Arginine Side‐Chain Hydrogen Exchange: Quantifying Arginine Side‐Chain Interactions in Solution

Abstract The rate with which labile backbone hydrogen atoms in proteins exchange with the solvent has long been used to probe protein interactions in aqueous solutions. Arginine, an essential amino acid found in many interaction interfaces, is capable of an impressive range of interactions via its guanidinium group. The hydrogen exchange rate of the guanidinium hydrogens therefore becomes an important measure to quantify side‐chain interactions. Herein we present an NMR method to quantify the hydrogen exchange rates of arginine side‐chain 1Hϵ protons and thus present a method to gauge the strength of arginine side‐chain interactions. The method employs 13C‐detection and the one‐bond deuterium isotope shift observed for 15Nϵ to generate two exchanging species in 1H2O/2H2O mixtures. An application to the protein T4 Lysozyme is shown, where protection factors calculated from the obtained exchange rates correlate well with the interactions observed in the crystal structure. The methodology presented provides an important step towards characterising interactions of arginine side‐chains in enzymes, in phase separation, and in protein interaction interfaces in general.


Introduction
The backbone of proteins has long been the main focus of solution state Nuclear Magnetic Resonance (NMR) spectroscopy, where a comprehensive toolbox of elegant methods is now available to quantify structure, [1][2][3][4][5] interactions, [6,7] and dynamics over many order of magnitudes of timescales. [8][9][10] An important method used to probe the formation of secondary structures and intramolecular interactions in proteins, such as hydrogen bonds, is the quantification of amide hydrogen exchange rates with the bulk solvent. [11] These exchange rates are typically measured either by dissolving the protein of interest in 2 H 2 O and following the decay of the amide proton signal-intensities in NMR spectra [12][13][14] or by magnetisation-transfer type experiments. [15][16][17][18][19] A comparison of the obtained hydrogen exchange rates obtained within proteins with the corresponding rates of small peptides yields a protection factor (PF), [20] which reports on the energy of interactions formed by the amide proton in question.
Whilst a knowledge of protein backbone behaviour is often imperative to understand many aspects of protein functions, it is typically the side-chains that directly mediate activity and participate in the important and functional interactions. Arginine residues are often crucial to many biological inter-action interfaces because the flexible arginine side-chain, consisting of a chain of aliphatic carbon atoms and a terminal guanidinium group, is capable of an array of hydrogen-bonds and other interactions. [21][22][23] The arginine guanidinium group has a very high pK a of 14 [24] and the delocalised positive charge is therefore present under all physiologically relevant pH values. [25] Each arginine guanidinium group has a large delocalised p-system for cationp and pÀp interactions [26,27] as well as five guanidinium protons that are available for hydrogen-bonding and salt-bridging, but generally labile and able to exchange with the bulk solvent. The hydrogen exchange along with restricted rotation about the C z ÀN e bond are unfortunately often a hinderance to obtaining conventional 1 H-15 N NMR correlation spectra at neutral or high-pH. [28,29] However, the rate of the hydrogen exchange can be dramatically reduced if the hydrogen in question is involved in a strong hydrogen-bond or a saltbridge [30,31] and a stronger interaction leads to a slower exchange rate. An accurate determination of the residuespecific side-chain hydrogen exchange rates therefore allows for a quantification of any such interactions involving an arginine side-chain.
Below, we present a new NMR experiment to measure the hydrogen exchange rate of the 1 H e proton of arginine sidechains, based on 13 C detection and the one-bond deuterium isotope shift of 15 N e , which generates two exchanging species in 1 H 2 O/ 2 H 2 O mixtures. [17] An application of the methodology to the 19 kDa protein T4 Lysozyme (T4 L) provides hydrogen exchange rates for 12 of the 13 arginine side-chains in the protein. The remaining residue, R95, is characterised using an established method for monitoring hydrogen exchange. A subsequent comparison of the obtained exchange rates with those of free arginine allows for the calculation of side-chain protection factors, which in turn report on the energetics of the interactions formed. Exchange rates between approximately 0.5À20 s À1 are accessible using the presented methods, how-ever, as the hydrogen exchange rates are exquisitely sensitive to pH and temperature, small changes to the sample conditions allows measurements of rates in a large range of arginine sidechains.

