Kinetic Constraints in the Specific Interaction between Phosphorylated Ubiquitin and Proteasomal Shuttle Factors

Ubiquitin (Ub) specifically interacts with the Ub-associating domain (UBA) in a proteasomal shuttle factor, while the latter is involved in either proteasomal targeting or self-assembly coacervation. PINK1 phosphorylates Ub at S65 and makes Ub alternate between C-terminally relaxed (pUbRL) and retracted conformations (pUbRT). Using NMR spectroscopy, we show that pUbRL but not pUbRT preferentially interacts with the UBA from two proteasomal shuttle factors Ubqln2 and Rad23A. Yet discriminatorily, Ubqln2-UBA binds to pUb more tightly than Rad23A does and selectively enriches pUbRL upon complex formation. Further, we determine the solution structure of the complex between Ubqln2-UBA and pUbRL and uncover the thermodynamic basis for the stronger interaction. NMR kinetics analysis at different timescales further suggests an indued-fit binding mechanism for pUb-UBA interaction. Notably, at a relatively low saturation level, the dissociation rate of the UBA-pUbRL complex is comparable with the exchange rate between pUbRL and pUbRT. Thus, a kinetic constraint would dictate the interaction between Ub and UBA, thus fine-tuning the functional state of the proteasomal shuttle factors.


Introduction
The ubiquitin-proteasomal system is essential for maintaining proteostasis in the cell. Substrate proteins conjugated with the ubiquitin (Ub) chain in a particular manner can be targeted to the proteasome for degradation. The targeting process is mediated by the interactions between Ub and the intrinsic Ub receptors in the proteasome [1][2][3]. Ub-modified substrate proteins can also be targeted to the proteasome with the assistance of proteasomal shuttle factors. A shuttle factor contains an Ub-like domain (Ubl) at its N-terminus and one or more Ub-associating domains (UBA) at its C-terminus. The Ubl interacts with the same receptors in the proteasome, often with higher affinity than Ub [2,4]. The UBA, on the other hand, transiently interacts with Ub. Together, the proteasomal shuttle factor bridges the interaction between the substrate protein and the proteasome.
Ubiqulin-2 (Ubqln2) and Rad23A are the two common proteasomal shuttle factors. Ubqln2 is one of the four proteins, Ubqln1-4, in the ubiquilin family. Ubqln2 is prone to self-assembly to form liquid droplets or insoluble aggregates [5,6] and is associated with amyotrophic lateral sclerosis with frontotemporal dementia [7] and Huntington's disease [8]. On the other hand, the interaction with Ub via the Ubqln2-UBA domain can shift the equilibrium towards the diluted phase and dissipate Ubqln2 coacervate [5]. UV excision repair proteins, including Rad23A and Rad23B, can also phase separate in the cell. But unlike Ubqln2, Rad23 self-assembly is facilitated with the addition Ub chain, resulting in the formation of proteasome foci in the cell [9]. The reason for the distinct coacervation behavior for the two proteasomal shuttle factors can be two-fold. First, a Rad23 protein harbors two tandem UBA domains, allowing multivalent interactions with Ub instead of just one UBA domain in Ubqln2. Second, Ub has a weaker binding for Rad23 than for Ubqln2 [10,11].
Ub not only modifies other proteins, Ub itself can also be modified [12]. Phosphorylation by kinase PINK1 at Ub residue S65 has been studied most intensively [13][14][15], thanks to its connection to the Parkinson's disease [16,17]. An increase of S65-phosphorylated Ub (pUb) level has been observed in neurons and brains of the aging population and neurodegenerative disease patients [18,19]. It has been suggested that Ub phosphorylation by PINK1 can inadvertently impair proteasomal activity and disrupt proteostasis [15]. Indeed, Ub phosphorylation can interfere with the synthesis and hydrolysis of the Ub chain [20][21][22], i.e., the writers and erasers of the Ub signaling cascade. In comparison, how Ub phosphorylation impacts the noncovalent interactions between Ub and other proteins is less clear [23]. A Ub phosphomimetic has been shown to bind to Rad23A much tighter than the wildtype Ub [21] in a quantitative proteomics study, but it is unknown how the wildtype pUb behaves.
