Supporting Information

Supporting Methods

NMR sample

OAA was expressed and purified as described in (Koharudin et al. 2011). The NMR sample consisted of 2 mM 15N-labeled OAA in 20 mM sodium acetate, 20 mM sodium chloride, 3 mM sodium azide, 90/10% H2O/D2O (pH 5).

NMR spectroscopy

15N-CEST experiments were recorded on a 700 MHz AVANCE III spectrometer equipped with 5 mm cryogenically cooled triple-resonance probe, at 277 K, with 160 and 1024 15 1 complex points and maximum acquisition times of 66.2 and 104.4 ms in the N (t1) and H

(t2) dimensions, respectively, using 4 scans per t1 increment. All experiments were performed as described in (Vallurupalli et al. 2012), using weak radio frequency field strengths of 15 and 1 75 Hz and a H decoupling field strength of 3.5 kHz during Tex = 0.4 s. A series of 2D data sets were recorded, corresponding to 15N offsets incremented in steps of 0.4 ppm (28 Hz). In addition, a reference experiment (Tex = 0 s) was acquired.

Data processing and analysis

The measured spectra were processed using NMRPipe (Delaglio et al. 1995) and analyzed with CARA (Keller 2004), to obtain CEST intensity profiles (major state peak intensity vs. 15N offset). Errors in the peaks intensity were estimated from duplicated measurements at five different 15N offsets.

The reduced CEST profiles composed of 26 15N offsets incremented in steps of 0.8 ppm (56 Hz) were generated from the conventional profiles (52 15N offsets incremented in steps of 0.4 ppm (28 Hz)). Each reduced CEST profile was first inverted by subtracting the largest I/I 0 ratio from all I/I0 values and then transformed into a time-domain signal by using inverse Fourier transform. The time-domain signal was extrapolated via linear prediction (LP) to double the number of points, using a prediction order of 2. The LP filter was calculated using a singular value decomposition (SVD) method. The extended time-domain was reconverted into frequency domain spectrum using Fourier transform. Finally the frequency domain is again inverted by subtracting the largest experimental I/I0 ratio from all I/I0 values, resulting in 15 a 52 N offsets CEST profile (FT-CEST profile). The error in I/I0 after the LP processing was estimated as:

(5)

where σexp is the experimental error and σLP is the error derived from the LP processing, estimated as the root mean square deviation (R.M.S.D) between the experimentally derived

I/I0 and the ones obtained after processing. The FT-CEST profile was processed using an in- house written python script, in which the linear prediction and Fourier transform functions were taken from the Nmrglue module. (Helmus and Jaroniec 2013)

All CEST profiles were analyzed using an in-house written python script that minimizes the target function:

(6)

in which exp is the experimental error to the experimental intensities Iexp, and Icalc refers to the calculated intensities. Intensities were calculated using the Bloch-McConnell equation as

(7)

(8)

a where Iz is the z-component of the angular momentum for the major state, M0 is a column matrix with the populations of the major and minor states (pa and pb, respectively), and A is the system of the Bloch-McConnell equation for a single spin-1/2 system exchanging between two states presented in Eq. 5 of (Vallurupalli et al. 2012).

Alternatively, intensities were calculated using the analytical R1expression (Baldwin and Kay 2013; Palmer III 2014; Trott and Palmer III 2002) as

(9)

where R1ρ is calculated using Eq. 1-4 of the main text, with the following coefficients:

For both models, 1 field inhomogeneity was taken into account by performing 10 calculations using different 1 fields evenly spaced between ± 2= 10%around the mean (15 or 75 Hz). The calculated intensities correspond to a weighted average of those 10 calculations assuming a Gaussian distribution. (Vallurupalli et al. 2012) All the fitted rates a b (kab, kba, R2 , R2 , and R1) were constrained to be positive during the minimization, where kab = a b pbkex and kba = pakex, and we assume R1 = R1 . Initial guesses for the fitting parameters were a b estimated as follows: R2 , R2 , and chemical shift difference between the major and the minor states () are user defined; R1 and the chemical shift of the major state are automatically estimated from the data (the former as where I is one of the experimental intensities measured off-resonance for both the major and the minor states and I0 is the intensity for Tex =

0, and the latter as the 1 offset for which the intensity is minimal); kab and kba are estimated based on a grid search. Uncertainties in fitting parameters were estimated using a Monte Carlo approach using the experimental errors.

Simulations

The effect of the radio-frequency field strength 1 is demonstrated on synthetic data sets created using the analytical solution (Eq. 8). Different datasets with various kex (50, 100, 200 -1 b -1 and 300 s ), R2 (10, 30, 50 and 100 s ), and pb (1 and 5%) values were generated. For all a -1 -1 datasets, a, b, R1 and R2 of 120 ppm, 125 ppm, 0.5 s and 20.0 s , were used. CEST profiles were created for a relaxation delay of 0.4 s and radio-frequency field strengths of 15, 30, 50, 75, and 100 Hz, considering a 70.12 MHz field for 15N. For each CEST profile, data points were created assuming a Gaussian distribution centered on the theoretical value with a standard deviation of 0.006, corresponding to 50 different offsets ranging from 110 to 130 ppm. The CEST profiles using each radio-frequency field strength were fitted either independently or simultaneously with the analytical solution, as described above (see Data processing and analysis). Supporting Tables

Table S1. Fractional error* of the fitting parameters derived from CEST experiments for Val 38, Asn 75, Trp 77, and Asn 104 of OAA at 277 K. Each CEST profile (reduced, FT, and conventional) was fitted to a two-state model using the analytical solution.

Reduced FT Conventional

Val 38

kex/kex (%) 78 49 28

pbpb (%) 100 67 33

 (%) 3 4 2

a a R2 R2 (%) 2 2 0.8

b b R2 R2 (%) 48 38 22

 R1R1 (%) 0.8 1.5 0.5

Asn 75

kex/kex (%) 16 12 12

pbpb (%) 23 19 15

 (%) 4 3 3

a a R2 R2 (%) 5 3 3

b b R2 R2 (%) 90 62 65

 R1R1 (%) 2 2 2

Trp 77

kex/kex (%) 15 11 12

pbpb (%) 18 14 14

 (%) 1 1 1

a a R2 R2 (%) 4 3 3

b b R2 R2 (%) 70 34 34

 R1R1 (%) 3 2 2

Asn 104 kex/kex (%) 47 38 19

pbpb (%) 60 40 20

 (%) 4 16 3

a a R2 R2 (%) 1 1 1

b b R2 R2 (%) 42 39 19

 R1R1 (%) 1.0 1.5 0.7

*Fractional errors were calculated based on the fitting parameters and uncertainties in Table 3 as P/P, where P is the uncertainty associated with parameter P.

Supporting Figures

b Figure S1. Comparison of the R.M.S.D. between the fitted kex and R2 and the real values for pb = 5% (A) and pb = 1% (B). For each pb various synthetic datasets were simulated using a, a -1 -1 b, R1 and R2 of 120 ppm, 125 ppm, 0.5 s and 20.0 s , respectively. Datasets were generated b -1 -1 for various R2 values (10, 30, 50 and 100 s ), with kex = 150 s and various kex values (50, -1 b -1 100, 200 and 300 s ), with R2 = 30 s . b Figure S2. Absolute difference between the R2 (A) and kex (B) values obtained using the reduced and FT-CEST datasets, and the values obtained using the conventional datasets for four residues of OAA.