The yeast strains were maintained on YEPD agar plates and stored at 4˚C. Cells were grown at room temperature with shaking in rich media (YEPD) for 1 - 2 days to attain ca 2 × 10⁸ cells/ml. ENOX proteins of yeast are exposed at the external surface of the yeast cells such that activities may be measured with unbroken cells. Additionally, the yeast cells were heated for 1 h at 70˚C to inactivate heat-sensitive enzymes prior to analysis. This was to prevent yeast contamination in the open laboratory. ENOX proteins resist heating at 70˚C for one h. Results were similar with unheated yeast cells.

Heat-inactivated yeast cells (ca. 10⁷ cells in 50 µl) were combined with 2.5 ml 50 mM Tris-Mes buffer (pH 7.0), 2 mM KCN and 150 µM NADH. To refold and renature the ENOX proteins of the heat-inactivated yeast, reduced glutathione (GSH) was added to a final concentration of 100 µM, and incubated for 10 min to reduce disulfides to allow for refolding. Next H₂O₂ was added to a final concentration of 0.03% followed by incubation for 10 min to reform disulfides to stabilize the protein in a correctly folded conformation.

NADH oxidation was measured in a Hitachi Model U3210 spectrophotometer at 340 nm, continuously for one min at 1.5 min intervals for two h using an extinction coefficient of 6.21 mM⁻¹∙cm⁻¹. Inhibitors were added at 60 min and data were collected for a further 60 min. A second machine of the same model with the vehicle alone added at 60 min served as the control.

Reduced coenzyme Q₁₀ was prepared fresh by addition of an equal volume of 0.25% NaBH₄ under nitrogen to a 7.5 mM stock solution of coenzyme Q₁₀ in ethanol. After several min of incubation, 0.l volume of 0.1 N HC1 was added to degrade the excess NaBH₄. The reaction mixture for measuring the oxidation of the reduced coenzyme Q₁₀ (Q₁₀H₂) contained heat-inactivated yeast, ca. 10⁷ cells in 2.5 ml of 50 mM Tris-Mes buffer, pH 7.0 and 0.08% Triton X-100 to maintain the Q₁₀H₂ in suspension. The reaction was started with the addition of 40 µl of 5 mM Q₁₀H₂. The disappearance of reduced CoQ was measured at both 290 and 410 nm using an extinction coefficient of 0.805 mM⁻¹∙cm⁻¹.

Heat-inactivated yeast (ca. 10⁷ cells in 50 µl) were added to 2.5 ml of 50 mM Tris-Mes, pH 7.0. The reaction was pre-incubated with 0.5 µmol of 2.2’-dithiodipyridine (DTDP) in 5 µl DMSO to oxidize residual thiols. After 10 min of incubation, a further 3.5 µmol of DTDP were added in 35 µl of DMSO to start the reaction. The increase in absorbance due to the cleavage of DTDP was monitored at 340 nm using a millimolar extinction coefficient of 6.21.

Yeast were grown in 200 ml minimal SD minus uracil or SR minus uracil media (Open Biosystems, Huntsville, AL) on a shaker at 200 rpm at room temperature for 2 - 3 days at 25˚C. Samples of 50 µl were collected every 2 h and snap frozen at −80˚C. Time windows were used to collect the samples, with the flow between collections returned to the flask. Although this was a batch culture, the small sample sizes did not reduce the total volume of the culture significantly, and each sample had approximately the same total protein content.

To prepare the samples for the assay, the yeast were thawed and 50 µl of Y-PER (Yeast Protein Extraction Reagent, Pierce) were added and the solution was vortexed for 20 min to lyse the yeast and release the cell contents. Glyceraldehyde-3-phosphate dehydrogenase activity was assayed in a reaction solution containing 100 µl lysed yeast, 0.1 M Tris-HC1, 0.5 mM EGTA, pH 8.0, 1 mM Na₂HAsO₄, 2 mM NAD⁺ and 3 mM glyceroldehyde-3-phosphate. NAD⁺ reduction was determined from the increases in absorbance at 340 nm at 37˚C measured over 5 min using a millimolar extinction coefficient of 6.21.

