The propensity of a protein for degradation is largely encoded in its state of ubiquitylation (
1,
2). The ubiquitylation process results in highly diverse configurations of ubiquitin chains on target proteins (
3). The 26
S proteasome recognizes ubiquitylated substrates and degrades them into short peptides (
4). Tests of defined configurations of ubiquitins on substrates for their influence on recognition and degradation showed that a substrate protein must generally be conjugated with a chain of at least four ubiquitins to interact tightly enough with the proteasome for degradation (
5). However, no compelling evidence supports the existence of a tetraubiquitin chain receptor on the proteasome. Alternative explanations for the tetraubiquitin chain selection rule mostly rely on the geometric distance between a pair of proteasomal subunits to gauge the length of a ubiquitin chain (
6,
7). The requirement for a tetraubiquitin chain for degradation also differs from substrate to substrate, without a predictable relationship to a substrate’s function or structure (
8–
11).
Exit from mitosis and passage into the G
1 phase of the cell cycle requires ubiquitylation mediated by the anaphase-promoting complex (APC) (
12). Substrates (such as cyclin B, securin, and geminin) typically contain multiple lysine residues, to which ubiquitin moieties are conjugated, providing a very large number of possible combinations of ubiquitin chain configurations (
3,
8,
13,
14). Mass spectrometry studies indicate that ubiquitin chains on cyclin B molecules generated in reconstituted reactions contain, on average, only two ubiquitins (
3). Moreover, multi-monoubiquitylation (referring to ubiquitylation on multiple lysine residues without chain formation) on cyclin B leads to efficient degradation. Multiple ubiquitylation sites are commonly found on substrates of other E3 enzymes (
15,
16); at least 56% of ubiquitylated human proteins contain more than one ubiquitylation site, though the relevance of these ubiquitylations to protein degradation has not been fully demonstrated (
17).
Ubiquitins conjugated to the substrate promote interaction with the proteasome; however, binding by itself is not sufficient to initiate degradation. Several known proteasome-interacting proteins (Usp14, Rad23, etc.) are stable (
18), and autoubiquitylated Cdc34 is not degraded, despite its strong interaction with the proteasome (
19). To facilitate initiation of substrate translocation, it has been proposed that substrates must have an unstructured terminal region of at least 30 amino acids (
20); multiple steps occur in the proteasomal degradation process, as suggested by cryo–electron microscopy (cryo-EM) structures (
6,
7,
21). Before or coincident with peptide translocation, conjugated ubiquitins are removed by deubiquitylating enzymes (DUBs) Rpn11, Usp14, and Uch37 on the proteasome (
22). Whereas Usp14 and Uch37 may have an editing role to tune the rate of proteasomal degradation, they are dispensable for the degradation process. The DUB Rpn11, by contrast, is required for efficient proteasomal activity. Rpn11 is located close to the substrate entry port, where it removes ubiquitin chains en bloc from the translocating peptide (
6,
23). It is unclear how the proteasome might use these features to establish selectivity in substrate recognition.
To understand the requirements for efficient protein degradation, we examined the kinetics of degradation of substrates with defined ubiquitin configurations. We found that, for APC substrates with multiple ubiquitylated lysine residues, tetraubiquitin chains were not required for efficient degradation. Rather, given the same number of total ubiquitins on a substrate molecule, diubiquitin chains were more efficient than tetraubiquitin chains in promoting degradation. To elucidate the molecular basis through which some ubiquitin configurations promote more efficient degradation than others, we investigated the intermediate steps in the degradation pathway using single-molecule (SM) methods. For substrates containing multiple lysines, the strength of interaction with the proteasome was determined largely by the total number of ubiquitins and was less sensitive to the ubiquitin configuration. However, substrate binding alone was not sufficient for rapid degradation for most substrates. Rather, degradation depended strongly on the initiation rate of passage into the substrate translocation channel, and this transition was promoted by the presence of ubiquitin chain structures on substrates.