When phosphorylated by PINK1 at S65, the resulting pUb can undergo a large conformational change to adopt a C-terminal retracted conformation (pUb RT ) [20]. The alternative conformation differs from the typical C-terminal relaxed conformation (pUb RL ), mainly in the hydrogen-bond register of the last β-strand (β5). The two conformational states are in slow exchange and about equally populated at the physiological pH [14,24]. Importantly, mutants mimicking the S65 phosphorylation cannot elicit the alternative conformation [24,25]. To understand how the phosphorylation impacts Ub noncovalent interactions with other proteins, we characterized the binding dynamics and kinetics between pUb and the two UBA domains from Ubqln2 and Rad23A. Our results indicate that Rad23A does not bind to pUb more tightly than to Ub. Moreover, we show that Ubqln2-UBA selectively interacts with and enriches pUb RL owing to a kinetic constraint.

Sample Preparation
Human ubiquitin was cloned to a pET11a vector and expressed in BL21 star cells. LB medium and M9-minimum medium were used to prepare unlabeled proteins and isotope-enriched proteins, respectively. Ubiquitin was purified through Sepharose SP and Sephacryl S100 columns (GE Healthcare, New Brunswick, NJ, USA) in tandem. For isotopic labeling, 1 g/L U-15 N-labeled NH 4 Cl (Isotec, Kürten, Germany) and/or 2 g/L U-13 C-labeled glucose (Isotec, Milwaukee, WI, USA) were added to the M9-minimum medium as the sole nitrogen and/or carbon source. PINK1 from body louse (phPINK1) was prepared as previously described [24]. To phosphorylate Ub, PINK1, Ub, MgCl 2 , and ATP were mixed at the molar ratio of 1:10:500:500 in 20 mM Tris HCl buffer, also containing NaCl 150 mM, 1 mM DTT at pH 8.0. The reaction was performed at room temperature for 4 h. The pUb product was further purified with the Source Q column (GE Healthcare, New Brunswick, NJ, USA). Successful phosphorylation of Ub by PINK1 was confirmed by ESI mass spectrometry (Bruker Daltonics, Billerica, MA, USA).
The genes encoding the human Ubqln2-UBA (residues 578 to 621) and human Rad23A-UBA2 (residues 315 to 363) were synthesized with optimized codons and sub-cloned into pET11a plasmid (a thioredoxin tag, a hexahistidine tag, and a TEV cleavage site were appended at the N-terminus of UBA). All proteins were expressed using BL21 (DE3) strain. LB medium and M9-minimal medium were used to prepare unlabeled and isotopeenriched proteins, respectively. After cell lysis, the protein was purified with a Ni-NTA agarose column (GE Healthcare, New Brunswick, NJ, USA) and a Sephacryl S100 column (GE Healthcare, New Brunswick, NJ, USA). The tags were removed with TEV protease at Biomolecules 2021, 11, 1008 3 of 12 4 • C overnight, followed by a second Ni-NTA agarose column (the desired protein was recovered in the flowthrough) and Sephacryl S100 columns column.

NMR Titration Experiments
For the titration of 15 N-labeled Ub or pUb with Ubqln2-UBA or Rad23A-UBA2, the initial NMR sample was prepared as 100 µM in 20 mM HEPES buffer (containing 150 mM NaCl at pH 7.4). A series of 1 H-15 N HSQC spectra were recorded for the 15  The NMR data were processed and analyzed using NMRPipe [26] and CCPNmr Analysis V2.4 [27], respectively. The CSPs were computed with [0.5 × ∆δH 2 + 0.1 × ∆δN 2 )] 0.5 , in which ∆δH and ∆δN were the chemical shift difference in 1 H and 15 N dimensions, respectively.

