Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome

Human ubiquitin C-terminal hydrolyase UCH-L5 is a topologically knotted deubiquitinase that is activated upon binding to the proteasome subunit Rpn13. The length of its intrinsically disordered cross-over loop is essential for substrate recognition. Here, we showed that the catalytic domain of UCH-L5 exhibits higher equilibrium folding stability with an unfolding rate on the scale of 10−8 s−1, over four orders of magnitudes slower than its paralogs, namely UCH-L1 and -L3, which have shorter cross-over loops. NMR relaxation dynamics analysis confirmed the intrinsic disorder of the cross-over loop. Hydrogen deuterium exchange analysis further revealed a positive correlation between the length of the cross-over loop and the degree of local fluctuations, despite UCH-L5 being thermodynamically and kinetically more stable than the shorter UCHs. Considering the role of UCH-L5 in removing K48-linked ubiquitin to prevent proteasomal degradation of ubiquitinated substrates, our findings offered mechanistic insights into the evolution of UCH-L5. Compared to its paralogs, it is entropically stabilized to withstand mechanical unfolding by the proteasome while maintaining structural plasticity. It can therefore accommodate a broad range of substrate geometries at the cost of unfavourable entropic loss.


Results
Folding equilibrium of UCH-L5 N240 monitored by intrinsic fluorescence and far-UV CD spectroscopy. To compare the folding stability of UCH-L5 N240 with that of UCH-L1 33 and -L3 27 , we analysed its chemical stability by urea-induced equilibrium unfolding analysis through intrinsic fluorescence and far-UV CD spectroscopy. UCH-L5 N240 has four tryptophan residues that are strategically distributed in the backbone topology that serve as ideal structural probes (Fig. 1). W8 and W36 are in proximity to the N-and C-termini that are involved in knot formation. W58 is adjacent to the catalytic site, encompassing C88, H164, and D179. W196 is located at the turn between β 5 and the longest helix, α 7. SVD analyses of the intrinsic fluorescence spectra of UCH-L5 N240 as a function of urea concentration indicate that UCH-L5 N240 unfolds in a two-state fashion without significant contribution from folding intermediates as in the case for UCH-L1 (Fig. 2). This is further confirmed by far-UV CD spectroscopy that monitors changes in secondary structures. The intrinsic fluorescence and far-UV CD unfolding data were global-fit to a two-state model ( Table 1). The free energy of unfolding of UCH-L5 N240 (9.21 ± 0.39 kcal mol −1 ) is higher than that of UCH-L1 (8.83 ± 0.10 kcal mol −1 ) 33 and UCH-L3 (7.11 ± 0.20 kcal mol −1 ) 27 , and the transition point of UCH-L5 N240 , [D] N-D,50% , is about 0.5 M higher than those of UCH-L1 and -L3 with comparable m-values (Table 1).
Folding kinetics of UCH-L5 N240 . We next evaluated the folding kinetics of UCH-L5 N240 in comparison with those of UCH-L1 and -L3 27,28 . Single-jump (SJ) stopped-flow fluorescence measurements of UCH-L5 N240 as a function of urea concentration yielded four linear refolding arms that we assigned as phases 1, 2, 3, and 4, corresponding to the slowest to the fastest kinetic phases, respectively. The slowest refolding phase 1 has the largest amplitude (A 1 ), indicating its association with global folding events (Fig. 3). In the case of unfolding kinetics, we only observed three linear unfolding arms that correspond to the kinetic phases 2-4 because the kinetics of Scientific RepoRts | 7:45174 | DOI: 10.1038/srep45174 phase 1 is too slow to be reliably measured by the stopped-flow mixing device. We therefore used manual mixing followed by far-UV CD measurements (Supplementary Results) to extract two unfolding kinetic phases, with the faster one being consistent with the kinetic phase 2 up to 4.4 M urea; above 4.4 M urea, the kinetic CD traces were fit to a single exponential function due to the limited time resolution to resolve the contribution of the faster kinetic phase. The slower kinetic phase observed in the CD measurements was then associated with unfolding phase 1 (open black circles in Fig. 3a).