The NMR Experiment
The NMR pulse scheme derived for the measurement of 1 H e / 2 H e exchange rates of arginine side-chains is shown in Figure 1. The experiment incorporates several aspects of the previously published SOLEXSY [17] Figure 1. Since the deuterated 15 N e species, 15 N e ( 2 H), lacks a directly bound proton the refocussed INEPT results in a selective polarisation of only the 15 N e ( 1 H) species, which leads to a density operator proportional to N e z ( 1 H) at point b using the product operator formalism [36] . During the variable mixing period between b and c, t mix , magnetisation is partially transferred from N e z ( 1 H) to N e z ( 2 H) via the chemical exchange (hydrogen exchange) with the bulk solvent. Between points c and d a sign-coding filter is present during which only the N e z ( 1 H) operator is inverted (f 3 = x) or not inverted (f 3 = -x) relative to the N e z ( 2 H) operator. Between d and e the chemical shift of 15 N e ( 1 H/ 2 H) is encoded in a semi-constant time manner, whilst the one-bond 13 C z À 15 N e coupling is allowed to evolve for a total duration of 1/(2J CN ) = 25 ms, resulting in a density operator proportional to 2C z z N e z ( 1 H/ 2 H) at point e. Frequency selective 13 C d and 13 C z pulses are used to ensure that only the desired 13 C z À 15 N e coupling evolves during this period. Simultaneous 1 H and 2 H WALTZ decoupling is applied throughout the indirect chemical shift period to suppress the scalar couplings associated with these nuclei. A final INEPT block between e and f, incorporating selective 13 C z and 15 N e pulses refocuses the magnetisations of interest to in-phase 13 C z at point f for detection under simultaneous 1 H and 15 N decoupling. Frequency discrimination in the indirect dimension is achieved by incrementing f 2 by 908 in line with the states-TPPI scheme. [37] The data are recorded as a pseudo-4D experiment (f 3 , t mix , t 1 , t 2 ), which after a two-dimensional Fourier transformation along t 1 and t 2 results in two cross-peaks, 13 C z À 15 N e ( 1 H) and 13 C z À 15 N e ( 2 H), for each arginine residue with the 13 C z frequency along the direct dimension (w 2 ) and the 15 N e frequency along the indirect dimension (w 1 ). With t mix~0 s, only the 13 C z À 15 N e ( 1 H) signals are observed ( Figure 2a) and the spectrum resembles a standard 13 C z À 15 N e HSQC experiment performed on a sample iñ 100 % H 2 O. Increasing the t mix delay causes initially the 13 C z À 15 N e ( 2 H) cross-peaks to appear for those residues undergoing the fastest exchange ( Figure 2b). Increasing the delay further allows time for the more slowly exchanging signals to appear (Figure 2c). The intensity of both the 15 N e ( 1 H) and 15 N e ( 2 H) signals decay due to longitudinal relaxation during the mixing time, which limits the experiment to accurately probe hydrogen exchange rates faster than~0.5 s -1 . Furthermore, the experiment begins with a 1 HÀ 15 N refocussed INEPT of~11 ms ( Figure 1) and significant exchange during this period will lead to a reduction in the amount of N e z ( 1 H) magnetisation present at the start of t mix , which limits the experiment to only probe hydrogen exchange rates slower than~20 s À1 . Non-selective 908 (1808) rf-pulses are shown as narrow (wide) black bars and are applied at the highest available powers. The delay t a is 1/(4J HN ) = 2.72 ms and the delay t b is 1/(4J CN ) = 12.5 ms. The 13 C frequency selective 1808 pulses, S' and S'', are applied with a Seduce [32] shape (300 ms at 18.8 T) and are selective for 13 C d and 13 C z respectively. The 13 C frequency selective 908 pulse, E, is applied with an EBURP-2 [33] shape (1.5 ms at 18.8 T). The 15 N 1808 frequency selective pulse (R) is applied with a REBURP shape (3.75 ms at 18.8 T). Proton decoupling during the indirect chemical shift period and during acquisition is achieved with a 4 kHz WALTZ-64 [34] scheme. 15 N decoupling during acquisition is achieved with a 0.7 kHz GARP4 [35] scheme. 