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

Abstract

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 (pUb_RL) and retracted conformations (pUb_RT). Using NMR spectroscopy, we show that pUb_RL but not pUb_RT 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 pUb_RL upon complex formation. Further, we determine the solution structure of the complex between Ubqln2-UBA and pUb_RL 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-pUb_RL complex is comparable with the exchange rate between pUb_RL and pUb_RT. Thus, a kinetic constraint would dictate the interaction between Ub and UBA, thus fine-tuning the functional state of the proteasomal shuttle factors.

1. 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.

2. Materials and Methods

2.1. 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-¹⁵N-labeled NH₄Cl (Isotec, Kürten, Germany) and/or 2 g/L U-¹³C-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, MgCl₂, 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 isotope-enriched 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 4 °C overnight, followed by a second Ni-NTA agarose column (the desired protein was recovered in the flowthrough) and Sephacryl S100 columns column.

2.2. NMR Titration Experiments

For the titration of ¹⁵N-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 ¹H-¹⁵N HSQC spectra were recorded for the ¹⁵N-labeled pUb sample with Ubqln2-UBA or Rad23A-UBA2 at 22.7 μM, 56.7 μM, 113.5 μM, 141.8 μM, 170.2 μM, 226.9 μM, 283.6 μM and 340.4 μM as the final concentration. The ¹H-¹⁵N HSQC spectra were recorded using a Bruker 600 MHz NMR spectrometer (Bruker Daltonics, Billerica, MA, USA) at 25 °C (298 K).

The NMR data were processed and analyzed using NMRPipe [26] and CCPNmr Analysis V2.4 [27], respectively. The CSPs were computed with [0.5 × ΔδH² + 0.1 × ΔδN²)]^0.5, in which ΔδH and ΔδN were the chemical shift difference in ¹H and ¹⁵N dimensions, respectively.

2.3. Determination of K_D Value for pUb-UBA Complex

The zero-order equilibrium between pU_RL and pUb_RT can be written as below:

$$pU{b}_{RL}\stackrel{R}{\leftrightarrow } pU{b}_{RT}$$

(1)

The ratio between pUb_RT and pUb_RL concentrations is a constant at a particular pH [26]:

$$R=\frac{\left[pU{b}_{RT}\right]}{\left[pU{b}_{RL}\right]}$$

(2)

Now we consider the UBA interaction with pUb_RL, and the entire equilibrium can be written as follow:

$$pU{b}_{RT} \stackrel{R}{\leftrightarrow } pU{b}_{RL}+UBA \stackrel{K_{D }}{\leftrightarrow } Complex$$

(3)

The dissociation constant (K_D) between pUb_RL and UBA is defined as:

$$K_D=\frac{\left[pU{b}_{RL}^{free}\right]\times \left[UB{A}^{free}\right]}{\left[Complex\right]}$$

(4)

The total concentration of pUb [M] is:

$$\mathrm{M}=\left[pU{b}_{RT}\right]+\left[pU{b}_{RL}^{free}\right]+\left[Complex\right]$$

(5)

The concentration of UBA added [T] at a given titration point is known and can be substituted in the following equation:

$$M=\left[pU{b}_{RT}\right]+\frac{\left[pU{b}_{RT}\right]}{R}+\left[T\right]-\left[UB{A}^{free}\right]$$

(6)

$$pU{b}_{RL}^{free}=\frac{\left[pU{b}_{RT}\right]}{R}=\frac{K_D\times \left(\left[T\right]-\left[UB{A}^{free}\right]\right)}{\left[UB{A}^{free}\right]}$$

(7)

Combining Equations (6) and (7), the [pUb_RT] is described as follow:

$$\left[pU{b}_{RT}\right]=\frac{-\left\{R\times \left(\left[T\right]-M\right)+K_D\times R\times \left(R+1\right)\right\}+\sqrt{{\left\{R\times \left(\left[T\right]-M\right)+K_D\times R\times \left(R+1\right)\right\}}^2+4\times M\times R^2\times K_D\times \left(1+R\right)}}{2\times \left(R+1\right)}$$

(8)

