Structural basis and mechanism of the unfolding-induced activation of HdeA, a bacterial acid response chaperone

The role of protein structural disorder in biological functions has gained increasing attention in the past decade. The bacterial acid-resistant chaperone HdeA belongs to a group of “conditionally disordered” proteins, because it is inactive in its well-structured state and becomes activated via an order-to-disorder transition under acid stress. However, the mechanism for unfolding-induced activation remains unclear because of a lack of experimental information on the unfolded state conformation and the chaperone–client interactions. Herein, we used advanced solution NMR methods to characterize the activated-state conformation of HdeA under acidic conditions and identify its client-binding sites. We observed that the structure of activated HdeA becomes largely disordered and exposes two hydrophobic patches essential for client interactions. Furthermore, using the pH-dependent chemical exchange saturation transfer (CEST) NMR method, we identified three acid-sensitive regions that act as structural locks in regulating the exposure of the two client-binding sites during the activation process, revealing a multistep activation mechanism of HdeA's chaperone function at the atomic level. Our results highlight the role of intrinsic protein disorder in chaperone function and the self-inhibitory role of ordered structures under nonstress conditions, offering new insights for improving our understanding of protein structure–function paradigms.

The role of protein structural disorder in biological functions has gained increasing attention in the past decade. The bacterial acid-resistant chaperone HdeA belongs to a group of "conditionally disordered" proteins, because it is inactive in its wellstructured state and becomes activated via an order-to-disorder transition under acid stress. However, the mechanism for unfolding-induced activation remains unclear because of a lack of experimental information on the unfolded state conformation and the chaperone-client interactions. Herein, we used advanced solution NMR methods to characterize the activatedstate conformation of HdeA under acidic conditions and identify its client-binding sites. We observed that the structure of activated HdeA becomes largely disordered and exposes two hydrophobic patches essential for client interactions. Furthermore, using the pH-dependent chemical exchange saturation transfer (CEST) NMR method, we identified three acid-sensitive regions that act as structural locks in regulating the exposure of the two client-binding sites during the activation process, revealing a multistep activation mechanism of HdeA's chaperone function at the atomic level. Our results highlight the role of intrinsic protein disorder in chaperone function and the selfinhibitory role of ordered structures under nonstress conditions, offering new insights for improving our understanding of protein structure-function paradigms.
Intrinsically disordered proteins (IDPs) 5 or proteins containing intrinsically disordered regions (IDRs) constitute about a half of human proteins and are often disease-related (1,2). In prokaryotic proteomes, IDRs are also found to be enriched in proteins involved in pathogenic pathways and essential for invasion of host immune systems (3,4). Elucidating the functional mechanisms of IDPs or IDRs is critical for understanding the pathogenesis mechanisms of many diseases and is also indispensable for a complete elucidation of the protein structurefunction paradigms. However, experimental information of disordered proteins is scarce and remains technically challenging to obtain, mainly due to the intrinsic "fuzziness" of the disordered regions. A group of stress-response chaperones in both eubacteria and eukaryotes have been found to adopt wellfolded structures under nonstress conditions and become activated via unfolding under stress conditions (5). These include the redox-regulated Hsp33, the temperature-regulated Hsp26, and the acid-activated chaperone HdeA and are termed "conditionally disordered proteins" (5)(6)(7)(8)(9)(10). These proteins represent a unique case of protein disorder, because they undergo an "order-to-disorder" transition during function, which is exactly opposite to the more commonly observed "disorder-to-order" transition either via the "folding-upon-binding" mechanism or by post-translational modifications (11,12).
The periplasmic chaperone HdeA in enteric bacteria plays a major role during acid stress in protecting a broad range of periplasmic proteins from denaturation-induced aggregation (13)(14)(15). The function of HdeA is critical for the survival of pathogenic bacteria when passing through the hosts' stomach, where it interacts with its native clients, including the outer membrane proteins (OMPs) as well as chaperones such as SurA and DegP that are essential in the OMP biogenesis pathways (16,17). HdeA exists as a well-folded homodimer in the inactive state, and its activation requires acid-induced protein unfolding accompanied by dimer dissociation, resulting in the exposure of hydrophobic surfaces for interaction with denatured client proteins (9 -10, 13, 18 -23). The molecular mechanism of the unfolding-induced HdeA activation is still unclear, and several long-standing questions remain unanswered concerning the following fundamental aspects. First, what is the active conformation of the HdeA chaperone? Second, where is (are) the client-binding site(s)? Third, how is HdeA activated and what is the structural basis for such an activation, or more specifically, how does acid induce the exposure of the binding site(s)?
To address the above issues, we herein employ several state-ofthe-art solution NMR techniques that have unique advantages in studying protein disorder and heterogeneous protein-protein interactions at atomic resolution (24 -26). The active-state conformation of HdeA has been characterized, which is largely disordered with local residual helical structures. Two hydrophobic segments with relatively extended conformations are identified to play central roles in binding client proteins, and a pH-regulated dynamic equilibrium between the well-folded inactive conformation and a sparsely-populated, partially unfolded conformation is observed. Three pH-sensitive structural regions are identified to function as "structural locks" in regulating the chaperone function activation. Our results provide molecular details of a multistep activation process of HdeA during acid stress, which demonstrates the central role of disordered regions in the chaperone function and the self-inhibitory role of ordered protein structure.

