Phase response curve

One of us examined the timely use of three factors (melatonin treatment, exposure to light, physical exercise) to hasten the resynchronization of the sleep-wake cycle in a group of elite sports competitors after a transmeridian flight across 12 time zones (Cardinali et al. 2002). Outdoor light exposure and physical exercise were used to cover symmetrically the phase delay and the phase advance portions of the phase-response curve. Melatonin taken at local bedtime helped to resynchronize the circadian oscillator to the new time. Individual actograms taken from sleep log data showed that all subjects became synchronized in their sleep to the local time in 24-48 h, well in advance of what would be expected in the absence of any treatment (Cardinali et al. 2002). More recently, a retrospective analysis of the data obtained from 134 normal volunteers flying the Buenos Aires - Sydney transpolar route in the past 9 years was published this further supports such a role for exogenous melatonin in resynchronization of sleep cycles (Cardinal et al. 2006). 

Van Gelder The Perl is not a normal oscillator. What we see in the cryptochromes is that Crj2 has an exaggerated phase response curve probably because the oscillator is not as robust. It may be the case that Perl is also a weak oscillator with an accordingly exaggerated phase response curve. 

Hardin You said the phase response curves (PRCs) are altered. Is that independent of which component you constitutively express ... 

Van Gelder It has to be something with a biphasic phase response curve, which may not be the case for some of these agents. 

Sharma VK, Chandrashekaran MK. Singaravel M, Subbaraj R. 1999. In the field mouse Mus booduga melatonin phase response curves (PRCs) have a different time course and wave form relative to light PRC. JPineal Res 26 153-157. 

Lewy AJ, Bauer VK, Ahmed S, Thomas KH, Cutler NL, Singer CM, Moffit MT, Sack RL. The human phase response curve (PRC) to melatonin is about 12 hours out of phase with the PRC to light. Chronobiol Int 1998 15 71-83. 

It should be noted that calculation of the amplitude response from the phase can only be done with an accuracy of some constant. Equations 1.301 and 1.302 lead us to the following conclusions. First of all, measurement of the phase response does not provide additional information on the geoelectric section when the amplitude response is already known. However, it may well be that the shape of the phase response curve more clearly reflects some diagnostic features of this section than does the amplitude response curve. 

A systematic determination of the phase delay (A< <0) or phase advance (A > 0) as a function of the phase of the oscillations yields the phase response curves of fig. 2.19. The two curves were established at different levels of the perturbation in product y. In both cases, a discontinuity occurs as a delay abruptly transforms into a phase advance. In the terminology of Winfree (1980), such phase response curves are of type 0. If the magnitude of the product perturbation were sufficiently small, a very weak phase shift would occur at all phases

large number of biological oscillations, including circadian rhythms (Winfree, 1980). 

Fig. 2.19. Phase response curve for the phosphofructokinase allosteric model, indicating the phase shift caused by ADP addition. The phase shift A(P corresponding to a delay (A

Fig. 5.13. Phase response curve showing the phase shift induced by pulses of cAMP applied in the course of oscillations. One period of the oscillations divides into a phase of weak or no response, a refractory phase corresponding to a delay, and an excitable phase corresponding to a phase advance of the oscillations. The bottom part of the figure shows a schematic representation of the time course of intracellular and extracellular (shaded area) cAMP (Gerisch etal, 1979).

If CICR release plays a prominent role in the mechanism of oscillations, then the latter should be particularly sensitive to perturbations in cytosolic Caf. The effect of pulses of cytosolic Ca has been determined by numerical experiments, the results of which are shown in fig. 9.15. In part a, an instantaneous, moderate increase in Z by some 0.2 p,M results in a delay of the next high-amplitude peak in cytosolic Ca. This delay occurs when the perturbation is applied shortly after the minimum of Caf oscillations. When the same Ca pulse is given a little later, as shown in part b, a phase advance is observed. The dependence of the phase shift on the phase at which the perturbation occurs is illustrated by the phase response curve shown in fig. 9.16. This curve, established at a fixed value of the perturbation equal to 0.18 xM, indi-... 