2 H decoupling between c and e is achieved with a 1 kHz WALTZ-16 scheme. Pulses are applied with x phase unless stated otherwise. The phase cycle used is f 1 : y, Ày, f 2 : 2(x), 2(Àx), f rec : x, 2(Àx), x. f 3 is cycled (x, Àx) to implement the sign-coding filter. Gradient pulses of 1 ms are represented by black rectangles and are applied with strengths of g1: 25.1 G/cm, g2: 25.1 G/cm, g3: 5.9 G/cm, g4: 9.1 G/cm, g5: 21.9 G/cm, g6: 16.6 G/cm, g7: 12.3 G/cm .  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57 The ubiquitous large 15 N one-bond deuterium isotope shift (0.7 AE 0.1 ppm in T4 L) makes assignment of the 13 C z -15 N e ( 2 H) cross-peaks trivial and ensures that the 13 C z À 15 N e ( 1 H) and 13 C z À 15 N e ( 2 H) cross-peaks are well-resolved. However, doubling the number of cross-peaks in the spectrum increases the chance of overlap. In the 13 C z À 15 N e spectrum of T4 L for example, R154 15 N e ( 2 H) partially overlaps with R148 15 N e ( 1 H), which hampers a quantitative analysis of either residue. To overcome this problem, a sign-coding filter ( Figure 1, c to d) is used immediately prior to the chemical shift evolution period to separate the 15 N e ( 1 H) and 15 N e ( 2 H) species into different subspectra ( Figure 3). Two experiments are recorded for each t mix delay with f 3 = AE x. The full pseudo-4D dataset is split into two pseudo-3D datasets after acquisition. The first dataset (f 3 = +x) results in the 15 N e ( 1 H) and 15 N e ( 2 H) cross-peaks having opposite sign, whilst in the second dataset (f 3 = À x) both cross-peaks have the same sign. Taking the difference of the two datasets thus provides a spectrum where only the protonated species, 13 C z À 15 N e ( 1 H), are present. Similarly, addition of the two datasets provides the corresponding spectrum for the deuterated species, 13 C z À 15 N e ( 2 H).

Deriving Hydrogen Exchange Rate Constants for T4 Lysozyme
In Figures 2 and 3 it is seen that the line-shapes are generally asymmetric, which is due to three-bond 15 N e and two-bond 13 C z isotope shifts originating from 1 H h / 2 H h . Peak volumes of 13 C z À 15 N e ( 1 H) and 13 C z À 15 N e ( 2 H) cross-peaks as a function of t mix were therefore obtained by a simple summation over a region of approximately two linewidths in each dimension around the cross-peak of interest. Examples of obtained build up/decay curves for R14, R154 and R54 of T4 L are shown in Figure 4, where hydrogen exchange rates are derived as described in the Experimental section.
The quality of the data is such that accurate exchange rate constants for both the protium to deuterium (k 12 ) and deuterium to protium (k 21 ) processes generally can be obtained. The ratio of these two rate constants is primarily dependent on the ratio of 1 H 2 O and 2 H 2 O present in the solution. For the data shown in Figure 4, where the amount of deuterium in the solvent was carefully maintained at 50 %, the ratio of the two processes (k 12 /k 21 ) for R14 and R154 is~1.1, which reflects the fractionation factor previously reported for backbone amides. [38,39] To avoid the need to very carefully control the relative amounts of protium and deuterium in the solvent, the total exchange constant is considered and defined to be the sum of the two contributing processes, k ex = k 12 + k 21 , which is independent of the protium/deuterium concentration. From the recorded data, accurate hydrogen exchange rate constants (k ex ) can be obtained, 4.6 AE 0.2 s À1 and 1.51 AE 0.10 s À1 for R14 and R154, respectively. The extracted rates for the remaining residues are shown in Table 1(a). Five of the 13 arginine sidechains in T4 L do not show any exchange in experiments performed at pH 5.5 and at 298 K with t mix up to 1 s. This is due to the fact that those hydrogens are engaged in interactions, such as a hydrogen-bond with a carbonyl oxygen or saltbridges between the guanidinium group and acidic side-chains, which is supported by the crystal structure of T4 L (PDB: 102L [40] ). However, the data at pH 5.5 does not provide any quantitative information on the strength of the interactions.
As for the hydrogen exchange of backbone amide protons [13] it is assumed that an arginine 1    where k op and k cl are the first-order rate constants for the reactions between the open and closed state, and k ch is the second-order rate constant for the base-catalysed chemical hydrogen exchange.