Results were analyzed using fast Fourier transform and decomposition fits [16]. To determine the period length of activity oscillations, the fast Fourier transforms were with a user-defined transform in Sigma Plot 8.0. Decomposition fits on both the enzyme activity and the growth determinations used MINITAB and were based on the period length established by Fourier analysis.

Standard NAD(P)H oxidase activity assays in which the disappearance of NADH was measured over one min at 1.5 min intervals in heat-inactivated yeast revealed two sets of oscillations based on the recurrence of two maxima separated by 6 min of similar but not identical period lengths. One set denoted by ① and ② in Figure 1(a) exhibited a period length of 24 min. The period length of the second set denoted by A and B in Figure 1(a) was longer and nearer to 25 min. This double period in yeast

increases the complexity of the data over that of mammalian cells and plants which normally exhibit only a single set of oscillations with a period length of 24 min.

To resolve the two oscillatory patterns, fast Fourier (Figure 1(d)) and time series analyses (decomposition fits) (Figures 1(e) and (f)) were employed as used conventionally to resolve patterns of oscillations that are neither sinusoidal nor monotonic [16]. Fourier analyses (Figure 1(d)) partially resolved the two oscillatory patterns with the pattern labeled A and B yielding a period with a slightly lower frequency (longer period) than the pattern labeled ① and ②. Decomposition fits for a 24 min period length based on the Fourier analysis clearly superimposed the maxima labeled ① and ② but not those labeled A and B (Figure 1(b)) whereas decomposition fits for a 25 min period length based on the Fourier analysis coincided with the maxima labeled A and B but not those labeled ① and ② (Figure 1(c)). The recurring patterns predicted by the time series analysis are reproduced in Figure 1(e) for the 24 min oscillations (maxima ① and ②) and in Figure 1(f) for the 25 min oscillations (maxima A and B). Statistical measures of accuracy are summarized and explained in Table 1. With the exception of Figure 2, Figures 3-8 were analyzed in a manner identical to that for Figure 1 with comparable measurements of accuracy.

To link the two ENOX activities and the extra maxima corresponding to a 40 min ultradian period to the circadian clock, glyderaldehyde-3-phosphate dehydrogenase (GAPDH) activity was used. GAPDH activity peaks once within each 24 h period making it an ideal marker of circadian day length [17]. Morré et al. [13] reported that the ENOX1 period in min equals the circadian day length in h for a series of site directed C ® A replacements in ENOX2 where ultradian period lengths of 22, 36 and 45 min resulted in circadian period lengths of 22, 36 and 45 h. Yeast cultures grown in glucose sampled every 2 h for 88 h and assayed for GAPDH activity revealed maxima of GAPDH activity at 24, 25 and 40 h (Figure 2). The two hour sampling interval was sufficient to resolve the different maxima observed as each maximum was represented by several points defining both the ascending and the descending limbs of each maximum. The observed two maxima of 24 and 25 corresponded to the 24 and 25 min ultradian rhythms based on NADH oxidation. The 24 min period is denoted by ① and ②, the 25 min period is denoted by A and B. The 40 min period, denoted by 40 in the figure, may correspond to the 40 min metabolic rhythm of yeast thus far observed only with continuous cultures.

As measured by cleavage of the substrate 2,2’-dithiodipyridine (DTDP), three maxia separated by 4.5 min were generated by mammalian ENOX1 [6]. Yeast also exhibited this activity (Figure 3), with two sets of 3 maxima labeled ③, ④ and ⑤ and, C, D and E, each separated by 4.5 min, an activity that alternates with the two peaks of the oxidative activity for the two sets of oscillations [1]. DTDP cleavage was analyzed statisticcally as for Figure 1 with a similar outcome and comparable accuracy values (Table 1).

Although externally-supplied NADH was used to assay ENOX activity, hydroquinones resident in the plasma membrane are most likely the natural substrate [10]. When reduced coenzyme Q₁₀ was assayed, two sets of oxidative maxima were seen (Figure 4) similar to those observed with NADH (Figure 1). Within each set, two maxima each separated by 6 min were observed. Statistical analyses of both Figures 4(a) and (b) resolved the two sets of oscillations into series having distinct period lengths and accuracy values similar to those of Figure 1 (Table 1).

