Compactness of Protein Folds Alters Disulfide‐Bond Reducibility by Three Orders of Magnitude: A Comprehensive Kinetic Case Study on the Reduction of Differently Sized Tryptophan Cage Model Proteins

Abstract A new approach to monitor disulfide‐bond reduction in the vicinity of aromatic cluster(s) has been derived by using the near‐UV range (λ=266–293 nm) of electronic circular dichroism (ECD) spectra. By combining the results from NMR and ECD spectroscopy, the 3D fold characteristics and associated reduction rate constants (k) of E19_SS, which is a highly thermostable, disulfide‐bond reinforced 39‐amino acid long exenatide mimetic, and its N‐terminally truncated derivatives have been determined under different experimental conditions. Single disulfide bond reduction of the E19_SS model (with an 18‐fold excess of tris(2‐carboxyethyl)phosphine, pH 7, 37 °C) takes hours, which is 20–30 times longer than that expected, and thus, would not reach completion by applying commonly used reduction protocols. It is found that structural, steric, and electrostatic factors influence the reduction rate, resulting in orders of magnitude differences in reduction half‐lives (900>t 1/2>1 min) even for structurally similar, well‐folded derivatives of a small model protein.


Introduction
Structurald isulfide (SS) bonds, which are stable in the harsh oxidative extracellulare nvironment, maintain the native fold of proteins by fixing and protecting them from thermal fluctuation induced by elevated internal dynamics. The SS bond formation is perhaps the most fundamental post-translational modification that stabilizes the 3D fold of globularp roteins. The absence of regulated SS formation leads to diseases including diabetes, [1] cancer, [2] neurodegenerativec onditions, [3] and cardiovascular diseases. [4] Non-native SS bond pairing evokes backbonem isfolding,w hich jeopardizes both function and bioactivity,a lthough some proteins may present alterna-tive SS states and still achieve similarly well-foldedf orms. [5] In protein evolution, the presence of SS bonds shows as ignificant correlation with the complexity of the organism. [6] Approximately 50 %o fa ll cysteine residues found in proteins form SS bonds, [7] and thus, these cysteiner esiduesb ecome the most conserved among all amino acids, despite being added late to the geneticc ode during protein evolution. [8] Duet ot he unique pairingp attern of cysteiner esidues,S Sb onds stabilize the 3D fold of proteins unambiguously. [9] Contrary to structural disulfides, redox-actived isulfides are highly dynamic, and their formation is reversible. The redox potentialo ft he surrounding environmentc ontrols the regulation and cellular localization of these proteins. [10] Intramolecular formation of these redox-active disulfides is common for oxidoreductases (thioredoxin [11] or glutaredoxin [12] family) and allostericd isulfides, [13][14][15] whereas an intermolecularS Sl inkage resultsi ng lutathionylated [16] or cysteinylated [17] small molecule-protein adducts.T he redox potential and stabilityo ft he SS bond is highly dependento ns everalf actors, such as the pK a of the thiols (the standard pK a is 8.5, but this can range from 3.5 to 12.8, depending on the local environment), [18] the strain introduced by the SS bond of the protein structure, and the entropic cost of SS bond formation. [19,20] The Cys residues of an SS bond are typicallyd istant in the primary sequence; 49 %o ft he SS-bond-forming cysteine residues are more than 25 residues apart from each other. [21] The SS-bond formation is thermodynamically more favorable if the cysteiner esidues are placedi ns patialv icinity by the native fold itself before oxidation, [22] otherwise-inthe absence of chaperones assisting folding [23] -the protein precipitates. Adjacent cysteiner esidues oxi-An ew approacht om onitor disulfide-bond reduction in the vicinity of aromatic cluster(s) has been derived by using the near-UVr ange (l = 266-293nm) of electronic circular dichroism (ECD) spectra.B yc ombiningt he results from NMR and ECD spectroscopy,t he 3D fold characteristics and associated reduction rate constants (k)o fE 19_SS,w hich is ah ighlyt hermostable, disulfide-bond reinforced 39-amino acid long exenatide mimetic, and its N-terminally truncated derivatives have been determined under different experimental conditions.
Single disulfide bond reduction of the E19_SS model (with an 18-fold excess of tris(2-carboxyethyl)phosphine,p H7, 3 7 8C) takes hours, which is 20-30 times longer than that expected, and thus, would not reach completionb ya pplying commonly used reduction protocols. It is found that structural, steric, and electrostatic factors influence the reductionr ate, resulting in orders of magnitude differences in reduction half-lives (900 > t1 = 2 > 1min) even for structurally similar,w ell-folded derivatives of as mall modelp rotein.
which is a3 9a mino acid protein of comparablebioactivity,b ut improved water solubility.Asa"natural tool" for enhancing the compactness of the 3D fold, we introduced two solventexposed Cys residues into E19, making E19_SS (Figure 1), and al oop from residues 18 to 39 in E19_A18C_S39C (E19_2SH). E19_2SH oxidized to E19_SS spontaneously with atmospheric O 2 dissolved in water at room temperature. The SS bond of E19_SS extendst he hydrophobic core of the native Trpf old in the spatial proximity of 22Tyr,w hich is surrounded by explicit negative charges (15Glu, 16Glu, 17Glu). Although E19_SS is small in size, (MW: 4334.9 gmol À1 ), its reduction takess everal hours to reach equilibrium with > 10 molar excess of TCEP in water at room temperature. Because the SS bond reduction time turned out to be significantly longer than that expected based on literatured ata and commonl aboratory practice, we launched ac omparatives tudy,i ncluding three designeda nd truncated analogueso fE 19_SS,n amely,E 11_SS, E5_SS, and E2_SS. Notably, the model systemst hus created( Figure 1) oxidize spontaneouslya nd rapidlya dopt the Trp-cage 3D fold. [56] Moreover, the "loop size" createdb yt he SS bond, in other words, the number of residues between the two reacting cysteine residues, is 20 amino acids long, which is close to the averagev alue ( % 17) observed in thousands of proteins. [57] E11_SS wasd esigned by removing the "HGEGTFTS"t ail, which wast he unstructured GLP-1R-activating N-terminal eight residues of E19_SS. Shortening by an additional six residues removes the outer helicalp art of E19_SS,n amely,t he "HGEGTFTS-DLSKQM" subunit, [56] affording E5_SS. Although 14 residues shorter than that of E19_SS,E 5_SS stilla dopts ac ompact Trp-cage fold and comprises the entire interface for bind- Figure 1. A) Structureensemble of E19_SS, and B) amino acid sequences of GLP-1; exenatide;p arent E19 and its truncated derivatives E11, E5, and E2; their SS analogues E19_SS, E11_SS, E5_SS,a nd E2_SS;a nd their reduced2 SH analogues E19_2SH, E11_2SH, E5_2SH, and E2_2SH. The position of the SS bridge is highlighted by stick representation and underlined as C. The sequences of E19 is divided into six majorp arts: 1) 2-8 unstructured Nterminus, 2) 9-14 outer helix, 3) 15-17 kink region, 4) 18-27 inner helix, 5) 28-34 3 10 helix, and 6) 35-39 polyproline region. This apportionmentoft he sequence coincides with the truncation of the peptides. ing to GLP-1R. [52] Finally,i nE 2_SS, the entire Nterminus preceding 18Cys of E19_SS was omitted,n amely," HGEGTFTS-DLSKQ-EEE" was cleaved, to give af olded protein with af ully exposed SS bond at itss urface; this is considered to be ac onstruct ready for ar apid SS bond reduction ( Figure 1).
