The 26S Proteasome utilizes a kinetic gateway to prioritize substrate degradation

Unnatural amino-acid labeling of the proteasome

To deconvolute individual steps of substrate degradation and track the coupled conformational changes of the proteasome, we sought to develop Forster resonance energy transfer (FRET)-based assays sensitive to specific processing events. One requirement for these assays was the ability to site-specifically attach fluorophores to the 19S regulatory particle with minimal perturbations. We thus devised a method for the incorporation and labeling of 4-azido-L-phneylalanine (AzF) in Saccharomyces cerevisiae base and lid sub-complexes using previously established heterologous expression systems (Fig. 1A) (Amiram et al., 2015; Bard and Martin, 2018; Beckwith et al., 2013; Chatterjee et al., 2013; Chin et al., 2002; Lander et al., 2012). To increase the labeling specificity, solvent-exposed cysteines were reversibly protected before reacting the incorporated AzF with a dibenzocyclooctyne-linked fluorophore (van Geel et al., 2012), leading to 50-80% labeling efficiency with minimal off-target reactions (Fig. 1A). Proteasomes reconstituted with these fluorescently labeled base and lid sub-complexes exhibited full activity in substrate degradation (Fig. 1B, Fig. S1A).

Tracking the Conformational State of the Proteasome

Published cryo-EM structures of the 26S proteasome revealed major conformational changes between the substrate-free and substrate-processing states, yet it remains unclear how these transitions are coupled to specific degradation steps. We identified the lid subunit Rpn9 and the N-terminal coiled-coil of the base subunits Rpt4 and Rpt5 as promising positions for the placement of a donor-acceptor pair to directly monitor the proteasome conformational dynamics through FRET (Fig. 1C). As the lid rotates relative to the base during the transition to a substrate-engaged state, the distance between Rpn9 and the N-terminal helix of Rpt5 decreases by almost 40 A, and we predicted that the FRET efficiency for fluorophores at these positions would increase accordingly.

Proteasomes were thus reconstituted using lid with donor-labeled Rpn9-S111AzF and base with acceptor-labeled Rpt5-Q49AzF, and bulk FRET efficiencies were measured under steady-state conditions (Fig. 1D). Incubation with the non-hydrolyzable nucleotide analog ATPγS has previously been shown to induce the substrate engaged-like s3 state (Sledz et al., 2013), and it correspondingly caused a significant increase in FRET compared to proteasome in ATP (Fig. 1D). Interaction with ubiquitin-bound Ubp6 has also been found to shift the conformational equilibrium towards the substrate-engaged state (Aufderheide et al., 2015; Bashore et al., 2015), which was confirmed by our assay showing an increase in FRET efficiency when catalytically inactive Ubp6 was added together with tetra-ubiquitin. There was no change in FRET, however, upon addition of 100 μM unanchored ubiquitin chains. Despite binding to proteasomal receptors, as indicated by their inhibition of substrate degradation (Fig. S1B), these unanchored chains hence do not induce a conformational change of the proteasome.

We then measured the FRET signal of actively degrading proteasomes and observed an increase similar to that of proteasomes trapped in the s3 state by ATPγS. The signal increased further upon addition of ubiquitinated substrate in the presence of 1,10-phenanthroline (oPA), an inhibitor of the deubiquitinating enzyme Rpn11 (Verma et al., 2002). Preventing Rpn11-mediated deubiquitination inhibits degradation by stalling substrate translocation through the central channel, most likely when the attached ubiquitin chain reaches the narrow entrance to the N-ring pore, thus trapping and synchronizing proteasomes in a substrate engaged state (Worden et al., 2017). We conclude that actively processing proteasomes spend most of the time in an s3-like conformation.

Rapid substrate engagement induces the proteasome conformational switch

While the steady-state FRET-based assay confirmed that actively degrading proteasomes switch away from the s1 state, it provided no information about when this switch occurs. To determine the relationship between the conformational change and specific processing steps, and to gain insight into the overall coordination of substrate degradation, we developed a series of fluorescence-based assays for measuring detailed kinetics (Fig. 2).