Active-state conformation of HdeA
The inactive HdeA is a homodimer under neutral pH conditions (13,18,23), although it becomes unfolded and dissociates into monomers at pH 2 with the estimated K d value of ϳ45 M (13). Under normal sample concentrations for NMR spectroscopy (ϳ100 M to 1 mM), the activated HdeA is in equilibrium between dimer and monomer conformations, both of which are largely unfolded and show significant signal overlap in the NMR spectra, which greatly hinders spectral analysis (Fig. S1). In this study, we identified a HdeA-F28W mutant that preserves the chaperone activity (Fig. 1, A and B, and Fig. S2A). This mutant is mainly monomeric at low pH judged by sizeexclusion chromatography (Fig. S2B), and its 2D 1 H-15 N HSQC spectrum at pH 1.5 shows a unique set of peaks essentially resembling those corresponding to the monomeric conformation of the activated WT-HdeA (Fig. S3). Therefore, the HdeA-F28W mutant can represent the monomeric activated state of HdeA and is used for chemical shift assignments and structural analysis.
By using conventional triple-resonance NMR experiments combined with experiments specifically optimized for disordered proteins, we obtained nearly complete backbone resonance assignments of HdeA-F28W at pH 1.5 (Fig. 1C). Analysis of the secondary structural propensity based on chemical shift information (27) confirms that the protein is largely disordered, whereas four short segments show different tendencies of forming local helical conformations (Fig. 1E). These residual helical regions generally correspond to part of the original helices ␣1 to ␣4 in the inactive HdeA structure, but are significantly shorter in length (Fig. 1, D and E). The two segments 20 -24 and 61-67 that are linked to each other via the strictly conserved disulfide bond between cysteine residues 18 and 66 show close to 40 and 70% helical contents, whereas the other two segments 35-43 and 79 -83 display lower helix-forming tendencies. The results are in accordance with the relaxation parameter R 2 /R 1 ratios, with higher R 2 /R 1 ratios indicating less structural flexibility. The averaged R 2 /R 1 value for segments 20 -24 and 61-67 is ϳ13.6, which is approximately two times the value of ϳ7.4 for segments 35-43 and 79 -83, and it is significantly higher than the N terminus of the sequence (Fig. 1E). This indicates that residual structures are present in the above regions, and the local conformation around the disulfide bond maintains the highest rigidity.

Site-specific 19 F labeling in HdeA
As demonstrated in our previous study (23), the majority of the backbone amide signals of HdeA in the 1 H-15 N HSQC spectra disappear upon binding to client proteins, and the remaining observable resonances correspond to the flexible, charged N and C termini (Fig. 1A). All signals throughout the 14 -72 region are unobservable, making it impossible to identify residues that are most critical for client interactions. We therefore used 19 F NMR spectroscopy to characterize the conformational properties of activated HdeA in both the client-free and -bound states by site-specifically introducing 19 F-labeled tryptophan into the protein sequence. Considering that the tryptophan residue contains a bulky hydrophobic side chain, which could potentially disrupt protein structure as well as affect chaperoneclient interactions, the conformational states and chaperone-like activities of all mutants were carefully examined and compared with WT-HdeA. A total of 15 mutants containing site-specifically incorporated 19 F-labeled tryptophan ( Fig. 2A) was selected and used for further 19 F NMR experiments, and the naming follows a "HdeA-xx-fluoro" pattern, where "xx" is the number for the amino acid position with the 19 F label in the protein primary sequence (Table 1). 1 H-15 N HSQC spectra were recorded to confirm that the mutations do not disrupt the overall structure of the inactive state and also do not interfere with client binding (Fig. S4). Isothermal titration calorimetry (ITC) experiments (Fig. S5) and antiaggregation assays (Fig. S6) further verified that the mutant retains chaperone activities essentially similar to WT-HdeA. One-dimensional 19 F NMR spectra were collected at pH 7.0 and 2.0 for all 19 F-labeling sites ( Fig. S7 and S8), and the results show that the 19 F chemical shifts are dispersed over a range of ϳ5 ppm (Ϫ47.7 to Ϫ52.5 ppm) at pH 7 while clustering around Ϫ48.3 ppm at pH 2, which is consistent with acid-induced unfolding (see more details in supporting Discussion).
It is worth mentioning that among the 15 sites for 19 F incorporation, 10 sites showed a unique peak in the 19 F NMR spectra of the free state at pH 2.0, whereas mutations to tryptophan in the remaining five sites (residue numbers 16, 24, 35, 78, and 82) resulted in the detection of two or more resonance peaks (Fig.  S8). In particular, the HdeA-24-fluoro, HdeA-35-fluoro, HdeA-78-fluoro, and HdeA-82-fluoro mutants show two peaks at pH 2, originating from a dynamic equilibrium between dimer and monomer conformations as indicated by concentration-dependent changes of peak intensities in both 19 F NMR and 1 H-15 N HSQC spectra. In addition, the HdeA-16-fluoro mutant appears to be structurally more stable at acidic pH compared with WT-HdeA, as it still harbors the folded conformation at pH 2.0 as shown by the 1 H-15 N HSQC spectra (Fig. S8A). This sample shows a total of four peaks in the 19 F NMR spectrum at acidic pH, as similarly observed in a previous study that identified the two peaks on the left as originating from the folded (or locally folded) conformation (28). Concentration-dependent 19 F NMR data further identified the monomeric and dimeric states of the unfolded conformation (Fig. S8B). For these mutants, chemical shift and line-shape analyses of the 19 F NMR data were performed using the peak corresponding to the monomeric unfolded conformation.

Client-binding sites identified by 19 F NMR
To identify the regions responsible for binding client proteins, we measured the solvent isotope shifts ⌬␦ ϭ ␦(D 2 O) Ϫ All ⌬␦ values are negative, and those closer to zero (smaller ͉⌬␦͉ values) indicate less solvent exposure. Therefore, we expect that the regions of HdeA in direct contact with the client protein to be buried show the smallest ͉⌬␦͉ values in the complex sample. In addition, we also expect to see a decrease of solvent exposure (thus negative ⌬⌬␦ values, when ⌬⌬␦ is calculated as The SSP scores were calculated based on the chemical shifts of 13 C ␣ and 13 C ␤ atoms using the program package SSP (27). SSP scores close to 1 indicate high propensity of ␣-helices. The R 1 and R 2 relaxation rates were measured on a 700-MHz spectrometer. For comparison, the SSP scores of the inactive HdeA based on the chemical shift assignments of WT-HdeA at pH 3.0 (23) is also shown (upper panel, helical regions shown in blue). The helical elements ␣1-␣4 in the inactive state (blue) and ␣1*-␣4* in the active state (red) are schematically shown on the top. The intramolecular disulfide bond is formed between cysteine residues 18 and 66.