Herein, we discusst he structure and properties of both the oxidizeda nd reduced forms of the four model proteins of different a-helical lengths, in comparison with the parent (Cysfree) miniproteins, and the kinetics of reduction. We introduce spectroscopic approaches that make the monitoring of the reductionp rogress fast and easy. The effect of the compactness of the protein fold, the accessibility,a nd the local explicit chargeso ft he SS bond and the reagent type on reduction rate and the mechanism are also explained herein.

Results and Discussion
Three-dimensional fold characterized by far-UVelectronic circulardichroism (FUV-ECD) spectra Circular dichroism (CD) spectroscopy is increasingly recognized as very sensitive indicator of protein conformation, [58,59] relying on ap lethora of electronic transitions. The FUV-ECD spectra of Trp-cage proteins( e.g.,E xenatide, E19, E19_SS)a re typically the weighted sums of the C-(folded and highly helical) and Utype (unfolded) base curves (Figure 2A), as assigned and verified by means of NMR spectroscopy. [60,61] As the temperature increases, the shapeo ft he FUV-ECD spectra changes:t hose of the parent proteins-E2, E5, E11, and E19-acquire more and more U-type characteristics, as they unfold gradually.T he tem-perature-dependentF UV-ECD spectra for all four SS bond enforced model peptides were recorded between 5a nd 85 8C( in steps of 5 8C, resulting in 17 spectra for each protein;F igure S1 in the Supporting Information). Aside from E2_SS, the SSbond-containing mutantsh ave similar FUV-ECD spectrat ot hat of their parent proteins at low temperatures. On the other hand, because the SS bond makes the 3D folds of SS variants more rigid, they preserve their C-type characteristics better and delay unfolding, even at higher temperatures. Once the SS bond is reduced (see below for details), the spectral properties of the SH variantsr evert to those of the parentp roteins.T heir 3D-scaffold compactness decreases as the temperature increases;t his is less apparent in the case of E2 and E2_2SH because they both already present an ensemble of dynamic backbone structures at 5 8C.
Ensemble deconvolution [62,63] of the 204 (12 17) ECD spectra, f(l, T), made the quantitative analysis of the relative abundance of secondary structural elements belonging to each peptidei ne ach state possible because the pure ECD curves were successfully assigned. [60,[64][65][66] The resultsi nF igure 2B indicate that 1) the SS bond stabilizes the less folded protein scaffolds more effectively,f or example, whereas the difference at 4 8Cb etween the E2 and E2_SS folded fraction is 48 %, the same difference between E5 and E5_SS is 14 %; in the case of E11a nd E11_SS, it is only 28 %, and for E19 and E19_SS it is 7% ( Figure 2D). 2) The ratio of the folded, helical components increases upon going from E2 to E5 and E11; however,t he compact a-helicalc ontent of E19_SS,E 19_2SH, and E19 is lower than those of E11_SS, E11_2SH, and E11b ecause the unfolded eight-residue-long N-terminal part elevates the overall Figure 2. A) Te mperature-dependent FUV-ECD spectra (204 in total) of the four primal peptides (E2, E5, E11, and E19) and their four reduced(_2SH)a nd four oxidized( _SS) variants. B) The two pure ECD curves were derived from the ensembleanalysis of the 204 ECD spectrabyu sing CCA + .Pure component 1 (red) represents that of the unfolded/U-type, whereas component 2( green)r epresents the folded/C-type backbone structure. C) The associated relativep ropensities [%] of the two pure components at each measured temperaturea re given for E19_SS as an example, D) as well for each 204 spectra starting from E2 (at 5 8C) up to E19_SS (at 85 8C). 3) All four reduced proteins (E2_2SH, E5_2SH, E11_2SH, E19_ 2SH) have ah igher helix content(% 7-15 %) than that of the parentp roteinso ver the entire temperature range.4 )The 3D folds stabilized by SS bonds are less sensitive to temperature ( Figure 2C,D ).
Three-dimensional folds of proteins determined and characterized by NMR spectroscopy The ensemble of the temperature-dependentF UV-ECD spectra confirmst hat SS bonds preserve the fold of the model proteins and increase thermostability.N MR spectroscopy analysisa t 15 8Ca llowed further characterization of the 3D structures of each variant. Fold, chemical shift, and secondary chemical shift (SCS) information [67] were derivedf rom the appropriate 2D homonuclear NMR spectroscopy experiments ( 1 H, 1 (Table 1).
Ac omparison of the helices of different lengthsi sm ore straightforward if the helical segment is divided into three parts:1 )the outer a-helix, 2) the kink region in the vicinity of the SS bond, and 3) the inner a-helix ( Figure 3).
The outerh elix compactness seems to be affected by the length of the a-helix. Interestingly,t his part of E11v ariants is slightly more structured, in spite of being the terminalp art (usually flexible and unstructured), as opposed to the outer helices of the E19 variants, where this helical segment is flanked( Figure 3A). The above tendency is alsot ruef or the kink region, but here the presence and state (_SS or _2SH) of the SS bond are also differentiated ( Figure 3B). These distant helical parts have generally lower [AECSD Ha ðiÞ ]/i values than those of the inner helix. The compactness of the inner helices is similar (expect for E2). Interestingly,r educed longer polypeptides show slightly increased [AECSD Ha ðiÞ ]/i values, whichm ay be the indicative of ring tension in the SS bond cyclized variants in these systems( Figure 3C). 1 HNMR spectroscopy studies also confirmt hat all model proteins,e xcept E2, have ac ommon, compact, and folded Trpcage core structure at T = 15 8C(Ta bles 1and S1 and Figure S2), regardless of the differentlys tructured tails attached to them ( Table 1). E2 is predominantly unfolded, even at low temperature (15 8C), but because the SS bond joins together the Na nd Cterminio fE 2_SS, the hydrophobic core folds properly.I nterestingly, even E2_2SH forms am ore compact Trpc age than that of E2. In agreement with data reported in the literature, cysteiner esidues promote and stabilize a-helices, if located at their Ntermini. [68] The cage values of the longerr educed peptides are close to that of their oxidized counterparts (Table 1).  [51,55] were used to correlate the fold of the protein. The following "H" atoms were involved in calculations: W25He1, L26Ha,G 30Ha2, P31Hb2, R35Ha,P 37Ha,P 37Hb2, P38Hd1, and P38Hd2.
