The Cdk1-APC/C cell cycle oscillator circuit functions as a time-delayed, ultrasensitive switch

Abstract

Despite the complexity and variety of biological oscillators, their core design invariably includes an essential negative feedback loop. In the Xenopus laevis embryonic cell cycle oscillator, this loop consists of the kinase cyclin B-Cdk1 and the ubiquitin ligase APC/C^Cdc20; active Cdk1 activates APC/C^Cdc20, which then brings about cyclin B degradation and inactivates Cdk1. Here we ask how this negative feedback loop functions quantitatively, with the aim of understanding what mechanisms keep the Cdk1-APC/C^Cdc20 system from settling into a stable steady state with intermediate levels of Cdk1 and APC/C^Cdc20 activity. We found that the system operates as a time-delayed, digital switch, with a time lag of ~15 min between Cdk1 and APC/C^Cdc20 activation and a tremendously high degree of ultrasensitivity (n_H ≈ 17). Computational modeling shows how these attributes contribute to the generation of robust, clock-like oscillations. Principles uncovered here may also apply to other activator-repressor oscillators and help in designing robust synthetic clocks.

Organisms from cyanobacteria through vertebrates make use of biochemical oscillators to drive repetitive processes like cell cycle progression and vertebrate somitogenesis. Oscillators also allow organisms to anticipate natural environmental rhythms, as exemplified by the circadian clock. The time scales of biological oscillations vary widely (over >10 orders of magnitude¹) and the components of oscillator circuits are highly diverse. Nevertheless, it is thought that all biological oscillators share certain common design principles.

For example, oscillators generally depend upon negative feedback². However, absent crucial elements, negative feedback circuits often settle into a stable steady state rather than oscillating³. Computational studies have enumerated several modifications of the basic activator-repressor circuit that can promote oscillations^{1, 4–8}. These include time delays, which can be generated by the addition of intermediary species to the negative feedback loop; ultrasensitivity in the steady-state responses of the loop’s components to their upstream regulators; and interlinked positive feedback loops, which can serve as a bistable trigger. This raises the question of which of these strategies are actually utilized in the complex biological oscillator circuits found in nature.

Here we focus on the Xenopus laevis embryonic cell cycle, which is driven by an autonomous biochemical oscillator^{9, 10}. The core of the oscillator is a negative feedback loop that includes the Cdk1-cyclin B protein kinase and the E3 ubiquitin ligase APC/C^Cdc20. Active Cdk1-cyclin B brings about activation of APC/C^Cdc20 through an incompletely understood mechanism¹¹. In turn, active APC/C^Cdc20 polyubiquitylates the mitotic cyclins, tagging them for degradation by the proteasome¹² and completing the loop.

The Cdk1 system also includes interlinked positive and double-negative feedback loops, involving the protein kinases Wee1A and Myt1 and the phosphatases Cdc25A and Cdc25C, which collectively function as a bistable trigger^{13, 14}. Compromising the bistable trigger suppresses oscillations in Xenopus egg extracts¹⁵, indicating that positive feedback can promotes oscillations. Here we examine the quantitative properties of the core negative feedback itself, with the aim of understanding how this loop contributes to the robust, autonomous oscillations seen in the early embryo.

We first examined how the steady-state rate of degradation of securin-CFP (a substrate of APC/C^Cdc20) varies with the activity of Cdk1, since ultrasensitivity in this response could promote oscillations. We made use of cycloheximide-treated interphase Xenopus egg extracts for these studies. We added various concentrations of non-degradable Δ65-cyclin B1 to the extracts in the presence of PD0166285, an inhibitor of Wee1A and Myt1 that effectively neutralizes the positive feedback loops of the mitotic trigger and allows intermediate levels of Cdk1 activity to be obtained (Fig. 1a–c). Securin-CFP was then added, and the time course of its degradation was monitored with a fluorescence plate reader. Securin-CFP fluorescence decreased exponentially with time in extracts treated with mitotic concentrations of Δ65-cyclin B1 (Fig. 1d). Similar results were obtained in the presence of the MEK inhibitor U0126 (Fig. S1), suggesting that any residual Mos is too low in concentration to exert a significant cytostatic factor effect.