Activation mechanism of an acid-resistant chaperone
⌬␦ free Ϫ ⌬␦ complex as shown in Fig. 2B) for residues involved in interaction when comparing the complexed state with the free state. Both criteria unambiguously support the identification of two hydrophobic regions 28 -35 and 49 -55 as the interaction sites. Residue Trp-16 also appears to contribute to client binding, suggested by the decreased ͉⌬␦͉ value in the complex state compared with the free state. However, this position exhibits limited solvent exposure in the free state as well, possibly due to the residual secondary structures around the disulfide bond region.
Furthermore, comparison of the signal line widths in the free and complexed states at pH 2.0 supports the participation of segments 28 -35, 49 -55, as well as residue 16 in binding client proteins (Fig. 2C). The significantly increased line widths of these residues in the presence of the client protein demonstrate direct involvement in binding, whereas the nearly unchanged chemical shifts for all positions reflect the heterogeneous (or promiscuous) nature of the binding. Particularly, site 55 shows significant line broadening and apparently comprises multiple conformations, indicative of heterogeneous binding (Fig. 3).
Taking all the above factors into consideration, it is clear that the two segments that are rich in hydrophobic residues, namely the 28 -35 and 49 -55 segments, play central roles in directly binding to unfolded client proteins under acid stress ( Fig. 2A). The 19 F-labeling sites identified to participate in client interactions are mapped onto the folded HdeA dimer structure in Fig.  2D, whereas space-filling representation of the two segments showing their locations in the dimer structure are depicted in Fig. 2E. Taking into account that the 28 -35 segment is more deeply buried in the core of the dimer, we herein term the 49 -55 segment as client-binding site I and the 28 -35 segment as client-binding site II (see below).
To further verify these two client-binding sites, four single mutants HdeA-F28K, HdeA-V33K, HdeA-V49K, and HdeA- The values ⌬␦ complex , ⌬⌬␦, and ⌬FWHM were independently used as criteria to judge whether the 19 F-labeled sites are involved in client binding, and the results are indicated below the protein sequence in A. 19 F-Labeled sites with ⌬␦ complex values satisfying 0 ppm Յ ⌬␦ complex Յ Ϫ0.07 ppm, ⌬⌬␦ values satisfying ⌬⌬␦ Յ Ϫ0.025 ppm, or ⌬FWHM values satisfying ⌬FWHM Ն 400 Hz are marked by "ϩϩ" in A; those with ⌬␦ complex values satisfying Ϫ0.07 ppm Ͻ ⌬␦ complex Յ Ϫ0.10 ppm, ⌬⌬␦ values satisfying Ϫ0.025 ppm Ͻ ⌬⌬␦ Ͻ 0 ppm, or ⌬FWHM values satisfying 200 Hz Յ ⌬FWHM Ͻ 400 Hz are marked by "ϩ" in A (see supporting Discussion for more details). D, mapping of the 19 F-labeled sites that show direct involvement in client binding onto the HdeA dimer structure. Residues from the two monomers are shown as green and red spheres, respectively. E, ribbon diagram of HdeA dimer structure with the client-binding sites from both molecules shown as spheres. Site I from both monomers are colored in light blue, and site II from the two molecules are colored in green and cyan.
Activation mechanism of an acid-resistant chaperone L50K were constructed and were observed to show decreased chaperone activity compared with WT-HdeA (Fig. S10, A and B and supporting Discussion). Notably, single mutation of either Val-33 in client-binding site II or Leu-50 in site I to lysine disrupts the folding of HdeA in its inactive form at pH 7, whereas the F28K and V49K mutants maintains the well-folded dimeric structure at neutral pH (Fig. S10C). These observations can be attributed to the facts that the side chains of Val-33 and Leu-50 largely contribute to packing of the hydrophobic core, whereas those of Phe-28 and Val-49 point toward the periphery of the dimer structure. Nevertheless, all four mutants are largely disordered at pH 1.5, which is similar to WT-HdeA. The four mutations do not prevent the acid-induced unfolding of HdeA, and the V33K and L50K mutations even result in constitutive unfolding at neutral pH. The deficiency of these mutants in preventing acid-induced client precipitation supports the role of these two sites in client binding.
Furthermore, it is worth noting that both client-binding sites are sandwiched between regions with relatively high propensities of residual helical conformations but display low propensities themselves (Ͻ20%) of forming helices in the active state ( Fig. 1E). Site II contributes to the formation of a large portion of the helix ␣2 in the inactive dimer structure, whereas the 52 VQGI 55 tetra-peptide in site I forms the N-terminal tip of helix ␣3. The transition from helical to the more extended random coil conformation may be important for exposure of the hydrophobic residues and thus interaction with client proteins.

pH-regulated order-to-disorder transition
The order-to-disorder transition of HdeA during acid stress that exposes the two client-binding sites can be probed by the pH-dependent solvent paramagnetic relaxation enhancement (sPRE) experiment, which uses soluble paramagnetic probes to characterize the solvent accessibility of each residue. The results show that the inactive HdeA dimer structure is relatively compact at pH 6, with the majority of the residues minimally affected by the paramagnetic probes, whereas several regions, including the N and C termini as well as the two client-binding sites, show significantly increased solvent accessibility at pH 4 and 3 ( Fig. 4) and is in general agreement with the NMR hydrogen/deuterium (H/D) exchange data previously reported (22).
To provide direct experimental characterizations of the partially unfolded intermediates along the pH-dependent unfolding pathway of HdeA, we further used the chemical exchange saturation transfer (CEST) NMR method that has special advantages in probing sparsely-populated protein conformations (25,29). Briefly, when the structure of a protein is in exchange between a highly-populated ground state and a sparsely-populated "invisible" (or "excited") state, saturation on the sparsely-populated state could be transferred to the ground state and result in the signal intensity reduction of the ground state, thus rendering the invisible state to become "visible." 15 N-CEST NMR spectra of the WT-HdeA were systematically recorded at pH values of 4.0, 3.5, 3.0, and 2.5 (Fig. S11). The HSQC spectra in the pH range of 4.0 -3.0 show a single set of peaks corresponding to the folded dimeric state, and therefore the 15 N-CEST profiles are probing conformational exchanges with the folded dimer as the ground state. However, the HSQC spectrum of WT-HdeA at pH 2.5 is highly heterogeneous and contains multiple sets of peaks, including one set corresponding to the folded dimer similar to that detected at pH 3.0, as well as those similar to the unfolded states (which is an equilibrium of unfolded dimer and monomer states) as detected at pH 2.0 (Fig. S12). Only the CEST profiles of resonances corresponding to the dimer species were analyzed, and thus the 15 N-CEST data at pH 2.5 presented herein also report on the conformational exchanges with the folded dimer as the ground state. The experiments detected no excited states for all residues at pH 4.0, whereas sparsely-populated excited conformations were observed for a certain number of residues in the pH range of 3.5 to 2.5, many of which show chemical shifts resembling random coils (Fig. 5, A and B, and Fig. S11) (30). The number of residues harboring the excited state increases as the pH decreases, and a drastic difference was observed between pH conditions of 3.0 and 2.5 (Fig. 5A). At pH 2.5, when HdeA is highly activated, over half of the total number of residues show exchanges between folded and unfolded conformations, and the residues are spread out in the protein sequence, suggesting that the exchange process corresponds to a global unfolding of Table 1 Summary of HdeA mutants used in this study Activation mechanism of an acid-resistant chaperone the protein structure. This is further supported by the high correlation between the excited state chemical shifts of WT-HdeA at pH 2.5 with the active disordered state chemical shifts obtained from the assignments of HdeA-F28W at pH 1.5 (Fig.  S13). Notably, the HSQC spectrum of WT-HdeA at pH 2.5 contains signals originating from the unfolded conformation, and thus the minor peaks detected in the CEST profiles should be detectable in the HSQC spectrum, although accurate identifications of these peaks are difficult due to the severe signal overlaps originating from dimer-monomer equilibrium of unfolded WT-HdeA. In contrast, order-to-disorder conformational exchanges occur only at local regions at pH 3.0 and above, and these partially unfolded conformations most prob-ably represent the unfolding intermediates along the pH-induced activation pathway.
Global fitting analyses of the CEST data using a two-state exchange model, G L | ; kGE kEG E, where G and E stand for the ground and the excited states, further show that the apparent exchange rate constant k ex (k ex ϭ k GE ϩ k EG ) between the folded and unfolded conformations decreases at lower pH, and the relative population p E of the excited state increases (Fig. 5A). The unfolding rate constant k GE is estimated to be ϳ1.5, 2.0, and 4.1 s Ϫ1 , whereas the folding rate constant k EG is estimated to be ϳ500, 218, and 66 s Ϫ1 at pH 3.5, 3.0, and 2.5, respectively (Table 2).