[f] The average CSD of backboneHa protons per residue. NMR spectroscopy data reveal that al onger a-helix results in a more structured Trpc age, in all cases studied.
In general,i ts eems that the core of the reduced (SH À )p roteins is almost as well folded as those that are SS bonded. The following3 Df old compactness order was established: CSD SS cage > CSD 2SH cage > CSD parent cage ,b ut the differences are small, aside from those of E2 (CSD E2 cage = 3.8)!E2_SS (CSD E2 SS cage = 11.3).
Oxidized and reduced states defined by near-UV (NUV) ECD data As shown above, reduction does not have ad ramatic effect on the tertiary structure content of the model systemsa tr oom temperature;t hus, to detect reduction, NUV-ECDs pectra (instead of FUV) had to be used. The interpretationo ft he changes to theo bserved chiroptical properties of the Trp/Tyr/ SS!Trp/Tyr/2SH ( Figure 4A)c omplex chromophores ystem is less straightforward because the assignment of "pure"N UV-ECD spectra has not yet been completed. The conformationdependentf ine structure of Tyr/Trp chromophores [60] (260 l 320 nm) comprises the 1 Lb of Tyr( l % 276 nm, with a shouldera tl % 287 nm), 1 Lb of Trp( l % 281 and % 293 nm), and 1 La of Trpt ransitions appearinga ss uperimposed broad bands. In addition, the SS bond may also contributei nf orm of ar elativelyw eak butb road band with am aximum at l % 260-270 nm. For the current proteins with SS bonds, al arger negative band was recorded ( Figure S3). The bands of Trpa nd Tyr in the SS-bond-containing proteins shifted to the negative ellipticity range, which was not observed in the case of the parentp roteins (E2, E5, E11, E19), [60] for which the bands of these amino acids were detected in the positive range (except the Trpb and at l % 293 nm). The reduction kinetics of E19_ SS!E19_2SH were monitored over time as the band intensities at l % 266, 281, 287, and 295 nm increased from larger negative to smaller negative and/or positivev alues, similar to those of the parentp roteins ( Figures 4A and S3). We were encouraged to use NUV-ECD spectral changes to monitor SS to SH reduction in proteins if embedded in as uitable molecular environment such as that of the Trpc age motif. Due to the acidic nature of TCEP,t oa void anyp Hs hift, a phosphate buffer (50 mm,p H7)w as used to sustain nearphysiological pH. The groups of Han [39] and Whitesides [37] described the chemical instabilityo fT CEP above pH 7i n3 00-400 mm phosphate buffer.T hey found that the autoxidation of TCEP depended on how the reagent was stored (open air or in capped vials), whether the solution is stirred, ando nt he elapsedt ime (24 t 72 h) during storage. However,h erein, we have monitored TCEP stabilityb ym eanso f 31 PNMR spectroscopyi n5 0mm phosphate buffer,a nd found no significant spectralc hanges connected to TCEP oxidation or degradation at room temperature over 14 days.
Reduction of the E19_SS protein was followed by recording NUV-ECD spectra( % 0.113 mm E19_SS,p H7,1 5 8C, 18-fold excess of TCEP,c ell length = 10 mm) at four different wavelengths (266, 281, 287, and 293 nm). Thus, by following band intensity changes of selected (one or more) 1 Lb transitions of Tyro rT rp, we could monitort he redox state of the SS/SH groups and determine the "end point" as as teady state. Thus, if as uitable aromatic residue (Tyr,T rp, Phe) is coupled to the SS bond as ac hromophore, it enables its reduction/oxidation state to be monitored, even if the molecular system shows no coupledb ackbone conformational changes (CSD E19 SS cage = 11.66; CSD E19 2SH cage = 11.07). The measured absorbance was converted into concentration by using Equation (1): Figure 4. A) NUV-ECD spectralchanges measured for the reduction of E19_ SS ( % 0.113 mm E19_SS, pH 7, 15 8C, 18-fold excess of TCEP) at four different wavelengths (l = 266, 281, 287, and 293 nm). No spectral changes were observed after about55h(3300 min). B) 1 HNMR spectra of E19_SS!E19_2SH reduction (c % 0.115 mm,p H7,158C, 18-fold excess of TCEP) in water.The chemical shift of the indole He1o fT rp25 was used to monitorreduction: He1s hifted upfield from d = 9.60 (SS) to 9.78 ppm (2SH duringt he reduction). Reaching steady state, the integral ratio of E19_2SH and E19_SS was found to be 92 to 8%.C )Concentration change of E19_SS [mm]m easured duringr eduction by different approaches plotteda saf unctiono ft ime. D) The calculated rate constants (see the discussion of modeling reduction kinetics).
Steadys tate was reached conclusivelya fter about 55 h. We determined the rate constant, k 1 ,a te ach wavelength by parameter estimation to be k l¼266 nm 1 = 4.11 10 À4 Lmmol À1 min À1 , k l¼281 nm 1 = 5.67 10 À4 Lmmol À1 min À1 ,a nd k l¼287 nm 1 = 5.98 10 À4 Lmmol À1 min À1 (Figures 4C and S4). The deviations of the fitted modelf rom the measured data at l = 293 nm were remarkably large;t herefore, parameter estimation was not performed on this dataset. NUV-ECD monitoringe nables one to observe the clean and clear changes in the spectra,b ut it does not make it possible to extract the absolute value of the concentration,[ SS] 1 ,a tt he end point of the reaction. Based only on the intensityo ft he molar ellipticity,i tc annotb ed ecided if reduction is fully completed or not. To ascertain the absolute values of the concentrationsi nt he redox system, reduction was repeated under the same conditions in NMR tubes with a diameter (Ø) of 5mm(% 0.113 mm E19_SS, pH 7, 15 8C, 18-fold TCEP) by recording 1 HNMR resonances ( Figure 4B). By using both SS and SH state integralso ft he signals at selected resonance frequencies (e.g.,H e Trp ), 1 HNMR spectroscopy driven quantitative analysis of the reduction was performed (Figure 3E)a nd the rate constant was determined to be k NMR 1 = 8.03 10 À4 Lmmol À1 min À1 .A lthough 18-fold excess of TCEP was used, 1 HNMR spectroscopy data showedt hat, at steady state, @[E19_SS]/@t % 0a nd @[E19_2SH]/@t % 0, reduction was incomplete and about 8% of E19_SS remained oxidized. Ac omparisono ft he calculated reactionr ates of the two methods (NMR and CD spectroscopy) shows that not only are the orders of magnitudest he same, but the values are also quite similar.The reduction rate of NUV-ECD measured at l = 287 nm is closest to that of k NMR 1 ( Figure 4C). Monitoring the intensity of the molar ellipticity by NUV is af ast and efficient method to define the end of the reaction. It also provides an approximate value of the reduction rate if the conversion is close to completion. Based on 1 HNMR spectroscopy integrals, it is possible to determine the rate of the conversion and obtain evidence for the reversibility of the redox system. Taking into account incomplete conversion, despite the presence of the 18-fold excess of RA, the role of dissolved oxygen and reoxidation should also be included in the kinetic mechanism.