By fitting to a two-state model, we obtained four refolding rates and four unfolding rates associated with the four kinetic phases. The fastest and slowest refolding rates were separated by four orders of magnitude, and the fastest and slowest unfolding rates were separated by six orders of magnitude, reflecting a very large dynamic range for the different folding events (Table 2). Amongst the four kinetic phases, the kinetic m-value (m kin ) and the associated free energy of unfolding of the phase 1 are essentially the same as those derived from equilibrium unfolding (Table 1), while the values for the other three kinetic phases are markedly smaller, suggesting that phase 1 is the dominant term that gives rise to the observed spectral changes in the equilibrium unfolding measurements. In other words, phase 1 reflects the unfolding of the native state (N) into one of the intermediates. Indeed, CD-derived A 1 associated with unfolding phase 1 is much larger than those of the second slowest phase (Supplementary Results); likewise, SJ fluorescence-derived A 2 is 4-10 times larger than A 3 and A 4 (Fig. 3b).
To compare the folding kinetics of UCH-L1, -L3, and -L5 N240 , we repeated the SJ stopped-flow fluorescence measurements for UCH-L1 and -L3 under the same experimental conditions and focused on the slowest and the most dominant kinetic phases to compare with that of UCH-L5 N240 (Fig. 3c and Table 3). While the m-values associated with the refolding arms of UCHs are similar, the m-value associated with the unfolding arm of UCH-L5 N240 is about twice that of UCH-L1 and -L3, resulting in a much slower unfolding rate in water (k u H O 2 = 8.1 * 10 −9 s −1 ) that is five and four orders of magnitude slower than those of UCH-L1 and -L3. The folding rate of UCH-L5 N240 in water (k f H O 2 = 0.14 s −1 ) is comparable with that of UCHL1 and is about 100 times slower than that of UCH-L3.
In an effort to establish the relationships between the four kinetic phases in the context of folding pathways, we used double-jump (DJ) interrupted refolding fluorescence analyses to obtain additional refolding rates through global fitting of the kinetic traces obtained with different aging times (t age ) in the presence of different urea concentrations (open blue circles for k 3 and open green triangles for k 4 in Fig. 3a). Unlike UCH-L1 and -L3, however, amplitude analyses of the kinetic phases 3 and 4 of UCH-L5 N240 as a function of the aging time (t age ) can be best fit to a linear three-state reaction with the microscopic forward and back reaction rates extracted through global fitting, although the results are noisy and a lag phase in the amplitude build up of the second fastest phase is barely visible. The results therefore suggest the presence of transiently populated intermediate corresponds to the fastest kinetic phase of UCH-L5 N240 (Supplementary Results). Completion of the kinetic folding pathway of UCH-L5 N240 for direct comparison with those of UCH-L1 and -L3 will require better instrument stability for kinetic measurements with a timescale that spans over five orders of magnitudes (Fig. 3a). . UCH-L5 N240 is colour-ramped from blue to red from the N-to C-termini and ubiquitin is coloured grey with its C-terminus shown in grey sticks. The side-chain atoms of the catalytic residues are shown in spheres with carbon, nitrogen, oxygen and sulphur atoms shown in white, blue, red and yellow, respectively, and their identities indicated accordingly. The tryptophan side-chains are shown in semi-transparent spheres. The cross-over loop was illdefined due to its flexibility and is indicated in dashed gold line. (B) Topological representation of UCH-L5 N240 illustrating the distribution of the tryptophan residues. The colouring scheme is the same as in (A). α -helices and β -strands are shown in rectangular and arrows, respectively.
Scientific RepoRts | 7:45174 | DOI: 10.1038/srep45174 NMR HDX reveals abundant local backbone fluctuations in UCH-L5 N240 . Having established the slow global folding kinetics of UCH-L5 N240 , we sought to obtain further structural insights into the origin of stability by solution state NMR spectroscopy. We first obtained near complete assignments of the fingerprint backbone 15 N-1 H HSQC spectrum of UCH-L5 N240 , which display highly dispersed cross-peaks corresponding to a well-folded structure, while a group of poorly dispersed cross-peaks with very strong intensities are ascribed to the highly disordered cross-over loop (residues 150-160) and the C-terminal extension beyond the UCH domain (residues 230-240) for which we did not have complete assignments (Supplementary Results). The structural disorder in the cross-over loop, the flanking residues, and the C-terminal region was confirmed by their low order parameters (S 2 ) reflecting fast local motions on the ps to ns timescale (Supplementary Results). This timescale however, is more than six orders of magnitudes faster than the fluorescence-based kinetics of UCH-L5 N240 . We    therefore resorted to NMR hydrogen-deuterium exchange (HDX) analysis to probe molecular dynamics on a much slower timescale by determining the rate of HDX for a specific amide group and comparing it with the expected value for a random coil to derive the corresponding PF that reflects the stability of the corresponding hydrogen bond (see Material and Methods) 34 .