Activation mechanism of an acid-resistant chaperone
The rate constant of unfolding increases about 3-fold when pH decreases from 3.5 to 2.5, whereas the rate constant of refolding decreases of about 10-fold. These results indicate that the energy barrier for the folding-to-unfolding transition decreases along with the decrease of pH, whereas the energy barrier for the reverse process dramatically increases. This results in a gradual increase of the excited state population, as well as the average lifetime for the excited state, which is ϳ2.0 ms at pH 3.5, 4.6 ms at pH 3.0, and 15.0 ms at pH 2.5. Moreover, the  Activation mechanism of an acid-resistant chaperone estimated unfolding rate constant of 4.1 s Ϫ1 at pH 2.5 is highly consistent with the kinetics parameter (k Ͼ 3.5 s Ϫ1 ) of HdeA unfolding and monomerization reported previously (20), further supporting that the excited states probed by the CEST experiments are on-pathway for HdeA activation.

Conformational transition "hot spots"
By comparing the number and locations of residues showing order-to-disorder exchanges under different pH conditions, we identified three essential acid-sensitive structural hot spots in which conformational transitions (dimer dissociation and unfolding) initially occur (Fig. 5C).
The first region (designated as "region a" hereafter) showing quick acid-response at pH 3.5 is the 46 ED 47 -49 VLD 51 segment, which clusters in the C-terminal end of the 50s loop and immediately connects to helix ␣3. At pH 3.0, one additional residue, Val-52, shows conformational exchanges, whereas at pH 2.5 all residues in the 46 EDAVLDV 52 segment undergo exchanges. Notably, the 49 VLDV 52 tetra-peptide is part of the client-binding site I and is involved in dimer formation by interacting with the N terminus of the other HdeA molecule in the homodimer via electrostatic interactions (Fig. 5D). Protonation of the three acidic residues Glu-46, Asp-47, and Asp-51 could break the electrostatic interactions and lead to local structural loosening. Asn-14 residue in the N-terminal loop region is spatially close to the 46 ED 47 -49 VLD 51 segment in the dimer structure (Fig.  5C), and its observed conformational exchanges at pH 3.5 could originate from local collective motions.
The second region ("region b") corresponds to segment 34 GFA 36 -39 LN 40 in the C-terminal end of helix ␣2. Compared with region a, this region shows less acid sensitivity because conformational exchanges could be detected for only Asn-40 at pH 3.5. When the pH decreases to 3.0, conformational exchanges can be observed for residues Gly-34, Phe-35, and Ala-36 located in the very center of the HdeA dimer. The 34 GF 35 dipeptide is part of the client-binding site II, and the Gly-34 and Leu-39 residues have essential contributions to dimer packing by interacting with Gly-34Ј and Leu-39Ј residues from the other HdeA monomer (here we use a Ј to indicate residues from the second HdeA monomer). Notably, residues Asp-43 and Lys-44 in the loop immediately connected to the C-terminal end of ␣2 show electrostatic interactions with Asp-43Ј and Lys-44Ј from the other HdeA monomer (Fig. 5D), forming an electrostatic "lock" that helps stabilize the dimeric structure. Protonation of Asp-43 could break this lock and promote the exposure of the client-binding site II.
The third region ("region c") corresponds to the 24 VD 25 -28 FQ 29 segment at the N-terminal tip of helix ␣2. This region shows relatively high acid sensitivity with four residues exhibiting exchanges at pH 3.5, and the number gradually increases with the decrease in pH values. Notably, the 28 FQ 29 dipeptide is part of the client-binding site II, and the Phe-28 residue contributes to dimer formation by interacting with the Pro-30Ј residue. Although the acidic Asp-25 and Glu-26 residues do not show electrostatic contacts with positively charged residues, the carbonyl group of Asp-25 is observed to form a hydrogen bond with the Ser-27 hydroxyl group based on the X-ray crystal structure (Fig. 5D). Protonation of the Asp-25 side chain could affect its ability in acting as an electron receptor and destabilize the local structure.
At pH 3.0 and 2.5, residues in other regions also start to show dynamic exchanges between folded and unfolded states, including the hydrophobic 55 IA 56 -V 58 segment in the ␣3 helix which may also participate in client interactions, and the densely-charged C-terminal region harboring the ␣4 helix (Fig. 5A).