A change in the sample conditions, which increases the exchange rate of free arginine therefore increases the exchange rate of interacting arginine side-chains and ought to allow the observation of residues engaged in interactions. Exchange rate constants were therefore also obtained for T4 L at pH 7.4 and 308 K and these are shown in Table 1(b). Values for four of the five residues missing from measurements at pH 5.5 and 298 K are obtained at pH 7.4; only R95 continues to elude detection of exchange. It is interesting to note that the residues observed in the previous experiment (pH 5.5, 298 K) are not detected at pH 7.4, 308 K because the exchange rates are so fast that the magnetisation vanishes in the first refocussed INEPT. Overall, a combination of the two datasets here allows the measurement of hydrogen exchange rates for 12 of the 13 arginine residues in T4 L.
Only an upper bound for the hydrogen exchange rate of R95 can be estimated from the exchange experiment above since no visible exchange was observed within the mixing time used. To measure the hydrogen exchange rate of R95, T4 L was lyophilised from 100 % 1 H 2 O at pH 5.5. The sample was subsequently dissolved in 100 % 2 H 2 O before repeated 1 H-15 N-HSQC experiments were recorded at 278 K over the course of two days or at 288 K overnight (Supporting Information). The intensity of the 1 H e À 15 N e cross-peak was measured as a function of time and fitted to a single exponential decay function. With these experiments the exchange rate of R95 1 H e can be estimated to 4.29 AE 0.02 10 À5 at 288 K, thus confirming that the side-chain of R95 is engaged in a particularly strong interaction.

Comparison with Other Methods for Measurement of Hydrogen Exchange
One commonly used method to characterise hydrogen exchange is to dissolve the protein of interest in a~100 % 2 H 2 O buffer and subsequently record 1 H-detected and 15 N-edited correlation spectra with regular intervals to quantify the timeconstant for the decay of the remaining 1 H. The limitations of this commonly used experiment are two-fold. Firstly, the dead time for dissolving the protein of interest in the 2 H 2 O buffer and secondly the time required for each spectrum. On the other very extreme, very fast hydrogen exchange rates of up to 10 5 s À1 can be measured using CPMG-type experiments with and without proton decoupling [41] and this approach has also been applied to arginine side-chains. Thus, these two methods are both complementary to the method presented above.
A commonly used method to quantify hydrogen exchange on a timescale similar to the presented method is the CLEANEX-PM [15,16] experiment. In this experiment, the water 1 H magnetisation is locked using a high-power spin-lock and the hydrogen exchange is quantified by observing an increase in the transferred proton magnetisation as a function of the time the water magnetisation is spin-locked. There are several advantages of the presented method compared to the CLEANEX-PM method. Firstly, in the method presented here the exchange takes place when the magnetisation is longitudinal and therefore there is no need to apply a long and strong spinlock field. The hydrogen exchange rate is very sensitive to temperature changes and the relatively high-power field required to cover the full range of arginine 1 H e chemical shifts can warm the sample significantly, [17] affecting the measurements. Secondly, the CLEANEX-PM experiment assumes the slow tumbling limit in order to achieve a cancelation of intramolecular NOE and ROE contributions. The effective correlation time of arginine side-chains [28] is often so that the slow-tumbling limit is not applicable, as for the backbone of intrinsically disordered proteins. [17] Thirdly, the use of 13 C detection neatly sidesteps the need to suppress the solvent during acquisition, which can also affect cross-peaks of interest. For example, in the 1 H-detected spectrum of T4 L, the 1 H e resonance of R96 is just~1 ppm downfield from the H 2 O signal and can be affected by water suppression.
A recent and elegant method to quantify hydrogen exchange is the SOLEXSY method by Skrynnikov and coworkers. [17] As for the SOLEXSY method, the method presented  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55 56 57 in Figure 1 also employs the exchange between a protonated and a deuterated species to quantify hydrogen exchange and as such the two methods bear resemblance. However, the method presented here utilises 13 C z detection such that much fewer magnetisation transfer steps are required in the pulse scheme and magnetisation is kept on slower relaxing nuclei, such as 13 C z and 15 N e . Moreover, the arginine side-chain does not contain a spin-system that resembles the 1 H a À 13 C a À 13 COÀ 15 N network utilised in the SOLEXSY method, which means that the original SOLEXSY method is not directly applicable to quantify hydrogen exchange in arginine sidechains.