Determination of K D Value for pUb-UBA Complex
The zero-order equilibrium between pU RL and pUb RT can be written as below: The ratio between pUb RT and pUb RL concentrations is a constant at a particular pH [26]: Now we consider the UBA interaction with pUb RL , and the entire equilibrium can be written as follow: The dissociation constant (K D ) between pUb RL and UBA is defined as: The total concentration of pUb [M] is: The concentration of UBA added [T] at a given titration point is known and can be substituted in the following equation: Combining Equations (6) and (7), the [pUb RT ] is described as follow: On the other hand, the sum of [pUb RL ] and the concentration of pUb RL in the complex form is defined in the following equation: For NMR titration, the relationship between the CSP and protein concentration is described as follow: in which δ obs is the observed CSP value at a given titration point, n is the stoichiometric ratio, [P] is the total concentration of pUb relaxed state, δ min is the minimum value of CSP, δ max is the maximal value of CSP. [T] is the concentration of the UBA domain. In Equation (10), [P] is described using Equation (9), the value of K D for the complex between UBA and pUb relaxed state could be calculated by fitting the concentration of UBA [T] against observed CSP δ obs .
The concentration of the free pUb RL can be calculated using Equations (2) and (4). The relationship between K D , k ex , k on , and k off is described in Equations (11) and (12), and thus can be calculated.
2.5. Acquisition of NMR ZZ-Exchange Data 15 N-labeled pUb (380 µM) and Ubqln2-UBA (280 µM) were mixed in 20 mM HEPES buffer at pH 7.4 containing 150 mM NaCl. As a control, 380 µM free 15 N-labeled pUb was prepared in the HEPES buffer. The experiments were performed on a Bruker 600 MHz NMR spectrometer (Bruker Daltonics, Billerica, MA, USA) at 30 • C. The delay times for the ZZ-exchange were set at 0 ms, 20 ms, 40 ms, 60 ms, 90 ms, 120 ms, 160 ms, 220 ms, 380 ms, and 450 ms. The signal intensities with different delays were evaluated and used to fit the exchange rates between pUb RL and pUb RT , using the established method [30].
The structure of the complex between the Ubqln2 UBA and the pUb RL was calculated using XPLOR-NIH [32]. The topology and parameter files for phosphorylated serine (SEP) were generated as previously described [14]. For the intra-molecular restraints of Ubqln2 Biomolecules 2021, 11, 1008 5 of 12 UBA (PDB code: 2JY6) and the pUb relaxed state (PDB code: 5XK5), the published data were used during the structure determination [24]. Intermolecular NOE and RDC restraints were used to restrain the complex structure. The RDC restraints of pUb RL with Ubqln2-UBA (85% complex at pUb and Ubqln2-UBA concentrations of 300 µM) and its free form were recorded separately in the same alignment medium. To determine the RDC values of pUb RL /Ubqln2 UBA complex, the contribution of the free form of pUb RL was subtracted from the observed data of the sample of pUb RL with Ubqln2 UBA, using the following equation: Two hundred forty structures each were calculated, and the top-ranked 20 structures with the lowest energy were selected. The structures were further subjected to water refinement. for further analysis. Structure figures were rendered using PyMOL Version 2.2 (The PyMOL Molecular Graphics System, Schrödinger). The complex structure of Ubqln2-UBA and pUb RL has been deposited at the PDB with the accession number of 7F7X.

UBA Selectively Interacts with pUb RL
We titrated the unlabeled UBA domain from Ubqln2 or the second UBA domain (UBA2) from Rad23A to 15 N-labeled pUb. The titration causes progressive chemical shift perturbations (CSPs) for a subset of peaks in pUb RL but almost negligible CSPs for the peaks corresponding to pUb RT . Though the CSP magnitude is similar for pUb RL when titrated with two UBA domains, the largest perturbed residues are found in β4 and β2 with the Ubqln2-UBA β5 and with the Rad23A-UBA2 ( Figure 1).