Multistep activation mechanism of HdeA chaperone function
Based on the above results, a multistep acid-induced activation mechanism of HdeA chaperone function is derived and schematically summarized in Fig. 6. The client-binding site I is located at a relative peripheral region in the HdeA dimer structure and is shielded by the N-terminal segment of the other HdeA molecule. The acidic residues Glu-46, Asp-47, and Asp-51 in the 50s loop have pK a values of 4.07, 4.14, and 3.83 (22) and are in the deprotonated state under neutral and nearneutral conditions (pH Ͼ 4), ensuring electrostatic interaction with the N-terminal region. As the pH decreases to lower than 4, protonation of these residues results in disruption of the intersubunit electrostatic contacts and exposure of the clientbinding site I. The self-inhibitory role of the N-terminal region is supported by the observation that an HdeA-N⌬9 mutant with the N-terminal nine residues deleted shows interactions with SurA, another native client of HdeA (13), under elevated pH conditions (Fig. S14, A and B). In addition, the HdeA-N⌬9 mutant also exhibits partial anti-aggregation activity toward the native client protein OppA (13) at pH 4.0, whereas both WT-HdeA and HdeA-F28W are inactive under this pH condition ( Fig. S14C and supporting Discussion). Local structural loosening is supported by the sPRE results revealing a drastic difference of the extent of solvent exposure for the N-terminal residues between pH 6 and 4 (Fig. 4), which was not observed in the H/D exchange experiments because all resonances from the N-terminal segment already disappeared even at pH 6 (22). This difference most probably originates from the larger size of the chelated solvent paramagnetic probes compared with water molecules (the probes in the H/D exchange experiments), thus rendering higher sensitivity in observing subtle changes for fast-exchanging amides in the N-terminal segment using the sPRE method.
The client-binding site II located in the ␣2 helix is tightly packed in the structural core of inactive HdeA dimer and could only be exposed via extensive disruption of the dimeric interface. At pH above 4, two acid-sensitive regions (region b and region c as shown in Fig. 5) present at both ends of the ␣2 helix stabilize the dimer interface via inter-and intrasubunit contacts. In addition, previous studies have shown that the protonation of Glu-37, an acidic residue showing an exceptionally high pK a value, maximally stabilizes the inactive HdeA dimer at pH 5 and protects residues in the client-binding site II from being accessed (10,22,31,32). At pH Ͻ 4, acid-induced orderto-disorder conformational exchanges in the b and c acid-sensitive regions loosen the structural locks and enable partial dissociation of the ␣2 helices of the two HdeA molecules. Notably, region b occupies more than half of the total length of the ␣2 helix, whereas region c locates only at the N-terminal tip of the helix. Therefore, upon acid-induced loosening of these two

Activation mechanism of an acid-resistant chaperone
regions, it appears that the C-terminal part of the ␣2 helix (the upper part as shown in Figs. 5C and 6A) becomes more destabilized. The sPRE data at pH 3-4 show that the solvent accessibility of residues in ␣2 increases rapidly toward the C-terminal end (Fig. 4), further suggesting that the C-terminal half is more significantly affected by pH changes and that dimer dissociation is most probably initiated from this end. This scenario is also supported by previously reported H/D exchange data and molecular dynamics simulations (22, 33).
Taken together, the acid-induced activation of HdeA is a multistep process, which involves the destabilization of three essential structural locks that inhibit the chaperone activity under nonstress conditions. The initial activation step is the dissociation of the N-terminal loop, which exposes the client-binding site I. The subsequent step involves local structural destabilization of helix ␣2 from both the N-and C-ends, which enables partial exposure of client-binding site II. Finally, when pH further decreases, the whole-protein structure collapses and becomes fully activated, with both sites exposed for client interactions. In the fully activated state, the N-and C-terminal regions of HdeA form two highly charged, flexible "tails" that help increase the solubility of the HdeA-client complexes, whereas the two essentially hydrophobic client-binding sites are held into a "ring" structure by the strictly conserved disulfide bond (Fig. 6, B and C). Both the spatial proximity of the two client-binding sites restricted by the disulfide bond, as well as the higher propensities of adopting random coil conformations for these two segments compared with other regions in the ring, Figure 6. Summary of acid-induced activation mechanism of HdeA. A, schematic illustration of the multistep pH-dependent activation process of HdeA. The two client-binding sites I and II are shown in light blue and deep blue, respectively. As pH decreases, the hydrophobic residues in client-binding sites I and II, as well as the Trp-16 residue, gradually become exposed and competent for client binding (illustrated by stars). The pH-sensitive region a and the N-terminal segment that regulate the exposure of site I are colored red, whereas the pH-sensitive regions b and c that regulate the exposure of site II are colored violet and purple, respectively. B, illustration of the "ring-tail" model of activated HdeA showing the highly charged hydrophilic tails, the relatively structured hinge containing the disulfide bond, and the hydrophobic ring harboring the client-binding sites I and II. The two sites are colored in light blue and deep blue as in A, and the segments with residual helical contents are colored in light yellow (segments 35-43 and 79 -83) and orange (segments 20 -24 and 61-67), respectively. C, mapping of all structural features essential to HdeA activation onto the dimer structure. One monomer is shown as a ribbon diagram, and the other is shown as the surface representation. The client-binding sites and the residual helical regions are colored as in B, and the pH-sensitive residues in regions a, b, and c are shown as spheres and colored as in A.

Activation mechanism of an acid-resistant chaperone
could sufficiently increase the effective hydrophobic surface area to facilitate client interactions.

