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Measurement and Characterization of Hydrogen-Deuterium Exchange Chemistry Using Relaxation Dispersion NMR Spectroscopy Gennady Khirich, Michael J. Holliday, Jasper C. Lin, and Aditya Nandy J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10849 • Publication Date (Web): 27 Jan 2018 Downloaded from http://pubs.acs.org on February 10, 2018

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The Journal of Physical Chemistry

Measurement and Characterization of HydrogenDeuterium Exchange Chemistry Using Relaxation Dispersion NMR Spectroscopy Gennady Khirich‡*, Michael J. Holliday♯, Jasper C. Lin§, and Aditya Nandy§,† ‡

Protein Analytical Chemistry, Genentech, Inc., 1 DNA Way South San Francisco, California

94080, United States ♯

Early Discovery Biochemistry, Genentech, Inc., 1 DNA Way South San Francisco, California

94080, United States §

Late Stage Pharmaceutical Development, Genentech, Inc., 1 DNA Way South San Francisco,

California 94080, United States relaxation dispersion, HDX, CPMG, hydrogen-deuterium exchange, HX, hydrogen-exchange, arginine, natural abundance, equilibrium isotope effect, kinetic isotope effect, nanosecond timescale, millisecond timescale

ACS Paragon Plus Environment

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Abstract One-dimensional heteronuclear relaxation dispersion NMR spectroscopy at

13

C natural

abundance successfully characterized the dynamics of the hydrogen-deuterium exchange reaction occurring at the Nε position in L-arginine by monitoring Cδ in varying amounts of D2O. A small equilibrium isotope effect was observed and quantified, corresponding to ∆G = ‒0.14 kcal mol-1. A bimolecular rate constant of kD = 5.1 × 109 s-1M-1 was determined from the pH*dependence of kex (where pH* is the direct electrode reading of pH in 10% D2O, and kex is the nuclear spin exchange rate constant), consistent with diffusion-controlled kinetics. The measurement of ∆G serves to bridge the millisecond timescale lifetimes of the detectable positively charged arginine species with the nanosecond timescale lifetime of the non-observable low-populated neutral arginine intermediate species, thus allowing for characterization of the equilibrium lifetimes of the various arginine species in solution as a function of fractional solvent deuterium content. Despite the system being in fast-exchange on the chemical shift timescale, the magnitude of the secondary isotope shift due to the exchange reaction at Nε was accurately measured to be 0.12 ppm directly from curve-fitting D2O-dependent dispersion data collected at a single static field strength. These results indicate that relaxation dispersion NMR spectroscopy is a robust and general method for studying base-catalyzed hydrogen deuterium exchange chemistry at equilibrium.


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Introduction Hydrogen exchange (HX) chemistry underlies many of the pivotal techniques used in the study of biomolecular dynamics. Initially investigated by Linderstrøm-Lang and coworkers in the 1950s1-4, and later further developed by various groups5-13, techniques based on this chemistry allow for detailed investigation of acid/base catalysis in small molecules as well as structural changes in macromolecules. Such experiments are typically performed in the presence of deuterium, which acts as an isotopic label throughout the course of an aqueous hydrogendeuterium exchange (HDX) reaction and measured using nuclear magnetic resonance (NMR) spectroscopy and/or mass spectrometry14-17. The kinetics of these reactions are highly sensitive to pH and span many orders of magnitude9, 17-20, ranging from sub-millisecond timescales to timescales on the order of years. NMR spectroscopy is a powerful tool that allows not only for the elucidation of molecular structure, but also the accurate quantitation and characterization of the kinetic and thermodynamic parameters that underlie a system’s dynamic equilibrium. Currently, the prevalent NMR method for studying HDX reaction kinetics relies on the monitoring of nonequilibrium integrated peak intensities in a one- or two-dimensional manner after a lyophilized sample is reconstituted in pure D2O. In contrast, NMR methods for studying HX chemistry at equilibrium exist and have been used successfully in many studies21-29. However, relaxation dispersion experiments, which are particularly amenable to studying equilibrium reactions, have not yet been applied to the study of HX reactions to the best of our knowledge. These experiments generally allow for the accurate and precise quantitation and analysis of dynamics that occur on the microsecond-millisecond timescale when there is a non-zero difference between the chemical shifts of the exchanging states. Although this requirement is not satisfied


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for HX reactions in non-isotopically enriched solvent due to the chemical and magnetic equivalence between the exchanging states, the deuterium content that is ubiquitously added to aqueous NMR samples for deuterium locking also serves to break this degeneracy, allowing for the application of relaxation dispersion methods to the study of HDX chemistry. Moreover, relaxation dispersion methods provide not only a means to monitor the directly observable millisecond timescale lifetimes of the reactants and products of base-catalyzed isotope exchange reactions, but also access to the faster picosecond-nanosecond timescale lifetimes of so-called invisible states which correspond to the low-populated intermediate species along the reaction coordinate. These invisible states are typically unobservable in practice. Thus, three-state chemical equilibria with such an intermediate state may be studied spectroscopically in terms of an effective two-state model between reactants and products. NMR experiments that fall under the relaxation dispersion category include the CarrPurcell-Meiboom-Gill-based (CPMG) and the R1ρ-based suites of pulse sequences30-35. These methods are sensitive to chemical exchange phenomena occurring on the millisecond and microsecond-millisecond timescales, respectively. Additionally, the successful application of CPMG-based methods to the study of dynamics on the seconds timescale has previously been demonstrated36. Historically, these experiments have been successfully used to study macromolecular dynamics33-34, 37-45. In particular, relaxation dispersion methods have been instrumental in characterizing the dynamics of ligand binding, aggregation, allostery, conformational changes, and intermediate and off-pathway states sampled during processes such as catalysis and folding. Additionally, a small number of examples exist in which these methods were applied to smaller molecules46-51. The application of relaxation dispersion techniques to small molecules offers multiple favorable experimental properties. For instance, high quality