Discussion
The multiple lysines on a substrate and on ubiquitin itself generate a large number of possible ubiquitin configurations. These configurations represent a “ubiquitin code” of unknown degeneracy that must be read by the proteasome and converted into a rate of substrate degradation. We have approached this problem with two methods: construction of substrates with defined ubiquitin configurations and SM techniques. We found that tetraubiquitin chains are not essential for rapid proteasomal degradation of APC substrates, which would explain why a tetraubiquitin receptor on a proteasome has not been found. In fact, ubiquitin chains on cyclin B, and possibly other APC substrates, are typically short (
3), and multiple ubiquitylatable lysine residues are a common feature of these substrates. A distributed array of short ubiquitin chains appears to be a superior and perhaps an optimal signal for proteasomal degradation; this conclusion could probably extend to substrates of other E3 ligases. Although a single ubiquitin chain may be sufficient for degrading certain substrates, such as Sic1 mutants and IκB (
16,
43), increasing the number of ubiquitylated lysine residues of the canonical single-chain substrate β-galactosidase greatly accelerates its degradation (
44). Similarly, WT cyclin B was degraded faster than mutants with fewer lysines at the same total amount of ubiquitylation (
Fig. 1F) (Ub = 7 to 8). Besides K48 chains, the APC also establishes K11 and K63 linkages on substrates (
3). We found that K48 chains promoted more efficient degradation than K11, K27, and K63 chains (fig. S6).
By studying cyclin B mutants, we found that proximity of the first ubiquitylated lysine to the N terminus was associated with faster degradation (
Fig. 1E), suggesting that the degradation rate is sensitive to the position of ubiquitylated lysine residues. There was a correspondence between long dwell times and elevated rates of degradation (fig. S33A), suggesting that ubiquitin chain position could control the rate of degradation, at least partially, through controlling affinity with the proteasome. Single-lysine mutants of cyclin B with a ubiquitin chain at different positions had indistinguishable binding kinetics to the proteasome, suggesting that monochain and multichain substrates may interact with the proteasome by different mechanisms (fig. S33B). For WT substrates, our current method of constructing defined ubiquitin configurations does not specify the chain positions. The results are understood as a populational average of all actual combinations of positions, of which the vast majority can promote efficient degradation.
Comparison of the
Kd values for tetraubiquitin chains measured by our SM methods with those from bulk assays suggests that surface immobilization of the proteasome is unlikely to distort kinetic rate constants. In addition, ubiquitylated securin took, on average, 10 s to complete translocation and possibly the degradation process on the surface-bound proteasome (fig. S34). This result is consistent with time for degrading similar-size proteins, such as dihydrofolate reductase and Sic1, measured in bulk assays (
45), suggesting that the surface-bound proteasome is unimpaired for unbiased kinetic studies.
The rate of degradation is determined by both binding (i.e.,
Kd effect) and postbinding (i.e.,
kcat effect) events on the proteasome. For APC substrates, multiple diubiquitin chains were more efficient degradation signals than tetraubiquitin chains, given the same total number of conjugated ubiquitins (
Fig. 1, B to D). The explanation for this distinction may be their different binding strength with the proteasome. Using SM methods, we observed weaker binding if ubiquitins were assembled into a single chain on K64–cyclin B when compared to that for WT cyclin B, which had short and distributive chain configurations (
Fig. 2B). High-resolution cryo-EM structures of the proteasome are consistent with the potential effectiveness of multiple short ubiquitin chains. Because proteasomal ubiquitin receptors Rpn10 and Rpn13 are distant from each other (
6,
7), distributive configurations of ubiquitins on a substrate molecule might promote the use of more ubiquitin receptors on the proteasome; a single ubiquitin chain might also be less effective due to steric constraint. Furthermore, Rpn10 and Rpn13 may not be the only ubiquitin receptors on proteasome because budding yeast can tolerate mutations of both (
46). Additional receptors or shuttle factors for the proteasome are also thought to contribute to the binding of ubiquitylated proteins (
47,
48) (see below).