Biomolecules 2021, 11, 1008 5 of 12 The structure of the complex between the Ubqln2 UBA and the pUbRL was calculated using XPLOR-NIH [32]. The topology and parameter files for phosphorylated serine (SEP) were generated as previously described [14]. For the intra-molecular restraints of Ubqln2 UBA (PDB code: 2JY6) and the pUb relaxed state (PDB code: 5XK5), the published data were used during the structure determination [24]. Intermolecular NOE and RDC restraints were used to restrain the complex structure. The RDC restraints of pUbRL with Ubqln2-UBA (85% complex at pUb and Ubqln2-UBA concentrations of 300 μM) and its free form were recorded separately in the same alignment medium. To determine the RDC values of pUbRL/Ubqln2 UBA complex, the contribution of the free form of pUbRL was subtracted from the observed data of the sample of pUbRL with Ubqln2 UBA, using the following equation: Two hundred forty structures each were calculated, and the top-ranked 20 structures with the lowest energy were selected. The structures were further subjected to water refinement. for further analysis. Structure figures were rendered using PyMOL Version 2.2 (The PyMOL Molecular Graphics System, Schrödinger). The complex structure of Ubqln2-UBA and pUbRL has been deposited at the PDB with the accession number of 7F7X.

UBA Selectively Interacts with pUbRL
We titrated the unlabeled UBA domain from Ubqln2 or the second UBA domain (UBA2) from Rad23A to 15 N-labeled pUb. The titration causes progressive chemical shift perturbations (CSPs) for a subset of peaks in pUbRL but almost negligible CSPs for the peaks corresponding to pUbRT. Though the CSP magnitude is similar for pUbRL when titrated with two UBA domains, the largest perturbed residues are found in β4 and β2 with the Ubqln2-UBA β5 and with the Rad23A-UBA2 (Figure 1).  Ubqln2-UBA not only selectively interacts with pUb RL and also enriches pUb RL to nearly 100%. When binding to Ubqln2-UBA, pUb undergoes a further equilibrium shift from pUb RT to pUb RL . In comparison, the addition of Rad23A-UBA2 causes little populational change for the pUb, even with the addition of a very high concentration ( Figure 2). are colored like a rainbow. (C,D) Chemical shift perturbations (CSPs) for the backbone amide of 100 μM 15 N-labeled pUbRL and pUbRT upon titration of 340 μM Ubqln2-UBA and 300 μM Rad23A-UBA2, with the secondary structure of pUb shown as a cartoon. The amide signals that disappear in the complex are indicated with asterisks. The gray columns indicate the residues of pUbRL and pUbRT have the same chemical shifts.
Ubqln2-UBA not only selectively interacts with pUbRL and also enriches pUbRL to nearly 100%. When binding to Ubqln2-UBA, pUb undergoes a further equilibrium shift from pUbRT to pUbRL. In comparison, the addition of Rad23A-UBA2 causes little populational change for the pUb, even with the addition of a very high concentration (Figure 2). In the standard one-site binding isotherm model, the concentration of the titrated protein is fixed. In a previous study by Fushman and coworkers, the titration points between pUb and the UBA domain from Ubqln1, a close homolog of Ubqln2 in the same family, were fitted with a simple one-site binding curve [25]. However, systematic deviations can be noticed from the fitting ( Figure S1). Upon UBA titration, the total pUbRL concentration changes, while the unbound pUbRL concentration should maintain a constant ratio with the pUbRT concentration. Thus, a revised model is needed to account for the coupled equilibria of the interconversion between pUbRL and pUbRT and the interaction between pUbRL and UBA, as described in the Methods section. Using this model, we obtained the KD values of 43.3 ± 3.6 μM and 403.5 ± 38.8 μM for Ubqln2-UBA and Rad23A-UBA2, respectively ( Figure 3A,C). Notably, the residuals are small and random from the fittings ( Figure S2).
As a control, we performed titrations of Ubqln2-UBA and Rad23A-UBA2 to 15 N-labeled unmodified Ub. The KD values are 33.0 ± 3.7 μM and 355.8 ± 56.0 μM for Ubqln2-UBA and Rad23A-UBA2, respectively. Thus, phosphorylation only slightly decreases the binding affinities of the UBA towards the pUbRL (Figure 3B,D). In the standard one-site binding isotherm model, the concentration of the titrated protein is fixed. In a previous study by Fushman and coworkers, the titration points between pUb and the UBA domain from Ubqln1, a close homolog of Ubqln2 in the same family, were fitted with a simple one-site binding curve [25]. However, systematic deviations can be noticed from the fitting ( Figure S1). Upon UBA titration, the total pUb RL concentration changes, while the unbound pUb RL concentration should maintain a constant ratio with the pUb RT concentration. Thus, a revised model is needed to account for the coupled equilibria of the interconversion between pUb RL and pUb RT and the interaction between pUb RL and UBA, as described in the Methods section. Using this model, we obtained the K D values of 43.3 ± 3.6 µM and 403.5 ± 38.8 µM for Ubqln2-UBA and Rad23A-UBA2, respectively ( Figure 3A,C). Notably, the residuals are small and random from the fittings ( Figure S2).
