Substrates of APC/CCdc20 have different times of degradation onset
In our previous work, we established a single-cell assay to track the degradation dynamics of APC/CCdc20 substrates in the budding yeast Saccharomyces cerevisiae. We tagged each substrate with green fluorescent protein (GFP) to follow its change in concentration over time. In the same strain, we also tagged the spindle-pole body (SPB) component Spc42 with mCherry. The SPB is seen as one dot in G1 and S phase, and separates into two dots at the onset of mitosis. At the metaphase-anaphase transition, the spindle begins to elongate and the two SPB dots move quickly away from each other. These two SPB events serve as single-cell timing references that allow us to align and compare GFP-tagged substrate degradation dynamics in different cells, either from the same strain or with different GFP-tagged substrates [6].
Previously, we estimated degradation timing by using the time point when 50 % of the GFP-tagged substrate was degraded. Here, we re-processed our previously published data to determine the timing of degradation onset. For each single-cell GFP trace, we smoothed and normalized the curve and calculated its first derivative (Additional file 1: Figure S2A). The minimum of the smoothed first derivative curve corresponds to the fastest declining point on the GFP trace during substrate degradation (Additional file 1: Figure S2A; yellow dots). Working backwards in time from that point, we identified the latest time point at which the smoothed first derivative was close to zero, which we used as our estimate of the time of degradation onset (Additional file 1: Figure S2A, B; green dots).
For all the substrates we analyzed, differences in substrate degradation timing were accompanied by significant differences in the timing of degradation onset (Additional file 1: Figure S3). Most relevant for this work are three substrates: Clb5, securin-2A, and Clb5-2A. The degradation onset of securin-2A, in which the inhibitory Cdk phosphorylation sites are mutated (T27A, S71A), begins an average of four min after Clb5 (Additional file 1: Figure S3A, Student's t-test, p-value <0.001). We focused on securin-2A instead of securin because these Cdk phosphorylation sites establish a positive feedback loop in securin degradation that could complicate our computational modeling [23]. Clb5-2A, in which the ABBA motif is mutated (I102A and Y103A), begins to be degraded three min later than wild-type Clb5 (Additional file 1: Figure S3B, Student's t-test, p-value <0.001). Since the ABBA motif allows Clb5 to compete with spindle assembly checkpoint (SAC) proteins for Cdc20 binding [6, 20], it is possible that the delay in Clb5-2A degradation relative to wild-type Clb5 is due to weak remaining SAC activity that does not inhibit Clb5 degradation. However, when we disable the SAC by deleting its key effector protein Mad2, Clb5-2A degradation is delayed relative to Clb5 to the same extent as it is in wild-type cells (Additional file 1: Fig S3C, D). Therefore, we attribute the delay in Clb5-2A degradation to a change in the Clb5-2A-APC/CCdc20 interaction that is independent of the SAC.
The onset of Clb5 degradation indicates the time at which the SAC is turned off and APC/CCdc20 first becomes active [6]. Thus, other substrates, such as Clb5-2A and securin-2A, are degraded several minutes after APC/CCdc20 becomes active. It is worth noting that in the strain where Clb5-2A degradation was monitored, wild-type Clb5 is deleted and there are no known APC/CCdc20 substrates that are better than Clb5-2A (Additional file 1: Figure S1C-E). Nevertheless, Clb5-2A degradation is delayed even though the timing of APC/CCdc20 activation should remain the same.
