Biophysical Journal, Volume 96. Supporting Material

Transcription

1 Biophysical Journal, Volume 96 Supporting Material NMR dynamics of PSE-4 β-lactamase: an interplay of ps-ns order and μs-ms motions in the active site Sébastien Morin and Stéphane M. Gagné

2 NMR dynamics of PSE-4 b-lactamase: an interplay of ps-ns order and µs-ms motions in the active site (Supplementary Material) Sébastien Morin Département de Biochimie et de Microbiologie and PROTEO Université Laval, Québec, QC, Canada Stéphane M. Gagné 1 Département de Biochimie et de Microbiologie and PROTEO Université Laval, Québec, QC, Canada 1 Corresponding author. Address: Bureau 3255, 1030, Avenue de la Médecine, Université Laval, Québec, QC, G1V 0A6, Canada, Tel.: (418) , Fax: (418) , stephane.gagne@bcm.ulaval.ca

3 S2 Order and motions in PSE-4 from NMR (Supplementary Material) Contents List of tables S3 List of gures S3 Example spectrum for PSE-4 S4 Methods details NMR data acquisition NMR data processing Veri cation for absence of concentration effects on global diffusion S5 S5 S5 S5 15 N spin relaxation S6 15 N spin relaxation statistics S6 15 N spin relaxation table S7 15 N spin relaxation gure S13 Consistency test S14 Model-free analysis S16 Local model-free models S16 Model-free minimization protocol S16 Flowchart of the model-free protocol S17 Model-free analysis table S18 Representation of the diffusion tensor and of the N-H vectors orientations used for optimization S24 Optimized model-free parameters S25 Comparison of order parameters with crystallographic B-factors S26 Comparison of PSE-4 and TEM-1 order parameters S27 Resistance to inhibitors and extended spectrum b-lactams S28 Limits in the analytical approach S29 Amide exchange Amide exchange table Amide exchange gure S30 S30 S34 Cavity lling motion for residues Glu 171 -Leu 177 of the W loop S35 References S36

4 Order and motions in PSE-4 from NMR (Supplementary Material) S3 List of Tables S1 15 N spin relaxation statistics S6 S2 15 N spin relaxation data S7 S3 Model-free analysis results S18 S4 Amide exchange data S30 List of Figures S1 Example spectrum showing the quality of the recorded data S4 S2 15 N spin relaxation data S13 S3 J(0) consistency test S14 S4 Flowchart of the model-free protocol S17 S5 Representation of the diffusion tensor and of the N-H vectors orientations used for optimization... S24 S6 Optimized model-free parameters S25 S7 Comparison of order parameters with crystallographic B-factors S26 S8 Comparison of PSE-4 and TEM-1 order parameters S27 S9 Amide exchange results S34 S10 Stereoviews of the cavity- lling motion for residues Glu 171 -Leu 177 of the W loop S35

5 S4 Order and motions in PSE-4 from NMR (Supplementary Material) Fig. S1: Example spectrum showing the quality of the recorded data (60.8 MHz R 1 at 10.9 ms delay).

6 Order and motions in PSE-4 from NMR (Supplementary Material) S5 NMR Data Acquisition Details For the measurement of the longitudinal relaxation rate ( 15 N-R 1 ), the sensitivity-enhanced inversion-recovery pulse sequence was from Lewis Kay's group (1). Relaxation delays were of 10.9, 21.8 (60.8 MHz), 43.6, 87.2 (50.6 and 60.8 MHz), 174.4, (50.6 and 60.8 MHz), 697.7, (50.6 and 60.8 MHz) and ms. With eight transients per FID and a recycle delay of two s, this acquisition scheme represented a total acquisition time of 13 h. For the measurement of the transversal relaxation rate ( 15 N-R 2 ), the pulse sequence was the implementation of Lewis Kay's sequence (2) within BioPack (Varian Inc., Palo Alto, CA). Relaxation delays were of 10, 30, 50, 70, 90, 110, 130, 150 and 190 ms. Heat compensation (3) was used. An interpulse delay of 575.6, and µs was used in the CPMG train (at 50.6, 60.8 and 81.0 MHz, respectively). Also, the RF eld strength for the 15 N 180 o pulses in the CPMG sequence was 5.061, (and and 5.952) and khz at 50.6, 60.8 and 81.0 MHz, respectively. These spectra were recorded by accumulating eight transients per FID using a recycle delay of three s for a total of 7 h at each magnetic eld. For the measurement of the steady-state heteronuclear NOE (f 1 Hg 15 N-NOE), the pulse sequence was from Lewis Kay's group (1). Spectra were recorded with and without 1 H saturation. A saturation time of 4 s was used and recycle delays were of 5 s for experiments with and without saturation (4 s of saturation + 1 s of blank delay, or 5 s of blank delay, respectively). NOE experiments being less sensitive, every experiment (with or without saturation) took 14 h for the recording of 44 transients per FID. Amide exchange experiments were performed with the INOVA 600 spectrometer, at a temperature of 31.5 o C as for spin relaxation experiments. At ph 7.85, the acquisition was at the following times (when half the acquisition had been completed): 35; 43; 51; 59; 67; 75; 83; 91; 99; 107; 119; 135; 150; 166; 182; 197; 213; 228; 244; 260; 276; 291; 307; 322; 338; 354; 369; 385; 408; 439; 470; 500; 531; 562; 593; 624; 655; 685; 717; 748; 778; 809; 840; 871; 1039; 1206; 1373; 1541; 1708; 2710; 2877; 2924; 3122; 3537; 3935; 4334; 5068; 5803; 6874 and 8974 min. Spectra up to 107 min were recorded with two transients; from 119 to 385 min, with four transients; from 408 to 2877 min, with eight transients; and from 2924 min to the end, with 16 transients. At ph 6.65, the acquisition was at the following times (when half the acquisition had been completed): 32; 40; 48; 56; 68; 76; 84; 92; 100; 108; 120; 136; 151; 167; 182; 198; 214; 229; 245; 260; 276; 291; 307; 323; 338; 354; 369; 385; 407; 438; 469; 500; 531; 562; 592; 623; 654; 685; 716; 746; 777; 808; 870; 1103; 1398; 1937; 2416; 3060; 3152; 5331; 6503; 8096; 12,492; 16,100; 37,334; 38,217; 44,253; 58,532; 77,293 and 115,559 min. Spectra up to 108 min were recorded with two transients; from 120 to 385 min, with four transients; from 407 to 2416 min, with eight transients; and from 3060 min to the end, with 16 transients. NMR Data Processing Details FIDs were shuf ed to yield pure absorptive two-dimensional line shapes from the sensitivity-enhanced (2, 4) data with the `rancey.m' macro. Water signals were subtracted with the function `SOL'. Linear prediction was performed in the indirect ( 15 N) dimension to extend the amount of data points by 50 % (70 % for amide exchange data). The baseline in each dimension was corrected using the function `POLY -auto -ord 0'. As stated above, the number of transients was higher as time proceeded for amide exchange experiments; thus, FIDs were scaled accordingly (so amplitudes were comparable between spectra with a different number of transients) using the NMRPipe function `MULT -c'. Veri cation for absence of concentration effects on global diffusion To assess the effect of concentration on diffusion, two samples of lower concentration were prepared (i.e and mm, with 0.5 mm for the main sample). A slight modulation of R 1 and R 2 relaxation rates was observed, corresponding to a lowering of the estimated correlation time by less than 5 % for this concentration range (data not shown). This small variation is expected due to viscosity changes as a function of protein concentration and excludes the possibility of concentration driven partial dimerization which could, if present, bias the analysis. In fact, a similar modulation of relaxation parameters was observed for 1 H-R 1 of imidazole as a function of protein concentration (data not shown). This variation was different than for PSE-4 because imidazole is in the fast tumbling regime ( w t m 1) while PSE-4 is in the slow tumbling limit (w t m > 1), but nevertheless showed that the apparent tumbling time of imidazole increased with increasing protein concentration, thus con rming the change in sample viscosity.