As a control, we performed titrations of Ubqln2-UBA and Rad23A-UBA2 to 15

The Complex Structure Explains the Binding Preference for Ubqln2-UBA
We collected the intermolecular NOEs between pUb and Ubqln2-UBA using a filtered/edited NMR pulse sequence. Consistent with the titration results, the NOE crosspeaks were only identified between the resonances associated with pUbRL and the resonances in Ubqln2-UBA ( Figure S3, Table S1). On the other hand, we could not observe intermolecular NOEs between pUb and Rad23A-UBA2. The failure to produce intermolecular NOEs can be explained by the short lifetime, i.e., fast dissociation rate, of the Rad23A-pUb complex, as will be discussed below. In addition to the NOEs, experimental restraints also include residual dipolar couplings (RDCs), measured for each subunit at an exact complex occupancy.
The structure of the complex between pUbRL and Ubqln2-UBA is well-converged with the root-mean-square deviations for all backbone heavy atoms of 0.81 ± 0.09 Å ( Figure S4 and Table S2). The structure is similar to those determined for other UBA-Ub complexes [11,33]. Formation of the complex buries solvent-accessible surface area of 1022.7 ± 139.7 Å 2 , which involves hydrophobic residues of L8, I44, and V70 in pUbRL and hydrophobic residues I611 and I615 in Ubqln2-UBA ( Figure 4A). Moreover, the β-sheet slightly bends upon complex formation, as the distance between the Cβ atoms of residues I44 and V70 is shortened from 6.3 ± 0.2 Å in the free pUbRL to 5.8 ± 0.2 Å in the UBA-bound pUbRL. Since β5 moves up by two residues in pUbRT [20,24], the interaction between V70 in pUbRL and I615 in Ubqln2-UBA would be abolished. This explains why the UBA selectively interacts with pUbRL.

The Complex Structure Explains the Binding Preference for Ubqln2-UBA
We collected the intermolecular NOEs between pUb and Ubqln2-UBA using a filtered/edited NMR pulse sequence. Consistent with the titration results, the NOE crosspeaks were only identified between the resonances associated with pUb RL and the resonances in Ubqln2-UBA ( Figure S3, Table S1). On the other hand, we could not observe intermolecular NOEs between pUb and Rad23A-UBA2. The failure to produce intermolecular NOEs can be explained by the short lifetime, i.e., fast dissociation rate, of the Rad23A-pUb complex, as will be discussed below. In addition to the NOEs, experimental restraints also include residual dipolar couplings (RDCs), measured for each subunit at an exact complex occupancy.
The structure of the complex between pUb RL and Ubqln2-UBA is well-converged with the root-mean-square deviations for all backbone heavy atoms of 0.81 ± 0.09 Å ( Figure S4 and Table S2). The structure is similar to those determined for other UBA-Ub complexes [11,33]. Formation of the complex buries solvent-accessible surface area of 1022.7 ± 139.7 Å 2 , which involves hydrophobic residues of L8, I44, and V70 in pUb RL and hydrophobic residues I611 and I615 in Ubqln2-UBA ( Figure 4A). Moreover, the β-sheet slightly bends upon complex formation, as the distance between the Cβ atoms of residues I44 and V70 is shortened from 6.3 ± 0.2 Å in the free pUb RL to 5.8 ± 0.2 Å in the UBA-bound pUb RL . Since β5 moves up by two residues in pUb RT [20,24], the interaction between V70 in pUb RL and I615 in Ubqln2-UBA would be abolished. This explains why the UBA selectively interacts with pUb RL .  The phosphorylated residue pS65 is located outside the interface between pUbRL and Ubqln2-UBA. This explains why Ubqln2-UBA binds to pUbRL only slightly weaker than the unmodified Ub ( Figure 4A). Interestingly, the interface does not involve residues in β2. Therefore, the observed CSP for β2 residues (Figure 1) is likely caused by the allosteric modulation of the β-sheet structure upon Ubqln2-UBA binding. Indeed, significant changes in the RDC values are observed for the interfacial residues and the backbone N-H bond vector of β2 residue L15 ( Figure S5). As a result, β1 and β2 strands curl slightly in the UBA complex ( Figure 4B).