Our model substrate, titin-I27^V15P-23-K-35, was constructed from a titin-I27 domain containing the destabilizing V15P mutation and a C-terminal unstructured region with a single lysine for ubiquitin-chain attachment in a defined position, leaving a 35-residue ‘tail’ for proteasome engagement (Fig. S1C) (Bashore et al., 2015; Saeki et al., 2005). The time required for degradation of this substrate was determined by tracking the anisotropy of a fluorophore attached to the N-terminus of the titin folded domain (Bhattacharyya et al., 2016). Gel-based assays confirmed the rapid degradation into peptides (Fig. 2B), and Michaelis-Menten analyses established the substrate affinity (K_M = 0.22 μM) and degradation rate (kcat = 2.34 sub enz⁻¹ min⁻¹) under multiple-turnover, steady-state conditions (Fig. S1D). In subsequent single-turnover degradation experiments with saturating concentrations of proteasome, we observed an initial fast increase in anisotropy, followed by a second increase and an exponential signal decay (Fig. 2C, Fig. S2A, Table S3). The observed two-step increase in signal is characteristic of multiple sequential kinetic processes. When the substrate was mixed with proteasomes containing the catalytically dead Rpn11^AXA mutant, the anisotropy signal also rapidly increased, but did neither show the second increase nor the exponential decay (Fig. S2A). Mixing with ATPγS-bound wild-type proteasomes led to no change in signal at all (Fig. 2C). The initial anisotropy increase is thus likely a result of ATP hydrolysis-dependent substrate engagement by the AAA+ motor, whereas the second, deubiquitination-dependent increase may report on the reduced substrate flexibility upon ubiquitin-chain removal and pulling of the folded domain against the motor entrance. The signal decay then reflects the mechanical unfolding, translocation, and cleavage of the substrate into small peptides. This decay (and all kinetic traces later measured for individual substrate-processing steps) fit best to a double exponential curve, consisting of a dominant fast phase and a low-amplitude slow phase. Since the slow-phase likely originates from a small population of partially aggregated or incompletely ubiquitinated substrate, we focused our analyses on the fast phase, as done in previous studies (Beckwith et al., 2013; Worden et al., 2017). Combining the time constant for the exponential decay in anisotropy (τ = 11 s) and the delay associated with the initial increase (to = 7 s) reveals that complete degradation of our titin model substrate occurs with a time constant of 18 s. The first step of substrate processing after ubiquitin binding requires the insertion of the unstructured initiation region into the pore of the proteasomal motor (Peth et al., 2010). We specifically tracked the kinetics of this tail-insertion process using a FRET-based assay that relied on the energy transfer between a donor fluorophore placed near the central channel of the motor, in the linker between the N-domain and the ATPase domain of Rpt1 (Rtp1-I191AzF), and an acceptor fluorophore attached to the substrate’s initiation tail (Fig. 2D, Table S4). To kinetically isolate tail-insertion from subsequent steps of substrate processing, we treated the proteasome with oPA, thereby preventing progression past the ubiquitin-modified lysine and trapping the proteasome with the inserted substrate in a high-FRET state. After stopped-flow mixing of acceptor-labeled substrate and donor-labeled, oPA-treated proteasome, we observed a rapid increase in FRET, as indicated by the quenching of donor fluorescence and the reciprocal increase in acceptor fluorescence (Fig. S2B), revealing a time constant of 1.6 s (Fig. 2D). Since ubiquitin binding to the proteasome was found to occur significantly faster, with τ ~ 0.4 s based on previous single-molecule measurements (Lu et al., 2015), we can conclude that the 1.6 s time constant is largely determined by substrate-tail insertion after ubiquitin interaction with a proteasomal receptor. Tail insertion thus occurred on a similar time scale as the change in anisotropy seen upon substrate mixing with Rpn11^AXA-containing proteasome (Fig. S2C). We confirmed that the fluorophore on the unstructured initiation region had no major effects on the degradation rate (Table S3), and no signal change was observed when mixing proteasome with substrate lacking a ubiquitin chain (Fig. 2D). Tail insertion was also prevented in the ATPγS-induced s3 state of the proteasome (Fig. 2D), in which the centrally positioned Rpn11 potentially obstructs access to the central pore.