The SM binding measurements suggest a model wherein a substrate molecule samples multiple modes of binding during its interaction with the proteasome (
Fig. 5). Evidence for such a mechanism comes from measurement of the dwell time as a function of ubiquitylation levels on the substrate. Beyond the ubiquitin-binding capacity of the proteasome, most likely limited to three or four ubiquitins by available ubiquitin receptors, a further increase of binding affinity relies on an increase in the local ubiquitin concentration on the substrate: the stochastic interaction. This stochastic mechanism stabilizes the bound state by increasing its entropy, or the number of microscopic states, because entropy is proportional to the logarithm of the number of these states. In this system, an increase in relevant entropy may occur if the substrate molecule can explore multiple conformations on the proteasome through intramolecular diffusion while remaining associated with the proteasome (
Fig. 5). Such dynamic sampling should also increase the likelihood that the peptide terminus would be captured by the substrate entry port on the ATPases, thereby facilitating initiation of translocation. A cooperative process is implied by the exponential increase of dwell time as a function of the number of conjugated ubiquitins, whereas a stochastic process is implied by a linear increase (
Fig. 2, C and D). A similar, biphasic binding relationship (1/
Ki ~ Ub number) was suggested in an early publication using competition assays, though the interpretation was different (
5) (fig. S35). An exponential increase of dwell time involving greater than three simultaneous interactions would further increase the discrimination of ubiquitin levels over a linear increase. Why, then, is the process no longer exponential after four ubiquitins? Cooperative mechanisms tend to promote tight binding, which has potential risks for the cell. If a highly ubiquitylated substrate could not be degraded by the proteasome, it would stably block the proteasome. Such an inhibition by stably binding complexes has been proposed to underlie the accumulation of ubiquitylated intermediates in various neurodegenerative diseases (
49). A linear increase in affinity at high-ubiquitin stoichiometry, though less discriminating, is also less prone to form unproductive, inhibitory substrate-proteasome complexes.
Although binding to the proteasome is a prerequisite for degradation, it does not in itself determine the rate of degradation. For example, WT Ub–conjugated securin and Ub0K-conjugated securin bind equally tightly, but the former is degraded much faster than the latter. The specificity of degradation must also reflect postbinding events. The SM analysis of Rpn11-dependent deubiquitylation indicates that the chain structure of ubiquitin promotes the initiation of translocation, a requirement for degradation. This effect of Ub chains also applies to cyclin B, a special substrate that can be degraded even without ubiquitin chains. We observed a shorter delay between binding and the initial deubiquitylation event for WT Ub–conjugated cyclin B than for Ub0K conjugates, consistent with the translocation-promoting activity of ubiquitin chains (fig. S36).
Most substrate-proteasome encounters do not lead to degradation, especially for substrates with a low number of conjugated ubiquitins (
Fig. 4C). Even for highly ubiquitylated substrates, binding events sometimes lasted for tens of seconds without leading to degradation. Thus, there may be a latent state of the proteasome, in which heterogeneous ubiquitin chain conformations might affect deubiquitylation (
50) or, perhaps more likely, might affect the orientation of a bound substrate, placing the translocation-initiating element far away from the substrate entry port. In this context, the presence of a short flexible domain at a substrate’s terminus should substantially accelerate its rate of degradation (
20,
51). Therefore, engagement of the translocation-initiating element by force-generating pore loops of the proteasomal ATPases, which are reached via the substrate entry port, may generally be a rate-limiting step in degradation. Translocation initiation has been proposed to underlie “commitment,” a hypothetical point at which substrates are irreversibly destined to degradation (
39). We argue that translocation initiation, sensitive to the configuration of ubiquitin groups on the substrate, is either the commitment step or is closely coupled to it.
To understand how ubiquitin chains promote translocation initiation, we propose a model based on our experimental observations (
Fig. 5). Conformational changes of the proteasome, driven by the ATPases quickly transiting through different nucleotide-bound states (
33,
40), may activate a ubiquitin chain receptor(s) that participates in substrate recognition (
52). Candidates for such a receptor include ATPase Rpt5, which can be cross-linked to bound ubiquitin chains (
53). The same result can also be explained by rearrangement of ubiquitin receptors (Rpn10 and Rpn13) into a higher-affinity state for ubiquitin chains. It would make sense if the additional ubiquitin chain receptor were closer to the substrate entry port than Rpn10 or Rpn13 to facilitate translocation initiation by engaging the substrate into a deeper conformation after the initial interaction involving mainly Rpn10 and Rpn13 (
Fig. 5). Such an intermediate step is indicated by the delay before deubiquitylation or translocation (fig. S30). Consistently, Rpt5 is very close to the substrate entry port, and conformational changes induced by ATP-γ-S dramatically reduce the distance between Rpn10 and Rpt4/5, indicating a possible direct transfer of substrates from initial binding to deeper engagement (
33,
54) (fig. S37).