Fig. 9.16. Phase response curve predicted by the minimal model for signal-induced Cif oscillations based on Ca nduced Csf release. Shown is the phase shift of Ca oscillations induced by a pulse of 0.18 j.M applied at different phases of the oscillations < = 0 corresponds to the peak in cytosolic Ca (Z) that is represented in the lower panel. A phase advance (A( > 0) occurs when the Ca peak resulting from perturbation exceeds 1 p,M. A phase delay (A< < 0) occurs when the resulting peak is less than that veilue (see also fig. 9.15a and b). The phase shift is expressed as a fraction of the period T. Parameter values are those of fig. 9.15 for these parameter values, T = 2.07 s. The phase response curve remains qualitatively unchanged when the period is of the order of minutes (Dupont et al, 1991).

Fig. 11.1. Phase response curves obtained in chick pineal cell cultures for 6 h pulses of light and anisomycin (Aniso.), an inhibitor of protein synthesis (Takahashi etal, 1989).

Fig. 11.2. Circadian rhythm of bioluminescence in Gonyaulax polyedra (Taylor et al., 1989b). The curves in (a) show phase-shifts of the rhythm by pulses of anisomycin, an inhibitor of protein synthesis. The concentration of anisomycin used is indicated along the vertical axis, as well as the time at which the drug is administered. Experiments shown indicate phase-shifts produced by 1 h pulses of 0.1 pM (vials 2 and 20) and 0.2 pM (vials 3 and 21) anisomycin. Vertical lines indicate positions of control peaks (vials 7 and 25). Drug pulses given between hours 11 and 12 (vials 2 and 3) resulted in phase delays as compared to control (vial 7) pulses given from hours 14 to 15 resulted in phase advances compared to control (vial 25). (b) A phase response curve for 1 h pulses of 0.3 pM anisomycin. Conditions are as in (a). Time on the abscissa denotes beginning of the pulses, in hours since cells were transferred to constant conditions. A positive phase shift denotes a phase advance.

The model for circadian oscillations in PER protein and per mRNA is closely related to the model proposed some 30 years ago by Goodwin (1963,1965), who discussed the conditions in which a protein repressing the transcription of its gene can produce sustained oscillations in the levels of that protein and its mRNA. A model of the Goodwin type was used explicitly for circadian rhythms, to determine phase response curves with respect to transient perturbations (Drescher et al, 1982). 

Drescher, K., G. Cornelius L. Reusing. 1982. Phase response curves obtained by perturbing different variables of a 24 hr model oscillator based on translational control. J. Theor. Biol. 94 345-53. 

Turek, F.W. 1987. Pharmacological probes of the mammalian circadian clock Use of the phase response curve approach. Trends Pharmacol. Sci. 

Type 0 phase response curve, 59,60,466 Type 1 phase response curve, 59,466 Type 1 and type 2 Ca waves, 396,402,... 

Vance and Ross [63] show that there is a close relation between the variation of the relative phase shift across the entrainment band and variation of the phase response curve provided that limit cycle oscillations are close to a supercritical Hopf bifurcation. 

Ruoff, R Forsterling, H.-D. Gyorgyi, L. Noyes, R. M. Bromous acid perturbations in the Belousov-Zhabotinsky reaction—experiments and model calculations of phase response curves. J. Phys. Chem. 1991, 95, 9314-9320. 

ABSTRACT. The principle features of the frequency-response i paratus developed at Imperial College is described. The apparatus has been used in both its a) full and b) single-step frequency modes to determine the diffiisivities of various hydrocarbons in silicalite-1. Die effect of temperature and loading of sorbate in the silicalite-1 has been ascertained. The effect of the introduction of A1 atoms into the framework of silicalite-1 on the diffusivity of benzene has been detmnined. The diffusion of benzene in NaX has been studied and diffusion coefficients obtained which agree with NMR pulsed field gradient measurements, n-Butane and 2-butyne hydrocarbons were found to generate out-of-phase response curves by the full FR method which could only be fitted by introducing two diffusion coefficients into the solution of the appropriate diffusion equation. 

Figures 12 and 13 show, for both n-butane and 2-butyne, that the maximum in the phase lag vs frequency curve shifts to higher frequency (i.e. to larger diffasion coefficients) when the temperature and concentration of sorbate increases. The out-of-phase response curves derived from...

Daan, S., and C. S. Pittendrigh, A Functional Analysis of Circadian Pacemakers in Nocturnal Rodents. II. The Variability of Phase Response Curves, J. Comp. Physiol., 106,253 (1976). 

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