It should be noted that there is an intrinsic sensitivity penalty in using the 13 C z nucleus for detection due to the lower gyromagnetic ratio when compared to 1 H. However, we believe that the favourable relaxation properties of 13 C z , the ability to encode a broad range of hydrogen exchange rates in relatively few 2D planes, and the inherent resistance to other transfer pathways clearly outweigh the intrinsic lower sensitivity associated with 13 C detection.

Side-Chain Protection Factors
The method described here allows for a determination of the two pseudo first-order rate constants, k 12 and k 21 . In order to derive quantitative information about the strength of the interactions formed by the H e in question, a reference rate corresponding to a non-interacting side-chain H e needs to be available under the same experimental conditions. As seen above in Table 1, there is a strong dependence of the exchange rates on both pH and temperature, whereas little dependence on the ionic strength is expected [30] . As a reference exchange rate, hydrogen exchange data for free [ 13 C 6 , 15 N 4 ]-L-arginine was obtained over a large temperature and pH range ( Figure 5).
Specifically, the pH dependence of log (k ex ) is linear with a slope of~1 as expected for a base-catalysed reaction, and the temperature dependence follows an Eyring dependence (DH ‡ = 78 AE 2 kJ/mol). In turn, this means that reference hydrogen exchange rates for arginine H e can be calculated over a large range of pH and temperature. For example, using the linear dependences of log (k ex ), the exchange rate of free arginine at pH 7.4 and 308 K was calculated to be 3100 AE 100 s À1 .
Hydrogen exchange rates were also measured for the methyl-ester of [ 13 C 6 , 15 N 4 ]-L-arginine to confirm that possible intermolecular interactions between the guanidinium group and the carboxylic acid in free arginine did not affect the obtained exchange rates. Rapid hydrolysis of the methyl-ester in the acidic aqueous conditions prevented a comprehensive analysis, but the results suggest that intermolecular interactions between the guanidinium group and the carboxylic acid, if present, are so weak that the hydrogen exchange rates are not affected.
Once the hydrogen exchange rate for free arginine is determined it can be used as a reference to calculate a protection factor, PF, in line with protection factors for backbone amide groups, as [Eq. (2)]: [13,20]  [g] The rate for free arginine at pH 7.4 and 308 K is extrapolated from the linear dependence in Figure 5.  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56 where k ex(free) and k ex are the hydrogen exchange rate constants obtained for free arginine and the arginine of interest, respectively. Calculated protection factors (PF) for the arginine side-chains in T4 L are shown in Figure 6a and in Table 1. It is clear from the data that R52, R95, R96, R145 and R148 are all engaged in interactions that prevent the exchange of H e to varying degrees. This finding is in good agreement with the crystal structure (Figure 6b-e) as well as previous investigations into the rotational rate of the C z ÀN e bond. [22] 3

. Conclusions
A new method for probing solution-state interactions of arginine side-chains in proteins has been presented. The presented 13 C-detected method allows measurements of the hydrogen exchange rate constant for the H e hydrogens of arginine side-chains; when these rates are between~0.5 s À1 and 20 s À1 . Thus, the method provides a means to quantify the interactions formed by the guanidinium group of arginine sidechains in proteins. The dependence of the hydrogen exchange rate for free arginine on temperature and pH was determined over a large range to provide a reference from which arginine side-chain protection factors can be calculated, similar to backbone amide protection factors that previously have been used widely to quantify interactions formed by the backbone in proteins. An application to the 19 kDa protein T4 Lysozyme was presented, which demonstrates the utility of the method and shows that for this protein protection factors for all bar one arginine side-chain can be obtained. It should be stressed that arginine side-chains that form salt-bridges and medium-strong hydrogen bonds are well captured under physiological conditions (pH 7.4, 308 K) using the presented method. Moreover, small changes in temperature and particularly in pH affect the rates substantially, thus generally allowing for a large range of arginine side-chains to be characterised. It is envisaged that the new method serves as a particularly valuable tool to characterise active sites in enzymes, [21,26] protein-protein or proteinnucleic acid interactions, [27] and phase separation, [23] where arginine residues are expected to play a crucial role for biological function.