Figure 1. Ultrasensitivity in the regulation of securin-CFP destruction by Cdk1.

a, Schematic depiction of the experimental approach. b–c, The response of Cdk1 to Δ65-cyclin B1 is all-or-none in the absence of PD0166285 (b) and graded in its presence (500 nM) (c). d, Degradation of securin-CFP in extracts. Extracts were treated with 8 concentrations of Δ65-cyclin B1 (shown in different colors) for 90 min to allow Cdk1 and APC/C^Cdc20 activities to reach steady state. In vitro-translated securin-CFP was then added and the securin-CFP fluorescence was monitored in a plate reader. The inset shows the apparent first order rate constant λ as a function of the Δ65-cyclin B1 concentration. Addition of the MEK inhibitor U0126 to the extracts had little apparent effect on securin-CFP degradation, suggesting that their is too little Mos left in these extracts to exert measurable cytostatic factor activity (see Fig. S1) e, Cdk1 activity (top) and securin-CFP degradation (bottom) as a function of the Δ65-cyclin B1 concentration. Data are from seven independent experiments, with each experiment designated by a different color. f, Pooled data on securin-CFP degradation versus Cdk1 activity. Data are from seven independent experiments and are scaled relative to the individual experiments’ maximum degradation rates and EC50 values. See also Fig. S1.

As shown in Fig. 1d, securin-CFP degradation was a switch-like function of the Cdk1 activity. The degradation rate was low in extracts treated with 0 or 17 nM Δ65-cyclin B1, and near-maximal in extracts treated with 33 nM Δ65-cyclin B1. These results fit well with earlier studies by Felix and co-workers¹⁶, and extend those studies by showing that even when Cdk1 activation is forced to be graded, the degradation of this APC/C^Cdc20 substrate is still highly ultrasensitive.

This experiment was repeated, and in all cases, the Cdk1 response was graded and the securin-CFP degradation response was switch-like, although the EC50 values for both responses varied substantially from experiment to experiment (Fig. 1e; see also the Supplementary Information). Similarly high variability was found for the responses of two other Cdk1 substrates studied previously, Wee1A¹⁷ and Cdc25C¹⁸, possibly because of varying amounts of phosphatase activity in different extracts¹⁹. Whatever the source of variability, we found that the APC/C^Cdc20 responses were ultrasensitive regardless of whether a high or low concentration of cyclin was required for APC/C^Cdc20 activation (Fig. 1).

To quantify the nonlinearity from all experiments, the data were scaled, pooled, and fitted to a single Hill function. The fitted Hill exponent n_H was 17, with a 95% bootstrap confidence interval of 9 to 200 (Fig. 1f). Therefore, securin-CFP degradation is essentially digital, switching from maximally off to maximally on over a tight range of Cdk1 activities. Similar results were obtained for the degradation of in vitro-translated cyclin B1-CFP, added at concentrations too low to yield significant Cdk1 activity (Fig. 2a, b).

Figure 2. Ultrasensitive degradation of cyclin A2-YFP and cyclin B1-CFP.

a–b, Cyclin B1 degradation. a, Cdk1 activity (top) and cyclin B1-CFP degradation (bottom) as a function of the Δ65-cyclin B1 concentration. In these experiments we used added Cdk1AF rather than added PD01166285 to make the Cdk1 response graded. b, Pooled data on cyclin B1-CFP degradation versus Cdk1 activity. Data are from six independent experiments, designated by different colors. Data are scaled relative to the individual experiments’ maximum degradation rates and EC50 values. c–d, Simultaneous measurement of the degradation of securin-CFP (c) and cyclin A2-YFP (d) in extracts. Extracts were treated with 8 concentrations of Δ65-cyclin B1 (designated by different colors) immediately before the addition of in vitro-translated securin-CFP and cyclin A2-YFP, to allow for monitoring and comparing the initiation of both APC/C substrates. For all Δ65-cyclin B1 concentrations that induced APC/C activation, the degradation of cyclin A2-YFP began about 25 to 40 min before the degradation of securin-CFP. e, Apparent first order rate constants for securin-CFP (red) and cyclin A2-YFP (black) degradation as a function of the Δ65-cyclin B1 concentration.