7 S6 Order and motions in PSE-4 from NMR (Supplementary Material) Table S1: 15 N spin relaxation statistics 50.6 MHz 60.8 MHz 81.0 MHz R 1 (s 1 ) R 2 (s 1 ) R 2 =R NOE Mean values with associated S.D. Last three residues excluded because of high mobility. (N = 228 at 50.6 MHz, 229 at 60.8 MHz, 235 at 81.0 MHz)

8 Table S2: 15 N spin relaxation data Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 22 ser n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 23 ser n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 24 ser n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 25 lys phe gln gln val glu gln asp val lys ala ile glu o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 38 val ser leu o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 41 ser ala o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l arg ile gly val ser val leu asp thr gln asn gly glu tyr trp asp tyr asn gly asn gln arg phe pro leu thr ser n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 71 thr phe o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 73 lys thr Order and motions in PSE-4 from NMR (Supplementary Material) S7

9 Table S2: 15 N spin relaxation data (continued) Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 75 ile ala cys ala lys leu o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 81 leu tyr asp ala glu gln gly lys val asn o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 91 pro asn ser thr val glu ile lys lys o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 100 ala asp leu val o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l thr o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 105 tyr ser pro val ile glu lys gln val gly gln ala ile thr leu asp asp ala cys phe ala o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 126 thr S8 Order and motions in PSE-4 from NMR (Supplementary Material)

10 Table S2: 15 N spin relaxation data (continued) Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 127 met thr thr ser asp asn thr ala ala asn ile ile leu ser ala val gly gly pro lys o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 147 gly val thr asp phe leu arg gln ile gly asp lys glu o.l. o.l. o.l. o.l. o.l. o.l thr arg leu asp arg ile glu pro asp o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 169 leu asn o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 171 glu gly lys o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 174 leu o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 175 gly asp leu arg Order and motions in PSE-4 from NMR (Supplementary Material) S9

11 Table S2: 15 N spin relaxation data (continued) Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 179 asp thr thr thr pro lys o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 185 ala o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 186 ile ala ser o.l. o.l thr o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 190 leu asn lys phe leu phe gly ser ala leu ser glu met asn gln o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 205 lys lys leu glu ser trp met o.l. o.l val asn asn gln val thr gly asn leu leu arg ser val leu pro ala gly trp asn S10 Order and motions in PSE-4 from NMR (Supplementary Material)

12 Table S2: 15 N spin relaxation data (continued) Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 231 ile ala asp arg ser gly ala n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 238 gly gly phe gly ala arg ser o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l ile thr ala val val trp o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 252 ser glu his gln ala pro ile ile val ser ile tyr leu ala gln thr gln ala o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 271 ser met glu glu arg asn asp o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 278 ala ile val lys ile o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l gly his Order and motions in PSE-4 from NMR (Supplementary Material) S11

13 Table S2: 15 N spin relaxation data (continued) Residue 50.6 MHz 60.8 MHz 81.0 MHz # a.a. R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe R 1 dr 1 R 2 dr 2 NOE dnoe (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) 285 ser ile phe o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l asp val tyr thr ser gln ser arg Exact magnetic elds were as follows: (50.6), (60.8), and (81.0) MHz. Values presented here are rounded to three decimals. Exact values can be obtained from the corresponding author or from the BMRB (accession number 6838). 81:0 R 2 were not used for model-free analysis. n.o.: non-observed N-H resonances. o.l.: overlapped N-H resonances. Important active site residues (Ser 70, Lys 73, Tyr 105, Ser 130, Glu 166 and Arg 234 ) are shown in bold red while the W loop is colored blue. S12 Order and motions in PSE-4 from NMR (Supplementary Material)

14 Fig. S2: 15 N spin relaxation data. Shown are the longitudinal (R 1 ) and transversal (R 2 ) relaxation rates as well as the R 2 =R 1 ratio and the steady-state heteronuclear NOE at 50.6 (light gray), 60.8 (dark gray) and 81.0 (black) MHz nitrogen frequency. Important active site residues are highlighted in light gray. Secondary structures are shown with helices as wide black boxes, and sheets as narrow gray boxes. Order and motions in PSE-4 from NMR (Supplementary Material) S13

15 S14 Order and motions in PSE-4 from NMR (Supplementary Material) Consistency test Consistency of spin relaxation datasets was assessed using the spectral density at the zero frequency (5): J(0) = 1:5 3d + c R1 2 R 2 + 0:6 (NOE 1) R 1 g N g H (1) where d = (1=4)(µ 0 =4p) 2 (~g N g H )=r 3 N-H )2 is the dipolar constant, c = (w N Ds) 2 =3 is the CSA constant, µ 0 is the permeability of free space, ~ is Planck's constant divided by 2p, and g N and g H are the gyromagnetic ratios of 15 N and 1 H, respectively. This function is eld independent in cases where µs-ms motions are absent. Fig. S3 shows that 50.6 and 60.8 MHz data possess high consistency whereas 81.0 MHz data possesses lower consistency. Model-free analysis (see corresponding section within the main document) shows that inconsistency for 81.0 MHz data is caused by R 2 data. Fig. S3: J(0) consistency test. Values are compared for datasets acquired at 50.6, 60.8 and 81.0 MHz (top: correlation plot; bottom: distribution plot of the ratios, with the mean value and standard deviation shown). On an individual basis, a few outliers are observed. These can arise because of ve principal reasons. First, modulation of the R 2 parameter can arise because of conformational exchange. Since this modulation is eld dependent, apparent consistency will be lower (residue Arg 234 is one of those). Second, consistency can appear lower as a result of some assumptions being erroneous. These include the assumption of constant r N-H and CSA. Third, residues can possess extremely high mobility yielding negative NOE values. Fourth, data for a given residue might be erroneous because of overlapping resonances. Fifth, one or more relaxation measurement at one eld strength could be prone to errors (probe imperfection, environmental instability, dif culty of carrying reliable data acquisition given the available hardware, etc). This may be the case for R 2 at 81.0 MHz. As was discussed in the main document, consistency of datasets recorded at 81.0 MHz was lower than for datasets recorded at 50.6 and 60.8 MHz (see Fig. S3 in the Supp. Mat.). Hence, to assess if datasets recorded at 81.0 MHz should be used, several tests were done with optimization of model-free models using a local correlation time

16 Order and motions in PSE-4 from NMR (Supplementary Material) S15 (local t m ) for each residue. When using all datasets, a high number of residues needed a R ex parameter (35 residues among the 134 located in regular secondary structure elements). This number was similar when removing either of the two consistent datasets (50.6 and 60.8 MHz). However, when removing the 81.0 MHz dataset, this number decreased signi cantly (from 35 to 17). Not surprisingly, the number of R ex parameters was still high when removing R 1 or NOE data at 81.0 MHz. However, when discarding R 2 at 81.0 MHz, the number of R ex decreased to the low number encountered when removing all three parameters at 81.0 MHz. Thus, R 2 recorded at 81.0 MHz were excluded from the subsequent model-free analysis. This is not surprising because, for molecules of 30 kda, R 2 have a high weight in the J(0) consistency test function. Despite our best efforts, which involved recording a total of three datasets at 81.0 MHz over a period of two years and carrying numerous parameter optimizations, we never succeeded to record R 2 at 81.0 MHz that was awless with the available hardware. The cause for the R 2 at 81.0 MHz to be slightly inconsistent with the rest of the data is still unknown although it could be caused by factors such as water saturation or probe stability during the CPMG pulse train. It could also be a high eld effect. Nevertheless, the inconsistency was detected and does not affect the quality of the extracted information. On the contrary, some studies could contain artifacts resulting from a failure to recognize such inconsistent datasets. We therefore believe some consistency test should always be done.