We have shown that there is no simple length threshold for ubiquitin chains for degradation by the proteasome. Rather, there are at least two requirements: a minimal number of ubiquitins to result in tight binding and a certain number or length of chains to promote translocation into the axial channel. The ultimate rate of degradation is probably set by ubiquitin stoichiometry, chain configuration, and properties of the substrate that affect not only the capacity to be ubiquitylated and the configuration of chains but also the orientation of the chains and translocation-initiating elements once bound to the proteasome.
Materials and methods
Protein purification and labeling
Recombinant, full-length human securin, Ube2S, GST-Emi1 (297-447), Xenopus geminin, Xenopus N-terminal cyclin B (amino acids 1 to 104), human N-terminal cyclin B (amino acids 1 to 88), and mutants were purified from Escherichia coli cells using an IMPACT kit (NEB, E6901S). A PKA (protein kinase A) site (RRASV) was also placed at the N terminus of the substrates used in degradation assays. Human ubiquitin, UbK48, Ub0K, UBK6A, and UbI44A mutants, each with a cysteine residue and a His tag at the N terminus, were purified from E. coli cells using cation-exchange chromatography (GE, 17-1152-01) labeled with DyLight 550 maleimide (Pierce, 62290). After removing unreacted dyes, labeled ubiquitin was subjected to anion-exchange chromatography (GE, 17-1153-01) to separate labeled and unlabeled species. Finally, the N-terminal His tag was cleaved off using thrombin.
Fluorescently labeled ubiquitin chains were synthesized using E2-25K in reactions containing 30 μM DyLight 550–labeled UbK48 and 10 μM DyLight 550–labeled Ub0K; carried out in UBAB buffer [25 mM Tris-HCl (pH 7.5), 50 mM NaCl, 10 mM MgCl2], 3 mM ATP, 1 μM E1, and 10 μM E2-25K; and incubated at 37°C for 16 hours. The product was purified and separated using anion-exchange chromatography. For binding assays with the proteasome, different fractions of ubiquitin chains were mixed as the sample.
Anti-20S antibody (MCP21) was biotinylated using biotin-NHS (Pierce, 20217) and was purified using desalting columns.
Radioactive 33P-ATP was used to label substrates with a PKA site at the N terminus for in vitro ubiquitylation and degradation assays.
E1, E2s (UbcH10, E2-25K), WT ubiquitin, biotin ubiquitin, methylated ubiquitin, K48-diubiquitin chains, and K48-tetraubiquitin chains were from Boston Biochem. Purified streptavidin was from Invitrogen.
For biotinylating substrates, a biotin-containing peptide (NEB, Bio-P1) was ligated to the substrate C terminus, which had been activated by intein cleavage during purification, resulting in ~90% ligation efficiency.
Ubiquitin chain methylation
Ubiquitin chain samples were buffer-exchanged into a mixture of 50 mM Hepes-Na (pH 7.5), 150 mM NaCl, and 2% glycerol. Dimethylamine borane and formaldehyde were added to the sample to final concentrations of 20 and 40 mM, respectively. After 2-hour incubation on ice, another 20 mM dimethylamine borane and 40 mM formaldehyde were again added, bringing final concentrations to 40 and 80 mM, respectively, and incubation was continued for 16 hours on ice. Methylated proteins were buffer-exchanged to tris-buffered saline [20 mM Tris-HCL (pH 7.5), 150 mM NaCl].
APC purification from HeLa cell G1 extract
HeLa cell G
1 extract preparation and APC purification were performed as described previously (
13). Briefly, 2L HeLa S3 cell spinner culture was synchronized at prometaphase using thymidine/nocodazole double block and was then released for 3 hours into G
1. Cells were harvested and subjected to nitrogen cavitation in 75% volume swelling buffer [20 mM Tris-HCl (pH 7.5), 5 mM KCl, 1.5 mM MgCl
2, 1 mM dithiothreitol (DTT), protease-inhibitor tablet (Roche, 05892953001)]. APC was purified from cell extracts using anti-Cdc27 (AF3.1, custom-made) agarose and eluted using a competitive peptide.