Contrary to expectations of a slower HDX of UCH-L5 N240 compared to UCH-L1 and -L3 based on the fluorescence-based equilibrium and kinetic data (Tables 1 and 2), UCH-L5 N240 exhibits significantly lower PF values, i.e., faster HDX, throughout its backbone amide groups compared to those of UCH-L1 and -L3 (Fig. 4). For instance, α -helix 3 of UCH-L1, which is packed against the central β -sheet as part of the hydrophobic core, is highly protected against HDX, and the C-terminal half of α -helix 3 of UCH-L3 exhibits partial protection against HDX; in contrast, α -helix 3 of UCH-L5 N240 shows negligible protection against HDX. Likewise, the PFs of the central β -sheet are higher for UCH-L1 than UCH-L3, both of which are higher than the minimal HDX protections of UCH-L5 N240 . In line with the crystallographic findings that indicated highly disordered structures in α -helix 6 for UCH-L3 and α -helix 2 for UCH-L5 N240 , we did not observe appreciable PF for any of the residues within these regions (shown in dashed lines in the top panel of Fig. 4). Consistent with our recent finding of the PUFs of UCH-L1 under native conditions, our current data on UCH-L3 and UCH-L5 N240 suggest the presence of highly populated PUFs as well: the degree of fluctuations for UCH-L5 N240 is much higher than that of UCH-L3, and even more so than that of UCH-L1, indicating a high degree of conformational plasticity for UCH-L5 N240 (Supplementary Results).
Thermodynamics associated with ubiquitin binding to UCH variants. Earlier studies on the enzyme kinetics of UCH-L1, -L3 and -L5 N240 have established that both UCHs bind to ubiquitin with sub μ M K M values [16][17][18][19]35,36 . While UCH-L1 exhibits higher binding affinity for ubiquitin compared to that of UCH-L3, its hydrolysis turnover rate (k cat ) is about two orders of magnitude slower than that of UCH-L3. We repeated and confirmed the previously reported parameters for UCH-L1, -L3, and -L5 N240 (Supplementary Results). Although the reported values have a rather broad range of distributions and our k cat value is at the higher end, the overall k cat /K M ratios are similar across different reports.
Having established that our recombinant UCHs are enzymatically active, we subsequently carried out isothermal titration calorimetry at four different temperatures (20,25,30, and 37 °C) to gain further insights into the ubiquitin binding process (Supplementary Results). For UCH-L1 and -L3, their binding affinities are not sensitive to temperature changes but the enthalpic contributions are clearly more favourable upon increasing temperature. For UCH-L1, the entropic contributions are favourable up to 30 °C and become unfavourable at body temperature, 37 °C. In contrast, for UCH-L3, the entropic contributions become unfavourable at 25 °C. ITC analysis is only applicable to UCH-L1 and -L3 due to the poor ubiquitin binding affinity of UCH-L5; the binding affinity between UCH-L5 and ubiquitin could only be determined by ITC in the presence of Rpn13 6 . Indeed, the addition of 1.2 molar equivalent of ubiquitin slightly increased the thermal stability of UCH-L1 and -L3, raising the melting temperature by 2.2 ± 0.1 °C and 0.9 ± 0.2 °C, respectively, while no significant change in thermal stability was observed for UCH-L5 N240 (Supplementary Results). The lack of significant thermal stability shift in UCH-L5 N240 upon the addition of its substrate is consistent with the expectation for weaker binding events 37 . As the CD melting analyses were carried out with only 5 μ M protein concentration, the addition of equal molar concentration of ubiquitin may not be sufficient to saturate UCH-L5 N240 . Even after the addition of six-fold higher amount of ubiquitin (30 μ M), we did not observe appreciable changes in melting temperature (data not shown).