17 S16 Order and motions in PSE-4 from NMR (Supplementary Material) Local model-free models Ten model-free models (with 0 to 5 adjustable parameters) were used to describe the internal dynamics as de ned previously (6): m0 : fg (1.1) m1 : fs 2 g (1.2) m2 : fs 2 ; t e g (1.3) m3 : fs 2 ; R ex g (1.4) m4 : fs 2 ; t e ; R ex g (1.5) m5 : fs 2 ; S 2 f; t s g (1.6) m6 : fs 2 ; t f ; S 2 f; t s g (1.7) m7 : fs 2 ; S 2 f; t s ; R ex g (1.8) m8 : fs 2 ; t f ; S 2 f; t s ; R ex g (1.9) m9 : fr ex g (1.10) where S 2 is the square of the generalized order parameter (7), t is the effective upper limit for the timescale of the motion characterized by S 2, R ex is the contribution to R 2 accounting for slow processes occurring on the µs-ms timescale and subscript e refers to the local motion characterized in models m2 and m4 whereas subscripts s and f refer to the slow (ns) and the fast (ps) motions (compared to the global tumbling) characterized in models m5 to m8, where the effective order parameter is a combination of order parameters for both timescales: S 2 = S 2 f S2 s. Models m9 and m0 are both limit situations where a residue respectively has its relaxation dominated by conformational exchange (m9), or displays very limited local motions (m0). Model-free minimization protocol A owchart of the model-free minimization protocol used in the current study is displayed in Fig. S4. A short discussion is presented here, justifying the use of different model selection approaches. Optimizing the diffusion tensor using only residues within well-de ned secondary structures takes advantage of the information contained in the crystal structure concerning secondary structures and avoids any bias of the global diffusion tensor which could arise from incorrect N-H orientations in loops caused by crystal packing or intrinsic exibility. After optimization of the different diffusion models, the AIC chosen diffusion tensor was used to minimize models for every residues, except for the three C-terminus residues (which were analyzed as diffusing independently of the rest of the protein, because their N-H vector orientation is unavailable). Final model selection for all residues (after the tensor had been xed) then proceeded using AICc (small sample size corrected AIC (8)) to minimize over- tting. Indeed, on a per residue basis, the sample size for relaxation data is quite small (n = 8) compared to the complete set used for diffusion tensor optimization (n = 1072), justifying the use of different statistical approaches suited for these two situations. Additionally, using AIC drastically increased the number of residues displaying non signi cant and isolated R ex terms. In fact, AIC yielded 52 residues with R ex terms and AICc yielded 32, with the 20 supplementary R ex terms from AIC being questionable because of both their low values and isolated distribution. For these reasons, AICc was used for the selection of local model-free models after the global diffusion tensor had been xed.

18 Fig. S4: Flowchart of the model-free protocol. This protocol employs the new approach proposed by d'auvergne and Gooley (9, 10) for the rst step with only residues from the core of regular secondary structures (a-helices and b-strands). In this step, model selection is performed using Akaike's Information Criteria (AIC = c 2 + 2k, where c 2 = å n i=1 [(R i R0 i )2 =s 2 i ] measures the goodness of t of experimental (R) and back-calculated data (R0 ), s is the experimental error, i is the residue number, and k is the number of parameters in a given situation) (11). In the second step, the diffusion tensor optimized rst is used for minimization of local model-free models for all residues. The best local model for each residue is chosen using the small sample size corrected AIC (AICc = c 2 + 2k + (2k(k + 1))=(n k 1) where n represents the size of the dataset (8)). In the current study, minimization of both local and global models was performed using the Newton algorithm. Order and motions in PSE-4 from NMR (Supplementary Material) S17

19 Table S3: Model-free analysis results # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s 1 22 ser n.o. n.o. yes n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 23 ser n.o. n.o. yes n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 24 ser n.o. n.o. yes n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 25 lys m2 S 2,t e phe m5 S 2 f,s2,t s gln m2 S 2,t e yes gln m5 S 2 f,s2,t s yes val m2 S 2,t e yes glu m1 S 2 yes gln m2 S 2,t e yes asp m1 S 2 yes val m1 S 2 yes lys m2 S 2,t e yes ala m3 S 2,R ex yes ile m1 S 2 yes glu o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 38 val m1 S 2 yes ser m2 S 2,t e yes leu o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 41 ser m1 S ala o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 43 arg m2 S 2,t e yes ile m2 S 2,t e yes gly m1 S 2 yes val m1 S 2 yes ser m1 S 2 yes val m1 S 2 yes leu m1 S 2 yes asp m2 S 2,t e yes thr m5 S 2 f,s2,t s gln m5 S 2 f,s2,t s asn m6 S 2 f,t f,s 2,t s gly m5 S 2 f,s2,t s glu m5 S 2 f,s2,t s yes tyr m5 S 2 f,s2,t s yes trp m4 S 2,t e,r ex yes asp m1 S 2 yes tyr m1 S 2 yes asn m1 S gly m1 S asn m1 S gln m1 S arg m1 S 2 yes phe m1 S 2 yes pro - - yes leu m1 S thr m1 S 2 yes ser n.o. n.o. yes n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 71 thr m1 S 2 yes phe o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 73 lys m1 S 2 yes S18 Order and motions in PSE-4 from NMR (Supplementary Material)

20 Table S3: Model-free analysis results (continued) # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s 1 74 thr m1 S 2 yes ile m1 S 2 yes ala m3 S 2,R ex yes cys m1 S 2 yes ala m3 S 2,R ex yes lys m1 S 2 yes leu o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 81 leu m1 S 2 yes tyr m1 S 2 yes asp m1 S 2 yes ala m1 S 2 yes glu m1 S 2 yes gln m1 S gly m1 S lys m2 S 2,t e val m2 S 2,t e asn o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 91 pro asn m1 S ser m3 S 2,R ex thr m1 S 2 yes val m2 S 2,t e yes glu m2 S 2,t e yes ile m2 S 2,t e lys m5 S 2 f,s2,t s lys o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 100 ala m2 S 2,t e asp m2 S 2,t e leu m2 S 2,t e val o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 104 thr o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 105 tyr m5 S 2 f,s2,t s ser m2 S 2,t e pro val m2 S 2,t e ile m1 S glu m3 S 2,R ex lys m5 S 2 f,s2,t s gln m2 S 2,t e val m2 S 2,t e gly m2 S 2,t e gln m2 S 2,t e ala m2 S 2,t e yes ile m2 S 2,t e yes thr m1 S 2 yes leu m3 S 2,R ex yes asp m3 S 2,R ex yes asp m1 S 2 yes ala m1 S 2 yes cys m3 S 2,R ex yes phe m1 S 2 yes Order and motions in PSE-4 from NMR (Supplementary Material) S19

21 Table S3: Model-free analysis results (continued) # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s ala o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 126 thr m1 S 2 yes met m3 S 2,R ex yes thr m3 S 2,R ex yes thr m1 S 2 yes ser m1 S asp m1 S asn m1 S 2 yes thr m3 S 2,R ex yes ala m1 S 2 yes ala m1 S 2 yes asn m3 S 2,R ex yes ile m1 S 2 yes ile m3 S 2,R ex yes leu m1 S 2 yes ser m1 S 2 yes ala m5 S 2 f,s2,t s yes val m1 S gly m1 S gly m1 S 2 yes pro - - yes lys o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 147 gly m1 S 2 yes val m3 S 2,R ex yes thr m2 S 2,t e yes asp m1 S 2 yes phe m1 S 2 yes leu m3 S 2,R ex yes arg m3 S 2,R ex yes gln m1 S 2 yes ile m5 S 2 f,s2,t s gly m1 S asp m1 S lys m1 S glu o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 160 thr m1 S arg m3 S 2,R ex leu m1 S asp m1 S arg m2 S 2,t e ile m1 S glu m1 S pro asp o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 169 leu m1 S asn o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 171 glu m1 S gly m1 S lys o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 174 leu o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 175 gly m1 S S20 Order and motions in PSE-4 from NMR (Supplementary Material)