Self-inhibitory role of the N terminus
In our previous work, we have hypothesized that the N-terminal charged region plays dual roles in HdeA function: one is to increase the HdeA-client complex solubility, and the other is to inhibit the chaperone function under neutral conditions (23). In this study, we show direct evidence that the N terminus protects one of the two essential client-binding sites under nonstress conditions. A previously reported constitutively active HdeA-D20A/D51A double mutant is also consistent with this scenario (10). Based on the solution NMR structure of the inactive HdeA dimer (23), both Asp-51 and Asp-20 play essential roles in stabilizing the N terminus. Asp-51 forms intermolecular contact with Lys-5Ј, whereas Asp-20 forms intramolecular contact with Lys-11. These two electrostatic interactions, together with the intermolecular electrostatic contacts between Asp-47 and Lys-10Ј described above, act in concert to anchor the N terminus onto the surface of the client-binding site I (Fig. S15). Disruption of these interactions could result in the release of the N-terminal region and expose site I under nonacidic conditions. However, we examined the 15 N HSQC spectra of the HdeA-D20A/D51A mutant and observed high content of unfolded conformations at pH 7.0 and 5.0 (Fig. S16), which complicates the interpretation of the constitutive chaperone activity at pH Ͼ 5 (10). The HdeA-N⌬9 mutant used in this study much better preserves the overall folded structure over the pH range of 7.0 to 3.5 (Fig. S16), and therefore, it provides more direct evidence for the self-regulatory role of the N-terminal segment. Moreover, our model of HdeA activation suggests that the first step of activation occurs at the clientbinding site I and involves a simple conformational switch of releasing the N-terminal segment. Thus, without the need for either dimer dissociation or large-scale protein unfolding, HdeA can use this patch of hydrophobic residues for initial contact with partially denatured clients under mild acidic conditions (pH 3.5-3). Actually, this can be supported by the appearance of a few N-terminal signals of HdeA (Lys-5, Ala-6, and Ala-7) when it initially interacts with client proteins at pH 3.0 -3.8, as reported in our previous study (23), which highlights the release of the N-terminal segment. No new signals from other regions of HdeA were observed upon client interaction, suggesting that the initial contact involves only site I. More intriguingly, protein sequence alignment of the HdeA and HdeB homologs reveals a nine-residue difference in their N-terminal regions (Fig. 7A). The HdeB protein is another acidresistance chaperone but with a less well understood functional mechanism. The dimeric structures of HdeA and HdeB are significantly different in terms of dimeric packing, although their monomeric structures are essentially similar (34 -37). Recent studies both in vitro and in vivo suggested that HdeB displays optimal chaperone activity at mild acidic pH values (pH ϳ4) (17,36). To date, it remains enigmatic as to why HdeB functions at a higher pH range when its overall 3D structure remains intact, whereas HdeA is activated only when it is partially unfolded at lower pH values. Sequence comparison between the two homologs reveals that the most conserved residues between these two proteins are clustered in three regions: the 17-24 and 60 -74 segments harboring the consensus cysteines and the 44 -58 segment harboring the client-binding site I of HdeA (numbered according to HdeA sequence). The sequence conservation in the first two regions may be important for maintaining structural stability, whereas the conservation in the third region implies that HdeB may also utilize the same site for interaction with client proteins. Because of the lack of the N-terminal nine residues in the HdeB sequence, this site is already exposed and competent for client interactions under nonacidic conditions without the need of protein unfolding (Fig. 7B).

Discussion
As Foit et al. (10) suggested previously, the activation of HdeA chaperone function may not require the protein to be completely unfolded and that "some of the pH-induced structural changes that accompany HdeA activation are by-products of acidification rather than an actual requirement for activity." Based on residue hydropathy analysis, the hydrophobic segments in the HdeA primary sequence contain 19 -41 and 45-65 and span through helices ␣1, ␣2, and ␣3 (19). Our results

Activation mechanism of an acid-resistant chaperone
show that the client-binding sites (28 -35 and 49 -55) comprise about only half the length of these segments, whereas hydrophobic residues close to the consensus cysteines are not directly responsible for client interactions. The identified binding sites are consistent with previous findings that hydrophobic residues Phe-35, Val-55, and Val-58 are essential for client interactions (19,20). Moreover, the two client-binding sites have distinct locations in the HdeA dimer structure and show different pH responses, indicating that HdeA activation follows a pH-dependent stepwise process in which the two sites are activated sequentially and that dimer dissociation (exposure of site II) is more stringently controlled and occurs only at a later stage. Therefore, it is possible that the two sites could act either independently (e.g. at mild acidic conditions when the dimer interface remains intact) or in concert with each other to gain higher chaperone activity (at low pH when HdeA is largely unfolded and the two sites are held in close proximity to provide a larger interaction surface). The sequential activation of HdeA may be important for fine-tuning the HdeA-client interactions under different pH conditions.
Although the existence of low-populated partially unfolded intermediates has been suggested by studies from different groups (22, 23,32,33,38,39), the exact identities of these intermediates and their correlations with chaperone function were poorly understood. Several molecular simulation studies have been carried out (31, 33, 38 -40), and a partially unfolded dimeric intermediate (I 2 ) of HdeA was captured showing the characteristics of an almost intact dimeric interface, whereas the helix ␣4 in one monomer is largely disordered (33). However, the location of the two client-binding sites indicates that unfolding and dissociation of helix ␣4 from the structural core does not play a profound role in exposing the hydrophobic surface responsible for client binding. Inspection of the HdeA dimer structure reveals that the side chains of Phe-74, Val-78, and Trp-82 from helix ␣4 form a hydrophobic core within a monomer with Phe-21 from helix ␣1, Val-33 from helix ␣2, and Val-58 and Ile-62 from helix ␣3, but are distal from either the Val-49/Ile-55 residues in client-binding site I or the bulky aromatic side chains of Phe-28/Phe-35 in client-binding site II (Fig.  S17). Therefore, unfolding of helix ␣4 within a monomer would not lead to significant exposure of the two hydrophobic binding sites. More importantly, the CEST data indicates that local structure loosening at the three pH-sensitive hot spots starts at a higher pH (pH 3.5) than the unfolding of helix ␣4 (pH 3.0). Unlike the drastic conformational change associated with helix ␣4 unfolding, these earlier structural loosening events at the pH-sensitive regions occur in a much more localized manner, but are directly involved in the exposure of client-binding sites and thus are more correlated with the chaperone activity. Taken together, the unfolding of ␣4 is more likely to be a byproduct of HdeA structural changes induced by acidification. Nevertheless, unfolding of ␣4 may contribute to increasing HdeA chaperone activity at low pH by exposing the 58 -63 segment in helix ␣3 as an extension to the client-binding site I. Additionally, it is also possible that ␣4 unfolding could indirectly affect the stability of the dimeric interface and facilitate dimer dissociation. It is worth mentioning that all computational studies aimed at characterizing the unfolding intermedi-ates of HdeA reported thus far start from the crystal structure lacking the first nine residues (10, 31, 33, 38 -40), and any local conformational changes involving the N-terminal segment would have gone unnoticed. Our current CEST data may hopefully provide an experimental basis and aid further molecular simulation studies.
Although the structural details of chaperone-client complexes are usually difficult to investigate due to the large molecular sizes and conformational dynamics, recent advances in solution NMR methods have enabled atomic-resolution structural determinations of the chaperones trigger factor (TF) and SecB in complex with unfolded clients (41,42). The bacterial acid-response chaperone HdeA exhibits some unique characteristics compared with these chaperone systems as it is largely disordered and dynamic in the activated state, whereas TF and SecB adopt relatively rigid three-dimensional structures with hydrophobic client-binding sites spread out on their surfaces. The two client-binding sites in HdeA are hydrophobic, which is a common feature shared among different chaperones. However, the extremely small molecular size of HdeA and the fact that the two client binding segments become largely disordered upon activation suggest that the HdeA-client binding mode could be much different from the above two chaperones. The disordered characteristics of the binding sites in HdeA may provide better exposure of the hydrophobic side chains and are favorable for client interactions. The observation that the binding sites show more extended conformations compared with neighboring regions suggests an inverse correlation between the helical-forming propensity and the client-binding activity and provides a unique demonstration of the link between structure disorder and chaperone function. Alternatively, the client-binding sites may adopt transiently formed or sparsely populated helical structures (in particular, residues in site I are estimated to have 10 -20% of helix-forming propensities), which may fine-tune the local conformation and facilitate promiscuous binding to a broad range of client proteins. Moreover, considering the results that segments outside the two client-binding sites show relatively high helixforming propensities under acidic conditions and that the HdeA-V33K and L50K mutations simultaneously destabilize inactive dimer structure and impair the chaperone activity, it is possible that a partially folded conformation of HdeA may be needed for sufficient chaperone-client complex formation. This scenario is also consistent with the observations that the disulfide bridge was important for chaperone function (20) and that the conformational transition hot spots identified by CEST cluster in space in the inactive state of HdeA. Under extremely acidic conditions when HdeA becomes largely unfolded, it remains possible that the chaperone transiently excurses to a partially folded state that facilitates complex formation with clients.
Taken together, our data highlight a complex interplay of both protein structural order and disorder in the regulation of the HdeA chaperone function. To fully understand the functional mechanism of HdeA, the atomic-level structural information concerning HdeA-client complexes is essential. The mode of HdeA-client interactions could be different under Activation mechanism of an acid-resistant chaperone mild acidic and highly acidic conditions, which have potential physiological implications regarding responses to different extents of acid stress, cooperation between HdeA and HdeB homologs, as well as the process of client release (21). However, the disappearance of NMR signals in the 1 H-15 N HSQC spectra of HdeA upon complex formation most probably reflects the promiscuous and dynamic nature of the binding, and it renders atomic-resolution structural determination of HdeA-client complexes through similar approaches as used in the studies of TF and SecB exceptionally difficult. Moreover, much less is known about the conformational states of acid-denatured client proteins and their chaperone-interacting sites, and further investigations focusing on the clients would hopefully shed more light on the HdeA-client interactions.