We next measured the kinetics of conformational switching after substrate addition to Rpn11-inhibited proteasomes, using the above-mentioned FRET-based assay that tracks the relative distance between the base and lid sub-complexes (Fig. 2E, Table S5). Because binding of unanchored ubiquitin chains alone had no effect on the conformational state of the proteasome, we hypothesized that engagement of the substrate’s unstructured region with the pore loops of the AAA+ motor is required to trigger the switch. Indeed, upon mixing proteasome with substrate, the acceptor fluorescence increased with a time constant of 2.2 s, closely tracking with the tail insertion event. A reciprocal signal change was observed in the donor channel, confirming the underlying FRET (Fig. S2D). Examination of early time points revealed that the FRET signal for substrate tail insertion increased immediately after mixing, whereas the signal for the conformational switch showed a 0.4 s delay (Fig. 2F). The delay indicates that the substrate tail is inserted first. Subsequent interactions with the motor pore-loops then lead to a rapid switch of the proteasome from the si to a substrate-engaged, s3-like state. This model is supported by our previous studies showing that the pore-loops of Rpt subunits at the top of the sl-state spiral staircase are particularly important for degradation, as they may make first contact with a substrate (Beckwith et al., 2013).

After substrate engagement, the proteasome must remove attached ubiquitin chains before proceeding to unfold and translocate the rest of the polypeptide. Therefore, a final FRET-based assay was designed to selectively monitor the deubiquitination event, this time by tracking the energy transfer between donor-labeled ubiquitin and an acceptor fluorophore attached to the substrate adjacent to the ubiquitinated lysine. Co-translocational ubiquitin removal from the substrate caused a loss in acceptor fluorescence, while pre-incubation of proteasomes with ATPγS abolished the signal change (Fig. 2G, Fig. S2E). Stopped-flow measurements of the FRET signal upon mixing substrate with saturating amounts of wild-type proteasome in the presence of ATP revealed that deubiquitination occurs with a total time constant of 6.8 s (Table S6), which reflects the sum of the time required for binding, tail insertion, and deubiquitination. This time constant also encompasses ubiquitin-chain release from the proteasome (which is expected to occur in less than 0.5 s, see below) or the time for translocation of the substrate polypeptide beyond the zone of FRET (which happens with a rate of at least 15 AA s⁻¹, see below). Mixing of the substrate with Rpn11^AXA-containing proteasome led to a more than 2-fold lower signal change that is likely caused by a change in fluorophore environment when ubiquitin binds to the catalytically-dead Rpn11 (Fig. S2F).

By comparing the various time constants described above, we can derive the first complete kinetic model of proteasomal substrate processing and estimate the time required for each step following substrate binding (Fig. 2H). Initial tail insertion proceeds with a time constant of 1.6 s, followed by a rapid conformational switch after 0.4 s. The removal of the ubiquitin chain then happens within ~ 5 s, and mechanical substrate unfolding, translocation, and cleavage take an additional 11 s.

The proteasome can quickly remove multiple ubiquitin chains, but is slowed down by stable domains

Our kinetic characterization revealed that most of the substrate processing time is spent on deubiquitination and unfolding or translocation. To further probe the relative contributions of these steps to overall degradation time, we modified our model substrate, either by changing the stability of the folded domain (Fig. 3A,B, Fig. S3) or by increasing the number of ubiquitin chains that need to be removed during degradation (Fig. 3C, Fig. S4).

