreted as indicating that anisomycin at sufficiently high doses causes an immediate strong (type 0) phase shift, then holds the clock stationary for a time interval that increases with concentration.the possibility that the 80 S ribosomal complex may be centrally involved in the fundamental circadian oscillation is put forward.Abbreviations DRC dose response curve - PRC phase response curve     

Melatonin-induced phase and dose responses in a diurnal mammal,Funambulus pennantii

ABSTRACT

Melatonin, an essential pineal hormone, acts as a marker of the circadian clock that regulates biological rhythms in animals. The effects of exogenous melatonin on the circadian system of nocturnal rodents have been extensively studied; however, there is a paucity of studies on the phase-resetting characteristics of melatonin in diurnal rodents. We studied the phase shifting effects of exogenous melatonin as a single melatonin injection (1 mg/kg) at various phases of the circadian cycle on the circadian locomotor activity rhythm in the palm squirrel, Funambulus pennantii. A phase response curve (PRC) was constructed. Adult male squirrels (N = 10) were entrained to a 12:12 h light-dark cycle (LD) in a climate-controlled chronocubicle with food and water provided ad libitum. After stable entrainment, squirrels were transferred to constant dark condition (DD) for free-running. Following stable free run, animals were administered a single dose of melatonin (1 mg/kg in 2% ethanol-phosphate buffered saline (PBS) solution) or vehicle (2% ethanol-PBS solution) at circadian times (CTs) 3 h apart to evoke phase shifts. The phase shifts elicited at various CTs were plotted to generate the PRC. A dose response curve was generated using four doses (0.5, 1, 2 and 4 mg/kg) administered at the CT of maximum phase advance. Melatonin evoked maximum phase advances at CT0 (1.23 ± 0.28 h) and maximum phase delays at CT15 (0.31 ± 0.09 h). In the dose response experiment, maximal phase shifts were evoked with 1 mg/kg. In contrast, no significant shifts were observed in control groups. Our study demonstrates that the precise timing and appropriate dose of melatonin administration is essential to maximize the amelioration of circadian rhythm–related disorders in a diurnal model.     

The effects of the general anaesthetic isoflurane on the honey bee (Apis mellifera) circadian clock

General anaesthesia administered during the day has previously been shown to phase shift the honey bee clock. We describe a phase response curve for honey bees (n=105) to six hour isoflurane anaesthesia. The honey bee isoflurane PRC is “weak” with a delay portion (maximum shift of –1.88 hours, circadian time 0 – 3) but no advance zone. The isoflurane-induced shifts observed here are in direct opposition to those of light. Furthermore, concurrent administration of light and isoflurane abolishes the shifts that occur with isoflurane alone. Light may thus provide a means of reducing isoflurane–induced phase shifts.