Sample preparations
The Escherichia coli hdeA, malE, surA, and oppA genes and all hdeA mutant genes were cloned into pET-28a(ϩ) plasmid (Novagen) and transformed into E. coli BL21(DE3)-T1R or BL21 Star(DE3)-T1R strains (Sigma) for protein expression. All protein expression and purification procedures were similar, as reported previously (23). The NMR samples were prepared in buffers containing 50 mM sodium phosphate and 45 mM citric acid at different pH conditions. The HdeA-client complex samples were prepared by mixing the HdeA and client protein samples at pH 7 and subsequently changing into buffers with various pH values using Millipore centrifugation tubes with a 3-kDa molecular mass cutoff.

Anti-aggregation assay
The chaperone activities of WT-HdeA, the HdeA-F28W mutant, and all 19 F-labeling mutants were tested by the antiaggregation assay as reported previously (9,43). MalE was used as the client protein and incubated in a buffer containing 45 mM citric acid, 50 mM sodium phosphate, and 150 mM sodium sulfate (pH 1.5) at 25°C for 60 min with or without the presence of HdeA and its mutants. The addition of 150 mM sodium sulfate was to achieve effective aggregation of MalE at low pH values (44,45). The MalE concentration was kept at 10 M, whereas four different concentrations (1, 2.5, 5, and 10 M) were used for HdeA and its mutants. The presence of MalE in the supernatant or the pellet was analyzed by SDS-PAGE.
For measuring the anti-aggregation activity of the HdeA-N⌬9 mutant at pH 4.0, the client protein OppA was used, and the incubation temperature was increased to 35°C. All other experimental conditions were the same. Control experiments were performed using WT-HdeA and HdeA-F28W at both pH 4.0 and 1.5.

Chemical shift assignments of the F28W mutant at low pH
For chemical shift assignments of the active monomeric state of HdeA, a sample containing 0.5 mM 13 C/ 15 N-labeled HdeA-F28W mutant was prepared at pH 1.5. NMR spectra were acquired at 25°C on Bruker Avance 700-MHz spectrometers, equipped with four RF channels and a triple-resonance cryoprobe with pulsed field gradients. Two-dimensional 15 N-edited HSQC spectroscopy, traditional three-dimensional HNCA, HN(CO)CA, HNCACB, HN(CO)CACB, HNCO, and HN(CA)CO for protein backbone assignments, as well as HNN and HN(C)N experiments especially designed for assigning unfolded proteins were collected (46, 47). All spectra were processed using the software package NMRPipe (48) and analyzed by the program NMRView (49).

F labeling
Site-specific incorporation of 19 F labels into HdeA was achieved by labeling tryptophan residues with 5-fluorotryptophan following published methods (50). Briefly, E. coli cells harboring plasmids containing the mutant genes were first grown in 1 liter of Luria-Bertani medium at 35°C. When the A 600 reached 0.8, the cells were collected by centrifugation at 4000 ϫ g and resuspended in 500 ml of M9 minimal medium with NH 4 Cl and glucose as the nitrogen and carbon sources, 60 mg/liter 5-fluoroindole, and with 50 mg/liter kanamycin. After shaking for 1 h at 35°C, protein expression was induced by adding isopropyl ␤-D-thiogalactoside to a final concentration of 0.4 mM. Cells were grown for another 8 h and harvested by centrifugation. 15 NH 4 Cl was used in the M9 media to simultaneously achieve site-specific 19 F incorporation and uniform 15 N labeling. The WT-HdeA protein sequence contains two tryptophan residues Trp-16 and Trp-82. For 19 F labeling in these two sites, the HdeA W82F or W16F mutants were used. For 19 F labeling in all other sites, additional mutations were made based on the HdeA W16F/W82F double mutant (e.g. for 19 F labeling in position 39, a HdeA W16F/W82F/L39W triple mutant was used). 19 F NMR experiments were performed at pH 7.0 or 2.0. The preparations for the samples containing 15 N/ 19 F-labeled HdeA mutants alone or in complex with unlabeled substrate MalE at pH 2.0 were similar to those reported previously (23). The samples were prepared with 0.5 mM 15 N/ 19 F-labeled HdeA mutants with or without 1.0 mM MalE for the free or complexed states, respectively. Trifluoroacetic acid (TFA) was added to a final concentration of 10 M as the internal chemical shift reference. All samples were prepared using the same stock of buffers with different pH values, and the exact pH value for each sample was further measured using microelectrode as well as 19 F NMR of a chemical shift-based pH sensor 4-fluoroaniline, as described previously (23). One-dimensional 19 F NMR spectra were acquired on a Bruker 600-MHz spectrometer equipped with a room temperature BBO probe at 25°C. For all 19 F-labeled mutants, the spectra of the inactive free state (pH 7), the active free state (pH 2), and the complex state (pH 2) were acquired sequentially, and a standard methanol sample was used for temperature calibration to ensure that the temperature control system of the spectrometer remained stable over time. A spectral width of 12 kHz and a relaxation delay of 1.5 s were used. A total of 4096 or 100,000 transients was recorded for the free state or HdeA-MalE complex samples, respectively.