Affinity purification of the 26S human proteasome
Human proteasomes were affinity-purified on a large scale from a stable human embryonic kidney 293 cell line harboring HTBH-tagged hRPN11 (a gift from L. Huang). The cells were Dounce-homogenized in lysis buffer [50 mM NaH2PO4 (pH 7.5), 100 mM NaCl, 10% glycerol, 5 mM MgCl2, 0.5% NP-40, 5 mM ATP, and 1 mM DTT] containing protease inhibitors. Lysates were cleared and then incubated with NeutrAvidin agarose resin (Thermo Scientific) overnight at 4°C. The beads were then washed with excess lysis buffer, followed by the wash buffer [50 mM Tris-HCl (pH 7.5), 1 mM MgCl2, and 1 mM ATP]. Usp14 was removed from proteasomes using the wash buffer plus 100 mM NaCl for 30 min. 26S proteasomes were eluted from the beads by cleavage, using TEV protease (Invitrogen).
In vitro ubiquitylation reaction
The APC ubiquitylation reactions were carried out in UBAB buffer [25 mM Tris-HCl (pH 7.5), 50 mM NaCl, 10 mM MgCl2] containing 5 nM APC, 100 nM E1, 2 μM UbcH10, 2 mg/ml bovine serum albumin (BSA), an energy regenerating system, and either ubiquitin or ubiquitin chains: 10 μM ubiquitin, methylated ubiquitin, or DyLight 550–Ub0K; 5 μM methylated K48-diubiquitin; and 1 μM methylated K48-tetraubiquitin. Reactions were incubated at 30°C. Results were quantified using a phosphorimager. For PKA-labeled substrates, calyculin A (EMD, 19-139), a broad-spectrum phosphatase inhibitor, was added at 10 μg/ml.
Ube2S autoubiquitylation reactions were carried out in UBAB buffer containing 6 μM Ube2S, 0.5 μM E1, and 5 mM ATP. 100 μM ubiquitin, methylated ubiquitin, or 40 μM methylated K48-diubiquitin chain were also added. Reactions were incubated at 37°C for 4 hours.
Quantitative degradation assay
PKA-labeled substrates (800 nM) were ubiquitylated by the APC using various forms of ubiquitin or ubiquitin chains for 45 min at 30°C. Reaction products were then mixed with proteasome-containing solution (UBAB buffer, 3 nM 26S proteasome, 2 mg/ml BSA, 1 μM GST-Emi1, 3 mM ATP, 10 μg/ml calyculin A) at a ratio of 1:4. The degradation reaction was sampled at 0, 3, 6, and 15 min at 37°C and was quantified using a phosphorimager.
To calculate the degradation rate, the intensity of each ubiquitylated species was quantified using ImageJ. These values were normalized to the intensity of the unmodified substrate (Ub0) to correct for loading error and nonspecific dephosphorylation. Finally, traces of the time course of degradation were fitted with an exponential decay function to obtain the rate constant.
Peptidase assay
Products of Ube2S autoubiquitylation reaction (6 μM) were mixed with proteasome-containing solution (UBAB buffer, 6 nM 26S proteasome, 2 mg/ml BSA, 3 mM ATP, 30 μM Z-GGL-AMC, 0.4 mM DTT) at a 1:1 ratio. Hydrolysis of GGL-AMC was monitored at 37°C using a fluorescence spectrometer.
Binding assay for ubiquitylated substrate
Wild-type securin was ubiquitylated in a standard APC reaction with either WT Ub or Ub0K in a total volume of 20 μl for 1.5 hours at 30°C. The product was incubated with GST-magnetic beads conjugated with GST-Rpn10 for 40 min at 4°C (
8). After 2× wash with buffer [25 mM Tris-HCl (pH 7.5), 100 mM NaCl, 0.5 mM EDTA, 0.05% Tween-20], the supernatant and bead-bound fraction were assayed for securin using anti-securin antibody by Western blot.