We also examined the degradation of cyclin A2, which interacts differently with APC/C^Cdc20 than cyclin B1 does²⁰, and hence could exhibit a qualitatively different stimulus-response relationship. To allow a direct comparison, we carried out two-color fluorescence studies using in vitro-translated securin-CFP and cyclin A2-YFP. As shown in Fig. 2c–e, cyclin A2-YFP was degraded more rapidly than securin-CFP, which could explain the observation that in Xenopus extracts, where the spindle assembly checkpoint is not operative²¹, cyclin B1 destruction still lags behind cyclin A2 destruction²². The two substrates exhibited similarly switch-like dose response curves, suggesting that ultrasensitivity is a general feature of the degradation of APC/C^Cdc20 targets.

Note that S. cerevisiae APC/C^Cdc20 has been reported to undergo intramolecular ubiquitination of its Cdc20 subunit, resulting in destruction of Cdc20 and auto-inactivation of the complex²³. If this is true of Xenopus APC/C^Cdc20, then both the auto-inactivation rate constant and the securin-CFP destruction rate constant would factor into the apparent first-order rate constant for securin-CFP destruction. However, Cdc20 appears not to cycle in abundance in Xenopus embryos (T. Tsai, unpublished results), and no obvious decreases were seen in APC/C^Cdc20 activity in Xenopus extracts over at least the first hour of incubation. For these reasons we infer that APC/C^Cdc20 auto-ubiquitination does not play a major role in terminating APC/C^Cdc20 activation in this system.

To examine the potential significance of this high ultrasensitivity, we carried out computational studies. We modeled the processes of cyclin synthesis and degradation and Cdk1 activation and inactivation (Fig. 3a) with two nonlinear ordinary differential equations (ODEs) (Supplementary Information). The two-ODE model has two nullclines, and the steady-state(s) of the system are found where the nullclines intersect²⁴ (Fig. 3b). The Cdk1 nullcline defines the steady-state activity of Cdk1 as a function of the total concentration of cyclin present in the system, and it is S-shaped due to the bistability of the mitotic trigger (Fig. 3b, blue curve). The Cyc nullcline is steeply sigmoidal because of the high ultrasensitivity in the response of cyclin degradation to Cdk1 activity (Fig. 3b, red curve). Initially we chose parameters for the degradation response such that the Cyc nullcline intersected the middle of the Cdk1 nullcline. The steady state at the intersection was unstable and all trajectories converged to a stable limit cycle (Fig. 3b). The result was saw-toothed oscillations in cyclin abundance and spiky oscillations in Cdk1 activity (Fig. 3c), similar to those reported from Xenopus extract experiments^{15, 25}. Note that the switch-like character of the Cyc nullcline made it easy to arrange for the two nullclines to intersect at a single unstable fixed point.

Figure 3. Ultrasensitive cyclin degradation allows limit cycle oscillations.

a, Schematic view of the Cdk1-APC/C^Cdc20 system. b, Phase plot of the two-ODE model. The Cdk1 nullcline (blue) was parameterized based on experimental work^{17, 18}, and its shape agrees well with the observed hysteretic steady-state response of Cdk1 to non-degradable cyclin B1^{13, 14}. The switch-like character of the Cyc nullcline (red) arises from the high Hill exponent found for the response of cyclin degradation to Cdk1 activity (Fig. 1). The two nullclines intersect at an unstable steady-state (open circle), and all trajectories converge to a stable limit cycle (black). c, Time course of cyclin accumulation and destruction and Cdk1 activation and inactivation in the two-ODE model. d, Phase plot of the two-ODE model assuming a Hill exponent of 1 for the response of cyclin degradation to Cdk1 activity. The system is now bistable; there are two stable steady-states (filled circles) and a saddle point (open circle). Sample trajectories are shown, with 15 approaching the interphase-like stable steady state (with low Cdk1 activity) and 6 approaching the M-phase-like stable steady state (with high Cdk1 activity). e, Time course of Cdk1 activation for the trajectories shown in panel d. f–h, Bifurcation analysis. The shaded region denotes the parameters compatible with oscillations and an unstable fixed point for the two-ODE model. i, Sensitivity analysis of the period and amplitude of oscillations as a function of one bifurcation parameter, EC50_deg, for various assumed Hill exponents n_H.

j–k, Stochastic simulations, based on Gillespie’s direct method, for various assumed Hill exponents n_H. (j) Time courses. (k) Variability of the period and amplitude of Cdk1 oscillations. Error bars denote standard deviations.