The experiments shown in Fig. 2 were performed with titin-I27^V15P-23-K-35, which has a thermodynamic stability of DG = −19 kJ mol⁻¹ (Fig. S3). Based on previously reported mutants of titin-I27 (Kenniston et al., 2003), we constructed and measured the degradation of a further destabilized variant, titin-I27^V13P/V15P-23-K-35 (DG = −8 kJ mol⁻¹), as well as the wild-type version, titin-I27-23-K-35 (DG = −24 kJ mol⁻¹). As seen for other substrates (Johnston et al., 1995; Kraut et al., 2012; Peth et al., 2013), increasing the stability of the folded titin domain significantly increased the overall time required for degradation. Analysis by SDS-PAGE showed that the most stable titin variant is rapidly deubiquitinated and then slowly unfolded and degraded (Fig. 3B). Hence, the unfolding event itself is the rate-limiting step of degradation for this substrate, which remains stably engaged after ubiquitin-chain removal and while the proteasome attempts to overcome the tough unfolding barrier. The less stable titin variants exhibited no accumulation of the deubiquitinated species on the proteasome, indicating that unfolding and deubiquitination occur on similar time scales for these substrates. Interestingly, the stability of the titin variants correlated with their ability to stimulate proteasomal ATP hydrolysis. The most stable substrate (titin-I27-23-K-35) showed the strongest stimulatory effect (Table S7), most likely because its slow unfolding caused the proteasome to spend the least time in the non-stimulated, substrate-free state during degradation under saturating conditions. The least stable titin-I27^V13P/15P variant was degraded with a total time constant of 15 s. Considering that all initial processing steps, including deubiquitination, take 6.8 seconds, and assuming rapid subsequent unfolding of the destabilized titin domain, we can estimate a minimum translocation rate of 15 AA s⁻¹ for the 116 amino acids that remain to be threaded after unfolding.

To test the effects of additional ubiquitin chains on substrate degradation, we added a second or third lysine into the unstructured tail of our model substrate. The modification of all three lysine was confirmed by SDS-PAGE after ubiquitination with methyl-ubiquitin (Fig. S4A,B) or by trimming poly-ubiquitin chains with the deubiquitinase AMSH (Fig. S4C), which does not remove the substrate-attached ubiquitin moiety (Michel et al., 2015). Michaelis-Menten analyses showed that substrates with one, two, or three ubiquitin chains have similar binding affinities and degradation rates (Fig. S1). Importantly, all three substrates also showed no difference in degradation rate under single-turnover conditions (Fig. 3C), suggesting that while the removal of the first ubiquitin chain takes 5 seconds, subsequent chains must be removed much more quickly. One model for this change in deubiquitination rate comes from our previous findings that the rate-limiting step of isopeptide cleavage by Rpn11 is a ubiquitin-induced conformational switch of its Insert-1 region (Worden et al., 2017). We propose that after Rpn11 removes the first ubiquitin chain, it does not immediately switch back to the inactive conformation, but is poised to bind and promote fast cleavage of nearby ubiquitin chains that rapidly approach Rpn11 as the substrate is translocated into the central pore.

Substrates with poor initiation regions fail to engage with the proteasome

It has been established that substrates with short (< 25 residues) or low-complexity initiation regions are not efficiently degraded in vitro and have extended in vivo half-lives (Fishbain et al., 2015; Fishbain et al., 2011; Inobe et al., 2011; Prakash et al., 2004; Yu et al., 2016). To investigate this phenomenon, we modified the initiation region of our model substrate by varying the length of the terminal tail following the single ubiquitinated lysine or by replacing it with a low complexity, serine-rich sequence previously shown to severely impair degradation (Fishbain et al., 2011; Yu et al., 2016). Tracking proteasomal processing by SDS-PAGE revealed that substrates with a 35 or 25 AA tail were completely degraded into peptides, whereas the truncated tail variants with 11 or 1 AA were primarily deubiquitinated and released (Fig 4A, Fig. S5). Deubiquitination and release of the short-tail substrates could be monitored by the decrease in anisotropy, albeit with a smaller amplitude than for complete proteolysis into peptides (Fig. S6A,B). Using this anisotropy readout in multiple-turnover titrations revealed that the short tails cause significant K_M defects for titin-I27^V15P-23-K-11 (K_M = 1.2 μM) and titin-I27^V15P-23-K-1 (Km = 2.7 μM), compared to titin-I27^V15P-23-K-35 (Km = 0.2 μM) (Fig. S1, Fig. S6D,E).

