Because these measurements are done on growing eyes, we devised
a method to separate the “cyclic component” from the “steady
state” growth component to assess the parameters of the rhythms:
phase, amplitude, and period.
2 In brief, we assume that
the growth curve (as in
Fig. 1A ) is composed of a diurnal rhythm superimposed on a steady rate of
growth. To separate these, a regression line is fit to the data for
each eye; the slope of this line yields the steady state rate of growth
(these data are used to compare rates of growth between groups). The
regression is then subtracted from the raw data; these residuals
represent the pure cyclic component for each eye. From these, one can
obtain phase, amplitude, and period by fitting a sine wave to these
data. For statistical comparisons of phase, a sine wave with a period
of 24 hours is fit to the data for each eye for the 4th day in
darkness. This cycle was chosen because the phase of the rhythm is less
variable over this last 24-hour period and because it could possibly be
a more accurate reflection of the true circadian (free-running) rhythm.
For statistical tests of phase, only those data meeting our inclusion
criterion, that the mean SD of the residuals of the sine wave fit to
the data were less than the SD of the raw data, and less than 60% of
the amplitude of the sine wave fit to the data (a similar method was
used in Ref.
2 ). These data and the number of eyes used
are shown in
Table 1 (“From individual eyes”). All descriptions of phase in
Results are obtained from these data. For graphical depictions, we show
the sine waves fit to the mean of the residuals for all eyes; the
period used for these fits was either 24 hours or was left
unconstrained, as indicated. The phases obtained from these “mean”
sine fits are shown in
Table 1 for comparison (“From averaged
data”). Amplitude is derived from these fits to the mean of the data.
t-Tests were used for all statistical comparisons.