Clb5 ABBA motif increases the catalytic rate of Clb5 ubiquitination
Our next goal was to develop computational models to help us understand how differences among substrates translate into distinct times of degradation onset. First, we needed to assess the parameters that might vary among substrates. The ABBA motif of Clb5 (or cyclin A in mammals) interacts with Cdc20, and for cyclin A this interaction is known to increase the binding affinity for Cdc20 [6, 20]. We tested an additional possibility that is based on our previous evidence that the D box and KEN box of securin increase the rate of ubiquitination once securin is bound to APC/CCdc20 [14]. We wondered whether the ABBA motif could also increase the catalytic rate of Clb5 ubiquitination. We carried out APC/CCdc20 ubiquitination reactions in vitro to directly measure the catalytic rate of Clb5 ubiquitination with or without the ABBA motif. We used a modified APC/C reaction in which the substrate is directly fused to the APC/C core subunit Apc10/Doc1 [14]. In this system, the enzyme is essentially saturated with substrate, and therefore differences in substrate affinity do not have an impact on the reaction rate. Some ubiquitination occurs in the absence of activator subunit, but addition of activator (Cdc20 or Cdh1) greatly enhances activity by improving the efficiency of the interaction with the E2 [14]. We fused the N-terminal 150 residues of Clb5 (containing the D box and the ABBA motif) to Apc10, generated radiolabeled fusion protein by translation in vitro, and incubated the fusion protein with purified APC/CCdc20 lacking the Apc10 subunit. As in our previous work [14], we carried out activity measurements over a broad range of E2 concentrations. Mutation of the ABBA motif caused a reproducible 1.5- to 2-fold decrease in maximal catalytic activity (Fig. 1). Thus, APC/C substrates can differ not only in their binding affinities for the APC/C, but also in their catalytic rate of ubiquitin transfer.
A simple dynamic model for APC/CCdc20-mediated substrate ubiquitination and degradation
We developed a computational model to determine whether it is possible, in principle, to generate a robust delay in substrate degradation by simply relying on the interaction between one substrate and APC/CCdc20 (Fig. 2a). The model includes the following molecular species: free APC/CCdc20 (A); free unmodified substrate (S0), free substrate with one, two, three or four ubiquitins attached (S1, S2, S3, S4, respectively); APC/CCdc20-bound unmodified substrate (AS0), and APC/CCdc20-bound substrate with one, two, three or four ubiquitins attached (AS1, AS2, AS3, AS4, respectively). These molecular species interact and interconvert by the following rate constants: APC/CCdc20 and free substrate associate with the rate constant k
a
; APC/CCdc20-bound substrates can either dissociate with rate constant k
d
or can be modified by the attachment of ubiquitin with the rate constant k
c
. Once a substrate carries four ubiquitins, regardless of whether it is bound to APC/CCdc20 or not, it is degraded by the proteasome with rate constant e. The amount of active APC/CCdc20 increases linearly at rate p
A starting from zero APC/CCdc20 at the zero time point. Substrate starts at a fixed amount and we assume no production of substrate, since our previous work showed that the level of Clb5-2A plateaus for several minutes before its degradation begins (Additional file 1: Figure S3B, D)[6]. The concentration change of each molecular species was determined by ordinary differential equations (Additional file 1: Figure S4), and all reactions were modeled as mass action since we considered binding and catalysis steps explicitly.
The initial concentration of the free substrate was set at 200 nM, based on previous estimates of Clb5 concentration in the cell [24]. We fixed the rate of APC/CCdc20 accumulation p
A
at 0.06 nM/sec, based on estimates of Cdc20 concentration obtained by single-cell analysis of GFP-tagged Cdc20 (Additional file 1: Figure S5). The degradation rate constant e was fixed at 1,000/sec, ensuring that substrate was degraded as soon as it was modified with four ubiquitins. All other parameters were varied across a range of values. We varied the substrate ubiquitination and dissociation rate constants k
c
and k
d
from 10−3/sec to 103/sec, based in part on previous enzymatic reaction results in vitro [9, 14, 25]. Substrate association rate constant k
a
varied from 10−4/(nM sec) to 10/(nM sec) (that is, 105 to 1010/[M sec]). Note that k
a
should be similar for different substrates as it is mostly determined by rates of random collisions, but we still analyzed a range of k
a
values to gain insights about the system.
We evaluated our model at 25 values for k
c
and k
d
and six values for k
a
, all evenly distributed on a log scale, so that each k
c
and k
d
value was changed by a factor of 1.8, and k
a
changed by a factor of 10, as compared to its immediate neighbors. For each set of parameters, we calculated the dynamics of substrate concentration over a period of 50 min, which is similar to the duration of a movie for experimental analysis (Fig. 2b).