As the Hill exponent’s assumed value decreased, the range of parameters over which a single unstable fixed point could be obtained decreased, and it was impossible to obtain oscillations when the Hill exponent was assumed to be 1; the system was always either monostable, excitable, or, as shown in Fig. 3d–e, bistable. Thus, the experimentally-determined shape of the Cdk1 nullcline necessitates that the Cyc nullcline be sigmoidal in shape, which in turn requires that the degradation of cyclin be an ultrasensitive function of the Cdk1 activity.

To explore the relationship between the degree of ultrasensitivity and the robustness of the oscillations to parameter variation, we carried out bifurcation analyses. Fig. 3f–h shows three of these, allowing the kinetic parameters for the negative feedback loop to vary for different assumed values of the Hill exponent n_H. In general, as the assumed ultrasensitivity increased, the range of parameters over which oscillations were obtained increased (Fig. 3f–h). In addition, we found that the oscillator’s period and amplitude were extremely sensitive to parameter changes for low n_H, but became stable as n_H increased to the high levels seen experimentally (Fig. 3i). Thus ultrasensitive negative feedback endowed the oscillator model with robust, clock-like oscillations.

A relatively low number of molecules in a chemical reaction can give rise to fluctuations around the deterministic dynamics, which can result in variation in both the period and amplitude of oscillations. The total number of cyclin and active Cdk1 molecules present in a Xenopus egg is not actually low (~10¹⁰ molecules per egg). However, it is possible that critical subpopulations of the Cdk1 complexes, such as those associated with the centrosome, may be small enough in number so that stochastic fluctuations become significant. Moreover, the same basic circuit functions in small cells (e.g. yeasts). We therefore asked whether ultrasensitivity in the negative loop affected the system’s robustness to stochastic fluctuations. We converted the two-ODE model into the master equation framework and carried out numerical simulations. Rate constants from the ODE model were converted such that the peak numbers of cyclin and active Cdk1 molecules were small enough to make the stochastic variations in cyclin and active Cdk1 readily apparent. As shown in Fig. 3i–j, ultrasensitive negative feedback made the period of the oscillations more resistant to intrinsic stochastic noise.

One longstanding hypothesis for how the order of cell cycle events is established is that early events require relatively low levels of Cdk1 activity, whereas late events require higher levels^{26, 27}. This hypothesis was originally inspired by studies in S. pombe, where a single cyclin-Cdk complex is primarily responsible for both S-phase and M-phase²⁶. In other organisms, where different cyclin-Cdks regulate different cell cycle phases, this hypothesis can be modified to apply to the ordering of events within a phase. For example, early mitotic events, like nuclear envelope breakdown, might require low levels of cyclin B1-Cdk1 activity, whereas late mitotic events like APC/C^Cdc20 activation might require high levels. This could keep Cdk1 and APC/C^Cdc20 activities out of phase with each other, and help ensure robust oscillations. However, previous experimental tests of this hypothesis have yielded mixed results. Clb2 titration experiments in S. cerevisiae support the differential threshold model²⁸, whereas live cell imaging studies in human cell lines indicate that the amount of Cdk1 activity required for APC/C^Cdc20 activation is lower, not higher, than the amount required for nuclear envelope breakdown²⁹.

Our modeling studies bear on this issue. Given the experimentally-determined shapes of the Cdc25 and Wee1 response functions, only a limited range of EC50 values for APC/C^Cdc20 activation are compatible with oscillations, and these values are similar to the measured values for the (early) Cdc25 and Wee1 responses (Fig. 4a).

