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A coupled pacemaker-slave model for the insect photoperiodic clock: interpretation of ovarian diapause data in Drosophila melanogaster

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Abstract

A coupled circadian oscillator model for the insect photoperiodic clock is described which consists of a hierarchically arranged pacemaker and slave. The pacemaker is self-sustained, temperature compensated, and entrainable by the light cycle; the slave is a damping oscillation receiving entrainment from two sources, from the pacemaker via a coupling factor, and also directly from the light. The damping slave oscillation is seen as the “photoperiodic oscillator”, equivalent to that proposed earlier by Lewis and Saunders (1987). The present simulations describe the effect of the strength of the coupling factor between hypothetical short- and long-period pacemaker oscillations (modelled on the “clock” mutants per sand per L2in Drosophila melanogaster) and a slave oscillation with a period of about 24 hours. The output is presented in terms of photoperiodic response curves and Nanda-Hamner, or resonance, plots. With a high coupling strength, the pacemakers strongly entrain the slave, but with a low coupling strength the slave's properties are more evident. The model is presented as a possible explanation for recent ovarian diapause data in D. melanogaster “clock” mutants (Saunders 1990), but also as a more general model for the role of the insect circadian system in seasonal time measurement.

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Abbreviations

T :

The period of the experimental light-dark cycle in hours

τ:

The free-running (unentrained) period of the circadian oscillation, in hours

CNL:

The critical night length, the amount of darkness in a 24 hour period which induces 50% of a population to enter diapause

CDL:

The critical day length, the reciprocal of CNL, i.e. if CNL = 10 h then CDL = (24 − 10) = 14 h

PPRC:

Photoperiodic response curve

PPTM:

Photoperiodic time measurement, the measurement of either day length or night length, the amount of light (or dark) being used as a signal which allows individuals to “tell” what time of year it is and to develop in a seasonally appropriate way

IPI:

Inter-peak interval, the length of time between peaks in a resonance plot, corresponding to the endogeneous period of the photoperiodic rhythm

φ i :

The photoinducible phase, a component of the external coincidence model of the photoperiodic clock. When illuminated during entrainment φ iinduces development in one way (non-diapause) whereas a different developmental path is taken (diapause) if this phase point is not illuminated Pittendrigh (1966)

P s :

The model photoperiodic system containing a short period central oscillator, or pacemaker

P L :

The model photoperiodic system containing a long period central oscillator, or pacemaker

c pace :

Hypothetical oscillating chemical of the pacemaker in the coupled model

c slave :

Ditto for the slave

INDSUM:

Induction sum, the accumulated value of the diapause inducing titre produced when φ iis not illuminated (Lewis and Saunders 1987)

CF:

The coupling strength between the pacemaker and the slave

SR:

Synthesis rate of oscillating chemical c

UB:

Maximum rate of synthesis of c, the Upper Bound

TD:

The time delay incorporated into the negative feedback control of the level of c

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  1. Institute of Cell, Animal and Population Biology, Division of Biology, University of Edinburgh, West Mains Road, EH9 3JT, Edinburgh, Scotland, UK

    S. W. Gillanders & D. S. Saunders

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  1. S. W. Gillanders
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  2. D. S. Saunders
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Gillanders, S.W., Saunders, D.S. A coupled pacemaker-slave model for the insect photoperiodic clock: interpretation of ovarian diapause data in Drosophila melanogaster . Biol. Cybern. 67, 451–459 (1992). https://doi.org/10.1007/BF00200989

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