Determining rotational dynamics of the guanidino group of arginine side chains in proteins by carbon-detected NMR† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cc04821a

A new NMR-based method is presented to determine the rotational dynamics around the Nε–Cζ bond of arginine to characterise the interactions mediated by arginine side chains.

: Exchange constants for free arginine as a function of temperature 2.5 Figure S5: Exchange rates for free arginine as a function of temperature 2.6 Figure S6: Extraction of exchange rate for T4L R14 at 298 K using spectra from 500 and 800 MHz together. 2.7 Figure S7: Extraction of exchange rate for T4L R52 at 298 K using spectra from 500 and 800 MHz together. 2.8 Figure S8: Extraction of exchange rate for T4L R96 at 298 K using spectra from 500 and 800 MHz together. 2.9 Figure S9: Longitudinal relaxation of Arg95 for determination of k ex 2.10 Table S1: Rotational exchange rates determined for arginine side chains of T4L99A 2.11 Table S2: Rotational exchange rates and DDG ‡ determined for R54 of human ubiquitin Electronic Supplementary Material (ESI) for ChemComm. This journal is © The Royal Society of Chemistry 2017

Protein Expression and Purification
Uniformly isotope labelled 13 C, 15 N T4 lysozyme C54T/C97A/L99A (referred to as T4L99A) was expressed from pET29b(+)--T4L L99A in E.coli BL21(DE3) cells. The expression and purification was performed as described previously 1 with minor modifications. Briefly, cultures were grown in 1 L M9 medium (containing 1 g 15 NH 4 Cl and 3 g 13 C 6 --glucose as sole nitrogen and carbon source, respectively) at 37 o C until they reached an OD 600 of 0.5 whereafter the temperature was reduced to 18 o C. At OD 600 of 0.7, protein expression was induced with 1 mM IPTG and cultures were grown overnight. Cells were harvested by centrifugation and lysed by sonication. The protein was purified via a 5 mL GE HiTrap SP--FF column, followed by a gel filtration via a 120 mL Superdex 75 column (GE). Fractions containing the protein were combined, buffer exchanged into T4L NMR buffer (50 mM sodium phosphate, 2 mM EDTA, 25 mM NaCl, 2 mM NaN 3 , 1 % D 2 O, pH 5.5) and concentrated to a final concentration of 1.1 mM (e 280 = 25440 M --1 cm --1 ).
The two--dimensional 1 H--detected zz--exchange experiments on free 13 C, 15 N--arginine were recorded on a Bruker Avance III 600 MHz spectrometer equipped with a room temperature TXI probe. The pulse sequence is depicted in Fig S3a. Briefly, an initial INEPT transfers magnetisation from 1 H to 15 N resulting in a two--spin order longitudinal 2H z N z matrix density element. During the following chemical shift evolution, t 1 , the 15 N chemical shift is encoded. Subsequently, magnetisation is converted to longitudinal magnetisation for the duration of the mixing time t m . Finally, magnetisation is transferred back to 1 H for detection.
Magnetisation that do not exchange during the mixing time give rise to diagonal peaks at {w 1 (N h1 ), w 2 (H h1 )} and {w 1 (N h2 ), w 2 (H h2 )}. Magnetisation that exchange during the mixing time resonate at a different frequency during t 2 detection, and give rise to cross peaks at {w 1 (N h1 ), w 2 (H h2 )} and {w 1 (N h2 ), w 2 (H h1 )}. For each experiment, spectra were recorded for 20 different mixing times t m in the range from to 2 to 300 ms. Spectra were analysed using nmrDraw 7 and visualized in CCPNMR 8 . Finally, the best--fit model parameters, I a,0 , I b,0 , R 1 , and k ex were determined by minimising the target function, c 2 , using in--house written software based on the LMFIT python library 13 .
In eq S6, i={a,b}, I i,calc (t) are calculated intensities, I i,exp (t) are the experimentally observed peak intensitites as a function of the relaxation delay T relax , and s is the uncertainty of the experimentally observed peak intensities. recorded per FID. The chemical shifts of the 13 C z --15 N h resonance of R54 were assigned via the 13 C z chemical shift observed in a 13 C z --15 N e spectrum. The 13 C z --15 N e spectrum was, in turn, assigned using a ( 13 C aliphatic , 13 C z ) 2D--plane of a CCNeCz--TOCSY experiment 14 and a previous assignment of ubiquitin 15 .