0.14 ± 0.03 0.80 ± 0.14 10.3 ± 1.8 1120 ± 740  Table 2. Kinetic parameters of UCH-L5 N240 derived from stopped-flow fluorescence measurements.   Despite our inability to obtain a stable binary complex of UCH-L5 N240 and ubiquitin in solution, we focused on the global analysis of the variable temperature ITC data to extract the heat capacity Δ C p in addition to the enthalpy, entropy, and thus free energy associated with ubiquitin binding for the UCH-L1 and -L3 in order to extrapolate the findings to correlate with potential characteristics of ubiquitin binding events for UCH-L5 N240 ( Table 4, Supplementary Results). Under standard conditions, 1 atm and 25 °C, UCH-L1 exhibits the strongest binding affinity towards ubiquitin, with a dissociation constant (K D ) of 0.26 μ M, while that of UCH-L3 is significantly weaker (Table 4). While UCH-L1 and -L3 bind to ubiquitin with comparable free energy change, the binding event is entropically favourable at 25 °C in the case of UCH-L1 and entropically unfavourable for UCH-L3, resulting in marked entropy-enthalpy compensation (Supplementary Results). As a result, the changes in heat capacity (Δ C p ) associated with ubiquitin binding is significantly larger for UCH-L3 (− 703 cal mol −1 K −1 ) compared to that of UCH-L1 (− 525 cal mol −1 K −1 ). Δ C p is associated with the changes in solvent accessible surface area (Δ SASA) upon binding. Indeed, UCH-L3 has a larger Δ SASA value (2691 Å 2 ) compared to that of UCH-L1 (2372 Å 2 ), according to their respective crystal structures in complex with ubiquitin (PDB ID: 1XD3 and 3KW5, respectively). This is accompanied by a large conformational change and cross-over loop ordering in UCH-L3 manifested in the large entropic penalty associated with ubiquitin binding. It is plausible to speculate that for UCH-L5 N240 , the entropic penalty associated with mono-ubiquitin binding is far greater that that for UCH-L3, hence the much weaker binding that is not accessible to ITC analysis.

Discussion
In this work, we have characterized in great detail the folding equilibrium and kinetics of the UCH domain of UCH-L5, i.e., UCH-L5 N240 , in comparison with previously reported results on UCH-L1 and -L3. Despite the apparent two-state folding equilibrium behaviour (Fig. 2), four well-resolved kinetic phases induced by urea could be observed by stopped-flow fluorescence measurements, indicating the presence of folding intermediates (Fig. 3). While the four kinetic folding phases have also been observed for UCH-L1 and -L3, and two parallel folding pathways were proposed to connect the native and denatured states, with two distinct folding intermediates being transiently populated along the two parallel pathways 27,28 , our interrupted refolding data suggest that the two fastest kinetic phases (k 3 and k 4 ) are connected sequentially rather than separately with two slower kinetic phases (k 1 and k 4 ) (Supplementary Results). Subsequent assignments of the connection(s) between the two fastest and two slowest phases were hindered because our stopped-flow instrumentation could not follow the large timescale separating the kinetic phases. The current data nevertheless suggest that the kinetic folding pathways of UCH-L5 N240 are different from those of UCH-L1 and -L3.
Human UCHs are important DUBs for maintaining cellular proteostasis 2 . Their unique domain architecture -a single domain that binds to and hydrolyses the isopeptide bond of ubiqutinated substrates -with very slow off-rates for releasing hydrolysed ubiquitin products 39 potentially increase the likelihood of encountering the proteasome machinery that actively unfolds ubiquitinated substrates for degradation. Indeed, it has been suggested by the recent single molecule mechanical unfolding study of UCH-L1 that the mechanical stability of the UCH domain may be beneficial for resisting UPS degradation 40 . Another important finding from the single molecule study is the consistent timescale of refolding triggered from mechanically and chemically unfolded states, implying that the intrinsic unfolding rates in the absence of chemical denaturant can be reliably derived from extrapolation of the linear dependency of chemical denaturant concentration (Fig. 3).