Slide passivation
We followed a basic slide passivation protocol using 5-kD PEG plus 2.5% 5-kD biotin-PEG (LaysanBio, MPEG-SVA-5000; Biotin-PEG-SVA-5000) in a “clouding-point” solution on amino-silanized slides for 4 hours, as described previously (
55,
56). In addition, we passivated them again using 1-kD PEG-NHS (Nacocs, PG1-SC-1k) for 1 hour, followed by 10% (w/v) BSA for 30 min before use. After passivation, slides were assembled into reaction chambers (
55). Streptavidin (0.2 mg/ml) was incubated with passivated slides for 5 min for immobilizing biotinylated substrates. The quality of slide passivation was tested by incubating with HeLa cell extracts supplemented with DyLight 550–Ub and measuring the level of nonspecific binding.
Single-molecule proteasome assay
Purified substrates (200 nM) were ubiquitylated by the APC with 5 μM fluorescent ubiquitin (WT Ub, Ub0K, UbK6A, or UbI44A) for 40 min (60 min for K64–cyclin B) at 30°C. The reaction product was diluted 100× into imaging buffer (UBAB, 3 mM ATP, 40 mM imidazole, 5 mg/ml BSA). Imidazole in the imaging buffer serves to reduce the nonspecific binding of fluorescently labeled proteins.
26S proteasome (15 nM) and biotinylated MCP21 antibody (15 nM) were mixed and incubated at room temperature for 15 min. The proteasome-antibody mix was loaded onto passivated slides coated with streptavidin. After a brief incubation, unbound protein was washed off and replaced with imaging buffer containing diluted ubiquitylation product. Image acquisition was started immediately with <15 s delay.
For experiments involving ATP-γ-S, ATP in imaging buffer was replaced with 2.5 mM ADP plus 0.5 mM ATP-γ-S. For experiments involving ADP, proteasome was incubated in 3 mM ADP buffer. ADP buffer and ubiquitylation product were also incubated with 30 mM glucose and 2 mg/ml hexokinase for 60 min at 30°C to remove residual ATP in the solution. For experiments involving 1,10-phenanthroline, 3 mM phenanthroline was added to the imaging buffer and proteasomal mixture; the sample was incubated for 20 min at room temperature before performing the experiment.
For the SM degradation assay, human cyclin B–NT was engineered with two cysteine residues close to its N and C termini and was labeled with DyLight 550–maleimide. Doubly labeled cyclin B was enriched via anion-exchange chromatography (HiTrap Q HP, pH 8.0). After ubiquitylation with unlabeled WT ubiquitin, 2 nM cyclin B was studied in the SM setup, as described above. Data analysis was identical to that described for the study of deubiquitylation.
We used a Nikon Ti TIRF microscope equipped with three laser lines of 491 nM (27 mW, full output from objective), 561 nM (30 mW), and 640 nm (59 mW), as well as an Andor DU-897 EMCCD camera. Time series were acquired at 200 ms per frame for 2 min, unless indicated.
Single-fluorophore intensity calibration
The fluorescence intensity of a single DyLight 550 molecule on ubiquitin was calibrated through photobleaching preformed ubiquitin chains (
27). Ubiquitin chains were synthesized in a standard E2-25K reaction (see above) containing 30 μM DyLight 550–labeled ubiquitin and 5 μM biotin-ubiquitin in UBAB buffer supplemented with 3 mM ATP, 1 μM E1, and 5 μM E2-25K. The reaction was incubated at 37°C for 16 hours.
The E2-25K reaction product was diluted 10,000× in imaging buffer (above) and loaded on a passivated slide via streptavidin. Photobleaching was observed with the use of a TIRF microscope, illuminated with a laser-intensity level 2.5× higher than that in proteasome experiments (to achieve faster photobleaching).
The uncertainty of measuring ubiquitin stoichiometry is ~30%, as suggested by the standard deviation of the intensity distribution of single fluorescent ubiquitin. This uncertainty is primarily due to uncorrected uneven illumination.
Single-molecule data reproducibility
To test the reproducibility of dwell time data as in fig. S13, the same experiment with slightly varying concentrations (±50%) of ubiquitylated substrates was repeated three times on the same coverslip but at different positions.