Concept of the reversible redox system
Physiological solutions contain dissolved O 2 from the air,a nd thus, Cys-SH groups of any protein might oxidize spontaneously to form the SS bond(s). The apparent rate constant depends on severalm icroequilibrium constants, which are explicitly not elaborated herein. [69] However,i tc ertainly depends on the width of the conformational space of the reduced molecular fold. Furthermore, the concentration of dissolved O 2 (and thus, T and p), the diffusion rate of TCEP,a nd the protein concentration are all rate-influencing factors. Because our model protein forms ac oupled reaction cycle, once E19_2SH is reduced by excess TCEP,E 19_SSw ill be instantaneously reoxidized by dissolved O 2 ( Figure 5). Before exploring the mechanism of these redox-cycle-relatede lectron-transfer processes, it should be noted that, at am acroscopic level, these coupled cycles remainh idden,a ss teady state (AE@x/@t = 0) is reached. Reduction concludes in a" normal way" if all dissolved O 2 is consumed;h owever,i ft he concentration of the RA declinesf aster than that of O 2 ,t hen oxidation will dominate the process and spectralp roperties will change accordingly ( Figure 5). It is hard to ap riori predict the end point of the latter process because, unlike the oxidized fold of ap rotein, the reduced one could have am ultitudeo fb ackbone conformers in exchange at various timescales (e.g., mst om s). Among these 3D folds of the reduced state, the "closed-SH" forms ( Figure S2 II), in which both the Ca nd Nterminia re close to each other,l ead only to In the case of the closedc onformer,i nwhich the ÀSH groups are closely fixed to eachother,i ntramolecular reoxidation can occur in the presence of O 2 ,w hereas the open conformer is more likely to aggregate due to intermolecular interactions. B) Threestagesoft he theoreticalredox setupsprovide the state at which reduction dominates the overall process (I), as teady state (II), and astate (III) in which excess dissolved O 2 and the absence of RA lead to oxidationb ack to the reduced state. The black square denotest he relative concentration of the oxidized form;g ray diamonds represent the reducedf orm. If precipitationo ccurs(k 3 > 0), then at the end pointoft he redox cycle the soluble protein concentrationhas decreased relative to the initial one.  Figure S2/XIII), then intermolecular oxidationw ill be more prevalent, giving rise to oligo-and polymer formation (see below).
Capturing internal backboned ynamics occurring on the timescale of micro-to milliseconds was successfully attempted by meanso fC arr-Purcell-Meiboom-Gill (CPMG) NMR spectroscopy. [70] Herein, we present the characterization of E5, E5_SS, and E5_2SH as examples. We found that only the backbone NH groups of Glu3, Cys4, Val5, Arg6, Tyr8, and Cys25 of E5_ 2SH partake in such slow motion. Considering the fact that all of these NH groups are close to both Cys residues (Figure 6), the CPMG data suggest that either E5_2SH presentsa lternative backbones tructures, which interconvert at as low exchange rate, or,d ue to incomplete reduction,t he remaining oxidized form (1-8 %, see ad iscussion of the conversion rate below) constantlyi nterconverts with the reduced form. The minor amount of coexisting oxidizedf orm (E5_SS)c ould contribute to the stabilization of the dominant backbonef old of E5_2SH. The conformational equilibrium between the oxidized and reduced states seems to be the most likely explanation for the above-described slow exchange;h owever, both scenarios of motion can occur in ac oncerted way.

Modelingo ft he SS bond reduction kinetics
The SS bond reduction by TCEP is ab imolecular nucleophilic substitution (S N 2) reaction. [37] Thus, both the concentration of the oxidized form of the protein [_SS] and that of the RA contributet ot he rate of the reduction.I na ni deal case, we should considero nly nucleophilic attack of the RA (k 1 ), but, as we explained previously,i np ractice, we also have to take into account back oxidation (k 2 ), which takes place simultaneously, and, in some cases, depending on the size and shape of the protein, precipitation (k 3 ;F igure 5). The mechanism of reduction, therefore, can be described by Equations (2), (3), and (4): By fitting this model to the concentration-timefunctions determined by meanso fN MR spectroscopy, k 1 , k 2 ,a nd k 3 can be determined, and half-livesc an be calculated. We focusedo n the determination of the reduction rate constants k 1 ;t herefore, sampling was more frequent in the reduction phase (stage I; Figure 5B). Based on parameter estimation (see the Experimental Section), k 2 and k 3 are very often either negligibly small, or, due to al ack of sufficient data, cannotb ec onfidently estimated. Obtaining keyk inetic parameters allowed us to describe and compare the reduction kinetics of the SS-containing miniproteins under various experimental conditions. Some protocols reported in the literature apply extreme conditions, such as high temperature (e.g.,5 0-80 8C), to obtain short reduction times;t his is clearly unsuitable for maintaining the integrity of the protein, or > 20-fold molar excesso fr eagent. By performing the reduction of E19_SS (0.8 mm)u nder such conditions (60 8Cw ith 18-foldT CEP excess), the reactions eemed almost instantaneous (t 1/2 < 5min), but the sample became opalescent and side reactions (e.g.,p recipitation) were instantly detected. Similarly to most globular proteins, the conformational ensemble of E19_2SH at 60 8Ci sd istinctly different from that of 15 8C; thus presenting many more unfoldeds tates.T he folded fraction of E19_2SH is 64 %a t1 58C, whereas it is 41 %a t6 08C, according to FUV-ECD analysis. Instead of intramolecular reoxidation, undesirable intermolecular reoxidation might occur between particles. (Reducing E19_SS for 120 min, followed by centrifugation gave practically zero soluble protein concentration.) In general,r eduction and reoxidation at higher T (e.g., ! 60 8C) is expected to be lesse ffective, and accompanied by multiple side reactions, such as b-elimination [71] (whicha lready occursa talower T), [72,73] racemization, [74,75] and aggregation.I n principle, the reduction rate can be enhanced at lower T by increasingt he TCEP molar ratio (15-20-fold molar excess);h owever,t his also triggers obscure unwanted processes ( Figure S5). Experiments were repeated at different temperatures (15,25, and 37 8C) with 0.8 mm protein and 18-fold excess of TCEP (Table 2a nd Figure S6).T he Arrhenius equation allows the activation energy (E a )oft he redox reaction to be derived, resulting in av alue of about 44.3 kJ mol À1 .F or comparison, the activa- tion energy of thiol-disulfide exchange between methylthiolate and oxidized DTT was calculated to be 62 kJ mol À1 . [76] Both FUV-ECDa nd NMR spectroscopy derived structural information support the high conformational similarityb etween E19_SS and E19_2SH;t herefore, E a is likely to be used for the redox reaction, rathert han for the conformational switch between the two conformational states (Table1). Based on the NMR spectroscopy derived signal integral analysis, the reduction was almost complete ( % 94 %) and no sign of precipitation was detected at anyt emperature. Additional experimentsw ere performed to investigate the effect of the protein/RA ratio as a practical perspective ( Figure S7). The above-described NMR spectroscopy methodology provides high-resolution information about the reduction mechanism, relative to that of the more rapid NUV-ECD approach, and thus, detailso ft he reduction of all four ÀSSÀ protein models were obtained through NMR spectroscopy.