Table 1. Accuracy measures as determined by decomposition (time series) analyses.^*

^*Decomposition analyses decompose a time series into trend, cyclic, and error components. The measured values of Table 1 evaluate the accuracy of the fitted values and include MAPE (mean of the average percent error), MAD (mean average deviation), and MSD (mean standard deviation). The fitted values by the additive model used agreed closely with the experimental data. Overall the accuracy measures provided show a strong positive relationship between the actual and predicted values. By the statistical criteria, the model performs exceptionally well with the r-values approaching zero for a reasonable level of precision [16].

Melatonin shifts the period of ENOX1 in mammalian cells [18]. When melatonin (final concentration 10 µM) was added to the NADH oxidase assay of mammalian ENOX1, a new maximum of NADH oxidase activity appeared exactly 24 min after melatonin addition. In yeast, the 24 min ENOX1 period responded to melatonin in this manner, denoted by ① and ② before melatonin addition and M after melatonin addition (Figure 5(a)). The initial 24 min period denoted ① and ② was suppressed immediately following melatonin addition (Figure 5(b)). The third maximum labeled ① just prior to melatonin addition was present but no third maximum ② was observed. The 24 min periodic oscillations then re-

sumed exactly 24 min following addition of melatonin 1.5 min out of phase with the original 24 min oscillations. In contrast, melatonin addition did not affect the oscillations with the 25 min period length (A and B) (Figure 5(c)).

An extract from the leaves and bark of Quassia amara L. containing the ENOX 1 inhibitor, simalikalactone D, that inhibits the activity of ENOX1 in mammalian and plant preparations [19], when added to the NADH oxidase assay inhibited the activity represented by the 24 min ENOX period (① and ②), Figure 6(b)) but was without effect on the ENOX activity represented by the 25 min period length (A and B, Figure 6(c)).

The mammalian form of ENOX1 binds 2 moles of copper/mole of protein and copper is essential for its activity

[6]. Alteration of the two copper sites by site-directed mutagenesis or copper removal by bathocuproine inactivated both human ENOX1 [6] and ENOX2 [7] such that little or no oscillatory activity remained. To determine if the yeast ENOX forms also required copper, to 500 µl heat-inactivated yeast were added 1 µl of trifluoroacetic acid to unfold the protein in the presence or absence of 15 µl of 10 mM bathocuproine, a copper chelator, to remove the copper. Yeast ENOX activity was diminished when bathocuproine was present (Figure 7). TFA alone did not reduce activity and activity could be restored to

TFA and bathocuproine treated preparations by addition of copper. In the presence of TFA, both ENOX1 activities were present (Figure 7(a)). In the presence of bathocuproine (Figure 7(b)), both ENOX1 activities were reduced or eliminated. All that remained were two maxima separated by 40 min which may correspond to the fundamental respiratory oscillation of 40 min normally seen only with continuous cultures [20,21].

The period lengths of the two ENOX forms in yeast were

temperature independent (Table 2), a hallmark of the biological clock and a characteristic of mammalian and plant ENOX1. The period length of the oscillations did not change over the range of 17˚C to 37˚C. In contrast, as is typical of both biochemical and chemical reactions, the amplitude doubled with a 10˚C increase in temperature.

A hallmark of the ENOX family of proteins is that of protease resistance. When the yeast ENOX forms were assayed after digestion with proteinase K or trypsin, the activity was unaffected even when unfolded in the presence of trifluoroacetic acid prior to addition of protease (Table 3).

Organisms grown in heavy water (deuterium oxide or D₂O) exhibit a circadian day lengthened in period length by about 25% [23,24]. When mammalian ENOX was assayed in heavy water, it exhibited a period length of about 30 min [25]. Heat-inactivated yeast assayed in heavy water yielded period lengths of approximately 30

Table 2. ENOX1 period length of Saccharomyces cerevisiae is independent of temperature (n = 4).

¹Period length monitored over time intervals as long as 6 h varied with a cumulative error of less than one min; ²Nanomoles/min/10⁶ cells.

Table 3. Protease resistance of yeast ENOX forms of heatinactivated Saccharomyces cerevisiae (n = 4).

^*Trifluoroacetic acid.

min for the maxima labeled ① and ② and of approximately 32 min (31.25 min) for the maxima labeled A and B (Figure 8).