We then analyzed the kinetics of tail insertion through increase of FRET between donor labeled, Rpn11-inhibited proteasome and acceptor-labeled substrate, as in Fig. 2D (Fig. 4B, Table 1). Shorter tails appeared to enter the central pore more rapidly, yet their FRET amplitude was severely reduced, with 11 and 1 AA tails showing only 25% and 16%, respectively, of the signal change detected for the 35-residue tail. These low amplitudes are most likely a consequence of the truncated tails being too short to reach from the narrow N-ring entrance to the pore loops, thus preventing a stable engagement with the AAA+ motor. After initial rapid insertion, these tails may quickly escape again from the central channel, which is consistent with the observed increase in the apparent rate constants for short tail insertion, k_app, that reflects the sum of both, on and off rates (Table 1). The elevated off rates lead to an increase in K_M for the processing of short-tailed substrates under multiple-turnover conditions, even though their ubiquitin targeting signal is unchanged (Fig. S6E). Based on the affinity for the 1-AA tail variant (K_m = 2.7 μM) and the previously determined on-rate for ubiquitin binding to the proteasome (8.5 10⁵ M ¹ s⁻¹, (Lu et al., 2015), we can approximate k_of ~ 2.3 s⁻¹ for the dissociation of tailless substrates or unanchored ubiquitin chains after Rpn11 cleavage.

Though short tails insert, at least briefly, into the pore of the motor, we found that substrates with those truncated initiation regions fail to trigger the conformational change of the proteasome (Fig. 4C). In contrast to the small amplitude and fast kinetics we observed for the tail-insertion traces, the conformational change traces for truncated tails exhibited almost no amplitude, supporting our model that interactions between the substrate polypeptide and the motor’s pore loops drive the switch in proteasome conformation. These data also confirm our results presented in Fig. 1D that binding of unanchored ubiquitin chains to proteasomal receptors does not induce the conformational change.

Despite their failure to engage and trigger proteasome conformational switching, shorttailed substrates are slowly deubiquitinated (Fig. 4A). The loss of anisotropy during the multiple-turnover processing of the 1 AA tail substrate (Fig. S6E) reveals a time constant of 45 s for this engagement-independent deubiquitination, which is significantly slower than the 6.8 s observed for translocation-coupled deubiquitination of the long-tailed substrate (Fig. 2G). The almost 7-fold difference in deubiquitination rate agrees well with the previously revealed acceleration of Rpn11-mediated ubiquitin cleavage by mechanical substrate translocation into the AAA+ motor (Worden et al., 2017). Since short-tailed substrates fail to induce the conformational switch of the proteasome, their slow deubiquitination likely occurs while the proteasome is in the s1 state or during brief, spontaneous sampling of s3-like conformation.

Like the short tails, the low complexity serine-rich tail also led to a significant KM defect in multiple-turnover processing and exhibited a decreased FRET amplitude for tail insertion (Fig. S6E, Fig. 4B). In contrast to the short tails, however, it also showed slower tail-insertion kinetics, with a kapp four times lower than that of a complex tail of the same length. Thus, in addition to having an elevated ratio of koff/kon (and therefore KM), the on-rate of the serine-rich tail is decreased. The conformational change induced by this substrate was also slow and of a low magnitude, with the defects again being amplified compared to those measured in tail insertion. Both the tail-insertion and conformational change assays rely on a stalled state, with the substrate’s initiation region stably engaged by the AAA+ motor. The small FRET-signal amplitudes for the serine-rich tail thus indicate a rapid substrate escape from the proteasome pore and a consequent low probability of commitment, explaining the observed slow degradation and frequent release (Fig. 4A). Low-complexity regions thus hinder substrate processing in several ways: by slowing the onset of tail insertion, inhibiting the conformational change, and likely by reducing the motor grip required for unfolding and translocation.