Kinetics of SS bond reduction influenced by steric factors
An appropriate reduction protocol was required to unambiguously determine the 3D structures of the above-introduced pure reduced states. Thus, in agreement with the above discussion, only mild conditions (15 8Ca nd twofold molar excess of TCEP) were used for the reduction of the four different miniproteins.D etermining the structuralp roperties andr eduction rates under the same conditions allowed us to elucidate the basis of the observed differences in the reductionr ates.W e found that, at T = 15 8C, the k 1 values of these four model proteins, comprising of identical core structures, but different lengths, were indeed different: their k 1 and t 1/2 values strongly depended on their sizes and/or molecular weights. It appears as if "cutting back" on the a-helicals egments trongly affects the SS bond reducibility,e ven though the SS bonds of all four modelsa re near the surfaces (Figure7A). To our great surprise, we recorded three orders of magnitude differences between the reduction rate constants ( Table 3). Whereas the reduction  % 909 min). The conversion rate was close to complete for the shorter peptide of E2_SS, whereas the reduction of E19_SS was only 88 %c omplete. The kinetic parameters of all four model proteins were determined by using at wofold molar excess of DTT,a tp H7,a nd T = 15 8C. The mechanism of SS bond reduction by DTT is also S N 2, [77] but the determined t 1/2 values are significantly longert han those obtainedb yusing the same molar excess of TCEP;h owever, the observed overall tendency and conclusion appear to be the same (Table 3).
Because the well-folded Trpc age motifs are identical (based on their CSD cage values;T able 1) in all four model proteins, the observed k 1 differences must be associated with the structural properties of their a-helicesa nd the eventually appearing unstructured tail. Although the dataset is limited( n = 3o r4 ), as the simplest approach, the length of the a-helix (n)a nd the half-lives( t 1/2 )o fr eduction could be correlated, leadingt oa n exponential dependence for both TCEP (t 1/2 = 2.06e 0, 371n , R 2 = 0.95) and DTT (t 1/2 = 50.47e 0, 377n , R 2 = 0.98) as the RA (Figure 7B). To take into account the additional structural descriptors for am ore complete characterization, we derived the steric factor (x)f or these protein models[Eq. (5)]: in which the reciprocal of the helicity ([AECSD Ha ðiÞ ]/i)a nd the bulkiness (RMSD) of the outer helical part were both calculated with respectt ot he length of the Nterminus (n;T able 3). We observed al inear dependence of the steric factors on the reductionh alf-lives as af unctiono ft he length of the Nterminus ( Figure 7C). Some, but not all, of the above k 1 (t 1/2 )d ifferences can be explained by structural differenceso ft he outer helix because both solvente xposure and local charges aroundt he Scheme1.Ageneralized mechanism of TCEP-and DTT-assisted mechanisms of SS bondreduction in proteins. Functionalg roupR À stands for the Nterminuso fthe protein systematically elongated here:i nE 19_SS the Rg roup is equal to H + -HGEGTFTSDLSKQMEEE-,i nE 11:H + -DLSKQMEEE-, in E5_SS: R = H + -EEE-, and in E2_SS it is simply H + .Abrief description of the detailed reaction mechanism is provided for both TCEP and DTT in the text.

Rate-determining steric and electronic factors of SS bond reduction
Apart from the steric effect of the helical parte mphasized above,t he S N 2m echanism of TCEP-driven reduction has to be discussed in terms of electrostatic effects. [19] In general, attack is more favorable and effective on those structures in which the Cterminus is neutral. According to the average pK a of the cysteinec arboxyl group (pK a = 1.92) at pH 7, the proportion of COOH/COO À is low: 1/12 000. The rate-determining step is cleavage of the SS bond. [78] During the S N 2r eaction, the nucleophilic Pa tom of TCEP attacks one of the SS bonds, forming a thiophosphomium salt (an S À ÀP + ion-pair complex;S cheme 1).
Nucleophilic attack (n!s*) is facilitatedb yt he favorable arrow-shaped (tetrahedral:1 058)s teric arrangement of the nonbonding electron pair of the Patom of TCEP.The main portion of the activation Gibbs free energy of reduction is consumed by splitting of the SS bond and not by the steric rearrangemento ft he intermediate structure. [79] Better solvation of the thiol and zwitterionr esultsi nalower activation Gibbs free energy of the reaction. Next, the positivelyc harged ÀSÀP + À [(CH 2 )ÀCOOH] 3 complex hydrolyzesr apidly and results in the phosphine oxide and free ÀSH groups of the protein.
Both chargeda nd aromatic side chains can participate,a nd thus, intimately influence the efficacy of TCEP-mediated reduction ( Figure 7A). The nucleophilic phosphine attacks the Cproximal cysteine because the intermediate cation can be stabilized by the proximal COO À group of the C-terminal cysteine. Apositive chargenear the SS bond could enhance the reaction throughe lectrostatic compensation of the N-proximal leaving thiolateg roup, whereas an egative charge might slow down the S N 2r eaction. [80,81] Direct through-bond effects of any chargeds ide chain can be ignored because they are separated by several s bonds from the negative COO À group. Although the inductiveo rd irect s-bond effects are negligible, both steric and spatial electrostatic effects in the vicinity of N-proximal cysteinep lay am ajor role in the reduction rate. At pH 7, the positivelyc harged Arg near the SS bond in the inner helix may facilitater eduction;h owever, it is distant from the SS bond ( Figure 7A), and thus, ad irect charge-controlled interaction is less likely to occur.O nt he other hand, the positively chargedN -terminal ÀNH 3 + can directly catalyze the instantaneous reduction [82] of E2_SS (t E2 SS 1=2 % 1min)b ecause HÀNÀC a ÀC b À Softhe cysteine forms afive-membered pseudo-ring that facilitates intramolecular NS protont ransfer. [83] Thus, upon TCEP attack, these ideal local electrostatic compensations may stabilize the intermediate thiophosphonium salt,s hiftingt he reaction equilibrium towards splitting of the SS bond. Furthermore, because the leaving thiolate anion is only positioned at the Nterminus of the well-folded a-helix, the positive charge of the a-helix macrodipole also promotes progress to the reduced state. [84,85] Moreover,d ue to the small protein size, the SS bond is most exposed to solventand reagent in E2_SS.