F NMR experiments
For measuring the solvent-induced isotope shifts, the samples were initially prepared in a buffer containing 90% H 2 O and 10% D 2 O for NMR spectra collection and subsequently lyoph-Activation mechanism of an acid-resistant chaperone ilized and re-dissolved in 100% D 2 O for another round of 19 19 F NMR spectra were well-reproduced and to estimate the data uncertainties. The solvent-induced isotope shifts ⌬␦ were also measured at pH 7.0 as a control, where we observed that residues in flexible regions show ͉⌬␦͉ values in the range of 0.10 to 0.17 ppm, whereas the ͉⌬␦͉ value for TFA in 100% D 2 O and in 90% H 2 O, 10% D 2 O was 0.14 ppm.
Apart from the solvent isotope shifts, the 19 F spectra of the HdeA mutants in complex with MalE acquired before and after lyophilization are essentially identical in terms of shape and line widths, indicating that lyophilization does not change the structure of HdeA in the complex or the mode of interaction between HdeA and the client. This was further verified by the essential similarity between the 1 H NMR spectra of the HdeA-MalE complexes at pH 2.0 before and after lyophilization (the samples were re-dissolved in H 2 O so that that no hydrogendeuterium exchange occurs).

ITC experiments
Binding of HdeA or its mutants to the client MalE was measured by ITC using a VP-ITC microcalorimeter (Micro-Cal, Northampton, MA) at 25°C according to the manufacturer's instructions. All protein samples were dialyzed overnight against a buffer containing 45 mM citric acid and 50 mM sodium phosphate (pH 1.5) and were degassed for 10 min before the titrations. A total of 283 l of concentrated WT-HdeA or its mutants (235 M) was used as the titrant and added into the MalE solution (1400-l, 19 M). The titrations were carried out with a preliminary 2-l injection (discarded in the data analyses) and followed by 24 injections of 10 l with an interval of 300 s. The control experiment by titrating HdeA into the buffer was subtracted before data analyses. Note that the buffer used for the ITC measurements does not contain the 150 mM sodium sulfate, which is different from the buffer used in the anti-aggregation assay, so that the MalE protein remains soluble under the experimental condition. All data were analyzed using the program package PEAQ-ITC analysis (Microcal) with different binding models, and the standard errors of the extracted parameters were derived from nonlinear least-squares fitting using the Levenberg-Marquardt algorithm.

sPRE experiments
Paramagnetic samples were prepared with 15 N-labeled HdeA (0.6 mM) with paramagnetic probe EDTA-Gd 3ϩ (0.5 mM), whereas the diamagnetic samples were prepared with 15 N-labeled HdeA alone. An excess of EDTA (1.0 mM) is added in both samples to eliminate the binding of Gd 3ϩ ions onto the protein. The 1 H-15 N HSQC spectra were collected for both samples at pH conditions of 6.0, 4.0, and 3.0 on a Bruker Avance 800-MHz spectrometer at 25°C. The spectra of the paramag-netic and diamagnetic samples at each pH condition were carefully compared to ensure that the addition of the EDTA-Gd 3ϩ probe did not affect the sample pH and that all signals were well overlaid. The sPRE effects were calculated as the intensity ratio for each residue in the spectra of the paramagnetic and diamagnetic samples. The experimental errors were determined from duplicated experiments.

N CEST measurements and analysis
The 15 N CEST experiment (29) for WT-HdeA was acquired at 35°C on a Bruker Avance 600-MHz spectrometer. Comparisons of the HSQC spectra and CEST profiles at three different temperatures, 15, 25, and 35°C, demonstrate that the structure and conformational exchanges are essentially similar, but acquiring CEST data at 35°C provided the highest sensitivity. The sample was prepared in buffers containing 50 mM phosphate, 45 mM citric acid, and 10% D 2 O at pH 4.0, 3.5, 3.0, and 2.5 with the protein concentrations of 2.0 mM. A total of 105 2D data sets were acquired with the 15 N carrier frequencies positioned from 101 to 132.2 ppm at a spacing of 0.3 ppm (18.24 Hz) during the irradiation time of t ex ϭ 800 ms. In all experiments, irradiation field strengths B 1 of 9.4 Ϯ 0.2 and 14.0 Ϯ 0.2 Hz were used, and a 2.7-kHz field 1 H decoupling composite pulse sequence (90 x -240 y -90 x ) was applied during the t ex period. Data without using the B 1 field during the t ex period was recorded as the reference experiment. B 1 calibration was carried out following the previously reported methods (51). All the data sets were processed using the NMRPipe program (48), and peak intensities were obtained by NMRView (49). The CEST profiles for the individual residues were generated by calculating the intensity ratios I/I 0 versus the varied 15 N carrier frequencies, where I 0 is the intensity measured in the reference spectrum, and I is the intensity measured with the application of the B 1 field. The CEST data were analyzed using the software package ChemEx (https://github.com/gbouvignies/chemex) 6 or in-house written Matlab scripts from B. Yu and D. Yang (52).
For a two-state exchange process, G L | ; kGE kEG E, G and E represent the ground state and sparsely populated excited state, respectively. The fractional populations of two states p G and p E satisfy the equations p G ϭ k EG /k ex and p E ϭ k GE /k ex , with k ex ϭ k GE ϩ k EG , p G ϩ p E ϭ 1, and p G Ͼ Ͼ p E . The lifetime of the excited state E is given by E ϭ 1/k EG , and the rate constants k GE and k EG can be calculated as k GE ϭ k ex ⅐p E and k EG ϭ k ex ⅐p G . The uncertainties of peak intensities were estimated from repeat measurements, and the standard errors of the extracted kinetic parameters were determined from data fitting by the ChemEx software using the covariance matrix.