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data may be obtained with a cryogenically-cooled probe on isotopically naturally abundant samples, which circumvents the necessity to obtain expensive isotopically enriched samples. Moreover, the CPMG relaxation period, Trlx, may be extended due to the relatively slower transverse relaxation time of the NMR signal of small molecule nuclei; this allows for an improved sampling of the low-pulsing frequency regime of relaxation dispersion profiles, which improves the accuracy with which dynamics parameters are measured. Lastly, many molecular systems are amenable to one-dimensional spectroscopy, resulting in significant reduction in data acquisition time relative to two-dimensional experiments. Here we present a novel application of the constant time relaxation-compensated CPMG (CT-rcCPMG) experiment to measure and characterize the millisecond and nanosecond timescale HDX reactions occurring in the sidechain of arginine as the fractional solvent deuterium content is varied. Of the twenty naturally occurring amino acids, arginine is the most basic, with a pK cited in the range 12.5 – 146, 52-53. This property of arginine contributes to its abilities to act as a protein refolding agent54-56 and control solution viscosity in drug formulations57. Indeed, studies have implicated arginine in participating in non-specific interactions with proteins58, as well as forming intermolecular clusters59-61 and like-charge dimers62 in aqueous solution. The large magnitude of the sidechain pK is also responsible for controlling the HX chemistry at Nε predominantly through a base-catalyzed mechanism6. The kinetics of this reaction have previously been studied by NMR via direct measurement of the widths of peaks63 and via measurement of apparent R1 values under low temperature conditions in 30% methanol, where exchange is slow on the chemical shift timescale64. HX kinetics measurements have also been performed on arginine sidechains in 13C/15N-labelled ubiquitin27. The CT-rcCPMG method for studying HDX chemistry circumvents these restrictions as it


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measures exchange-induced line broadening quantitatively and directly through the transverse relaxation rate constant over a wide range of temperatures without the necessity of adding freezing point depression agents or the necessity of isotopically labelled samples. The experiment is relatively simple to implement, works in one- and two-dimensional modes with naturally abundant 13C, and overcomes many of the analytical challenges traditionally associated with parameter correlations that occur when using the Carver-Richards (CR) equation of twostate exchange65 in the fast exchange limit (See Supporting Information S1 and S2). This method also reports on isotope-induced changes to the immediate magnetic environmental of the spin probe during the course of the exchange reaction, which may correlate with local hydrogen bonding interactions and perturbations. As shown below, it is also possible to detect and accurately quantify any equilibrium isotope effects that may potentially be present for a given isotope exchange reaction, as well as provide insight into the faster nanosecond timescale dynamics of low-populated non-observable intermediates.

Theoretical Background Two variants of the CT-rcCPMG experiment were used for all relaxation dispersion measurements in the course of these studies. The IS pulse sequence35 was used to generate dispersion data on the CαH spin system and the I2S pulse sequence66 was used to generate dispersion data on the CβH2, CδH2, and CγH2 spin systems. The basic principle behind a CPMG experiment is to measure the effective transverse relaxation rate constant, R2,eff, as τcp (the delay between consecutive π-pulses in an echo train) is varied. Variation of τcp modulates the extent to which Rex, the component of transverse relaxation originating from chemical exchange,


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contributes to R2,eff, such that R2,eff = R2,0 + Rex, with Rex = f(1/τcp). In the limit of fast CPMG pulsing (i.e. 1/τcp → ∞), Rex → 0 such that R2,eff = R2,0. In the limit of slow CPMG pulsing (i.e. 1/τcp → 0), Rex → Rex,max, such that R2,eff = R2,0 + Rex,max, where Rex,max is the maximum exchange contribution to transverse relaxation and may be estimated from the surrogate measurement of ∆R2,eff = R2,eff(1/τcp → 0) − R2,eff(1/τcp → ∞). This exchange contribution is sensitive to the chemical exchange parameters kex, pa, and ∆ω, which are, respectively, the NMR exchange rate constant, the fractional population of one of the two exchanging states, and the magnitude of the difference of chemical shifts between the two exchanging states. The details of the models employed in the analysis of experimental NMR relaxation dispersion data, as well as the typical peak behavior encountered throughout the experiment, are presented in Supporting Information S1. In pure protio- or deutero-solvent the HX exchange reaction at Nε is symmetric with respect to the chemical shift of the adjacent Cδ, thus rendering such chemistry undetectable by means of relaxation dispersion because ∆R2,eff = 0 when ∆ω = 0. The addition of solvent deuterium breaks the degeneracy between the carbon chemical shifts (∆ω ≠ 0) such that ∆R2,eff ≠ 0. However, the addition of deuterium also requires consideration of a potentially non-zero ∆G between the exchanging states, which has not previously been measured in arginine, though it is not expected to be large67. This is manifest as kinetic and equilibrium isotope effects (KIE and EIE, respectively), the hallmarks of which are induced changes in the rate constants such that the fractional populations of the protonated and deuterated states of Nε do not directly mirror the fractional isotopic composition of the solvent. It is noteworthy that non-relaxation based methods involving triple resonance NMR have previously been successfully employed68 to measure ∆G