As the Nterminus is elongated on the a-helix from E2_SS toward E19_SS, the "catalyzing" ÀNH 3 + group of the Nterminus moves further away from the SS bond, andt he effect of the macrodipole gradually vanishes;t hus, the reduction rate is reduced (t 1/2 increases; Ta ble 3). The role of this positivec harge was directly probedb ya cetylating the Nterminus, Ac-E2_SS, and, as expected, the half-life of reduction increased significantly: t E2 SS 1=2 % 1min!t Ac-E2 SS 1=2 % 8min (in both cases, ap rotein concentration of 1.7 mm and twofold excesso fT CEP were used).
The N-terminal elongation of E2_SS by three Glu residues results in E5_SS. As expected, the reduction rate is slower: t E5 SS 1=2 % 14 min. Although only at ripeptide is added to the dynamic Nterminus, reaching the SS bond still becomes harder for both reagent and/or solventm olecules. In addition, the 3D structure ( Figure 7A)s hows that the three negativelyc harged Glu side chains (at pH 7) are flanked by the N-proximal cysteine and the positivelyc hargedNterminus, and thus, effectively neutralize the catalytic effect. The structure of the ensemble determined by means of NMR spectroscopys hows a distance fluctuation from 3.7 to 10.7 between 4Cys Cb and 1Glu NH 3 + ,w hereas that of 4Cys Cb and 1Glu COO À fluctuates between 3.4 and 12.4 ( Figure 7). Thus, SS bond protonation requires an active contribution from the medium; but proton transfer is perturbed by the proximity of the negatively chargedg lutamate side chains.
Further elongation of E5_SS by the hexapeptide-DLSKQMleads to E11_SS. Under the same conditions, the reduction of this even larger model protein occurs more slowly (t E11 SS 1=2 % 67 min). The glutamate side chainsa re more oriented by the longer a-helix of E11_SS ( Figure 7): whereas 8Glu À turns outward, both 7Glu À and 9Glu À flank the SS bond from two sides. Residues 7Glu À with 4Lys + and 9Glu À with 12Arg + are capable of forming salt bridges in close vicinity,a nd thus, could partly compensate for the slowing effect of the negatively charged side chains. E11w as found to be more helical than that of longer E19; [56] thus we find here that both E11_SS andE 11_ 2SH have more compact a-helices than those of E19_SS and E19_2SH, according to both [AECSD Ha ðiÞ ]/i NMR spectroscopy measurements and FUV-ECD spectralp roperties. We believe that, in addition to partly compensated for negative electrostatic effect(s), mainly sterice ffects of the elongated and stiffer a-helix causet he longer value of t E11 SS 1=2 with respect to that of t E5 SS 1=2 .
Finally,E 11_SS elongated by the -HGEGTFTS-octapeptide results in E19_SS-the largestm odel protein used herein-for which the longest half-life (t E19 SS 1=2 = 909 min) is measured. E19_ SS has the same electrostatic pattern in the vicinity of the SS bond as that of E11_SS, but its reduction rate is about 15 times slower than that of E11_SS. Although the -HGEGTFTSsegment is far from the SS bond (d 7Thr-18Cys = 11-14 ;F igure 7) and cannot influence reductionb ye lectrostatic interactions, its higher internal dynamics( low S 2 value), [56] as as teric effect, must slow the SS bond reduction rate further. In fact, the latter increase, in terms of t 1/2 ,isagood estimation of the magnitude of ap urely steric effect of an unstructured polypeptidec hain on reduction rate. Differencesinr eduction kinetics and mechanism with alternative reagents There are af ew distinct differences in terms of the general mechanism of SS reduction by TCEP andD TT (Scheme 1). 1) As an initializings tep, deprotonation of the thiol group of DTT is required for successful nucleophilic attack, which depends on the pH of the medium. According to the Henderson-Hasselbach equation, [86] taking into account the acidic dissociation constanto fD TT (pK a1 = 9.2 and pK a2 = 10.1) at pH 7, deprotonated thiolatec oncentrationi sa bout three to four times lower than that of the overall DTT concentration. After successful nucleophilic attack on the SS bond, al inear ÀSÀSÀSÀ transition complex has to be formed, in which the negative charge is located on the two leaving Sa toms. [87] An intramolecular protonation, as for TCEP,a lso stabilizes the thiol anion leaving group if DTT is used, and thus, enhances the reactionr ate. Therefore, ap ositive inductive/sterice ffecti ncreases, whereas an egative effect decreases the reduction rate. 2) Contraryt oT CEP,t he active species of DTT has an egative charge. Therefore, chargeda minoa cid side chains close to the SS bond will directly affect attack by the nucleophilic RA. In line with these observations, both the negative Cterminus and the SS bond flankingg lutamate side chains repel DTT;t hus contributing to as ignificant and large-scale decrease in reactionr ate (Table 3).
3) Moreover,c omplete reduction by DTT consists of two steps: after the first attack, the free SH group of the peptide-DTT complexh as to cleave the previously formed SS bond, whereas DTT closes into as ix-membered ring (Scheme 1). All of these factors jointly decrease the reduction rate if DTT is used instead of TCEP (Table3). These considerations make it even more striking that, although severalproteins with variousnumbers of SS bonds per molecule, such as a-lactalbumin, lysozyme, and oxytocin, were reported to be completely reduced in 5min by 10 mm DTT at pH 5.5 and 70 8C, [88] we found that the reduction of miniproteins (e.g.,E 11_SS) with as ingle and exposed SS bond might take up to 138 h(Ta ble 3).

Spontaneous SH reoxidation accompanied by polymerization
Incomplete conversion, despite the presence of al arge excess of the RA, providede videncef or the reoxidationo ft he reduced SS bond of the studied model systems. To study this process in detail, the in situ reoxidation of the DTT-reduced protein samples at room temperature in sealed NMRt ubes (pH 7, 15 8C, twofold excess of DTT) was monitored for several weeks. Spontaneousr eoxidationo fE 2_2SH, E5_2SH, and E11_ 2SH by dissolved O 2 was clear after four weeks (Figure 8). The reoxidation rates (k 2 )h ave comparable orders of magnitude to that of the reduction rates (lowerb yo ne order of magnitude), but reoxidation has ap ronouncedr ole only after reaching steady state, at whicht he concentration of the already reduced peptides becomes significant.