22 Table S3: Model-free analysis results (continued) # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s asp m1 S leu m2 S 2,t e arg m3 S 2,R ex asp m1 S thr m1 S 2 yes thr m1 S 2 yes thr m1 S 2 yes pro - - yes lys o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 185 ala o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 186 ile m1 S 2 yes ala m1 S 2 yes ser o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 189 thr o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 190 leu m1 S 2 yes asn m1 S 2 yes lys m1 S 2 yes phe m1 S 2 yes leu m1 S 2 yes phe m1 S 2 yes gly m5 S 2 f,s2,t s ser m2 S 2,t e ala m5 S 2 f,s2,t s leu m2 S 2,t e ser m2 S 2,t e glu m1 S 2 yes met m2 S 2,t e yes asn m1 S 2 yes gln o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 205 lys m1 S 2 yes lys m1 S 2 yes leu m3 S 2,R ex yes glu m1 S 2 yes ser m1 S 2 yes trp m1 S 2 yes met o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 212 val m1 S 2 yes asn m1 S asn m2 S 2,t e gln m1 S val m2 S 2,t e thr m2 S 2,t e gly m asn m1 S leu m3 S 2,R ex leu m3 S 2,R ex arg m1 S ser m1 S val m1 S leu m1 S pro Order and motions in PSE-4 from NMR (Supplementary Material) S21

23 Table S3: Model-free analysis results (continued) # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s ala m2 S 2,t e gly m2 S 2,t e trp m2 S 2,t e asn m4 S 2,t e,r ex yes ile m1 S 2 yes ala m1 S 2 yes asp m3 S 2,R ex yes arg m3 S 2,R ex yes ser m9 R ex yes gly m3 S 2,R ex yes ala n.o. n.o. yes n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. n.o. 238 gly m2 S 2,t e gly m1 S phe m1 S gly m1 S ala m1 S arg m3 S 2,R ex yes ser o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 246 ile m1 S 2 yes thr m1 S 2 yes ala m1 S 2 yes val m1 S 2 yes val m1 S 2 yes trp o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 252 ser m1 S 2 yes glu m2 S 2,t e his m5 S 2 f,s2,t s gln m5 S 2 f,s2,t s ala m2 S 2,t e pro ile m1 S 2 yes ile m1 S 2 yes val m1 S 2 yes ser m1 S 2 yes ile m1 S 2 yes tyr m1 S 2 yes leu m4 S 2,t e,r ex yes ala m2 S 2,t e yes gln m1 S thr m2 S 2,t e gln m1 S ala o.l. o.l. - o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 271 ser m2 S 2,t e met m1 S 2 yes glu m1 S 2 yes glu m1 S 2 yes arg m2 S 2,t e yes asn m3 S 2,R ex yes asp o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 278 ala m1 S 2 yes ile m1 S 2 yes S22 Order and motions in PSE-4 from NMR (Supplementary Material)

24 Table S3: Model-free analysis results (continued) # a.a. Model Parameters Diffusion S 2 ds 2 S 2 f ds 2 f S 2 s ds 2 s t e dt e t f dt f t s dt s 60:8 R ex d 60:8 R ex core? ps ps ps ps ps ps s 1 s val m1 S 2 yes lys m3 S 2,R ex yes ile o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 283 gly m1 S 2 yes his m1 S 2 yes ser m1 S 2 yes ile m3 S 2,R ex yes phe o.l. o.l. yes o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. o.l. 288 asp m1 S 2 yes val m2 S 2,t e yes tyr m1 S 2 yes thr m5 S 2 f,s2,t s yes ser m6 S 2 f,t f,s 2,t s gln tm5 t m,s 2 f,s2,t s ser tm6 t m,s 2 f,t f,s 2,t s arg tm5 t m,s 2 f,s2,t s Exact magnetic elds were as follows: (50.6), (60.8), and (81.0) MHz. Values presented here are rounded to three decimals. Exact values can be obtained from the corresponding author or from the BMRB (accession number 6838). R ex parameters are calculated for a magnetic eld of 60.8 MHz. The diffusion tensor associated with these local model-free parameters is an ellipsoid with the following characteristics (12): correlation time t m = ( 0.024) ns anisotropy D a = D z (D x +D y )=2 = 3.75 ( 0.19) x 10 6 s 1 asymmetry (or rhombicity) D r = (D y D x )=(2D a ) = ( 0.022) s 1 isotropic component of diffusion D iso = 1=6t m = 1=3(D x +D y +D z ) = 13.1 ( 2.4) x 10 6 s 1 diffusion constants for the three principal diffusion axes D x = ( 0.10) x 10 6 s 1, D y = ( 0.11) x 10 6 s 1, D z = ( 0.13) x 10 6 s 1 orientations: q = 166:2( 8:4) o, f = 146:8( 1:1) o and y = 131:6( 2:6) o. This diffusion tensor was minimized using residues in secondary structures (134). Other residues (96) were excluded from diffusion tensor optimization. Local model-free models were selected using AICc as well as with manual modi cations for residues Gly 175, Leu 199, Glu 201, Arg 234 and Thr 291. Residues Gln 293, Ser 294 and Arg 295 from the C-terminus, which were absent from the crystal structure, were tted using a local t m parameter: 7.49 ( 0.22) ns, ( 6.44) ns and 3.58 ( 0.19) ns, respectively). n.o.: non-observed N-H resonances. o.l.: overlapped N-H resonances. Important active site residues (Ser 70, Lys 73, Tyr 105, Ser 130, Glu 166 and Arg 234 ) are shown in bold red while the W loop is colored blue. Order and motions in PSE-4 from NMR (Supplementary Material) S23

25 S24 Order and motions in PSE-4 from NMR (Supplementary Material) Fig. S5: Representation of the diffusion tensor and of the N-H vectors orientations used for optimization. Parameters for the ellipsoidal diffusion tensor are as follows: Diso = ( 0.024) x 106 s 1, Da = 3.75 ( 0.19) x 106 s 1, Dr = ( 0.022) s 1, tm = ( 0.024) ns, Dx = ( 0.10) x 106 s 1, Dy = ( 0.11) x 106 s 1 and Dz = ( 0.13) x 106 s 1. N-H vectors orientations are shown as surface on arti cial vectors of length 20 Å placed at the center of mass of the protein. Moreover, these vectors are duplicated in the opposite direction because of symmetry in the ellipsoidal diffusion tensor. Missing residues in the crystal structure (Ser22, Ser23, Gln293, Ser294 and Arg295 ) were added for visualization of the whole protein; their exact position being unknown.

26 Fig. S6: Optimized model-free parameters. Shown are the S 2, t (on both slow, t s, and fast, t e and t f, timescales) and R ex (at 60.8 MHz) values. Important active site residues are highlighted in light gray. Secondary structures are shown with helices as wide black boxes, and sheets as narrow gray boxes. Order and motions in PSE-4 from NMR (Supplementary Material) S25

27 Fig. S7: Comparison of order parameters (S 2 ) with crystallographic B-factors from PDB 1G68 (13). Important active site residues are highlighted in light gray. Secondary structures are shown with helices as wide black boxes, and sheets as narrow gray boxes. Qualitative dynamics information can be extracted from crystallographic B-factors (or temperature factors). However, compared to model-free order parameters, differences originate because B-factors are dominated by lattice disorder (14). Moreover, they are often recorded at very low temperatures compared to NMR, as in the case of PDB 1G68 (13) for which X-ray diffraction data was recorded at 100 K. Other possible differences might also arise from crystal packing or translational motions. Finally, B-factors do not report on a speci c timescale and thus can be in uenced by motions much slower than the ps-ns timescale probed by order parameters obtained from 15 N spin relaxation data. Hence, in our case, some differences are seen while some parts show better agreement (Fig. S7). This is the case for both N- and C-termini, the Thr 51 Gly 54 loop, the Leu 225 Trp 229 loop and the Glu 254 Pro 258 loop. On the other hand, the Leu 102 Val 108 loop, which displays fairly low order parameters (compared to the rest of the protein), possesses low nitrogen amide B-factors (low exibility); these may be artifacts due to crystal packing interactions. S26 Order and motions in PSE-4 from NMR (Supplementary Material)

