University of Groningen
External Time–Internal Time
Daan, Serge; Merrow, Martha; Roenneberg, Till
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Journal of Biological Rhythms
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2002
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Daan, S., Merrow, M., & Roenneberg, T. (2002). External Time–Internal Time. Journal of Biological
Rhythms, 17(2), 107-109.
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JOURNAL OF BIOLOGICAL RHYTHMS / April 2002
EDITORIAL
EDITORIAL
External Time–Internal Time
Every school kid learns the rules: Time runs from
the middle of the dark to the middle of the next dark in
24 equal steps. We inherited the system from the
priests in antique Egypt—12 hours for the night, 10 for
the day, and 2 for the twilights—until Islamic astronomers in the Middle Ages made the steps equal in duration. The Washington Conference of 1883 fixed the
time zones and thereby the world agreement on time
of day. Later economic considerations led to the adoption of daylight savings time. It is a reasonable working system. Time 0 is not exactly the middle of the
night, but it is thereabouts. Ten steps rather than two
dozen might have been easier in our decimal world,
but one gets used to the 24.
The only corner of society in which the simple rules
for counting the progress of the earth’s rotation are not
obeyed is that of the professional students of time, the
guild of chronobiologists. They invented their own
system. They measure the progress of time in hours of
zeitgeber time (ZT) or in circadian hours (CT). It is
hard to clarify the system to science journalists; it is
next to impossible to explain it to our fellow inhabitants of the world. Worse, it is raising recurrent confusion at our own meetings. But we stubbornly persist.
We write this while sitting on the sprawling lawns
of Salve Regina University, Newport, Rhode Island
(71°20’ W, 41°30’ N) at 2:00 PM EDT. It is 9 August
2001, the last day of the fascinating Gordon Conference on Chronobiology. Sunrise this morning was at
5:49 AM EDT. Hence, present ZT is 8:11, or, if one
wishes to count from civil twilight, ZT 8:42. We woke
up around 7:00 EDT this morning, so our internal
clocks now indicate something like CT 7. In the park
around us lives a family of wood mice and some squirrels. The squirrels’ present circadian time is 8:11 hours
after sunrise, hence CT 8.18. The mice will become
active at sunset (7:53 PM EDT), which is by convention
at their CT 12. Hence, their current circadian time is CT
6:07. For Northern and Southern points on the same
longitude, both CT and ZT systematically vary.
These examples show the confusion inherent in our
system of the notation of time. This system is not only
difficult to communicate—it is inadequate and obsolete. Both CT and ZT go back to Pittendrigh, whose
JOURNAL OF BIOLOGICAL RHYTHMS, Vol. 17 No. 2, April 2002
© 2002 Sage Publications
contributions to the field we respect beyond
anybody’s. Pittendrigh and Minis (1964) originally
introduced the two scales as SCT (subjective circadian
time) and AZT (arbitrary zeitgeber time), respectively.
Their definitions were “SCT 00 is that point in the
cycle which occurs when dawn would have fallen on
the first day of a DD freerun following a light-dark
cycle of 12:12. SCT 24 occurs one full cycle later” and
“AZT 00 is the onset of the light in the main (or only)
photoperiod in that cycle.” Pittendrigh was well
aware that the entrained circadian oscillation changes
its phase relationship with photoperiod of the
light-dark (LD) cycle, and that the definition of circadian time is therefore only unambiguous when the situation in LD 12:12 is known. He also realized that in
different photoperiods, ZT always refers to dawn but
the ZT at which dusk occurs varies. The ZT/CT formalism may have been useful for the eclosion of
Drosophila pseudoobscura rhythm, which peaks at
dawn, but for other rhythms it is often cumbersome,
confusing, and unfit for photoperiods other than
12:12.
To remedy the situation, we hereby introduce alternative time scales, replacing CT and ZT. These scales
are applicable under all photoperiods and, hence, for
all latitudes for both diurnal and nocturnal organisms,
and they easily fit in with the established 24-h clock.
We designate them as external time (ExT) and internal
time (InT). ExT is the number of hours × 24/T elapsed
since the middle of the dark period, where T is the
duration of the LD cycle in hours. In natural conditions, T equals 24 hours, and ExT always corresponds
with sidereal time. InT is the number of hours × 24/τ
elapsed since the middle of the subjective night, that
is, to the midpoint of the dark portion of the prior LD
cycle. InT equals [CT – 18]mod 24. It might have been biologically more relevant to define InT 0 as the breakpoint of the phase response curve for brief light pulses.
The breakpoint of course empirically converges on CT
18 or on InT 0. This definition would have the drawback of being dependent on prior measurement of a
phase response curve (PRC) and, hence, less generally
applicable. Figure 1 depicts how the new definitions
work out for several sets of fruit fly and hamster data.
107-109
107
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JOURNAL OF BIOLOGICAL RHYTHMS / April 2002
Figure 1. Comparison of circadian and zeitgeber time with internal and external time. (Upper four panels) Phase response curve of the
pupal eclosion rhythm of Drosophila pseudoobscura plotted as a function of subjective circadian time (A) and of internal time (B). Peak of
the pupal eclosion rhythm of D. pseudoobscura plotted as a function of arbitrary zeitgeber time (C) and of external time (D). Gray shading
indicates the dark phase (C, D, G, and H). (Lower four panels) Phase response curve of the hamster activity rhythm plotted as circadian time
(E) and internal time (F). Onset of hamster activity in photoperiods plotted with lights on as the zeitgeber time 0 (G) versus midnight as
external time 0 (H). Data for (A) through (D) from Pittendrigh and Minis (1964); for (E) and (F) from Daan and Pittendrigh (1976); and for (G)
and (H) from Elliott (1976).
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EDITORIAL
The new formalism is in two ways more intuitive than
the old. First, it corresponds to local time. Second, the
CT fixation to dawn does not correspond to our subjective experience. When moving from winter to summer, we experience both dawn as appearing earlier
and dusk as appearing later. We also anticipate additional benefits: Experimental conditions that mimic a
natural dawn and dusk, rather than artificial square
wave light cycles, are overdue. In these protocols, pegging the data to a discrete lights-on/lights-off signal
will be problematic.
We are aware that at 2 PM on the 9th of August,
2001, in Newport different organisms would still have
slightly different InTs. These discrepancies would be
attributable to differences in their clocks or their
behavior rather than to the definition of time, and thus
would serve a comparative function. We encourage
chronobiologists to use InT and ExT and abandon the
concepts of CT and ZT. Scientists of course loathe to
discontinue deeply rooted habits. For the internal as
109
well as the external transparency of our field, it is
worth the effort.
1
Serge Daan
Zoological Laboratory, University of Groningen
Martha Merrow
Till Roenneberg
Institut für Medizinische Psychologie, Universität München
REFERENCES
Daan S and Pittendrigh CS (1976) A functional analysis of
circadian pacemakers in nocturnal rodents: II. The variability of phase response curves. J Comp Physiol A
106:253-266.
Elliott JA (1976) Circadian rhythms and photoperiodic time
measurement in mammals. Fed Proc 35:2339-2346.
Pittendrigh CS and Minis DH (1964) The entrainment of circadian oscillations by light and their role as photoperiodic
clocks. Am Nat 48:261-294.
1. To whom all correspondence should be addressed:
Zoological Laboratory, University of Groningen, P.O. Box
14, 9750 AA Haren, the Netherlands; e-mail: daans@biol.
rug.nl.
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