UCH-L1
UCH-L3 a  Our comparative kinetic analysis of UCH-L1, -L3 and -L5 N240 highlighted the large dynamic range of the intrinsic unfolding rates (k u H O 2 ) of the most dominant folding events, i.e., unfolding of the native state to one of the intermediate states, amongst the three UCHs. UCH-L5 N240 has the longest cross-over loop and exhibits the slowest global unfolding rate, four orders of magnitude slower than those of UCH-L1 and -L3 ( Fig. 3 and Table 3). The length of the cross-over loop is essential in substrate recognition for UCHs. The longer cross-over loop of UCH-L5 is necessary for binding and hydrolysing the isopeptide bond of K48-linked di-ubiquitin 15 . According to the crystal structure of UCH-L5 in complex with ubiquitin and Rpn13 6 , UCH-L5 binds to mono-ubiquitin in the same pose as other UCHs, but with partially resolved electron density for the cross-over loop (Fig. 5a). However, the cross-over loop and the structural elements around the ubiquitin binding, site such as α -helix 7, need to undergo significant configuration rearrangement in order to accommodate a compact K48-linked di-ubiquitin without steric clashes between the cross-over loop and the substrate (Fig. 5b and c). We deduced an intrinsic structural plasticity from the NMR HDX analysis (Fig. 4), presenting the solution to this issue. Our findings also echo the conformational plasticity implicated in the regulation of the UCH-L5 DUB activity underscored by the recent crystallographic studies of UCH-L5 in complex with different auxiliary factors such as Rpn13 and INO80G for up-and down-regulating the DUB activity of UCH-L5, respectively 6,7 .
Generally speaking, longer loop lengths result in higher contact orders and thus slower folding rates 41 . However, the differences in the contact orders between UCH-L1, -L3, and -L5 N240 are too small to account for the four orders of magnitudes difference in refolding and unfolding rates; the relative contact orders of UCH-L1, -L3, and -L5 N240 are 0.137, 0.144, and 0.139, respectively (Fig. 3c). The differences in sequence compositions and the folding stabilities of individual secondary structure elements within different UCHs may have more significant contributions to the folding dynamics and kinetics than the contact orders per se. Indeed, despite the abundant internal dynamics within UCH-L5 N240 in the absence of ubiquitin, it is highly stable thermodynamically and kinetically in terms of chemical stability compared to UCH-L1 and -L3 (Tables 1 and 3). The stabilization effect may be attributed to the higher configurational entropy of UCH-L5 N240 with respect to that of UCH-L1 and -L3. Indeed, our NMR HDX analysis revealed that the individual secondary structural elements within UCH-L5 N240 are much less protected from solvent exchange, indicative of abundant local fluctuations (Fig. 4). Rapid HDX in secondary structure elements (mostly peripheral helices) of UCH-L1 has been attributed to highly populated PUFs under native conditions 28 . It is therefore plausible that UCH-L5 N240 also exhibits abundant PUFs under native conditions in solution, which help stabilize the folding of UCH-L5 N240 .
The extent to which local fluctuations occur within the PUFs of UCH-L5 may be far greater than what was observed in the crystal structure of UCH-L5, which shows structural disorder limited to the cross-over loop in all reported crystal structures and α -helix 2 in the apo form ( Fig. 1) 6,7,11 . Similar loop dynamics was observed in UCH-L5 from Trichinella spiralis 42 . Indeed, cross-over loop flexibility was observed in apo UCH-L3, but it was fully resolved in the ubiquitin-form 13 . In contrast, the cross-over loop of UCH-L1 was resolved both in the apo-and ubiquitin-bound forms 9,10 . The entropic cost of structural ordering in UCH-L3 is confirmed in our ITC analysis (Table 4 and Supplementary Results). There is a strong correlation between the free energies of unfolding of UCH-L1, -L3 and -L5 N240 with the lengths of the cross-over loops (Table 3). In addition, the degree of local fluctuations deduced from NMR HDX analysis is proportional to the length of the cross-over loop (Fig. 4).