Figure 4. The EC50’s for APC/C^Cdc20 activation, Cdc25 phosphorylation, and Wee1 phosphorylation are similar.

a, Nullclines for the two-ODE Cdk1-APC/C^Cdc20 model showing the range of cyclin degradation EC50 values over which the model yields unique limit cycles. At an EC50 value of approximately 28 nM, oscillations arise through a supercritical Hopf bifurcation. At EC50 ≈ 38 nM, the system goes through a subcritical Hopf bifurcation and oscillations begin to disappear. Thus, oscillations are possible only for a tight range of EC50 values similar to those assumed for Cdc25 (35 nM) and Wee1 (30 nM). b, Steady-state stimulus-response studies for Cdk1 activation, Cdc25 hyperphosphorylation, Wee1 T150 phosphorylation, and Cdc27 phosphorylation. The top panel is an autoradiogram of an H1 kinase assay. The three other panels are immunoblots. The band designated by an asterisk on the Cdc25 blot is a background band. Full gel scans are shown in Fig. S3. c, Steady-state dose-response curves.

We therefore set out to directly test whether securin-CFP degradation requires a relatively high level of Cdk1 activity, as predicted by the differential threshold hypothesis, or a low level, as predicted by the two-ODE model. To this end we simultaneously assessed the stimulus-response relationships for securin-CFP degradation, Wee1 T150 phosphorylation and Cdc25 hyperphosphorylation (two early mitotic events), and Cdc27 (APC3) phosphorylation (a late mitotic event)^{30, 31}. The concentration of Δ65-cyclin B1 and the level of Cdk1 activation required to half-maximally activate securin-CFP degradation were found to be comparable to that required for half-maximal Cdc25 and Wee1 phosphorylation (Fig. 4b, c). Thus, although differential thresholds are important for ordering some cell cycle events^{26, 27, 32, 33}, a different strategy must be employed in the Xenopus embryonic cell cycle. Interestingly, Cdc27 phosphorylation did require higher levels of Cdk1 activity than did the other mitotic events, and there was little Cdc27 phosphorylation at concentrations of Δ65-cyclin B1 that were just sufficient to induce maximal APC/C^Cdc20 activation (Fig. 4b, c). This indicates that there is not a simple relationship between the overall phosphorylation of this APC/C subunit and APC/C^Cdc20 activity.

As mentioned above, time delays in negative feedback loops tend to promote oscillations^5–7 and, in the case of the Xenopus embryonic cell cycle where a differential thresholds strategy is not applicable, such time delays could also help ensure that Cdk1-dependent mitotic events are completed before Cdk1 inactivation and mitotic exit take place. In most cells, the spindle assembly checkpoint provides a time delay in the degradation of the critical substrates cyclin B1 and securin (but not cyclin A, Nek2A, or HoxC10³⁴). However, in Xenopus eggs and embryos the checkpoint is not operative²¹. We therefore asked if an intrinsic time delay was built into the Cdk1-APC/C^Cdc20 loop and, if so, which step in the loop (APC/C activation or cyclin degradation) generated the delay.

The total time lag between Cdk1 activation and securin-CFP degradation was assessed by simultaneously adding both Δ65-cyclin B1 and securin-CFP to an interphase extract, measuring the time course of Cdk1 activation and securin-CFP degradation, and asking by how much the latter lagged behind the former (Fig. 5b, c). A mitotic concentration of Δ65-cyclin B1 (89 nM) was used and the inhibitor PD0166285 was included, which minimized the time needed for Cdk1 activation to plateau (Fig. 5c). To obtain a quantitative estimate of the apparent first order rate constant for securin-CFP degradation, the securin-CFP fluorescence data were smoothed using the Gaussian kernel technique (Fig. 5b, solid line), degradation rates were calculated by numerical differentiation, and rate constants were calculated.

Figure 5. Time lags in the Xenopus embryonic cell cycle oscillator’s negative feedback loop.

a, Schematic view of the experimental design. Interphase Xenopus egg extracts were prepared. A non-degradable cyclin protein (Δ65-cyclin B1) was added to activate Cdk1 and APC/C^Cdc20. PD0166285, an inhibitor of Wee1A and Myt1, was included to allow a graded range of Cdk1 activities to be obtained. b–c, Time lag between Cdk1 activation and securin-CFP degradation. These data imply that τ₁+τ₂ ≈ 15 min. d–e, Time lag between APC/C^Cdc20 activation and securin-CFP degradation. The upper bound for τ₂ is estimated to be 2 min. See also Fig S2. f–j, Computational analysis. f, Phase plot of the two-DDE model, assuming τ=15 min. The two nullclines are the same as those shown in Fig. 3b. All trajectories converge to a stable limit cycle (black). The limit cycle for the two-ODE model (i.e., τ=0) is shown as a dashed curve for comparison. g, Time course of cyclin accumulation and destruction and Cdk1 activation and inactivation in the two-DDE model. h–j, Bifurcation analysis. The light blue shading denotes the parameters compatible with oscillations the two-DDE model, but not for the two-ODE model. The dark blue shading denotes parameters compatible with oscillations for both the DDE and ODE models.