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(in the form of fractionation factors) at the backbone amides of labelled ubiquitin, as well as ∆ω (in the form of a tertiary isotope shift) on 13Cα of neighboring residues. The overall HDX chemical equilibrium between the Nε in arginine and water is presented in scheme 1. In this reaction, HOX and DOX represent any species of water with at least one proton or at least one deuteron attached, respectively. The reaction is catalyzed by OX– (X = H or D) through a base-catalyzed mechanism where the rate-limiting step is the abstraction of the proton at Nε by base, followed by the rapid protonation or deuteration of Nε by solvent, as well as the regeneration of catalytic hydroxide ion. The equilibrium constant describing this reaction is  ArgD +  [ XOH ] α p ArgD + K eq = = .  ArgH +  [ XOD ] 1 − α p ArgH +

(1)

Here, [ArgH+] and [ArgD+] are the concentrations of arginine that are protonated and deuterated at Nε, respectively, and [XOH]/[XOD] is the ratio of solvent protons to solvent deuterons, with α defined as the fraction of H2O in a mixture with D2O; p ArgH + and p ArgD + correspond to the fractional populations of ArgH+ and ArgD+, respectively, with p ArgD + = 1 − p ArgH + . Using the equilibrium relation ∆G = − RTlnKeq , the dependence of pArgH+ on α and ∆G is given by

pa =

α , α + (1 − α ) e −∆G / RT

(2)

where T is the absolute temperature in units of K. From scheme 2, the rate constants ki ( i ∈ {1, −2} ) may be written as


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ki = k D χ i OX −  ,

(3)

where kD is the diffusion-controlled bimolecular rate constant (in units of s-1M-1) that describes the formation of the collision complex between arginine and base, and

χi =

10∆pKi . 1 + 10 ∆pKi

(4)

This represents the probability of a successful abstraction of a proton/deuteron by OX‒ upon formation of the encounter complex with arginine, with ∆pKi (and all subsequent ∆pK terms) written in the form pKi(acceptor) – pKi(donor). Thus, ∆pK1 = pKXOH – pKArgH+ and ∆pK-2 = pKXOD – pKArgD+, and for arginine, χ i ≈ 1 . The rate constants k j

( j ∈{−1, 2}) describe re-

protonation and re-deuteration of the neutral Arg species by solvent, respectively, and are given by k −1 = k Dα (1 − χ1 ) [Water ]

(5a)

k2 = k D (1 − α )(1 − χ −2 ) [Water ] .

(5b)

and

Here, [Water] represents the concentration of water regardless of isotopic composition (55.6 M). For arginine, both k-1 and k2 are much larger than both k1 and k-2, since [Water] >> [OX‒]. The net rate constant describing the decay of the neutral Arg species (to either ArgH+ and ArgD+) is given by kArg = k-1 + k2. Thus, the lifetime of the neutral Arg species, which depends on α, may −1 be gleaned from τ Arg = k Arg .


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Scheme 3 describes the HDX kinetics as they are observed by NMR on arginine. Here,

kl ( l ∈ { f , r} ) are the net forward and reverse NMR-observed rate constants, respectively, and are given by k f = k D χ1ξ f OX −  = ξ f k1

(6a)

k r = k D χ −2ξ r OX −  = ξ r k −2 ,

(6b)

and

where −∆pK 1 − α )10 ( ξf = −∆pK

1 + 10

f

f

 α10 −∆pK r (1 − α )10 −∆pK f +  −∆pK f  1 + 10 −∆pKr 1 + 10 

−1

  ,  

(7a)

and

ξr =

α10 −∆pK  α10 −∆pK r

r

 1 + 10 −∆pK r  1 + 10 −∆pKr

−∆pK 1 − α )10 ( +

1 + 10

−∆pK f

−1

f

  .  

(7b)

ξf and ξr, respectively, represent the probabilities with which the neutral Arg species successfully abstracts a solvent deuteron or a proton. The ∆pKi terms are defined as pKi(acceptor) – pKi(donor), with ∆pKf = pKXOH – pKArgH+ and ∆pKr = pKXOD – pKArgD+. Thus, the NMRobserved exchange rate constant kex, which is always given by kex = ∑ l kl = k f + kr for a twostate exchange process69, may be expressed as kex = ( χ f ξ f + χ rξ r ) k D OX −  = γ kexchem .


(8)

10

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Here, γ ≡ χ f ξ f + χ r ξ r is the KIE, the value of which is approximately unity for arginine (see supporting information S3), and kexchem = k D OX −  is the canonical base-catalyzed exchange rate constant in the absence of both isotope effects (i.e. ∆G = 0) and protection factors70-71. By rearranging eq 8, kD may be obtained from the pH-dependence of kex via

logkex = pH + logγ kD KW

(9)

if both γ and Kw (the auto-ionization constant of water) are known. In our pH*-dependent study, we assume that KW is not significantly perturbed in 10% D2O from its nominal value of 10-14 in pure H2O, as well as that pH* is a suitable surrogate for pH under these experimental conditions72 (vide infra). Moreover, all results reported in this study assume that the pK of water is 15.7 for consistency with the historical literature. The dependence of pArgH+ on α provides a means by which ∆pK may be measured for the entire HDX reaction (scheme 1). By relating ∆G to ∆pK using

∆pK =

( log10 e ) ∆G ,

(10)

RT

it is possible to determine pKArgD+, the pK of deuterated arginine at Nε, via

pK ArgD+ = ∆pK water + pK ArgH + − ∆pK ,

(11)

where ∆pK water ≡ pK XDO − pK XHO . Knowledge of pKArgD+, along with previously published values of pKArgH+, pKXOH, and pKXOD, provides an experimental avenue for estimating τArg as a function of α.