Delay in degradation onset and fast degradation rate are opposing constraints
Using the one-substrate APC/CCdc20 model, we first searched for the parameter space that generated two behaviors seen in our previous in vivo studies: a significant delay in degradation onset and a rapid degradation rate. For each set of parameters, we quantified the delay in degradation onset by measuring the duration from time zero (i.e., the onset of APC/CCdc20 activity) to the time when substrate concentration declined to 95 % of its initial value (T95). To estimate the rate of substrate degradation, we measured the duration from T95 to the time when 50 % of the substrate was degraded (Td = T50 - T95) (Fig. 3a). Based on our experimental data, we were looking for the set of model parameters that had a T95 greater than 200 sec as well as a Td of less than 600 sec. It was immediately clear that these two criteria are satisfied by opposing constraints. At any fixed substrate association rate constant k
a
, a long T95 requires a small ubiquitination rate constant k
c
and/or a large substrate dissociation rate constant k
d
, whereas a short Td requires a large k
c
and/or a small k
d
(Fig. 3b). Therefore, the parameter space where both criteria are satisfied is restricted to a small overlap zone. Within this zone, we can easily reproduce Clb5-2A or securin-2A degradation dynamics like those observed in vivo (Fig. 3c).
Deubiquitination helps establish a delay at a cost to degradation rate
The ubiquitination state of a protein is determined by the relative rates of ubiquitination and deubiquitination. We thus analyzed the role of deubiquitination in our model by incorporating a deubiquitination reaction for all substrates with ubiquitins attached, bound to APC/CCdc20 or not. This led to an increase in the delay of degradation onset but also reduced the degradation rate, and was not essential to reproduce the experimentally observed delayed substrate degradation onset (Fig. 3d). We also tried allowing deubiquitination only for free substrates, only for APC/CCdc20-bound substrates, or only for substrates with one ubiquitin attached [26], and obtained similar results (Additional file 1: Figure S6).
Varying the dissociation rate constant k
d
influences degradation timing when free APC/CCdc20 is available
To address how the timing of degradation might be changed for different substrates, we quantified the delay in degradation onset (T95) for substrates with different k
c
and k
d
. We fixed k
a
at 0.01/(nM sec) and calculated T95 for each combination of k
c
-k
d
(Fig. 4a). As expected, increasing k
c
(rightward along x axis) or decreasing k
d
(downward along y axis) generally accelerated the ubiquitination process and decreased T95.
To measure the change in T95 that results from a small change in k
c
, we calculated the relative decrease in T95 following an increase in k
c
by a factor of 1.8 (Fig. 4b, left panel), starting with every k
c
-k
d
combination (Fig. 4b, middle panel). Increasing k
c
decreased T95 significantly throughout the parameter space, except in the region where degradation occurs extremely fast due to large k
c
.
Similarly, we calculated the relative decrease in T95 after a decrease in k
d
by a factor of 1.8 (Fig. 4b, right panel). Decreasing k
d
caused a significant decrease in T95 primarily in the area where free APC/CCdc20 is available (Fig. 4c; see also Additional file 1: Figure S7). In the lower left parameter region where varying k
d
does not significantly influence T95, all APC/CCdc20 molecules are occupied by substrate, ubiquitination occurs at the maximum rate, and varying k
d
does not significantly change the amount of substrate-bound APC/CCdc20.
A model system with two substrates sharing the same pool of APC/CCdc20 readily generates differences in degradation onset
Since the amount of Cdc20 is not in large excess over substrates in vivo (Additional file 1: Figure S5), competition among substrates for APC/CCdc20 is possible. To understand how competition might influence substrate degradation timing, we analyzed a model with two substrates, C and S, that are based on the yeast substrates Clb5 and securin-2A. The two substrates start at the same concentration and interact with the same pool of APC/CCdc20. The only difference is that C is a better substrate than S, either by having: (1) a smaller dissociation rate constant k
d,C
that is 1/10 the k
d,S
of S; or (2) a larger catalytic rate constant k
c,C
that is 10-fold greater than the k
c,S
of S.