As shown in Fig. 5b, securin-CFP degradation was initially slow and then accelerated, with the time lag between Cdk1 activation and securin-CFP degradation estimated to be ~15 min (Fig. 5c). This value agrees well with the time lags seen in previous studies of cyclin degradation in Xenopus extracts supplemented with active starfish Cdk1-cyclin B¹⁶. The observed delay includes both the time between Cdk1 activation and APC/C^Cdc20 activation (τ₁) and the time between APC/C^Cdc20 activation and securin-CFP degradation (τ₂). Lower concentrations of Δ65-cyclin B1 yielded longer time lags (Fig. S4).

To determine whether a time lag between APC/C activation and the onset of securin-CFP destruction (τ₂) contributed to the observed delay, the experiment was repeated with the securin-CFP added 80 min after Δ65-cyclin B1, at a time when APC/C^Cdc20 activity should be close to its steady state level. We then asked how quickly the securin-CFP fluorescence began to decrease. As shown in Fig. 4e, the measured fluorescence began dropping as soon as the securin-CFP was added to the extract. The apparent rate constant was maximal by the first time points, and τ₂ was estimated to be no greater than 2 min (Fig. 5e). Similar results were obtained with other Δ65-cyclin B1 concentrations; the time lag between addition of securin-CFP and its degradation was always too short to measure.

Taken together, these experiments demonstrate that there is a substantial (~15 min) time delay in the Cdk1-to-APC/C^Cdc20 leg of the negative feedback loop, and no detectable (< 2 min) delay in the APC/C^Cdc20-to-Cdk1 leg.

To explore the potential significance of the time lag, we modified the two-ODE model to include an explicit time delay between Cdk1 activation and cyclin degradation, yielding a pair of delay differential equations (DDEs) (Supplementary Information). With all other parameters held unchanged, a 15 min time delay slowed the period and increased the amplitude of the oscillations (Fig. 5f, g), without dramatically affecting the qualitative character of the oscillations (sawtooth oscillations in cyclin, spike-like oscillations in active Cdk1). The time delay also increased the robustness of the oscillations to parameter variation (Fig. 5h–j). Nevertheless, even with the time delay, ultrasensitivity in the degradation response was still required to obtain oscillations.

Alternatively, we modeled the time lag as arising from a multistep mechanism for the activation of APC/C^Cdc20 by Cdk1 (Supplementary Material). Again we found that time lags contributed to the robustness of oscillations (Fig. S5).

In summary, we have quantitatively characterized the negative feedback loop upon which the embryonic cell cycle oscillator is built. We found that Cdk1-induced degradation of securin, cyclin A2, and cyclin B1 is extremely switch-like, with steady-state responses equivalent to those of a cooperative process with a Hill exponent of at least 17 (Figs. 1 and 2). In addition, there is a substantial delay (~15 min) between Cdk1 activation and APC/C^Cdc20 activation (Fig. 5). Thus, even when the bistable trigger is eliminated from consideration, the core negative feedback loop functions as a time-delayed digital switch. Early theoretical studies of generic oscillator circuits established that both time delays and ultrasensitivity can help keep a negative feedback loop from settling into a stable steady-state^{1, 4, 5}. The present work shows that both of these design features are in fact present, and present to a remarkable degree, in the Xenopus embryonic cell cycle oscillator. ODE and DDE models of the circuit argue that the ultrasensitivity and time delays endow the circuit with a clock-like period, a constant amplitude, and robustness with respect to fluctuations in component concentrations and changes in kinetic parameters (Figs. 3, 5, and S5).