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Experimental All samples of L-arginine that were used in pH*-dependent and temperature-dependent studies were prepared in 10% D2O, with pH* representing the electrode reading in the presence of 10% D2O. The pH* of these solutions was adjusted accordingly with HCl or NaOH, and was measured in quintuplicate to a precision of 0.01 pH* units for each sample in the range 6.76 – 7.28 using a calibrated pH meter electrode. All measurements of ∆R2,eff were performed on a 150 mM arginine sample in 10% D2O. Samples used in D2O-dependent studies were prepared by diluting a 300 mM aqueous arginine solution two-fold by addition of an appropriate H2O/D2O mixture; pH* was not measured in these samples. NMR measurements were performed on Bruker 500 and/or 600 MHz spectrometers with cryogenically cooled probes. All sample temperatures were calibrated relative to methanol-d4 (CD3OD) within the probe. Data were typically collected in a heteronuclear one-dimensional fashion, with 1024 complex points collected in the direct dimension at maximum receiver gain, with a proton spectral width of 4 ppm, and the carrier frequency centered at 2 and 35 ppm in the proton and carbon dimensions, respectively. Water suppression was achieved by an echo/antiecho coherence selection scheme73-74 inherent to the pulse sequences used. A constant relaxation period of Trlx = 160 ms was used in all CPMG experiments, as this gave the desired ~50% signal attenuation at the slowest pulsing frequency during the relaxation period. This ensures that the exponential relaxation decay curve is adequately sampled during each iteration of τcp, resulting in an accurate measurement of R2,eff according to R2,eff = −

1  I (τ cp )   , where Io is the intensity ln  Trlx  I o   

of a reference signal (no CPMG period) and I(τcp) is the intensity of the same signal after a CPMG relaxation period with inter-echo spacing τcp. Each relaxation dispersion profile was


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collected with the following values of τcp, including duplicates at three τcp values: 1.000, 1.111 (×2), 1.250, 1.429, 1.667, 2.000, 2.500 (×2), 3.333, 5.000, 6.667, 8.000, 10.000, 13.333, 20.000, and 40.000 (×2) ms. Rex,max was estimated using ∆R2,eff = R2,eff (τcp = 40 ms) - R2,eff (τcp = 1 ms) in temperature-dependent studies. Uncertainties74 in the measured R2,eff values were estimated using σ ( R2 ) = σ ( I o ) + σ ( I (τ cp ) ) , where ߪ(‫ܫ‬௢ ) and ߪ(‫߬(ܫ‬௖௣ )) are the uncertainties from signal-to2

2

noise measurements in ‫ܫ‬௢ and ‫߬(ܫ‬௖௣ ), respectively. Uncertainties that were estimated as < 2% were set to a minimum value of 2% to account for any underestimation75. Spectra were processed with either Bruker’s TopSpin software or Mestrelab’s Mnova software. Each Monte Carlo simulation was performed in GraphPad Prism v7.00 by simulating 500 2%-random-noise-corrupted datasets from a model of interest with a nominal set of input parameters, fitting each generated dataset to the model of interest, and analyzing the resulting statistics of the best-fit parameters. All experimental dynamics parameters from relaxation dispersion data that were obtained from fits to the CR equation were validated via the above procedure, using the best-fit experimental parameters as both the input for the simulations and the initial values during curve-fitting. Additional information regarding Monte Carlo simulations to validate the best-fit dynamics parameters obtained from relaxation dispersion analysis is provided in Supporting Information SI.


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Results Detection and Verification of Chemical Exchange A classic hallmark of chemical exchange occurring on the millisecond timescale is the detection of a static field-dependent exchange contribution, Rex, to the transverse relaxation rate constant R2,0. Figure 1a shows dispersion profiles collected for Cα and Cδ of arginine, each at 500 and 600 MHz. The dispersion profiles of Cδ fit well with the Luz-Meiboom (LM) model of fast exchange (eqs S1-1 – S1-4), under the constraints that kex and Φex≡ pa pb ∆ω 2 are, respectively, field- independent and field-dependent parameters. Conversely, the very low amplitude dispersion profiles of Cα were not fit well with these constraints, as the Cα dispersion amplitude (Rex,max) remained field-independent. To test whether the Cα profiles were a result of spurious dispersion and to estimate the exchange regime of the observed Cδ dispersion profile, the temperature dependence of Rex,max was measured for Cα and Cδ at 600 MHz, using ∆R2,eff (vide supra), the results of which are presented in Figure 1b. The resulting trends are consistent with the field-dependent data of Figure 1a, thus providing confidence that the Cα dispersion profiles are spurious and that those of Cδ represent bona fide chemical exchange. Moreover, the decrease in ∆R2,eff with increasing temperature confirms that the exchange event detected at Cδ is fast on the chemical shift timescale, thus validating the initial use of eq S1-4. It was reasoned that the observed Cα profiles are most likely an artifact of the long relaxation period used in these studies, as shown in Supporting Information S4. Hydrogen Deuterium Exchange To test for the presence of any potential millisecond timescale aggregation dynamics in aqueous arginine60-61, the dependence of kex on arginine concentration was measured. As shown