Extraction of k ex from D--Evolution based experiments
The evolution of magnetisation during the D--evolution element is described by the Bloch equations 11,12,16 . Directly after the transfer of magnetisation to 15  where R 2 is the intrinsic transverse relaxation rate assumed to be identical in the two sites, k ex is the exchange rate constant defined as the sum of the forward and reverse rate constants, and Δ is the difference in peak position between the two exchanging sites in (rad/sec). Scalar couplings between 15 N h and 13 C z are refocused during the D--Evolution element due to the 180° 13 C pulse and can therefore be ignored. The CPMG 180° pulses refocus the magnetisation, which was considered by taking the complex conjugate of the current magnetization state matrix. The final magnetisation state (the FID) in the 15 N dimension was subjected to the same spectra processing as the actual recorded spectra, i.e. application of a Lorentzian--to--Gaussian window function followed by a phase correction and zero--filling.
Fourier transformation of the calculated FID yielded the theoretically derived spectra as a function of the model parameters described in the Liouvillian G in Eq (S7), that is R 2 , k ex and Δ . Experimental data were fitted to this set of theoretical spectra via a minimisation of the target function, c 2 ,: with N being the number of points in the dataset. We used the noise estimate of the spectra obtained from nmrDraw for the uncertainty . For the experimental data, 1D 15 N spectra were extracted for each plane separately (usually three 1D slices were summed up for each peak to obtain higher signal intensity) using FuDA and imported into Matlab. The noise was scaled according to the number of spectra summed up for each peak. Uncertainties for the obtained model--parameters were calculated using the covariance method 17  . Set CNST25 [15Nepsilon] to 84.5 ppm ; . Set effective scalar coupling to CNST2 = 40 Hz, which is 2*JCN. ; This will generate a density element proportional to ; 2CzNz ( ; Define pulse lengths define pulse pwc "pwc=p1" define pulse pwc_sel "pwc_sel=p12" define pulse pwc_chirp "pwc_chirp=p13" define pulse pwn "pwn=p3" define pulse pwn_sel "pwn_sel=p31" ; ; Define delays define delay taua "taua=1s/(cnst2*4)" define delay eta define delay tt "d11=30m" "d12=2u" "d13=2u" "in0=inf2/2" "tt=in0" "cnst21=o1/bf1" "cnst23=0.5*(cnst21+cnst22)" "cnst24=o3/bf3" "cnst26=0.5*(cnst24+cnst25)" #ifdef HALFDWELL "d0=in0/2−0.5*pwc_chirp−0.63662*pwn" #else "d0=in0−0.5*ppwc_chirp−0.63662*pwn" #endif /*HALFDWELL*/ "spoal12=1.0" "spoffs12=0.0" "spoal13=0.5" "spoffs13=0.0" "spoal31=0.5" "spoffs31=0.0" ; ; Automatic calculation of powers for selective pulses. Not that the ; powers have been optimized for best performance of Eburp and Reburp ; pulses, which is not a perfect inversion at zero frequency, and not ; using the integration factors in the headers. #ifdef AUTOCAL "spw12=(pwc/pwc_sel)*(pwc/pwc_sel)*plw1/(0.05813*0.05813)" "spw31=(pwn/pwn_sel)*(pwn/pwn_sel)*plw3/(0.041920*0.041920)" "plw32=(pwn/pcpd3)*(pwn/pcpd3)*plw3" #endif /* AUTOCAL */ ; ; Hard−code zero powers "plw0=0" "plw30=0"    Figure S2: Carbon--detected 13 C ζ --15 N ε HSQC spectrum of T4L99A. The spectrum was recorded at a field of 18.8 T at 298 K. The assignment shown is taken from ref 14 and it was used to assign the 13 C z -- 15 15 N decoupling during acquisition was achieved using a WALTZ16 scheme applied at a field of 0.7 kHz. (b) Extraction of the exchange rate for free arginine (100 mM in 50 % H2O/50% MeOH) using longitudinal 1 H--15 N zz--exchange spectra recorded at 600 MHz at 273 K. Intensities of crosspeaks and diagonal peaks were extracted using FuDA 9 . The ratios of crosspeak intensity to diagonal peak intensity as a function of the mixing time t mix are plotted in black. An exchange rate k ex of 200.1 ± 0.6 s --1 was obtained by least--square fitting (red). Figure S4: Exchange constants for free arginine in the temperature range from 275 to 293 K, measured using D--evolution. Spectra were recorded at 500 MHz and analysed as described above to extract the exchange rates. ln(k ex ) is plotted versus 1/T and shows a linear relationship as expected based on the Arrhenius equation. From the linear fit, DH ‡ = 48.7±0.6 kJ/mol (11.64 ± 0.15 kcal/mol) Figure S5: Extraction of exchange rate for T4L R14 at 298 K by a simultaneous analysis of spectra from 500 and 800 MHz. Black lines correspond to the experimental 1D spectra extracted along the 13 C z chemical shift of R14 and red lines are results of the least--squares fit. Figure S6: Extraction of exchange rate for T4L R52 at 298 K by a simultaneous analysis of spectra from 500 and 800 MHz. Black lines correspond to the experimental 1D spectra extracted along the 13 C z chemical shift of R52 and red lines are results of the least--squares fit. Figure S7: Extraction of exchange rate for T4L R96 at 298 K by a simultaneous analysis of spectra from 500 and 800 MHz. Black lines correspond to the experimental 1D spectra extracted along the 13 C z chemical shift of R96 and red lines are results of the least--squares fit.   a) From simultaneous analysis of D--evolution experiments at 11.7 T and 18.8 T. b) Calculated as described in Fig. 4.