Long-term (<1 year) reproducibility tests of the results of binding measurements carry 10 to 20% variation, probably due to batch-to-batch variability of proteasome samples or laser intensity drifts. Therefore, to minimize systematic variation in the measurements, each experiment with its controls was performed on the same slide using the same batch of proteasome and substrates.
Data analysis
The workflow of data analysis is illustrated in fig. S38.
Image processing
Raw images were first corrected for stage drifting after subtracting a uniform-intensity background. Stage drifting was corrected by subtracting the stage motion, which was derived using successive image registration to calculate the shift (step 1 in fig. S38). A custom-built algorithm was applied to identify binding spots of ubiquitylated molecules to the proteasome on the basis of their absolute intensity and local signal-to-noise ratio (step 2 in fig. S38). The spot-identification algorithm is based on finding the local maxima of ubiquitin fluorescence intensity in a field of view by applying a filter requiring the local signal-to-noise ratio to be larger than 6 and no other spots within four pixels around it. In this way, >90% of substrate-binding events can be identified compared with a blind manual identification (fig. S10). The false-positive rate is less than 5%, as shown by the nonsubstrate control, considering that one ubiquitin generates an average of ~20 photons on the camera per frame. After each substrate-binding spot has been recognized in a time lapse, spots are registered along the time axis according to their coordinate to designate substrate-binding events (step 3 in fig. S38). Specifically, if the coordinates of two substrate spots in two consecutive frames are less than or equal to one pixel apart, they are considered to be the same binding event. The absolute intensity of each spot was obtained by fitting the SM diffraction pattern with a two-dimensional Gaussian function, which generates both the signal intensity I(s) and the local background level I(bg) (step 4 in fig. S38). The signal intensity I(s) is then corrected for inhomogeneous illumination (step 5 in fig. S38). Inhomogeneous illumination was corrected by a self-adaptive algorithm that separates the entire field of view into 15-by-15 identical squares and uses the average fluorescent spot intensity in each square as a surrogate for the relative illumination intensity in the center of that square. Because the illumination intensity varies slowly across the field of view, we interpolated the illumination intensity at a given position from the center values in each square. The corrected signal intensity was then converted to absolute ubiquitin numbers by normalizing with the intensity value of a single ubiquitin obtained in the calibration step. The resulting traces were directly used for subsequent analysis or represented in figures, with no further processing.
Dwell-time analysis
A custom-built algorithm was used to measure the duration of substrate-binding events (dwell time), based on the background noise intensity plus a cutoff of 0.7 Ub level. The binding measurement is insensitive to the choice of the cutoff (0.5 to 0.9 Ub) or laser intensity (fig. S14). The maximal fluorescence intensity (converted to the number of ubiquitins using a calibrated single-fluorophore intensity value) during each binding event was measured and plotted versus the dwell time.
Stepped-event identification
A custom-built step-detection algorithm was used to identify stepped events (fig. S39). The formal definition of a stepped event is as follows: If two consecutive drops of fluorescent signal (>0.7 Ub) occur within 5 s, this is designated as a stepped event. Also, it is required that each intermediate state must last longer than one frame. Traces (~80%) can be identified correctly as compared with manual identification. Obvious classification errors were later corrected manually.
For counting the fraction of stepped events, only those events whose ubiquitin number was ≥3 were included in the analysis. We also excluded binding events that lasted longer than 90 s (5 to 10% of total binding events).
The same step-detection algorithm was also used in the analysis of photobleaching traces, to extract single-fluorophore intensity values.
Curve fitting in Fig. 2D
Segments of the curve (indicated in the figure) showing dwell time versus number of ubiquitin relationships were fitted with a linear function or an exponential function. A χ2 test (yi, data point i; , data point on the fitted line; ei, standard error) was performed to obtain the P value for each fitting model.
Photobleaching experiment on ubiquitylated substrates
Biotinylated securin was ubiquitylated by APC using DyLight 550–Ub and was immobilized on passivated coverslips via streptavidin. Time-lapse images were acquired under conditions identical to the SM proteasomal assay, but in the absence of proteasome. The total signal intensity in a central region of the field was analyzed to extract photobleaching information (fig. S26).