Kinetic Constraints for pUb Interaction
The addition of Ubqln2-UBA enriches pUbRL. However, the addition of Rad23-UBA largely failed to promote pUb conformational conversion. To account for the different selectivity for the UBA domain, we performed a detailed kinetics analysis during the formation of the pUb-UBA complex.
We first performed CPMG relaxation dispersion measurement for 15 N-labeled Ubqln2-UBA, with the unlabeled pUb added to ~10% and ~50% saturation of the complex ( Figure 5). The measurements were performed at two different magnetic fields, and the kex values for the exchange rate between free and bound proteins can be obtained in a global fit. At 1382.9 ± 3.7 s −1 and 320.3 ± 13.9 s −1 , the kex value is nearly four times larger at the higher concentration level. Using the kex values and the KD value (the zero-order interconversion equilibrium constant between pUbRL and pUbRT is set to 0.67), we obtained the concentration of the unbound pUbRL and determined the kon and koff values-6.8 ± 0.6 μM −1 s −1 and 293.1 ± 27.5 s −1 at the low saturation level, and 15.6 ± 1.4 μM −1 s −1 and 677.8 ± 61.0 s −1 at the high saturation level. The phosphorylated residue pS65 is located outside the interface between pUb RL and Ubqln2-UBA. This explains why Ubqln2-UBA binds to pUb RL only slightly weaker than the unmodified Ub ( Figure 4A). Interestingly, the interface does not involve residues in β2. Therefore, the observed CSP for β2 residues (Figure 1) is likely caused by the allosteric modulation of the β-sheet structure upon Ubqln2-UBA binding. Indeed, significant changes in the RDC values are observed for the interfacial residues and the backbone N-H bond vector of β2 residue L15 ( Figure S5). As a result, β1 and β2 strands curl slightly in the UBA complex ( Figure 4B).
Rad23A-UBA2 is highly homologous to Ubqln2-UBA. However, the interfacial residues I611 and I615 in Ubqln2-UBA are substituted with glutamate and alanine residues, respectively, in Rad23A-UBA2. Therefore, Rad23A-UBA2 interacts with pUb RL much weaker than Ubqln2-UBA. Moreover, Rad23A-UBA2 likely adopts a slightly different conformation in the complex, which would explain the different CSP profile (Figure 1).

Kinetic Constraints for pUb Interaction
The addition of Ubqln2-UBA enriches pUb RL . However, the addition of Rad23-UBA largely failed to promote pUb conformational conversion. To account for the different selectivity for the UBA domain, we performed a detailed kinetics analysis during the formation of the pUb-UBA complex.
We first performed CPMG relaxation dispersion measurement for 15 N-labeled Ubqln2-UBA, with the unlabeled pUb added to~10% and~50% saturation of the complex ( Figure 5). The measurements were performed at two different magnetic fields, and the k ex values for the exchange rate between free and bound proteins can be obtained in a global fit. At 1382.9 ± 3.7 s −1 and 320.3 ± 13.9 s −1 , the k ex value is nearly four times larger at the higher concentration level. Using the k ex values and the K D value (the zero-order interconversion equilibrium constant between pUb RL and pUb RT is set to 0.67), we obtained the concentration of the unbound pUb RL and determined the k on and k off values-6.8 ± 0.6 µM −1 s −1 and 293.1 ± 27.5 s −1 at the low saturation level, and 15.6 ± 1.4 µM −1 s −1 and 677.8 ± 61.0 s −1 at the high saturation level. Reciprocally, we performed CPMG relaxation dispersion measurements for 15 N-labeled pUb, with the unlabeled Ubqln2-UBA added at ~10% or ~50% saturation. However, the fitting was poor, especially at 10% saturation. We managed to obtain the kex value using residue L71 in the pUbRL conformational state ( Figure S6A,B), and the exchange rate at 50% saturation is also much higher than that at 10% saturation. As a control, we performed CPMG relaxation dispersion measurement for 15 N-labeled pUb alone. The change in the 15 N R2 value for L71 in the free pUb is negligible, indicating a lack of μs-ms timescale, which has been noted for the unmodified Ub [34].