28 Fig. S8: Comparison of PSE-4 and TEM-1 order parameters. Differences are shown for either the published TEM-1 order parameters of Savard and Gagné (15) (S 2 S&G ) or the order parameters using the same analytical approach as in the current study (S2 T, submitted elsewhere). Important active site residues EM-1 are highlighted in light gray. Secondary structures are shown with helices as wide black boxes, and sheets as narrow gray boxes. Order and motions in PSE-4 from NMR (Supplementary Material) S27

29 S28 Order and motions in PSE-4 from NMR (Supplementary Material) Resistance to inhibitors and extended spectrum b-lactams Extended spectrum b-lactams such as oximino-b-lactams and monobactams have allowed for a better ght against the resistance phenomenon. However, their bene cial effect was diminished by the rapid appearance of resistance to these molecules. The mutations include those at positions 69, 237, 240 and 276 (16). Additionally, b-lactamase inhibitors have been useful in the ght against b-lactam antibiotics resistance. However, since the introduction of b-lactamase inhibitors, several mutations appeared that provided resistance to those compounds which include the widely used clavulanic acid, sulbactam and tazobactam. Several mutations have been documented which include those at positions 69, 130, 165, 275 and 276 (17). Most of these mutations were found in TEM-like b-lactamases. However, even if the actual effects of such mutations are unknown in PSE-4, the differential dynamics for these conserved residues in either TEM-1 or PSE-4 might help understand what is happening. Here is a short discussion of dynamics at positions relevant to resistance to inhibitors and extended spectrum b-lactams. Thr 69 In homologous protein TEM-1, residue at position 69 (Met 69 ) was shown to be of high importance with regard to resistance against both extended-spectrum b-lactams and b-lactamase inhibitors (17). This is no surprise as this residue is located next to the catalytic Ser 70. In PSE-4, residue 69 is not a methionine, but a threonine. Thr 69 ts model m1 with a very high S 2 ( ). In TEM-1, Met 69 had also a high order parameter ( ) (15). Given the very high S 2 at position 69 and for residues nearby, mutations at this position might loosen the region around Ser 70 so catalytic residues can reposition according to these evolved compounds. Ile 165 Inhibitor resistance was shown to be sometimes caused by mutations at position 165 (17) which is occupied by a tryptophan residue in TEM-1. As for position 164, N-H backbone order parameter for Ile 165 is low relative to most residues in PSE-4 ( ). This contrasts with the catalytic Glu 166 which displays a S 2 of The joint exibility of residues at position 164 and 165 may allow Glu 166 to move slightly toward Ser 70 as could be needed for its activity in the acylation step of the mechanism. Hence, the exibility of Trp 165 in TEM-1 could be increased in mutants resistant to inhibitors allowing a speci c positioning of Glu 166. Ala 237 Mutations of residue Ala 237 are found in resistance to extended-spectrum b-lactams (17). In PSE-4, this residue has not been assigned probably due to broadened resonances, thus preventing gathering of dynamic information at this position. Nevertheless, µs-ms motions could be affecting Ala 237 and nearby residues such as Asp 233, Arg 234, Ser 235 and Gly 236 which are all tted using a R ex. The same situation is found in TEM-1 where no N-H cross-peak is observed for Ala 237, thus supporting the conservation and importance of such slow motions. It will be interesting to see if mutants for Ala 237 modify these slow motions affecting Ala 237 and its neighbors. Gly 240 Position 240 is another position mutated in extended-spectrum b-lactamases (17). It is occupied by a glycine in PSE-4 (as in most carbenicillinases (13)) and is quite ordered (S 2 = 0:91 0:01). However, in TEM-1, Glu 240 is much more ordered with a S 2 of Motions might be more released in PSE-4 as a result of Gly 240 's side chain being smaller, comparatively to Glu 240 in TEM-1. Moreover, mutations in TEM-1 might allow more movement at this position, as is the case in PSE-4. Arg 275 Even though it is quite far from the active site (>15 Å), residue Arg 275 is often mutated in inhibitor resistance cases (17). In PSE-4, this residue is tted using model m2 with a pretty high order parameter of The situation is similar in TEM-1 where the order parameter is A loosening of motional restriction might cause the augmented resistance for Arg 275 variants. Asn 276 Asn 276 is found in mutants resistant to extended-spectrum b-lactams and inhibitors in TEM-1 (17). In PSE-4, residue Asn 276 ts, as residue Arg 244 (also often mutated in cases of resistance), model m3 with a S 2 of and a R ex of s 1. In TEM-1, where this mutation was identi ed as clinically relevant, model m1 is chosen with a fairly high order parameter of This points to a potentially important difference in TEM-1 with regards to PSE-4. Maybe mutations at position 276 tend to reproduce motions already present in PSE-4. Looking at the dynamics of such mutants could be of high interest for understanding resistance to broad spectrum b-lactams.

30 Order and motions in PSE-4 from NMR (Supplementary Material) S29 Limits in the analytical approach Here are further discussions on the CSA and r N-H within the model-free formalism. Variations of the CSA Within model-free analyses, the CSA is generally held xed with an assumed value of -172 ppm as in this study. However, several studies (18 20) showed that the CSA varies among different residues in a given protein. Variations of the CSA, although limited, in uence results extracted using the model-free formalism. Thus, trying to optimize the CSA as part of the model-free analysis is a potential avenue to extracting better dynamics information because the CSA directly affects several parameters such as the extracted order parameters. Despite this, one needs to be really careful with such an analysis because optimizing the CSA could lead to artifacts. We tried such an optimization with models m1 to m5 to which the CSA was added as an additional parameter. After model selection using AICc and exclusion of outsiders (S 2! 1 and CSA! 0), a value of ppm was reached, with values ranging from to ppm. The associated S 2 values extracted using this approach were slightly more elevated than those using the standard approach with a mean S 2 of This is certainly related to the large variation of CSA obtained which contrasts to published data where a narrower distribution of the CSA was measured (20). Results obtained by Lee and Wand (21) who also optimized the CSA as part of their model-free analysis of ubiquitin yielded such a narrow distribution of CSA values. We are thus aware that some bias and artifacts could arise in our description of the dynamics of PSE-4 by introducing a varying CSA. Hence, all results presented in this study did not include such a parameter. Variations of the N-H bond length As for the CSA, r N-H is generally assumed constant throughout the sequence. In the current study, a value of 1.02 Å was used. The order parameters extracted with such a value will incorporate contributions from bond vibration and libration, hence the proposal by Ottiger and Bax (22) of a value of 1.04 Å for extraction of pure angular motions from spin relaxation data within the model-free framework. These different r N-H have been equivalently proposed (1.02 Å (23), and 1.04 Å (22), respectively). Using the rst value, S 2 values are 12 % lower than with the second (0.85 vs 0.95, respectively, for residues within rigid secondary structures) (24). This is due to the fact that the value of 1.04 Å is an effective bond length which incorporates quantum mechanical zero-point motions of the proton. Hence, S 2 parameters extracted using this value only report on motions of the peptide plane. However, the difference between both values is only a matter of scaling and doesn't in uence the conclusions resulting from the corresponding model-free analysis. Moreover, dynamics of two different proteins analyzed with the same N-H bond length (either 1.02 or 1.04 Å) will compare equivalently, irrespective of whether r N-H is 1.02 or 1.04 Å (23), as behaviors of vectors with S 2 of 0.85 (from r N-H = 1:02 Å) and 0.95 (from r N-H = 1:04 Å) are indistinguishable (25). As stated in the Methods section of the main document, the 1.02 Å value is widely used in the community with most model-free studies using it and many programs having it as default parameter. Moreover, the study of TEM-1 dynamics was performed using this value (15). Hence, for comparison purposes, we chose to set r N-H to 1.02 Å.