We first analyzed the differences in degradation onset (T95) between C and S in two-substrate systems. Regardless of the way in which C is a better substrate, we found a large parameter region in which there was a robust, significant difference in the timing of their degradation onset (red regions in Figs. 5a and 6a). The region where the difference in T95 was small had either: (1) a small k
d,S
, such that the difference between k
d,S
and 1/10 k
d,C
was too small to distinguish C and S and the two substrates were degraded with similar timing; or (2) a large k
c
, such that the degradation of both substrates was extremely fast (i.e., T95 was very small; white regions in Figs. 5a and 6a).
We then analyzed the differences in degradation rate (Td) between C and S (Figs. 5b and 6b). C generally had a higher degradation rate than S (TdC/TdS < 1), whether its affinity for APC/CCdc20 was higher (Fig. 5b) or its rate of catalysis was higher (Fig. 6b), which is consistent with our previous observation that the rate of Clb5 degradation in vivo is slightly higher than that of securin-2A (Additional file 1: Figure S1F) [6]. Only one parameter region did not generate this result: when C had higher affinity for APC/CCdc20, the degradation rate of C was slower than that of S at some low values of k
d,S
and k
c,S
(Fig. 5b; yellow and orange region, TdC/TdS > 1).
Substrate competition could delay degradation by decreasing available APC/CCdc20
We next explored in more detail how two different substrates influence each other’s degradation timing and rate, by comparing degradation of S in a two-substrate system to that in a one-substrate system with the same parameter values. We reasoned that in parameter regions where C has little effect on S degradation, the timing and rate of S degradation are determined primarily by its interaction with APC/CCdc20 as in a one-substrate system, and all the properties of a one-substrate system apply.
We first analyzed the two-substrate system in which C binds APC/CCdc20 with ten-fold higher affinity than S (k
d,C
is 1/10 k
d,S
), as described above. We calculated the relative increase in the T95 of S following the addition of C to the system, compared to S being the only substrate. In one parameter region, the addition of C significantly delayed the degradation of S (Fig. 5c; left and middle panel, red region). Under these conditions, C competitively inhibits S degradation by occupying a large amount of APC/CCdc20, thereby reducing the amount of APC/CCdc20 available to S (Fig. 5d). In the other parameter regions, k
d,S
is sufficiently large to allow more free APC/CCdc20 in the one-substrate system (see Fig. 4c), and the additional C in the system occupies only a small fraction of APC/CCdc20. This helps buffer against the effect of adding C to the system, and C does not delay S degradation significantly (Fig. 5c; right panel).
Interestingly, C did not have a significant impact on S in our alternate two-substrate system in which C is 10-fold more efficiently ubiquitinated once bound to APC/CCdc20. Addition of C to this system had very little effect on the degradation of S in the entire parameter region (Fig. 6c). In this scenario, when C is bound to APC/CCdc20, the substrate either dissociates or is rapidly ubiquitinated and destroyed. This short life-time of the C-APC/CCdc20 complex results in a very small population of C-bound APC/CCdc20 (Fig. 6d). Thus, C does not sequester APC/CCdc20 away from S and has little influence on S degradation, and the delayed degradation of S is primarily established by the parameters of its interaction with the APC/CCdc20 as in the one-substrate system. Interestingly, in some parameter regions in this scenario, S is more efficient in occupying APC/CCdc20 and can delay degradation of C (Fig. 6c; left panel).
The two-substrate systems we analyzed are both extreme cases. In reality, Clb5 could be better than securin-2A due to relatively small improvements in both k
d
and k
c
. For instance, our biochemical studies showed that the ABBA motif of Clb5 can increase its k
c
(Fig. 1), and others have shown that the ABBA motif of cyclin A can decrease its k
d
[18]. Other APC/C-interacting motifs are also likely to have similar effects on both k
d
and k
c
[14]. These parameters influence both the substrate-APC/CCdc20 interaction and the effect of competition for limited amounts of APC/CCdc20. For the Clb5-2A mutant that lacks the ABBA motif, the delayed degradation onset compared to Clb5 might be a combined result of being a less efficient APC/CCdc20 substrate and possibly less efficient in competing with other substrates for APC/CCdc20 binding.