Binding to Ubqln2-UBA also perturbs the exchange dynamics between pUbRL and pUbRT. The interconversion between the two Ub states occurs at ms-s timescale and can be probed with ZZ-exchange spectroscopy [20]. Binding to Ubqln2-UBA causes slight retardation of the back exchange from pUbRL to pUbRT compared to the free pUb ( Figure S7).
We also performed CPMG relaxation dispersion measurements for the 15 N-labeled Rad23-UBA2 with the unlabeled pUb added to ~5% saturation. The 15 N R2 values only decreases slightly at an increasing CPMG pulsing frequency ( Figure S8). Thus, only a lower limit could be estimated for the kex value for the exchange rate between free and bound forms, which is ~40,000 s −1 .

Discussion
Ub is an important signaling molecule and performs its function by modifying other proteins, the post-transitional modification process known as ubiquitination. Discoveries made in the past ten years have shown that Ub itself can be modified, and Ub modifications can profoundly remodel Ub signaling [12,15]. Ub is phosphorylated at residue S65 by PINK1 [13]. The pUb slowly interconverts between two distinct conformational states, namely pUbRL and pUbRT [20]. Using NMR titrations, we have shown that the UBA from Ubqln2 and Rad23A selectively interacts with pUbRL but not pUbRT. We have thus characterized the complex structure between Ubqln2-UBA and pUbRL and provided an atomic explanation for the UBA selectivity of the particular pUb state. Interestingly, Ubqln2-UBA selectively enriches pUbRL at the expense of pUbRT during the interaction. Prompted by this finding, we revised the one-site binding model to account for the changing concentration of pUbRL during UBA titration. The KD values from the Reciprocally, we performed CPMG relaxation dispersion measurements for 15 Nlabeled pUb, with the unlabeled Ubqln2-UBA added at~10% or~50% saturation. However, the fitting was poor, especially at 10% saturation. We managed to obtain the k ex value using residue L71 in the pUb RL conformational state ( Figure S6A,B), and the exchange rate at 50% saturation is also much higher than that at 10% saturation. As a control, we performed CPMG relaxation dispersion measurement for 15 N-labeled pUb alone. The change in the 15 N R 2 value for L71 in the free pUb is negligible, indicating a lack of µs-ms timescale, which has been noted for the unmodified Ub [34].
Binding to Ubqln2-UBA also perturbs the exchange dynamics between pUb RL and pUb RT . The interconversion between the two Ub states occurs at ms-s timescale and can be probed with ZZ-exchange spectroscopy [20]. Binding to Ubqln2-UBA causes slight retardation of the back exchange from pUb RL to pUb RT compared to the free pUb ( Figure S7).
We also performed CPMG relaxation dispersion measurements for the 15 N-labeled Rad23-UBA2 with the unlabeled pUb added to~5% saturation. The 15 N R 2 values only decreases slightly at an increasing CPMG pulsing frequency ( Figure S8). Thus, only a lower limit could be estimated for the k ex value for the exchange rate between free and bound forms, which is~40,000 s −1 .

Discussion
Ub is an important signaling molecule and performs its function by modifying other proteins, the post-transitional modification process known as ubiquitination. Discoveries made in the past ten years have shown that Ub itself can be modified, and Ub modifications can profoundly remodel Ub signaling [12,15]. Ub is phosphorylated at residue S65 by PINK1 [13]. The pUb slowly interconverts between two distinct conformational states, namely pUb RL and pUb RT [20]. Using NMR titrations, we have shown that the UBA from Ubqln2 and Rad23A selectively interacts with pUb RL but not pUb RT . We have thus characterized the complex structure between Ubqln2-UBA and pUb RL and provided an atomic explanation for the UBA selectivity of the particular pUb state. Interestingly, Ubqln2-UBA selectively enriches pUb RL at the expense of pUb RT during the interaction. Prompted by this finding, we revised the one-site binding model to account for the changing concentration of pUb RL during UBA titration. The K D values from the fitting show that thermodynamically, the UBA binding to pUb RL is only slightly weaker than to the unmodified Ub. This is consistent with the fact that pUb RL and Ub are structurally similar, and the phosphorylated residue is away from the binding interface ( Figure 4).