Although the details of the APC/C^Cdc20 activation mechanism are incompletely understood, some mechanisms that can generate ultrasensitivity also generate substantial time lags. For example, the observed steady-state and dynamic behaviors the negative feedback loop are consistent with a multistep phosphorylation activation mechanism (Fig. S5), with the nominal number of steps being approximately 25–30. If the phosphatase that reverses these phosphorylations is regulated by Cdk1, as is the case for PP2A-B55δ¹⁹, this regulation could also contribute to the ultrasensitivity and time lag. In any case, both high Hill exponents and time lags appear to be commonplace in the cell cycle oscillator circuit^{16–18, 35, 36}.

In summary, the present work shows that the negative feedback loop upon which the Xenopus embryonic cell cycle oscillator is built functions as a time-delayed, ultrasensitive switch. Given the diversity of biological oscillations, it will be of great interest to see whether this proves to be a recurring design strategy for biological clocks.

ONLINE METHODS

Preparation of Xenopus egg extracts

Undiluted interphase egg extracts treated with 100 μg/mL cycloheximide were prepared as described^{37, 38}, except that eggs were activated with calcium ionophore A23187 (200 ng/μL) rather than electric shock. In these extracts, endogenous cyclin B1 has been degraded and Cdk1 is inactive. Some experiments used frozen stocks of interphase extracts, with no noticeable decrease in Cdk1 and APC activities. The freezing procedure is described as follows. Freshly prepared extracts^{37, 38} were mixed with 80% glycerol to give a final concentration of 3%, then fast-frozen in 50 μL aliquots in liquid nitrogen, and stored at −80°C refrigerator for up to 6 months.

To drive the interphase extracts into a series of intermediate Cdk1 activity states, an inhibitor of Wee1 and Myt1 (PD0166285) was included (500 nM), and various concentrations of purified recombinant Δ65-cyclin B1 ranging from 0 to 200 nM (to interrupt the negative feedback and to drive Cdk1 activation) were added. In a few experiments (Fig. 2 and data not shown) we used Cdk1AF (200 nM) rather than PD0166285 to make the Cdk1 response graded. The Δ65-cyclin B1-supplemented extracts were incubated at room temperature for 90 to 120 min until they reached steady state and were then taken for simultaneous measurements of both Cdk1 and APC/C activities. Generally we did not add sperm chromatin to the extracts.

H1 kinase assay and automatic gel image analysis

Histone H1 kinase assays were carried out as described^{38. 32}P-labeled histone was detected using a PhosphorImager. To allow for consistent quantification, gel images were analyzed by an automatic gel image processing program written in MATLAB, based on a marker-controlled watershed algorithm. Assays were typically carried out in duplicate or triplicate.

Real-time fluorescence assay for APC/C^Cdc20 substrate degradation in Xenopus extracts

Fluorescent APC/C substrate proteins have been used to monitor APC/C^Cdc20 and APC/C^Cdh1 activities in real time in mammalian cell lines³⁹. Here we developed a similar real time assay for Xenopus egg extracts. We constructed cDNAs for various fluorescent (YFP-, CFP-, tdimer2-, or BODIPY-tagged) APC/C substrates and expressed them in vitro in a wheat germ system (TNT SP6 High Yield Protein Expression, Promega). In general the CFP-tagged substrates showed the best signal-to-noise values, well above the background of the extracts’ auto-fluorescence.

A small amount (0.5–1 μl out of the 50 μl reaction) of the in vitro-translated securin-CFP, cyclin B1-CFP, and/or cyclin A2-YFP was added into each (15–20 μl) of the extracts with varying steady-state levels of Cdk1 and APC/C^Cdc20 activity. Extracts were immediately loaded in a small volume 384-well black plate (Greiner, Germany) and the degradation of securin-CFP, cyclin B1-CFP, and/or cyclin A2-YFP was monitored in real time using a fluorescence microplate reader (FLEXstation II 384). Duplicates or triplicates were typically performed. Control experiments established that photobleaching was insignificant (Fig. S1).

Bootstrapping techniques

To avoid having one experiment dominate the curve fitting, we used a bootstrap resampling method to calculate 95% confidence intervals for the pooled data shown in Figs. 1 and 2. We created 1000 samples by sampling with replacement from each pooled dataset. Histograms of fitting parameters from 1000 bootstrap samples corresponding to Fig. 1F indicated significant ultrasensitivity in the response of APC/C^Cdc20 to Cdk1.