How are proteasomes in vivo able to rapidly turn over high priority substrates, such as cell-cycle regulators, while ubiquitinated proteins with poor initiation regions and therefore slow processing kinetics compete for proteasomal ubiquitin receptors? To test this scenario in vitro, we performed competition experiments, in which the degradation of a fluorescently labeled, ubiquitinated titin-I27^V15P-23-K-35 substrate was tracked in the presence of unlabeled ubiquitinated substrates with varying tail architectures (Fig. 4D). While the unlabeled titin-I27^V15P-23-K-35 effectively inhibited degradation of its labeled counterpart, substrates with short or serine-rich initiation regions were poor competitors, even at concentrations above their measured KM values. Conversely, the long-tailed substrate effectively prevented the slow deubiquitination of substrates with poor initiation regions (Fig. S6C). These results can be explained by the high off rates and poor engagement of short or low-complexity tails with the ATPase motor. Their inability to compete also suggests that the ubiquitin-chain interactions with receptors on the proteasome is short lived. In contrast to these ‘poor’ substrates that do not prevent the proteasome from degrading other targets, non-degradable substrates such as amyloid-like fibers have been shown to recruit and stall proteasomes (Bauerlein et al., 2017), likely by efficiently engaging with the AAA+ motor but then resisting mechanical unfolding.

Substrates with ubiquitin-obstructed initiation regions depend on additional ubiquitin chains for degradation

The titin-I27^V15P-23-K-11 substrate described above contains a 11 AA tail C-terminal to the lysine-attached ubiquitin chain, and slow deubiquitination during proteasomal processing creates a 35-residue unstructured region that would otherwise be sufficient for processive degradation. Nevertheless, this substrate largely escapes degradation, likely because the flexible initiation region is not stably engaged with the AAA+ motor when the single, affinity-conferring ubiquitin chain is removed. In contrast to this model substrate, many proteins in the cell are modified with multiple ubiquitin chains, which has been shown to increase substrate affinity for the proteasome (Lu et al., 2015; Shabek et al., 2012). We therefore wondered whether the translocation-independent removal of ubiquitin chains obstructing flexible initiation regions could enable complete substrate degradation, provided that an additional ubiquitin modification maintains the substrate’s affinity for the proteasome during subsequent engagement. We tested this hypothesis by using SDS-PAGE to compare the proteasomal processing of an obstructed, short-tailed titin-I27^V15P-43-K-11 substrate with that of its double-lysine variant, titin-I27^V15P-23-K-19-K-11, containing an extra site for ubiquitin modification (Fig. 5). The presence of the second ubiquitin chain decreased the K_M from 2 μM to 1 μM (Fig. S6E), which is in contrast to the long-tailed substrates whose proteasome affinity is already high with a single ubiquitin chain and changes only minimally upon attachment of additional chains (Fig. S1D). Adding a second ubiquitin chain on the short-tailed substrate did not increase the velocity of processing, as titin-I27^V15P-43-K-11 and titin-I27^V15P-23-K-19-K-11 showed similar time constants (if_ast = 46 s ± 13 s) for the disappearance of ubiquitinated species (Table S8). For both substrates, slow, translocation-independent ubiquitin removal by Rpn11 appears to be rate-limiting and the first step of substrate processing. However, while titin-I27^V15P-43-K-11 was primarily deubiquitinated and released from the proteasome, titin-I27^V15P-23-K-19-K-11 was mostly degraded, as indicated by considerably stronger formation of peptide products and less accumulation of deubiquitinated protein (Fig. 5). These findings suggest that slow deubiquitination can make substrates with ubiquitin-obstructed initiation regions accessible for degradation, if additional ubiquitin chains keep the substrates associated with the proteasome. Accessory factors that modify the ubiquitination state of proteasome-bound substrates, such as Ubp6 and Hul5, may further act in concert with the proteasome’s intrinsic mechanisms described here (Crosas et al., 2006).

CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Andreas Martin (a.martin@berkeley.edu).

EXPERIMENTAL MODEL AND SUBJECT DETAILS

All proteins, except for the 20S core particle, were expressed in Escherichia coli using T7 expression vectors. The genes for all yeast proteins were cloned from Saccharomyces cerevisiae strain S288C. Usp2 and SENP2 are derived from H. sapiens, AMSH and Uba1 from M. musculus, sortase A from S. aureus, and all other genes are artificial. The Bl21-star(DE3) or Rosetta2(DE3)pLysS E. coli strains were used for protein expression as indicated for each protein. Cultures were grown in 2.5 L Ultra-Yield flasks (Thomson Instrument Company Cat#931136-B) shaking at 180 rpm at 37 °C. Induction times and temperatures are noted for individual proteins.

The 20S core particle was purified from the S. cerevisiae strain yAM54 (see below). Cultures were grown in YPD (Yeast extract, Peptone, and Dextrose) in 2.5 L Ultra-Yield flasks at 30 °C for 2 - 3 days harvested by resuspension in lysis buffer (see below) and popcorned into liquid nitrogen.

METHOD DETAILS

QUANTIFICATION AND STATISTICAL ANALYSIS

All curve fitting was done using Origin (Originlab, Northampton, MA) while plotting was done using Graphpad Prism. The fits were performed by least squares fitting, and visually evaluated by the distribution of the residuals to ensure there were no significant deviations from zero. For Michaelis Menten calculations, the initial rates from substrate degradation or deubiquitination experiments were fit to the Michaelis-Menten equation to determine kcat and KM. Exponential curves from single-turnover measurements were fit to either a double exponential increase/decay (y=y₀ + A₁*e^−t/τ1 + A₂*e^−t/τ2) or a delayed double exponential increase/decay (y=y₀ + A₁*e^{−(t−t0)/τ1} + A₂*e^{−(t−t0)/τ2}), in which the delay was determined by visual inspection of the curves. In general, the fluorescence channel with the largest signal change was used for fitting and representative traces. Some curves were smoothened by the Savitsky-Golay method for visualization, but all data analysis was done on the raw traces. The plotted curves were normalized to the initial fluorescence value for each trace.

The slow phase of the double exponential fit was not used in the analyses, because it is thought to arise from a small population of partially aggregated or incompletely ubiquitinated substrate. In support of this, the fast phase of the single-turnover degradation kinetics match well with the kcat values measured in multiple turnover. The time constants for both phases and their relative distribution of amplitudes are reported in Tables S3–S8.

The stability measurements (Figure S3) were fit to the following system of equations: y=(A+B*k)/(1+k); A=A₀+m_A*[urea]; B=B₀+m_B*[urea]; k=e^(−ΔG(RT); AG= m*(c_m-[urea]) All variables were fit globally across the three substrates, except for the cm values. The AG0 was then calculated using the equation AG₀= m*c_m.

The quantification in Figure 5 was done using Imagequant TL (GE), with each gel being internally normalized as noted before calculating the mean. All of the individual data points were used in the curve fitting of the ubiquitinated species. Because the titin-43-K-35 substrates gets degraded so quickly it was not possible to fit the data to a double exponential and thus a single exponential was used.

The number of technical replicates (N) and the relevant statistical parameters for each experiment (such as mean or s.d.) are described in the figure captions. Tables S3–S8 also report the mean and s.d. for all technical replicates performed. Occasionally, curves which were visually identified as large outliers were excluded from the analysis. No statistical methods were used to verify that the data met the assumptions of the statistical approach.