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:

$$\left[P\right]=\left[pU{b}_{RL}^{free}\right]+\left[Complex\right]=M-\frac{-\left\{R\times \left(\left[T\right]-M\right)+K_D\times R\times \left(R+1\right)\right\}+\sqrt{{\left\{R\times \left(\left[T\right]-M\right)+K_D\times R\times \left(R+1\right)\right\}}^2+4\times M\times R^2\times K_D\times \left(1+R\right)}}{2\times \left(R+1\right)}$$

(9)

For NMR titration, the relationship between the CSP and protein concentration is described as follow:

$${\delta }_{obs}={\delta }_{min}+n\times \left({\delta }_{max}-{\delta }_{min}\right)\times \frac{\left(\left[T\right]+\frac{\left[P\right]}{n}+K_D\right)-\sqrt{{\left(\left[T\right]+\frac{\left[P\right]}{n}+K_D\right)}^2-\frac{4\times \left[T\right]\times \left[P\right]}{n}}}{2\times \left[P\right]}$$

(10)

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.

2.4. CPMG Relaxation Dispersion Experiment

¹⁵N-edited CPMG measurement was performed for the NMR sample of the complex between Ubqln2-UBA and pUb prepared as concentrations (in 150 mM NaCl, 20 mM HEPES pH 7.4 buffer); one with 32 μM pUb and 300 μM Ubqln2 UBA (~10% saturation), and the other with 228 μM pUb and 300 μM Ubqln2 UBA (~50% saturation). The complex samples of Rad23A-UBA2 and pUb were also prepared with 54 μM pUb and 300 μM Rad23A-UBA2 (~5% saturation). The NMR sample of the complex between Ubqln2-UBA and ¹⁵N-pUb prepared as concentrations (in 20 mM HEPES pH 7.4 buffer with 150 mM NaCl); one with 39 μM Ubqln2 UBA and 300 μM ¹⁵N-pUb (~10% saturation), and the other with 229 μM Ubqln2 UBA and 300 μM ¹⁵N-pUb (~50% saturation). The CPMG experiments were recorded using Bruker 600 MHz, 700 MHz, and 850 MHz NMR spectrometers (Bruker Daltonics, Billerica, MA, USA) using the standard pulse sequence [28]. The CPMG spin-echo pulsing frequency includes 0 Hz, 40 Hz, 120 Hz, 200 Hz, 280 Hz, 360 Hz, 600 Hz, and 760 Hz. The NMR data were processed using NMRPipe and fitted using Glove [29].

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.

$$k_{ex}=k_{on}\times \left[pU{b}_{RL}^{free}\right]+k_{off}$$

(11)

$$K_D=\frac{k_{off}}{k_{on }}$$

(12)

2.5. Acquisition of NMR ZZ-Exchange Data

¹⁵N-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 ¹⁵N-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].

2.6. Calculation of the UBA-pUb Complex Structure

The ¹³C-edited F1-filtered NOESY spectra were recorded with a 120 ms mixing time on a 600 MHz NMR spectrometer at 25 °C. The ¹⁵N/¹³C-labeled Ubqln2-UBA (500 μM) and pUb (750 μM) were mixed in 20 mM HEPES buffer pH 7.4 with NaCl 150 mM. For the RDC sample, ¹⁵N-labeled pUb (300 μM) and Ubqln2 UBA (700 μM) were mixed in the same buffer. Residual dipolar couplings (RDC) were recorded for backbone amide bond vectors in PEG (C₁₂E₅)/hexanol (6%; Sigma-Aldrich, Saint-Louis, MO, USA) alignment medium [31], using the in-phase/anti-phase scheme.

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 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:

$$RD{C}_{complex}=\frac{\left(RD{C}_{complex-measured}-RD{C}_{free-measured}\times \%free\right)}{\%complex}$$

(13)

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.

3. Results

3.1. UBA Selectively Interacts with pUb_RL

We titrated the unlabeled UBA domain from Ubqln2 or the second UBA domain (UBA2) from Rad23A to ¹⁵N-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).

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).

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 ¹⁵N-labeled unmodified Ub. The K_D 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 pUb_RL (Figure 3B,D).

3.2. 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 cross-peaks 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 Ų, 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 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).

3.3. 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 ¹⁵N-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 ¹⁵N-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 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 ¹⁵N-labeled pUb alone. The change in the ¹⁵N 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 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 ¹⁵N-labeled Rad23-UBA2 with the unlabeled pUb added to ~5% saturation. The ¹⁵N R₂ 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.

4. 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.