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in Supporting Information S5, no detectable changes were observed in both kex and Φex at arginine concentrations of 10 and 300 mM, both at 281 and 300 K. Consequentially, it was reasoned that the origin of the Cδ dispersion data was most likely an isotope effect from an HDX event at the adjacent Nε. To test this hypothesis, 150 mM arginine samples were prepared in 10, 25, and 50% D2O. As illustrated in Figure 2a, the amplitudes of these dispersion profiles exhibit sensitivity towards solution D2O content at a static field strength of 600 MHz. By fitting the dispersion data with the LM model at 10, 25, and 50% D2O, kex was found to be 214, 205, and 209 s-1, respectively. Indeed, an excellent fit of the data was obtained with a single global best-fit kex of 208 s-1. This observed invariance of kex across multiple values of α is consistent with the theoretical prediction of eq 8 (vide supra) in conjunction with the predicted virtual invariance of γ for arginine across α (see Supporting Information S1). Thus, it was reasoned that the dependence of the dispersion amplitudes on α must originate from modulation of the fractional isotopic populations of Nε in arginine. Since ∆ω does not depend on α, the dispersion data were fit to the CR equation with both kex and ∆ω constrained to be globally shared across the datasets, and with pa ≡ pArgH+ constrained by eq 2 (with T = 298K and α = 0.90, 0.70, and 0.50) such that ∆G was a globally fit parameter as well. The best-fit values for the dynamics parameters were found to be kex = 213 s-1, ∆ω = 0.12 ppm, and ∆G = -0.14 kcal/mol. These results were validated with noise-corrupted Monte Carlo simulations, with each parameter being well defined by highly localized Gaussian distributions centered on the respective experimentally determined values, as shown in Figures 2b, 2c, and 2d. Monte Carlo simulations were also performed to test the integrity of the best-fit dynamics parameters from D2O-dependent dispersion profiles under the assumption that the isotopic populations of Nε exactly mirror the solvent isotope composition in the presence of EIEs in the


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range -0.5 < ∆G < 0.5 kcal mol-1 (see Supporting Information S6). Using our experimentallydetermined values of ∆ω and kex as input parameters for the generation of the synthetic data, it was found that the average best-fit values of ∆ω and kex do not stray far from the nominal input values (relative error in kex ≤ 5%, relative error in ∆ω ≤ 15%), thus suggesting that neglecting equilibrium isotope effects in D2O-dependent relaxation dispersion analysis of base-catalyzed HDX reactions still results in relatively faithful estimates of the true dynamics parameters. The pH*-dependence of kex was measured by collecting Cδ relaxation dispersion profiles in the pH* range 6.76 – 7.28 in 10% D2O, as shown in Figure 3. The use of either the CR model or the LM model to obtain exchange kinetics does not influence the pH*-dependence of logkex via eq 9 (see Supporting Information S2). Both analyses yield the statistically identical value of γkD = (5.1 ± 0.2) × 109 s-1M-1 for the isotope-perturbed rate constant. Under our experimental conditions, γ = 0.998 and does not vary with pH, corresponding to kD = 5.1 × 109 s-1M-1, a value which is in agreement both with previously reported values for arginine64 as well as the theoretical diffusion-limited Debye value of 1010 s-1M-1

6, 76

. Thus, the fact that nearly each

collision between ArgH+/D+ and base results in a fruitful abstraction of either H or D is substantiated. Additionally, the pH* dependence of Φex in 10% D2O was measured as a control; the experimental observation that Φex does not vary with pH* is consistent with theoretical prediction, as changes in pH* affect only kex, not the populations or ∆ω. Using our experimentally determined ∆G = -0.14 kcal mol-1 we find via eq 10 that ∆pK = -0.10. By combining ∆pK with pKXOH77 = 15.74 and pKXOD77 = 16.65, the difference in pKs between the ArgD+ and ArgH+ is found to be 1.0 (eq 11). By using pKArgH+6, 53 = 13, we find that pKArgD+ = 14 (all pK values assume a temperature of 298 K). As described by eqs 3 – 5, the lifetimes of the ArgH+, ArgD+, and neutral Arg species are dictated by their relative affinities for


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protons/deuterons with respect to water, as described by their relative pK values. Our experimentally determined values of kD and pKArgD+ were used concomitantly with the known values of the aforementioned pKs to estimate the lifetimes of the three arginine species in solution, as shown in Figure 4. Since both ArgH+ and ArgD+ are detected spectroscopically via the non-zero ∆ω on Cδ, their associated spectroscopic lifetimes (τArgH+ and τArgD+, respectively) correspond specifically to the average times between the hetero-isotopic (H/D) exchange events, and not the chemical lifetimes which report on both hetero-isotopic and homo-isotopic (H/H and D/D) back-exchange events. At 298 K, pH* = 7, and α = 0.90, we find that τArgH+ = 16 ms and τArgD+ = 2.2 ms. The lifetimes of these charged arginine species do not simply swap when α = 0.10 relative to their values at α = 0.90, due to the fact that ∆G ≠ 0. Indeed, we find that τArgH+ = 2.1 ms and τArgD+ = 24 ms when α = 0.10. Since kex does not depend significantly on α in arginine, τex too is not expected to vary with α. As α is varied from 0.10 to 0.90 at pH* 7, τex remains a constant 2.0 ms (Figure 4). These spectroscopic lifetimes are consistent with the millisecond timescale typically probed by CPMG relaxation dispersion experiments, as the dispersion amplitudes are modulated by kex and not solely by either kf or kr, both of which do vary with α. The chemical lifetime of the neutral Arg species at pH* 7 was found to be some 6 orders of magnitude shorter than τex,, with τArg = 1.9 ns when α = 0.90 and τArg = 1.6 ns when α = 0.10. Thus, while consideration of ∆G results in only a small modification in the determination of τArg, we anticipate that other situations amenable to this analysis may exist where the isotope effect, and therefore ∆G, is appreciably larger, such as reactions involving tritium-hydrogen exchange67. The relaxation dispersion method provides a simple and convenient way to accurately measure this effect.