31 S30 Order and motions in PSE-4 from NMR (Supplementary Material) Table S4: Amide exchange data Residue EX2? ph 7.85 ph 6.65 # a.a. k ex dk ex k ex dk ex k c logsf K op DG HX (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (kcal mol 1 ) 22 ser n.o. n.o. n.o. n.o. n-ter 23 ser n.o. n.o. n.o. n.o. 4.4e+2 24 ser n.o. n.o. n.o. n.o. 1.1e+1 25 lys o.l. o.l. >1e-3 >1e-3 8.4e-1 26 phe >1e-3 >1e-3 >1e-3 >1e-3 2.3e+0 27 gln >1e-3 >1e-3 >1e-3 >1e-3 5.6e+0 28 gln o.l. o.l. >1e-3 >1e-3 2.3e+0 29 val >1e-3 >1e-3 >1e-3 >1e-3 2.0e+0 30 glu EX2 1.8e-4 3.0e-5 1.7e-5 3.8e-7 1.3e e gln o.l. o.l. o.l. o.l. 6.6e+0 32 asp EX2 5.9e-4 9.3e-5 4.2e-5 6.6e-7 8.1e e val EX2 1.1e-5 4.8e-7 1.3e-6 7.6e-8 5.6e e lys EX2 2.3e-5 7.8e-7 2.8e-6 7.9e-8 6.7e e ala EX2 5.1e-4 2.2e-4 4.8e-5 1.0e-6 1.3e e ile EX2 3.5e-5 1.7e-6 2.8e-6 1.1e-7 4.2e e glu o.l. o.l. o.l. o.l. 4.8e+0 38 val o.l. o.l. 3.6e-5 8.2e-7 5.6e e ser >1e-3 >1e-3 >1e-3 >1e-3 8.5e+0 40 leu o.l. o.l. o.l. o.l. 1.2e+0 41 ser >1e-3 >1e-3 >1e-3 >1e-3 3.3e+0 42 ala o.l. o.l. 1.3e-4 2.5e-6 4.5e e arg EX2 4.8e-4 1.3e-4 3.2e-5 9.0e-7 2.7e e ile EX2 2.9e-4 3.8e-5 1.6e-5 5.3e-7 7.0e e gly o.l. o.l. 1.6e-6 7.5e-8 2.3e e val EX2 7.7e-6 7.0e-7 1.2e-6 5.1e-8 4.8e e ser EX2 7.1e-6 5.0e-7 1.9e-6 5.6e-8 8.5e e val EX2 6.8e-6 5.7e-7 1.4e-6 5.7e-8 3.9e e leu EX2 6.6e-6 6.8e-7 9.7e-7 3.5e-8 9.6e e asp o.l. o.l. 2.6e-5 8.1e-7 5.0e e thr o.l. o.l. o.l. o.l. 5.6e+0 52 gln >1e-3 >1e-3 >1e-3 >1e-3 3.6e+0 53 asn >1e-3 >1e-3 >1e-3 >1e-3 2.3e+0 54 gly >1e-3 >1e-3 >1e-3 >1e-3 4.0e+0 55 glu >1e-3 >1e-3 >1e-3 >1e-3 2.0e+1 56 tyr o.l. o.l. >1e-3 >1e-3 3.5e+0 57 trp EX2 6.1e-4 2.8e-4 3.9e-5 1.4e-6 9.9e e asp EX2 >1e-3 >1e-3 1.7e-3 3.7e-4 6.3e e tyr EX2 8.6e-6 7.6e-7 1.6e-6 6.4e-8 3.5e e asn >1e-3 >1e-3 >1e-3 >1e-3 2.6e+0 62 gly >1e-3 >1e-3 2.5e-4 8.6e-5 4.0e e asn >1e-3 >1e-3 >1e-3 >1e-3 5.6e+0 64 gln EX2 >1e-3 >1e-3 9.5e-5 2.8e-6 2.3e e arg >1e-3 >1e-3 >1e-3 >1e-3 2.7e+0 66 phe EX2 3.3e-4 1.4e-4 2.4e-5 1.7e-6 6.6e e pro pro pro pro pro pro 68 leu EX2 >1e-3 >1e-3 3.3e-5 3.3e-6 6.0e e thr >1e-3 >1e-3 >1e-3 >1e-3 1.2e+0 70 ser n.o. n.o. n.o. n.o. 8.5e+0 71 thr >1e-3 >1e-3 >1e-3 >1e-3 3.9e+0 72 phe o.l. o.l. o.l. o.l. 6.3e+0 73 lys >1e-3 >1e-3 5.2e-4 7.3e-5 1.0e e thr EX2 >1e-3 >1e-3 1.0e-3 5.7e-4 1.2e e ile EX2 2.9e-4 7.5e-5 2.1e-5 9.9e-7 6.7e e ala EX2 1.2e-4 9.2e-6 9.1e-6 5.4e-7 1.3e e cys EX2 1.3e-4 3.4e-5 1.3e-5 5.0e-7 8.1e e ala EX2 1.3e-4 2.0e-5 1.0e-5 2.1e-7 6.6e e lys EX2 9.1e-5 6.9e-6 9.8e-6 3.3e-7 4.2e e leu o.l. o.l. o.l. o.l. 3.6e-1 81 leu EX2 4.4e-5 4.3e-6 5.6e-6 3.4e-7 3.7e e tyr EX2 6.3e-5 6.1e-6 7.0e-6 4.1e-7 7.5e e asp EX2 1.2e-4 4.7e-5 1.3e-5 5.6e-7 9.1e e ala EX2 1.8e-4 3.1e-5 1.3e-5 5.1e-7 6.6e e glu EX2 >1e-3 >1e-3 6.7e-5 2.1e-6 8.1e e gln o.l. o.l. >1e-3 >1e-3 6.6e+0 87 gly >1e-3 >1e-3 >1e-3 >1e-3 4.0e+0 88 lys >1e-3 >1e-3 >1e-3 >1e-3 1.0e+0 89 val EX2 >1e-3 >1e-3 5.9e-4 4.2e-5 1.2e e asn o.l. o.l. o.l. o.l. 3.6e+0 91 pro pro pro pro pro pro 92 asn >1e-3 >1e-3 >1e-3 >1e-3 2.3e+0 93 ser >1e-3 >1e-3 >1e-3 >1e-3 5.3e+0 94 thr >1e-3 >1e-3 >1e-3 >1e-3 3.9e+0