Similar conclusions are reached in models with constant APC/CCdc20 activity
In the modeling described thus far, we used linearly increasing APC/CCdc20 activity as a simple approximation of the condition in the cell. To explore further the effects of different patterns of APC/CCdc20 activation, we carried out computational studies of one- and two-substrate systems with a constant level of APC/CCdc20 (100 nM, half the initial concentration of substrates), as might be the case when APC/CCdc20 activity increases abruptly (perhaps due to SAC inactivation) to maximal levels. The major effect of constant APC/CCdc20 activity is that the system has a smaller parameter region with both delayed degradation onset and rapid degradation rate (Fig. 7a). We explain this result as follows: larger amounts of APC/CCdc20 activity exist at earlier time points in this system than in the system with gradually increasing APC/CCdc20 activity, and this reduces the delay in degradation onset. At later time points, APC/CCdc20 is not increasing and this reduces the degradation rate. Other than these changes, however, all other conclusions from our previous models remain unchanged: one substrate can still exhibit a robust delay in its degradation onset, and adding a second substrate may or may not increase this delay, depending on how APC/CCdc20 is partitioned among the substrates (Fig. 7b).
Clb5 does not significantly delay securin degradation
If competition from Clb5 contributes significantly to the delay in securin-2A degradation, then the delay should be reduced by removing Clb5 and increased by adding more Clb5. Direct deletion of Clb5 causes DNA replication defects and slows cell-cycle progression, which would complicate our measurement of mitotic timing [27]. We therefore decided to add more Clb5 to the cell by introducing an extra copy of CLB5, driven by its own promoter, into cells with securin replaced by the securin-2A allele. These cells maintain their endogenous copy of Clb5. The extra copy of Clb5 was tagged with GFP to confirm its expression in the cell (Fig. 8a). The presence of the extra Clb5 did not delay spindle elongation relative to SPB separation (Fig. 8b). Since spindle elongation is directly driven by securin-2A degradation, we conclude that the timing of securin-2A degradation was unaffected by extra Clb5. These results are most consistent with a two-substrate model in which Clb5 has a higher k
c
, does not occupy a significant fraction of the APC/CCdc20, and therefore does not compete effectively with securin in vivo (Additional file 1: Figure S8).
Processivity is determined by a subset of the factors that determine degradation timing and dynamics
The APC/C is processive: more than one ubiquitin can be attached during a single substrate-binding event (i.e., when the catalytic rate exceeds the substrate dissociation rate) [9]. Differences in processivity with different substrates are thought to influence the order of substrate degradation timing [10]. We explored this issue by analyzing the relationship between processivity and substrate degradation timing and dynamics with a modified one-substrate model. Processivity is measured as the number of ubiquitins attached to a substrate before it dissociates from APC/CCdc20. Thus, a simple model to calculate processivity can start with S-bound APC/CCdc20 (AS0) as the sole molecular species and does not require an association rate constant, in which case the concentration of free substrate or APC/CCdc20 becomes unimportant (Fig. 9a). In the same k
c
-k
d
parameter space that we analyzed in our other studies, we calculated the average number of ubiquitins per substrate molecule after the system reached steady state for each parameter combination. As expected, processivity, as a steady state property, is determined by the relative strength of k
c
and k
d
(Fig. 9b). However, higher processivity did not always correlate with earlier or faster degradation (Fig. 9c). We believe this is the case because T95 and Td, as dynamic properties, are determined not only by the absolute strength of k
c
and k
d
but also by additional factors, including the association rate constant k
a
and the concentrations of free S and APC/CCdc20. Thus, processivity is related to substrate degradation timing and dynamics but is not the sole determinant.