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Discussion HX chemistry is of significant interest in a wide variety of chemical disciplines as it provides a means to probe the kinetics of various acid- and base-catalyzed reactions, which in turn may report on transition states, structural changes, solvent-accessible surface area, and other dynamics in molecular systems. The purpose of the current study is to describe the successful application of relaxation dispersion NMR spectroscopy to the study of these important reactions in an aqueous arginine model system in the presence of solvent deuterium. Although linebroadening experiments based on measurements of resonance full-widths at half-height have successfully been employed in the past to measure equilibrium HDX kinetics in various amino acids63 (including arginine), the use of relaxation dispersion methodology allows for accurate and reproducible quantitation of bona fide exchange contributions to transverse relaxation rates without added complications arising from the contribution of field inhomogeneities to line widths. This results in the unambiguous measurement of not only the exchange kinetics, but also ∆ω, which contains information about local structure and/or chemical environment, and ∆G which reports not only on isotope effects at equilibrium, but also serves as a connection between the directly observable millisecond timescale lifetimes of the products and reactants, as well as the much shorter lifetimes of invisible intermediate states. This makes for a novel and powerful approach to the study of HDX chemistry. Although the millisecond kinetic window probed by the CT-rcCPMG experiment corresponds to a relatively narrow pH* range due to the sensitive dependence of kex on pH*, the pH* range of ~0.5 used in this study suggests that this is not a hindrance to the characterization of HDX chemistry using this method. The sensitivity of the CT-rcCPMG experiment to minor changes in exchange kinetics has thus been demonstrated. A general scheme for measuring the


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rate constant kD with relaxation dispersion experiments for a given HDX reaction may be described by the following procedure: (1) a screening study is conducted to identify the basic pH* region that results in millisecond timescale HDX dynamics (i.e. ∆R2,eff > ~2 s-1); (2) samples are prepared by varying the pH* within the identified millisecond pH* region and full relaxation dispersion profiles are collected; (3) the pH*-dependence of logkex is analyzed to extract kD. This procedure is amenable to other relaxation dispersion studies, such as R1ρ-based experiments, which allow for the sampling of even wider pH* ranges due to the sensitivity of the experiment to faster timescale exchange kinetics (kex < ~50,000 s-1)17, 32, 74. The correlation between the solvent deuterium content and the equilibrium fractional isotope populations (but not kex) greatly facilitates the analysis of HDX relaxation dispersion data. Traditionally, the exchange regime of a reaction is estimated from the field- or temperaturedependence of ∆R2,eff and an appropriate model of chemical exchange is chosen to fit the data78-79. Although the CR equation (eq S1-1) is valid for all exchange regimes, in general the dynamics parameters inherently exhibit significant interdependencies on one another. Therefore, each relaxation dispersion profile is typically collected at two static fields to break these correlations, allowing the dynamics parameters to be accurately quantified. Moreover, as the exchange approaches the fast limit, the populations and ∆ω merge into a product, which is exemplified explicitly in the LM model as Φex (eq S1-3). In such cases, pa, pb, and ∆ω cannot be separated from two-field curve-fitting alone, and other means of breaking these correlations must be implemented80 if information other than kex, Φex, and R2,0 is pertinent. However, the D2O dependence of HDX dispersion profiles disentangles the interdependence of ∆ω and pa, thus allowing for accurate quantitation of ∆ω and the fractional isotopic populations at a single static field strength. Moreover, the CR equation may be used to globally fit a series of dispersion


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datasets that are in the fast exchange regime, as any pre-existing correlations between dynamics parameters are broken by the solvent deuterium content (figure 2). The dependence of the equilibrium fractional isotopic populations on α may be used to increase the amplitude of the dispersion profiles during the course of experiments without perturbing kex, thus improving the accuracy with which HDX dynamics parameters may be measured. Moreover, this effect may be used in the initial screening and characterization of site-specific HDX reactions by providing a means to distinguish HDX from other confounding factors, such as conformational changes. However, when kex is measured at five pH* conditions, with all data sets fit globally, some residual inter-parameter correlations are still present from the CR equation. Best-fit values of ∆ω and pa are sensitive to their initial values during fitting. When both parameters are constrained to be globally fit, ∆ω remains sensitive to initial conditions when pa is constrained to mirror the fractional H2O content during fitting. We also note that the best-fit exchange kinetics are generally independent of the model used in analyzing fast exchange data. However, multimodalities in ∆ω during fitting may generate multimodalities in kex when correlations from the CR equation are not fully suppressed (Supporting Information S2) and parameter values are sensitive to initial fitting conditions. Thus, it is strongly advised that in the course of pHdependent studies both ∆ω and kex be initially extracted as fitting parameters from the LM model (either globally or dataset-specific) to be used as reference values for gauging their accuracy when obtained from the CR equation. Moreover, use of the LM model renders Monte Carlo data validation unnecessary, as it faithfully reproduces accurate dynamics parameters from noisecorrupted data (Supporting Information S2). This significantly simplifies analysis, interpretation, and validation of dispersion data. Alternatively, ∆ω may be accurately measured from a D2O-