32 Order and motions in PSE-4 from NMR (Supplementary Material) S31 Table S4: Amide exchange data (continued) Residue EX2? ph 7.85 ph 6.65 # a.a. k ex dk ex k ex dk ex k c logsf K op DG HX (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (kcal mol 1 ) 95 val EX2 >1e-3 >1e-3 3.4e-4 3.5e-5 3.1e e glu >1e-3 >1e-3 o.l. o.l. 1.3e+1 97 ile >1e-3 >1e-3 >1e-3 >1e-3 1.2e+0 98 lys >1e-3 >1e-3 >1e-3 >1e-3 2.5e-1 99 lys o.l. o.l. o.l. o.l. 2.5e ala >1e-3 >1e-3 >1e-3 >1e-3 1.3e asp >1e-3 >1e-3 >1e-3 >1e-3 8.1e leu >1e-3 >1e-3 >1e-3 >1e-3 1.7e val o.l. o.l. >1e-3 >1e-3 1.2e thr o.l. o.l. o.l. o.l. 3.1e tyr >1e-3 >1e-3 >1e-3 >1e-3 1.9e ser >1e-3 >1e-3 >1e-3 >1e-3 6.0e pro pro pro pro pro pro 108 val >1e-3 >1e-3 >1e-3 >1e-3 2.0e ile >1e-3 >1e-3 >1e-3 >1e-3 6.7e glu >1e-3 >1e-3 >1e-3 >1e-3 4.8e lys >1e-3 >1e-3 >1e-3 >1e-3 1.2e gln >1e-3 >1e-3 >1e-3 >1e-3 1.3e val >1e-3 >1e-3 >1e-3 >1e-3 2.0e gly >1e-3 >1e-3 >1e-3 >1e-3 6.3e gln >1e-3 >1e-3 >1e-3 >1e-3 5.6e ala >1e-3 >1e-3 >1e-3 >1e-3 2.3e ile EX2 >1e-3 >1e-3 1.4e-4 1.2e-5 4.2e e thr EX2 >1e-3 >1e-3 1.2e-4 1.4e-5 1.2e e leu EX2 >1e-3 >1e-3 1.4e-4 1.1e-5 9.6e e asp o.l. o.l. 1.1e-5 9.2e-7 5.0e e asp EX2 3.7e-4 1.4e-4 1.0e-4 5.3e-6 2.3e e ala EX2 2.1e-4 3.4e-5 1.6e-5 6.3e-7 6.6e e cys EX2 3.7e-4 7.9e-5 2.2e-5 7.9e-7 8.1e e phe EX2 2.1e-4 5.4e-5 3.7e-5 6.5e-7 1.1e e ala o.l. o.l. o.l. o.l. 5.6e thr EX2 >1e-3 >1e-3 1.8e-4 1.7e-5 2.0e e met o.l. o.l. 3.6e-4 6.3e-5 3.6e e thr EX2 >1e-3 >1e-3 6.4e-4 1.6e-4 2.0e e thr >1e-3 >1e-3 >1e-3 >1e-3 3.1e ser >1e-3 >1e-3 >1e-3 >1e-3 8.5e asp >1e-3 >1e-3 >1e-3 >1e-3 1.6e asn >1e-3 >1e-3 >1e-3 >1e-3 6.6e thr >1e-3 >1e-3 >1e-3 >1e-3 2.0e ala >1e-3 >1e-3 >1e-3 >1e-3 3.6e ala >1e-3 >1e-3 >1e-3 >1e-3 2.3e asn o.l. o.l. >1e-3 >1e-3 2.3e ile >1e-3 >1e-3 >1e-3 >1e-3 4.2e ile EX2 2.0e-4 8.0e-5 1.8e-5 7.6e-7 2.5e e leu EX2 1.9e-4 2.4e-5 1.7e-5 7.2e-7 3.6e e ser EX2 >1e-3 >1e-3 1.2e-4 4.6e-6 3.3e e ala EX2 >1e-3 >1e-3 6.6e-5 1.5e-6 4.5e e val EX2 2.2e-4 3.1e-5 1.7e-5 5.4e-7 2.0e e gly >1e-3 >1e-3 >1e-3 >1e-3 6.3e gly EX2 3.6e-4 2.1e-4 4.7e-5 1.6e-6 9.7e e pro pro pro pro pro pro 146 lys o.l. o.l. o.l. o.l. 4.2e gly >1e-3 >1e-3 >1e-3 >1e-3 2.3e val EX2 2.9e-4 6.1e-5 3.4e-5 8.6e-7 4.8e e thr EX2 2.6e-4 5.3e-5 4.0e-5 1.6e-6 3.1e e asp EX2 2.8e-4 1.2e-4 3.7e-5 1.2e-6 1.3e e phe EX2 1.9e-4 5.2e-5 2.1e-5 9.8e-7 1.1e e leu EX2 7.4e-5 3.0e-5 1.2e-5 8.5e-7 1.5e e arg EX2 >1e-3 >1e-3 1.9e-5 6.7e-7 1.7e e gln EX2 >1e-3 >1e-3 9.9e-5 5.7e-6 3.8e e ile EX2 2.6e-4 7.9e-5 1.6e-5 6.0e-7 4.2e e gly >1e-3 >1e-3 >1e-3 >1e-3 2.3e asp EX2 >1e-3 >1e-3 2.3e-4 1.7e-5 2.0e e lys >1e-3 >1e-3 >1e-3 >1e-3 1.2e glu o.l. o.l. o.l. o.l. 4.8e thr EX2 8.4e-4 3.9e-4 9.1e-5 3.7e-6 5.6e e arg EX2 >1e-3 >1e-3 8.4e-5 5.2e-6 4.3e e leu EX2 >1e-3 >1e-3 6.5e-5 3.7e-6 1.0e e asp EX2 >1e-3 >1e-3 2.2e-5 3.4e-6 5.0e e arg EX2 >1e-3 >1e-3 4.4e-5 4.8e-6 7.8e e ile >1e-3 >1e-3 5.3e-5 2.9e-6 7.0e e glu >1e-3 >1e-3 1.8e-5 1.7e-6 4.8e e-6 7.6

33 S32 Order and motions in PSE-4 from NMR (Supplementary Material) Table S4: Amide exchange data (continued) Residue EX2? ph 7.85 ph 6.65 # a.a. k ex dk ex k ex dk ex k c logsf K op DG HX (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (kcal mol 1 ) 167 pro pro pro pro pro pro 168 asp o.l. o.l. o.l. o.l. 8.1e leu EX2 >1e-3 >1e-3 7.0e-5 4.3e-6 1.7e e asn o.l. o.l. o.l. o.l. 1.4e glu >1e-3 >1e-3 >1e-3 >1e-3 8.1e gly >1e-3 >1e-3 >1e-3 >1e-3 1.1e lys o.l. o.l. o.l. o.l. 1.0e leu o.l. o.l. o.l. o.l. 3.6e gly o.l. o.l. >1e-3 >1e-3 2.4e asp >1e-3 >1e-3 >1e-3 >1e-3 2.0e leu n.o. n.o. >1e-3 >1e-3 1.7e arg EX2 >1e-3 >1e-3 6.7e-4 3.9e-4 1.7e e asp n.o. n.o. 5.9e-5 6.3e-6 1.3e e thr EX2 >1e-3 >1e-3 4.9e-5 1.2e-6 5.1e e thr EX2 2.4e-4 1.2e-4 6.3e-5 3.9e-6 3.1e e thr EX2 3.3e-4 7.8e-5 3.5e-5 1.3e-6 3.1e e pro pro pro pro pro pro 184 lys o.l. o.l. o.l. o.l. 4.2e ala o.l. o.l. o.l. o.l. 1.3e ile EX2 1.9e-4 2.1e-5 1.4e-5 6.6e-7 4.2e e ala EX2 2.0e-4 3.1e-5 1.9e-5 6.6e-7 1.3e e ser EX2 >1e-3 >1e-3 6.0e-5 2.8e-6 5.3e e thr o.l. o.l. o.l. o.l. 3.9e leu EX2 1.4e-4 4.0e-5 1.4e-5 6.5e-7 9.6e e asn EX2 1.6e-4 4.8e-5 2.0e-5 7.3e-7 1.4e e lys 2.8e-4 5.7e-5 o.l. o.l. 4.2e phe EX2 1.0e-4 1.2e-5 1.0e-5 4.4e-7 2.3e e leu o.l. o.l. 7.9e-6 4.2e-7 1.5e e phe EX2 1.0e-4 4.2e-5 1.4e-5 5.1e-7 2.4e e gly >1e-3 >1e-3 >1e-3 >1e-3 9.7e ser o.l. o.l. >1e-3 >1e-3 1.3e ala >1e-3 >1e-3 >1e-3 >1e-3 4.5e leu EX2 >1e-3 >1e-3 2.6e-4 1.2e-5 6.0e e ser >1e-3 >1e-3 >1e-3 >1e-3 3.3e glu >1e-3 >1e-3 >1e-3 >1e-3 1.6e met >1e-3 >1e-3 >1e-3 >1e-3 6.6e asn >1e-3 >1e-3 >1e-3 >1e-3 2.3e gln o.l. o.l. o.l. o.l. 2.3e lys o.l. o.l. o.l. o.l. 4.2e lys EX2 >1e-3 >1e-3 2.0e-4 1.6e-5 2.5e e leu EX2 1.7e-4 4.2e-5 1.7e-5 5.9e-7 3.6e e glu o.l. o.l. 1.9e-5 6.5e-7 5.0e e ser EX2 5.1e-4 7.5e-5 7.4e-5 2.3e-6 1.5e e trp EX2 2.9e-4 4.2e-5 1.9e-5 7.3e-7 1.8e e met o.l. o.l. 1.3e-5 9.5e-7 1.8e e val EX2 1.3e-4 5.0e-5 1.2e-5 7.4e-7 2.0e e asn o.l. o.l. o.l. o.l. 3.6e asn >1e-3 >1e-3 >1e-3 >1e-3 2.3e gln >1e-3 >1e-3 >1e-3 >1e-3 2.3e val >1e-3 >1e-3 >1e-3 >1e-3 2.0e thr >1e-3 >1e-3 >1e-3 >1e-3 3.1e gly n.o. n.o. >1e-3 >1e-3 6.3e asn n.o. n.o. >1e-3 >1e-3 5.6e leu >1e-3 >1e-3 >1e-3 >1e-3 6.0e leu >1e-3 >1e-3 >1e-3 >1e-3 3.7e arg >1e-3 >1e-3 >1e-3 >1e-3 1.7e ser >1e-3 >1e-3 >1e-3 >1e-3 8.9e val EX2 >1e-3 >1e-3 4.6e-4 7.9e-5 3.9e e leu EX2 >1e-3 >1e-3 1.9e-4 9.1e-6 9.6e e pro pro pro pro pro pro 227 ala >1e-3 >1e-3 >1e-3 >1e-3 2.3e gly n.o. n.o. >1e-3 >1e-3 4.0e trp EX2 >1e-3 >1e-3 4.3e-5 9.2e-6 2.2e e asn EX2 9.8e-4 3.0e-4 6.5e-5 5.1e-6 1.8e e ile o.l. o.l. 1.7e-4 9.0e-6 4.2e e ala EX2 5.6e-4 2.0e-4 3.8e-5 3.1e-6 1.3e e asp EX2 >1e-3 >1e-3 1.7e-4 1.2e-5 8.1e e arg >1e-3 >1e-3 o.l. o.l. 7.8e ser n.o. n.o. >1e-3 >1e-3 8.9e gly >1e-3 >1e-3 >1e-3 >1e-3 7.9e ala n.o. n.o. n.o. n.o. 5.6e gly >1e-3 >1e-3 >1e-3 >1e-3 4.0e+0