Reoxidation can take place both intra-and intermolecularly. Whereast he former leads to ad ecrease of overall conversion rates, the latter results in the formation of random molecular clusters, which may lead to precipitation. According to our semiquantitative analysis based on the recorded 1 HNMR spectra, the integral changes of the TrpH e1r esonances both in the oxidizeda nd reduced forms of the protein during reduction with DTT show ad ecrease in concentrationo ver the observed period of redox time for both E2_SS and E5_SS. Precipitation can be more intense if the protein concentration is higher. According to our present observations, increasing the length of the a-helix within the Trpc age proteins stabilizes the soluble protein fraction. This meanst hat the elongated Nterminus, namely,t he outer helix in the case of E11_2SH, effectively shields the free SHÀ groups of the reduced protein, and thus, prevents any intermolecularr eoxidation, whereas shorter variants, such as E2_2SH and E5_2SH, yield as ignificant amount of polymer formation. Due to the diversity of open 3D folds of both E5_2SH and E2_2SH, spontaneous intramolecular ring closure is hindered and less likely to happen. The N-terminal Cys of E11_2SH is placed and fixed at the highly orderedi nner Figure 8. The 50-membered structure ensembles of A) E11_SSQE11_2SHa nd B) E5_SSQE5_2SH. The fold of E11_2SH is morecompact than that of E5_ 2SH, which has more"open" conformers, in which the Cys residuesa re far from each other.T his allows intermolecular,rathert han intramolecular,r eoxidation.The dissolved oxidized and reduced protein concentrations of C) E11_SSQE11_2 SH and D) E5_SSQE5_2SH (oxidized:b lue;reduced:green) as af unction of time. In the case of E5_SSQE5_2SH, the initial concentration decreased by 68 %, whereas, at the end of ac omplete redox cycle, the concentration of E11_SSQE11_2SHr emained the same. E) Estimated parameters of the complete redox cycles.( The k 1 valuesare slightly different from those in Ta ble 3, for which the estimation comprisesd ata only for phase 1.) Notably,int hesel ong-term experiments, the rate of O 2 diffusion characterized by the rate constant k 4 was also involved. Figure S11c ontainsa ll data for parameter estimation of E11_SS, E5_SS, and E2_SS.
ChemBioChem 2020, 21,681 -695 www.chembiochem.org helix, with ar educed internal mobility of Cys18, and thus, mostly intramolecularr ing closures take place. In the case of E5_2SH, intermolecular SS bond formation is allowed,b ut may be limitedj ust by Brownian motion and concentration.Acomparisono ft he polymerization rates (k E11 SS 3 < k E5 SS 3 )w ith different N-terminal lengths also supports this concept ( Figure8E).
E2_SS was N-acetylated to eliminate the reduction rate-enhancinge ffect of the positively charged Nterminus, ÀNH 3 + ,i n the vicinityo ft he SS bond. Upon acetylation, t 1/2 has indeed increased (t E2 SS 1=2 = % 1min t Ac-E2 SS 1=2 = % 8min), but, in addition, the reaction reaches its steady state at al ow conversion rate (50 %). During reduction, almost immediately,b oth of the appropriate signali ntegrals of Ac-E2_SS and Ac-E2_2SH start to decrease, with af oamy precipitateg radually forming in the NMR tube. The isolated and HPLC-purified precipitant was identified as ap olymer of the parentm iniprotein by meanso f MS ( Figure S12). Oligomer formation and soluble protein concentration decrease werem ore advanced for Ac-E2_SS than that of E2_SS ( Figure S13). Due to the absence of the shielding effect of the outer a-helix, the free thiol moiety of the Nterminus is accessible for additionally reduced peptides in which the two free SH groups can hook peptide chains together.T he polymerc an grow until another free Nterminus and acetylated C-terminal thiol-containing peptidec loses polymerization. In addition, for Ac-E2_2SH, intramolecular N!Sa cyl transfer could take place, [89] blockings ome of the SH groups from promoting oligo-and polymerization through intermolecular SS bond formation.

Conclusion
The SS-bond cyclized exenatide derivate and its variants were synthesized. Both the oxidized (E19_SS)a nd reduced (E19_ 2SH) forms,a long with the parent molecule, E19, and all three of their truncated variants (E11_SS, E11_2SH, E11, E5_SS, E5_ 2SH, E5, E2_SS, E2_2SH, and E2) comprised the same Trpc age/ SS/SH bond motif as that of their core structures.T he SS bond stabilized model proteins showedi mprovedt hermostability and 3D fold compactness, with respectt ot heir reduced and parentf orms. Key residues for receptor binding remained in positioni na ll of these models;t herefore, E19_SS might be promisinga gonists for GLP-1R and as al ead compound for type 2d iabetes mellitus.
The reduction rate of E19_SS was found to be unexpectedly slow compared with that reported in the literature. Ther eaction takes hours (t 1/2 = 48 min), even at 37 8C, although the protein is small, and its single SS bond is exposed at the surface, and thus, accessible for reducing reagents. All four Trpc age variants studied herein have an almoste qually compact core structure, with a-helical segmentsofd ifferent length and internal mobility. By performing ac omplete NMR spectroscopy based structure elucidation,w ef ound that the progress of reductionc ould be monitored by means of 1 HNMR by using selected resonance frequencies. We have established that these four model proteins of different a-helical lengths have significantly different reduction rate constants. Although it is generally complicated to discriminate each factor that affects the SS bond reduction rate, the present set of miniproteins enabled them to be deciphereds eparately.W eh ave focused special attention on the importance of the intramolecular protonation of the SS bond;t his step greatly enhances the reactionr ate. From CPMG measurements, we found that, at steady state, selected residues in the vicinity of the SS bond presented as low exchange on the micro-to millisecond timescale of motion. This redox cycle lasts as long as active RA can be found in solution.W ef ound that structural, steric, and electrostatic factors influenced the reduction rate greatly,r esulting in almost three orders of magnitude differences in reduction half-lives (t 1/2 )f or otherwise structurally similar and globularly folded model proteins.
Notably,i na ddition to intramolecular reoxidation within the redox cycle, intermolecularo xidation could also occur.T he rate of these two concerted reactions depended on 1) the internal dynamics of the backbone conformers in the proximity of the SS bond, and 2) the shielding effecto ft he a-helixo nt he SS bond. Intramolecular N!Sa cyl transfer in Ac-E2_SS inhibits intramolecular reoxidation, but increases intermolecularr eoxidation,which leads to oligo-and polymerization.
We found that easy-to-collect NUV-ECD spectralp roperties were indeed useful for monitoringt he SS!SH reaction, even quantitatively,w ithout the time-consuming assignment of the high-resolutionN MR spectroscopy data. If the SS bond were situated in the vicinity of an aromatic cluster,NUV-ECD spectral changes could be used to monitort he transformation, which was proportional to the extent of reduction and clearly signaled when steady state hadb een reached. Thus,w ee ncourage the use of CD spectroscopy for monitoring protein reduction rate in the manufacture of recombinant proteins( e.g.,i nsulin, human monoclonal IgG antibodies) on al arge scale, to control and providei nformation on the state of SS-SH bonds.