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dependent study (vide supra), thus simplifying the pH*-dependent relaxation dispersion analysis to one involving only kex and Φex. The ability to obtain isotope shifts directly from single-field relaxation dispersion experiments under intermediate-fast chemical exchange conditions is a powerful feature that is greatly simplified by the dependence of the populations on α. Moreover, when the approximation that pa = α is invoked, the best-fit value of ∆ω from a D2O-dependent dispersion series is not greatly perturbed in the presence of an EIE. Isotope-induced chemical shifts can provide valuable information regarding local hydrogen bonding interactions, because the magnitude of such a shift on a nucleus that is adjacent to the site of HDX typically correlates with the number and/or strength of hydrogen bonds with which it is involved81-82. Although more pronounced in primary isotopic shifts (i.e. isotopic exchange occurs directly on the nucleus being observed, such as 1H – 15

N experiments involving glutamine and asparagine sidechains in proteins), the relatively

weaker secondary isotopic shift has shown to be accurately probed. Indeed, our experimentally determined magnitude of ∆ω = 0.12 ppm is in the expected range of a secondary two-bond isotope shift on Cδ 81, 83-84. Previous measurements of tertiary isotope shifts at 13Cα positions in ubiquitin68 yielded ∆ω = 0.08 ppm, which is consistent with the expectation that a secondary isotope shift induces a greater change in the 13C chemical shift than a tertiary one. This application may prove useful for the study of local hydrogen bonding interactions and their dependence on structural dynamics in proteins, as well as on the study of solute-solvent and solute-solute interactions. In particular, site-specific isotopic shifts via ∆ω, in conjunction with site-specific HDX rates, may act as reporters on local structure as a system is shifted across binding, conformational, and/or pH-dependent equilibria.


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The capability to directly measure millisecond timescale exchange events and infer the significantly faster nanosecond timescale exchange events provides insight with respect to the dependence of the lifetimes of the various arginine species in solution on solvent deuterium content. The decrease (increase) in τArgD+ (τArgH+) with increasing α is predominantly due to a change in the frequency of collisions between two hetero-isotopic species and not due to any existing differences in the pK values involved. On the other hand, the observed trend in τArg with respect to α is primarily a pK effect. By considering the differences between ∆pKf and ∆pKr, the propensity of Arg to abstract a solvent deuteron over a proton is ~26% higher. Although these propensities are further modulated by the respective abundancies of each isotope in the solvent, the net result is the observed gradual increase in τArg with increasing α. The virtual independence of τex in arginine with respect to α becomes apparent when the interpretation of kex is considered. Generally, kex = ∑ i ki 69 and although its exact chemical interpretation is typically elusive, it sets the characteristic timescale for exchange of nuclei between magnetically distinct environments for a given reaction. However, in the case of basecatalyzed HDX, kex = γ kexchem (eq 8) and since γ ≈ 1 for arginine (Supporting Information S3), the approximation kex ≈ kexchem holds. Thus, no significant changes in either kex or τex are expected as α is varied since the total base concentration remains fixed, and the interpretation of the NMRdetected kex becomes clear. As shown in Supporting Information S1, even the presence of a significant isotope effect ( ∆G ≤ 2 kcal mol-1) does not induce significant changes in τex (and thus in kex). Inherent in these arguments is the reasonable assumption that OH‒ and OD‒ each abstract protons and deuterons from arginine with equal proclivity.


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Overall, our results are in agreement with the general conclusions reached by Connelly et al67 regarding isotope effects in HDX measurements. Although the fractional isotopic populations are governed by ∆pK overall, they are effectively governed by ∆pKsolute – the difference in pKs between protonated and deuterated solute – because ∆pKwater remains fixed. Since |∆pKsolute| for small molecules is not expected to deviate significantly from |∆pKwater|, the condition ∆pK ≈ 0 will generally be true, which is manifest as negligible deviations between equilibrium fractional isotopic solute populations and the fractional solvent isotope composition. The proof-of-concept reported herein to measure equilibrium HDX using relaxation dispersion at natural abundance is quite general and should, in principle, be applicable to any system of interest where a 1H-13C correlation may be established adjacent to a nucleus that is prone to hydrogen exchange (i.e. nitrogen). This may prove to be particularly beneficial in the study of natural products and small molecule pharmaceutics such as peptides, antibiotics, and macrocycles, which are not readily amenable to isotopic labelling. In practice, however, the application of this technique to proteins and other macromolecular systems is not without its own set of challenges. Even with the advent of modern cold probe technology and high-field spectrometers, data acquisition may prove to be a bottle neck due to the necessity of collecting each point on the dispersion profile as a two dimensional dataset. This may at least be partially mitigated by leveraging non-uniform sampling schemes85-86 to shorten acquisition times. The application of RD to protein systems at natural abundance may further be hindered through decreased spectral quality owing to the enhanced transverse relaxation due to dipolar interactions. This may necessitate the judicial (and often undesirable) choice of an appropriate perdeuteration labelling scheme which leaves the carbon of interest protonated while deuterating the remaining aliphatic carbons. Moreover, the CPMG relaxation period, Trlx, would need to be


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shortened relative to the 160 ms period used in this study due to the elevated R2s of proteins relative to small molecules; this results in limited sampling of the crucial slow-pulsing regime of the dispersion profile, which may have an effect on the accuracy of the obtained dynamics parameters. Even so, such studies would most likely be limited to surface-exposed residues owing to the large protection factors associated with buried side chains. Pending these experimental hurdles, this method may be applied to any event in which kex is perturbed, such as at a binding/aggregation interface, or a conformational change that involves the making or breaking of a hydrogen bond with the exchangeable proton of interest. Care must be taken to analyze the data within the context of an appropriate exchange model, as a two-state conformational change may exhibit effective three-state or four-state dynamics depending on the sensitivity to the fractional isotopic populations of each structural state.