34 Order and motions in PSE-4 from NMR (Supplementary Material) S33 Table S4: Amide exchange data (continued) Residue EX2? ph 7.85 ph 6.65 # a.a. k ex dk ex k ex dk ex k c logsf K op DG HX (s 1 ) (s 1 ) (s 1 ) (s 1 ) (s 1 ) (kcal mol 1 ) 240 gly >1e-3 >1e-3 >1e-3 >1e-3 9.7e phe >1e-3 >1e-3 >1e-3 >1e-3 9.7e gly >1e-3 >1e-3 >1e-3 >1e-3 9.7e ala >1e-3 >1e-3 >1e-3 >1e-3 5.6e arg >1e-3 >1e-3 >1e-3 >1e-3 2.7e ser o.l. o.l. o.l. o.l. 8.9e ile EX2 1.5e-5 1.5e-6 2.9e-6 1.1e-7 8.4e e thr o.l. o.l. 5.0e-5 3.1e-6 1.2e e ala EX2 6.4e-6 4.5e-7 1.0e-6 4.2e-8 3.6e e val EX2 3.9e-6 4.1e-7 4.8e-7 3.6e-8 2.0e e val EX2 3.8e-6 5.1e-7 3.8e-7 4.5e-8 3.1e e trp o.l. o.l. o.l. o.l. 1.4e ser EX2 >1e-3 >1e-3 4.8e-4 3.4e-4 4.1e e glu o.l. o.l. >1e-3 >1e-3 1.6e his o.l. o.l. >1e-3 >1e-3 2.8e gln >1e-3 >1e-3 >1e-3 >1e-3 1.1e ala >1e-3 >1e-3 >1e-3 >1e-3 2.3e pro pro pro pro pro pro 259 ile EX2 9.4e-7 4.9e-7 2.6e-8 6.0e-9 4.2e e ile EX2 5.6e-7 1.3e-7 2.6e-8 5.1e-9 2.5e e val EX2 5.6e-7 1.4e-7 6.6e-8 2.1e-8 1.2e e ser EX2 2.7e-6 6.4e-7 6.1e-8 9.4e-9 8.5e e ile EX2 1.2e-6 2.7e-7 3.6e-8 2.5e-8 8.4e e tyr EX2 1.6e-6 4.6e-7 9.1e-8 3.2e-8 7.2e e leu o.l. o.l. 4.7e-6 2.3e-7 6.8e e ala EX2 1.4e-4 2.5e-5 1.3e-5 4.6e-7 1.4e e gln >1e-3 >1e-3 >1e-3 >1e-3 2.3e thr >1e-3 >1e-3 >1e-3 >1e-3 2.0e gln o.l. o.l. >1e-3 >1e-3 3.6e ala o.l. o.l. o.l. o.l. 2.3e ser o.l. o.l. >1e-3 >1e-3 5.3e met n.o. n.o. >1e-3 >1e-3 4.5e glu >1e-3 >1e-3 >1e-3 >1e-3 8.1e glu >1e-3 >1e-3 >1e-3 >1e-3 2.3e arg o.l. o.l. o.l. o.l. 7.8e asn >1e-3 >1e-3 >1e-3 >1e-3 3.8e asp o.l. o.l. o.l. o.l. 8.1e ala EX2 >1e-3 >1e-3 1.3e-4 2.9e-6 6.6e e ile EX2 2.5e-4 4.7e-5 1.2e-5 3.1e-7 4.2e e val EX2 1.3e-5 6.0e-7 1.1e-6 6.6e-8 1.2e e lys o.l. o.l. 2.8e-6 7.3e-8 6.7e e ile o.l. o.l. o.l. o.l. 2.5e gly EX2 1.1e-5 8.3e-7 3.0e-6 6.7e-8 2.3e e his o.l. o.l. 4.5e-6 1.3e-7 2.4e e ser EX2 7.3e-5 2.7e-5 1.2e-5 2.7e-7 2.6e e ile EX2 8.4e-6 6.6e-7 3.8e-6 6.0e-7 8.4e e phe o.l. o.l. o.l. o.l. 2.3e asp o.l. o.l. 7.8e-6 2.0e-7 2.0e e val EX2 >1e-3 >1e-3 2.0e-4 1.5e-5 5.6e e tyr EX2 >1e-3 >1e-3 2.5e-4 2.0e-5 1.9e e thr >1e-3 >1e-3 >1e-3 >1e-3 2.2e ser >1e-3 >1e-3 >1e-3 >1e-3 8.5e gln >1e-3 >1e-3 >1e-3 >1e-3 4.5e ser >1e-3 >1e-3 >1e-3 >1e-3 5.3e arg >1e-3 >1e-3 >1e-3 >1e-3 8.6e-2 Values presented here are rounded. Exact values can be obtained from the corresponding author or from the BMRB (accession number 6838). n-ter: N-terminus amine. n.o.: non-observed N-H resonances. o.l.: overlapped N-H resonances. Important active site residues (Ser 70, Lys 73, Tyr 105, Ser 130, Glu 166 and Arg 234 ) are shown in bold red while the W loop is colored blue.

35 Fig. S9: Amide exchange results. Shown are amide exchange rates (k ex ) at ph 6.65 (blue) and 7.85 (red). Protection factors (SF), equilibrium constants (K op ) and apparent free energies for the opening of the protecting structure (DG HX ) are also shown for ph 6.65 (i.e. in the EX2 regime). Important active site residues are highlighted in light gray. Secondary structures are shown with helices as wide black boxes, and sheets as narrow gray boxes. S34 Order and motions in PSE-4 from NMR (Supplementary Material)

36 Order and motions in PSE-4 from NMR (Supplementary Material) S35 Fig. S10: Stereoviews of the cavity- lling motion for residues Glu 171 -Leu 177 of the W loop. (A) Order parameters (S 2 colored as in Fig. 2, A of the main document). (B) Conformational exchange (R ex colored as in Fig. 2, B of the main document). (C) Apparent free energies of exchange (DG HX, colored as in Fig. 4 of the main document). (D) The cavity between the W loop and the protein core which the motion of residues Glu 171 -Leu 177 (yellow) would ll is shown in gray surface. Residues from the hinge (Arg 161 and Arg 178 ) are colored red and shown in the stick representation as well as residues Arg 65 and Gly 175 (orange) which would form a hydrogen bond once the motion (black arrow) is completed. Catalytic Glu 166 is also shown in the stick representation.