Using model systems, the effects of loop insertions have been investigated, generally through inserting repeating glycine residues [43][44][45] . Based on the findings, an empirical function was proposed to probe residual structures in the denatured states with the assumptions that the inserted loop residues marginally destabilize the proteins, that the insertions do not interact with the remaining structure in the denatured, transition, or native states, and that the energetic changes are predominantly entropic 46 . Indeed, such assumptions were met for several other model systems 47,48 . Loop elongation however, is not always destabilizing for proteins. A recent study showed that polyglycine loop insertion could in fact significantly increase the entropy of the native state of an acylphosphatase, thereby increasing the native state stability without perturbing the transition and denatured states 49 . In contrast to the artificial manipulation of the loop lengths of model systems, our current results present a biologically relevant example, which has likely evolved to maximize the structural plasticity of UCH-L5 by a longer substrate recognition loop and peripheral helical elements. The structural plasticity therefore contributes to an entropic gain in thermodynamics while the higher flexibility is beneficial for recognizing a broad range of substrates with potentially different ubiquitin linkages without steric clashes with the cross-over loop (Fig. 5). Our NMR titration data (Supplementary Results) strongly suggest that UCH-L5 N240 remains dynamic in complex with ubiquitin, which may be the underlying reason for its poor K M value (Supplementary Results). The entropically stabilized native state of UCH-L5 N240 significantly reduces the unfolding rate that could be essential for withstanding the potential mechanical unfolding driven by the proteasome when it is associated with the regulatory subunit Rpn13 for DUB activity activation. It is therefore plausible that the functional contribution of the cross-over loops of UCHs that are part of the knotted elements is to balance the need for structural plasticity in substrate regulation and kinetic folding stability that is needed for withstanding proteasome-mediated degradation.

Methods
Recombinant protein purification. The pGEX-6P1 vector-based expression construct of UCH-L5 N240 was a kind gift of Dr. Chittaranjan Das (Purdue University, USA). The resulting recombinant protein construct contains a glutathione S-transferase (GST) fused at the N-terminus of UCH-L5 N240 . The expression vector was transformed into a BL21 (DE3) E. coli strain and cultured in LB medium containing 0.1 mg/mL ampicillin for antibiotic selection. Recombinant protein over-expression was induced by adding 0.5 mM isopropyl thio-β -d-galactoside (IPTG) when the optical density of bacterial culture at 600 nm (OD 600 ) was close to 0.8, followed by overnight incubation with shaking at 16 °C. The cells were harvested and purified by a standard protocol for GSTbased affinity column purification, followed by fusion tag removal using PreScission protease (GE Biosciences, USA), as described previously 11 . The resulting recombinant protein was subjected to size-exclusion chromatography using a gel-filtration column (Superdex 75 26/60, GE Biosciences, USA) in 20 mM Tris-HCl (pH 7.6), 100 mM NaCl and 5 mM DTT. The purity of the recombinant protein was higher than 95% judging from SDS-PAGE by visual inspection.
Intrinsic fluorescence spectroscopy. The intrinsic fluorescence of UCH-L5 N240 was monitored by exciting the samples at 260 nm and recording the emission spectra between 300 and 450 nm at 25 °C using a temperature-controlled fluorimeter (FP8500, JASCO, Japan). Urea-induced equilibrium unfolding was monitored by generating 41 aliquots of protein solution containing a gradient of urea (0-6 M) concentrations with a linear increment step of 2.5% made by a two-channel liquid dispenser (Hamilton, USA) to minimize manual pipetting errors.
Far-UV CD spectroscopy. Urea-induced equilibrium unfolding was also monitored by far-UV CD between 200 and 260 nm at 25 °C using a temperature-controlled CD spectrometer (J-815, JASCO, Japan). The spectra were collected with a bandwidth of 1 nm, a data interval of 0.5 nm, and an averaging time of one second. Thermal denaturation of UCH-L5 N240 was monitored by analysing the CD signal changes at 215 nm between 25 and 80 °C while the changes at 222 nm were monitored for UCH-L1 and -L3. In all cases, 5 μ M of protein was used and 1.2 molar equivalent of ubiquitin was added to assess the effect of ubiquitin binding. The resulting isotherms were normalized and fitted to a two-state equilibrium unfolding model to extract the thermodynamics parameters, i.e., melting temperature (T m ), enthalpy (Δ H), entropy (Δ S) and changes in heat capacity (Δ C p ) as described previously 50 .