The selective enrichment of pUb RL by Ubqln2-UBA not only has to do with the thermodynamics of the binding equilibrium but has to do with the association/dissociation kinetics. The interconversion between the free and bound forms for Ubqln2 complex is much slower than that for the Rad23A complex. A slower off-rate means a longer lifetime for the Ubqln2-pUb complex, allowing intermolecular NOEs to build up ( Figure S3). The slower interconversion rate also means that Ubqln2-UBA is more capable, kinetically, of driving the conversion from pUb RT to pUb RL .
However, the experimentally determined k on and k off rates of the Ubqln2-pUb complex are larger than the interconversion timescale between pUb RT and pUb RL by over an order of magnitude. Interestingly, the k on and k off rates decrease when the saturation level of the complex is lower. Upon extrapolation, the k off rate would be even lower at the start of the binding process, comparable to the timescale of pUb RT /pUb RL interconversion. Moreover, upon Ubqln2 binding, the back conversion from pUb RL to pUb RT is slightly slowed ( Figure S7). Together, owing to the kinetic constraint, pUb RL can be efficiently enriched by Ubqln2 but not by Rad23A.
The acceleration of the binding kinetics at higher complex occupancy can be explained by the conformational restriction of pUb RL . Ub undergoes a so-called pincer-like movement, with the residues in β1 and β2 experience large fluctuation at sub-µs timescale [35,36]. The association of a UBA stabilizes one of the preexisting conformations of the β-sheet structure. However, Ub does not simply bind to UBA through conformational selection; an induced fit or conformational restriction mechanism also plays an important role in the interaction between Ub and its partner protein, especially towards the end of the binding process [37,38]. The increased exchange rate between free and bound proteins at an increasing saturation level of the complex is characteristic of an induced-fit mechanism [39]. Microscopically, the interaction with Ubqln2-UBA induces and stabilizes a UBA-complementary conformation of pUb RL (Figure 4), which would permit rapid association and dissociation. In a sense, Ub phosphorylation by PINK1 can be likened to Ub mutations specifically introduced that ultimately drive the Ub-binding mechanism to induced fit [40]. Nevertheless, a precise dissection of the two binding mechanisms warrants further analysis [41,42].
As such, phosphorylation at Ub residue S65 provides additional kinetic and dynamic constraints for Ub-UBA noncovalent interactions, which would determine whether the proteasomal shuttle factor remains monomeric for proteasomal targeting or phase-separate to form liquid or solid coacervate.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/biom11071008/s1, Figure S1: Reanalysis of the NMR titration data between pUb and the UBA domain of ubiquilin1, published by Fushman and coworkers [25]; Figure Figure S4: Superposition of the 20 lowest-energy conformers calculated for Ubqln2-UBA (cyan) and pUb RL complex (green), shown in two perspectives; Figure S5: Comparison between observed and calculated RDC values for pUb RL ; Figure S6: CPMG relaxation dispersion measurements were performed for 15 N-labeled pUb at two different magnetic fields; Figure S7: The interconversion rate between pUb RL and pUb RT analyzed with NMR ZZ-exchange experiment; Figure S8: CPMG relaxation dispersion measurements performed for 15 N-labeled Rad23A-UBA2 at 600 MHz with the unlabeled pUb added to~5% saturation; Table S1: Intermolecular distance restraints for the structure calculation of Ubqln2-UBA/pUb RL complex.; Table S2: Structure statistics for the Ubqln2-UBA/pUb RL complex; Table S3: The fitted values of k ex , k on , and k off of pUb RL /Ubqln2 UBA complex.