Experimental Section
ECD:F UV-ECD spectra were recorded on aJ asco J810 spectrophotometer by using a1 .0 mm path length cuvette with protein concentrations of 20-30 mm.D ata accumulation was performed over a range of 185-260 nm, with 0.2 nm step resolution at as can rate of 50 nm min À1 with a1nm bandwidth. The spectral accumulations were resolved between 5a nd 85 8Ci ns teps of 5 8C. The temperature was controlled by using aP eltier-type heating system. Each spectrum baseline was processed by subtracting the solvent spectrum from that of the protein and the raw ellipticity data were converted into mean residue molar ellipticity units, Reduction monitoring by NUV-ECD:T he spectra were recorded on aJ asco J810 spectrophotometer by using a1 0mmp ath length cuvette with protein concentrations of 120-150 mm.D ata accumulation was performed over ar ange of 240-325 nm, with 0.2 nm step resolution at as can rate 50 nm min À1 with a1nm bandwidth. The sample was tempered by using aP eltier-type heating system. Each spectrum baseline was processed by subtracting the solvent spectrum from the peptide spectrum and the raw ellipticity data were normalized by the concentration [V]. Reduction was followed for 75 h. Each intensity [V]a t2 66, 281, 287, and 293 nm was converted into concentration by using Equation (6). Monitoring reduction kinetics:P eptide samples were prepared between 0.8 and 1.8 mm in 50 mm NaH 2 PO 4 -Na 2 HPO 4 buffer (600 mL, pH 6.95), with 10 %D 2 O. A0 .1 m solution of NaOH was used to set the pH to 7. Sodium trimethylsilylpropanesulfonate (DSS) was added as the internal proton reference standard, set to d = 0.0 ppm under all conditions. 1 H, 1 H2 Dh omonuclear spectra were recorded for the oxidized peptide;t hereafter,u pon the addition of ad ifferent excess of 0.5 m TCEP or DTT,r eduction was observed by recording as eries of 1D 1 Hs pectra (ns = 64 or 128 scans). Finally,a tt he end point, 1 H, 1 Hh omonuclear 2D spectra were recorded on the reduced peptide. Data sets were processed by using To pSpin 3.2 software. The conversion rate was determined by using the relative integral of the TrpH e1s ignal in the oxidized (Int OX )a nd reduced (Int RED )f orm. Each integral was normalized to the integral of DSS. The concentrations were determined by the ratio of the oxidized and reduced integrals and the initial protein concentration.
Structure determination: 1 HNMR spectroscopy assignations were completed by using 1 H, 1 HC OSY and 1 H, 1 HT OCSY spectra, and then the distance restraints were determined based on 1 H, 1 HN OESY spectra. Spin locks for 1 H, 1 HT OCSY were 80 ms, whereas the mixing time for 1 H, 1 HNOESY was 150 ms. CCP NMR [90] spectroscopy was used for resonance assignment, crosspeak calibration, and structure refinement. CNS Solve 1.3, [91] Aria 2.0 standard iteration protocol, and water refinement were used for 10-membered structure ensemble calculations. All structural figures were illustrated by using PyMOL software.
CPMG effect:B ackbone 15 N-longitudinal (R 1 )a nd transverse (R 2 )r elaxation rates and the heteronuclear 1 H, 15 Nc ross-relaxation rate constant (NOE) of E5, E5_SS, and E5_2SH were measured at 288 K. For each crosspeak (i), R 2,i values were calculated by using Equation (7): in which I i is the intensity of the given crosspeak in the i th spectrum, I ref is the intensity of the given crosspeak in the reference spectrum, and t CPMG is the relaxation period of the CPMG measurement. The R 2 values per residues were plotted against n CPMG [Hz]. Quantitative analysis of the CPMG graph reveals those residues that show CPMG effects in the protein.
Peptide synthesis and purification:P roteins were prepared by means of standard solid-phase peptide synthesis or bacterial expression methods, as published previously. [92] Proteins were purified by means of reversed-phase HPLC on aC 18 column by using a gradient of water/acetonitrile eluents. (Eluent A: 0.1 %t rifluoroacetic acid (TFA) in water;e luent B: 0.08 %TFA and 80 %a cetonitrile in water.) Parameter estimation:K inetic parameter estimation was based on the integral of selected NMR signals considered to be proportional to the concentration of the relevant species. The mechanism taken into account is that given by Equations (8), (9), (10) and (11): in which SS is the reduced model protein with an intramolecular SÀSb ond;2SH is the same protein with the SÀSb ond reduced to two ÀSH groups;a nd the symbol Øm eans ad ifferent phase from that of the reaction mixture, that is, the polymer aggregate as a sink in the first case and the gas phase as as ource in the second case. Notably,i ns ome cases, in which polymer precipitation (k 3 ) and/or oxygen diffusion (k 4 )f rom the gas phase proved not to be present (indicated by largely nonsignificant estimated parameters concerning these processes), these steps have been omitted from the fitted mechanism.
For parameter estimation, the COPASI 4.16 (Build 104) Biochemical System Simulator software (http://copasi.org/) was used, with the parameter estimation option of the Levenberg-Marquardt method. The result of the estimation procedure did not depend on the choice of the initial parameters within al arge interval;t hus, there was one stable optimum for the fit of the model only.C onfidence interval half-widths and relative standard deviations based on them were calculated from the estimated standard deviations, which suggested aS tudent distribution with nÀp degrees of freedom, in which n is the number of data points in the concentration versus time measurements and p is the number of parameters estimated.
To determine the half-life and initial concentration of the SS species, ak inetic analysis of the temporal evolution of the reactions was performed. Both reduction and oxidation proved to be second-order reactions, which was not only supported by the good fit of the model, but also by the fact that, with this mechanism, the measured ([SS] 0,meas )a nd calculated ([SS] 0,calcd )i nitial concentrations of the model proteins were in very good agreement. From the kinetic analysis, the initial concentration of oxygen ([O 2 ] 0 ) could also be estimated, except for one case in which the uncertainty of this parameter was very large, due to the lack of sufficient experimental data.
Because reduction follows second-order kinetics, the half-life (t 1/2 ) of model proteins also depends on the actual concentration of the RA in the reaction mixture [Eq. (12): in which k 1 is the rate constant of reduction, c SS,0 is the initial concentration of the model protein, and c Red,0 is the initial concentration of the RA. [Notably,E q. (12) is valid only if c Red,0 is greater than c SS,0 -as in the current case. If c SS,0 exceeds c Red,0 ,b ut it is not higher than that of twice the value of c Red,0 ,t hen the two initial concentrations should be flipped in both the difference and the fraction. If c SS,0 exceeds c Red,0 by more than af actor of two, then the SS protein concentration cannot become as low as half of the initial concentration, due to reduction.] For this reason, the half-life is less indicative of the rate of hydrolysis;t he correct comparison