Conclusion We have demonstrated the successful application of relaxation dispersion NMR spectroscopy at 13

C natural abundance and a single static field to quantitatively characterize an HDX reaction

occurring at the Nε position of arginine. The pH*-dependence of kex yielded a diffusion-limited base-catalyzed rate constant kD = 5.1 × 109 s-1 M-1, consistent with the theoretical Debye magnitude of ~1010 and in agreement with previously published values. This method was also capable of identifying the presence of a weak equilibrium isotope effect (∆G = ‒0.14 kcal mol-1), which was shown to not significantly influence the interpretation of HDX chemistry at the Nε position in arginine. The millisecond timescale spectroscopic lifetimes of protonated and deuterated positive arginine species were successfully measured as the fractional solvent


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deuterium composition was varied. The shorter nanosecond chemical lifetime of the neutral arginine species was indirectly measured as well, serving as a proof-of-concept that relaxation dispersion NMR spectroscopy may be used to successfully access events occurring in the submicrosecond regime during base-catalyzed isotope exchange reactions. Overall, the results of this study suggest that relaxation dispersion is a powerful and robust approach for the general study of base-catalyzed HDX chemistry at equilibrium, and provides an additional experimental path to the ever-growing field of measuring HDX by NMR methods.


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Scheme 1. The net equilibrium describing the base-catalyzed HDX reaction occurring between Nε in L-arginine and water.

K → ArgD+ + HOX ArgH + + DOX ← eq

Scheme 2. The kinetic scheme describing the equilibrium states of L-arginine during the course of a hydrogen-deuterium exchange reaction occuring at Nε.

k → k → +   ArgH + ←  Arg ←  ArgD k 1

2

k

−1

−2

Scheme 3. The kinetic scheme describing the NMR-observed hydrogen-deuterium exchange reaction occuring at Nε in L-arginine.

kf

 → ArgD + ArgH + ←  k r


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Figure 1. (A) Relaxation dispersion profiles of Cδ (solid line) and the lack of relaxation dispersion in Cα (broken line) in arginine in 10% D2O at 500 (squares) and 600 MHz (circles). (B) The temperature dependence of the dispersion amplitude for Cδ and Cα at 600 MHz, estimated by the difference in ∆R2,eff between the highest and lowest CPMG pulsing frequencies. The decreasing dispersion amplitude with increasing temperature confirms that the chemical exchange event detected at C δ is fast on the chemical shift timescale. The solid and dotted lines are provided to guide the eye only and are not quantitative. Both A and B confirm that a bona fide exchange event is occurring on the millisecond timescale at Cδ but not at Cα.


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Figure 2. (A) The dependence of the Cδ relaxation dispersion profiles in arginine on the solvent deuterium content at 600 MHz. Global fitting of the data yielded kex = 213 s-1, ∆ω = 0.116 ppm, and ∆G = -0.14 kcal mol-1, with the latter being a measure of the equilibrium isotope effect that exists between Nε and water with respect to protons and deuterons. (B) – (D) The results of 500 Monte Carlo simulations seeded with the experimentally determined dynamics parameters at the 2% random noise level. The resulting distributions all fit well with a Gaussian function, each of which was found to be centered at the experimentally-determined respective value of each of the three fitting parameter (red dotted lines).


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Figure 3. (A) The dependence on pH* of the relaxation dispersion profiles of Cδ in arginine in 10% D2O and 298 K. (B) The pH*-dependence of kex. A value of kD = 5.1 × 109 s-1 M-1 was obtained for the base-catalyzed rate constant, in close agreement with the theoretical Debye value of 1010 s-1M-1 for a diffusion-controlled reaction.


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Figure 4. The dependence on the fractional protio-solvent content of the spectroscopic and chemical lifetimes of various arginine species in solution that are at equilibrium with respect to one another during an HDX reaction occurring at Nε. τArg is the dashed black curve; τArgH+ is the solid light blue curve; τArgD+ is the solid red curve; and τex is the dotted green curve.


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AUTHOR INFORMATION Corresponding Author *Gennady Khirich Email: [email protected] Present Addresses †

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts.

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources N/A Notes The authors declare no competing financial interests. Acknowledgment The authors would like to thank the following people for helpful discussion and suggestions during the course of these studies: Dr. Benjamin Walters, Ken Skidmore, Dr. Wayne Fairbrother, Noah Wake, Kyle East, Dr. Natalie Garcia, Dr. Yung-Hsiang Kao, and Dr. John Stults. GK is particularly indebted to Prof. Aaron Bloomfield for the many hours and late nights spent engaging the author in critical and pedantic discussions, without which much of the manuscript would have been untenable.


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Abbreviations NMR, nuclear magnetic resonance; CT-rcCPMG, constant time relaxation-compensated CarrPurcell-Meiboom-Gill; HX, hydrogen exchange; HDX, hydrogen-deuterium exchange; EIE, equilibrium isotope effect; KIE, kinetic isotope effect Supporting Information Relaxation dispersion analysis, simulation results, and results of relevant control experiments

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