Thermodynamic parameters of equilibrium unfolding of UCH-L5 N240 induced by urea. All equilibrium unfolding data were subjected to singular value decomposition (SVD) analysis using an in-house written script for MATLAB (MATLAB and Statistics Toolbox Release 2012b, The MathWorks, USA) as described previously [29][30][31] . The titration series were used to generate an m × n matrix, M, as inputs for SVD analysis, where m corresponds to the number of recorded wavelengths and n corresponds to the number of titration points. SVD reconstruction generates an m × m unitary rotation matrix U r , an n × n unitary rotation matrix V r , and an m × n diagonal singular value matrix S to reconstruct the input matrix M as follows where U r corresponds to the basis function of the observed spectral patterns, and V r corresponds to the basis coefficient as a function of denaturant concentration. To determine the number of significant components necessary for reconstructing the input matrix, the normalized correlation coefficients of individual singular values were calculated and a threshold of 0.8 was used, leading to the conclusion that UCH-L5 N240 unfolds in a two-state model. The fluorescence and CD data were subjected to a two-state equilibrium-unfolding model as described previously [28][29][30][31] . The intrinsic fluorescence and far-UV CD data were fit separately and globally. Additionally, the changes of maximum fluorescence emission wavelength as a function of denaturant concentration were fitted to the same model for comparison.
Stopped-flow fluorescence spectroscopy. The folding kinetics of UCH-L5 N240 was monitored using a stopped-flow spectrometer in fluorescence detection mode (SX18 stopped-flow spectrometer, Applied Photophysics, UK) as described previously [28][29][30][31] . Changes in total fluorescence were monitored using an excitation wavelength of 280 nm with a 320 nm cut-off filter. All experiments were carried out at 25 °C. 20 μM UCH-L5 N240 was buffered in 20 mM Tris-HCl (pH 7.6), 100 mM NaCl with 8 M urea for unfolding or without urea for refolding measurements. For single-jump kinetic measurements, the folding reactions were triggered by rapidly mixing the folding or unfolding buffer with protein solution at an asymmetric mixing ratio of 10:1. After the 11-fold dilution, the final protein concentration was 1.8 μM. For double-jump kinetic measurements, three different modes were employed: interrupted refolding, interrupted unfolding, or sequential refolding kinetic measurement.
For the interrupted refolding measurements, 7.7 M urea-denatured protein solution was first mixed with refolding buffer to initiate refolding over different aging periods, followed by the second mixing step with denaturing buffer containing 8 M urea immediately before we took kinetic fluorescence measurements under denaturing conditions. The first mixing step was achieved by mixing protein solutions with unfolding or refolding buffer with a 1:5 mixing ratio. After a specific aging period, a second mixing step was carried out by mixing the aged protein solution with an equal amount of unfolding or refolding buffer (1:1 mixing ratio) immediately before kinetic fluorescence measurements. The resulting kinetic traces were subjected to global fitting in which the folding rates were shared amongst all the kinetic traces of different aging times, and the amplitudes corresponding to different kinetic phases were shown as a function of aging time, and the rates at which the corresponding amplitudes built up were extracted by single exponential fitting to the observed amplitude as a function of aging time (t age ).
For all kinetic analyses, the observed reaction rates were extracted by fitting the kinetic traces to a single, double, or triple exponential function with an offset using the software package GraphPad Prism (GraphPad Software, USA). The choice of model, i.e., number of kinetic phases, was decided using the F-test statistics by Prism.
Scientific RepoRts | 7:45174 | DOI: 10.1038/srep45174 Isothermal titration calorimetry (ITC). A Microcal 200 instrument (GE, USA) was used for the ITC measurements. The protein concentrations of UCHs and human ubiquitin were set to 27.5 and 275 μ M, respectively. The latter was used as the titrant to be injected into the UCH solutions. The ITC experiments were carried out at 20, 25, 30, and 37 °C, and the resulting ITC data were individually analysed using NITPIC 60 and subsequently exported to Sedphat 61 for global fitting to extract the associated thermodynamics parameters. DUB activity analysis. The enzyme kinetics of UCH variants were assessed by UbAMC as a model substrate as described previously [16][17][18][19] . The enzyme concentrations were set to 1 nM, and UbAMC substrate concentrations ranged from 1 to 1000 nM. The fluorescence as a function of time was recorded individually using a temperature-controlled fluorimeter (FP8500, JASCO, Japan). The results were analysed using the built-in Michaelis-Menten equation of the software package GraphPad Prism (GraphPad Software, USA).