Kinetic Isotope Effects for Fast Deuterium and Proton Exchange Rates

By monitoring the effect of deuterium decoupling on the decay of transverse 15 N magnetization in D-15 N spin pairs during multiple-refocusing echo sequences, we have determined fast D-D exchange rates k D and compared them with fast H-H exchange rates k H in tryptophan to determine the kinetic isotope effect as a function of pH and temperature.


Introduction
In the parlance of magnetic resonance, chemical exchange is a process where a nucleus undergoes a change of its environment. 1The determination of the exchange rate of labile protons can provide valuable insight into both structural and dynamic aspects of a wide range of molecules, 2,3,4 such as the opening of base-pairs in nucleic acids and protection factors in protein-ligand complexes. 5,6In this paper, we shall focus on measurements of D-D exchange rates kD and their comparison with H-H exchange rates kH in tryptophan. 7The knowledge of kinetic isotope effects, i.e., of the ratio kH/kD that expresses the reduction of D-D exchange rates kD compared to H-H exchange rates kH, may contribute to the characterization of reaction mechanisms. 8,9The kinetic isotope effect can give insight into the stability of hydrogen-bonded secondary structures in biomolecules. 10In this work, we shall consider exchange processes involving labile D N deuterons and H N protons that are covalently bound to nitrogen atom in the indole ring of tryptophan.

Experimental Section
We have adapted to the case of deuterium (spin I = 1) a scheme that was originally designed to determine fast exchange rates of protons 7,11,12 (spin I = 1/2) by monitoring the effect of proton decoupling on the decay of transverse 15 N magnetization during multiple-refocusing sequences (CPMG). 13,14The modified pulse sequence is shown in Fig. 1.The scheme requires isotopic enrichment with 15 N and 13 C, since the 15 N coherence is excited by transfer from neighboring protons through two successive INEPT transfer steps via 1 J( 13 C, 1 H) and 1 J( 15 N, 13 C).The decay of the 15 N coherence is monitored indirectly after returning the coherence back to the proton of origin.The 15 N, 13 C-labelled isomers of tryptophan are dissolved in either D2O or H2O to determine the H/D kinetic isotope effect of the following reactions: N-D + D' + → N-D' + D + rate kD (1) N-H + H' + → N-H' + H + rate kH (2)   Where kD and kH are the pseudo-first order rate constants since the concentration of the solvent D2O or H2O, which is the source of the incoming D' + or H' + ions, is constant and much higher than the concentration of the solute.The first and last parts of the pulse sequence in Fig. 1 lead to a transfer of the magnetization from the blue non-exchanging 'spy' proton to 15 N and back, via the adjacent 13 C nuclei, by two successive pulse sequences for Insensitive Nuclei Enhanced by Polarization Transfer (INEPT). 15The first INEPT sequence transfers longitudinal proton magnetization Hz into two-spin order 2HzCz.The second INEPT sequence converts 2HzCz into 2CzNz.WALTZ-16 proton decoupling 16 is used to suppress the evolution under 1 J( 1 H, 13 C) coupling during the intervals of the INEPT sequences where the coherence is transferred from 13 C and 15 N.The antiphase coherence 2NyCz excited at the beginning of the multiple-refocusing CPMG interval decays in the course of this pulse train.At this point, two variants (A and B) of the experiments must be performed.In experiment B, continuous wave (CW) deuterium decoupling is applied during the CPMG pulse train, while in experiment A the deuterium irradiation is applied for the same duration but prior to the CPMG pulse train in order to avoid differences in temperature.Please do not adjust margins

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The remaining coherence 2NyCz is transferred back to the 'spy' proton for detection.The intensity of the resulting peak near 7.22 ppm in the proton spectra is proportional to the magnitude of the nitrogen 2NyCz coherence that remains at the end of the CPMG interval.In order to extract kD one can determine the ratio IA/IB of the peak intensities recorded without decoupling during the CPMG pulse train (experiment A) and with deuterium decoupling (experiment B).The delay τ is defined as one-half of the interval between consecutive nitrogen π-pulses.The τ delays need to be long enough to ensure that the ratio IA/IB is significantly different from 1. Typically, values of τ = 10.6 or 21.1 ms have been used.The scalar coupling is 1 J( 15 N, 2 D) = 15.4Hz, smaller than 1 J( 15 N, 1 H) = 98.6 Hz by the factor  2 D)/ 1 H) ≈ 0.15, but 1 J( 15 N, 2 D) is still large enough to act as an efficient vehicle of scalar relaxation.We can construct the matrix representations of the 4 x 9 = 36 Cartesian operators that span a complete basis set for a system comprising a 15 N nucleus with spin I = ½ and a 2 D nucleus with spin S = 1. 17When a CPMG multiple echo sequence is applied to the 15 N spins with an on-resonance rf field at the chemical shift of 15 N, while deuterium decoupling is applied with an amplitude 1 D at an offset  with respect to the chemical shift of 2 D. The rf pulses applied to the 15 N spins are considered to be ideal.Starting from an operator Ny, coherent evolution leads to the following terms 18

Physical Chemistry Chemical Physics Accepted Manuscript
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Please do not adjust margins The matrix representation of the Liouvillian L in the basis of Eq. 4 is: The matrix representation of   represents a πy pulse applied to the 15 N spins: [ 1 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 ] If the rf field for deuterium decoupling is applied on resonance, the evolution of the density operator can be described in a simplified base comprising only 6 product operators: In this reduced base, the matrix representation of the Liouvillian is: For the πy pulse applied to the 15 N spins one obtains in this reduced base: In the experiment of Fig. 1, the amplitude ν1 D of the continuous-wave rf field applied to the deuterium spins should be chosen carefully.The higher the rf amplitude ν1 D , the more efficient the decoupling, although one should avoid excessive heating.On the other hand, if the rf amplitude is too low, the ratio IA/IB is affected in a manner that can lead to erroneous measurements of the exchange rates.By way of illustration, at pD 7.5 and T = 300 K, for τ = 10.6 ms and nCPMG = 2, the ratio IA/IB has been determined as a function of the rf amplitude.For these experimental conditions, the amplitude can be attenuated as low as ν1 D =1 D /(2) = 100 Hz without affecting drastically the ratio IA/IB.For lower amplitudes the ratio is very sensitive to the exact amplitude.An rf field with an amplitude ν1 D = 3 kHz seems to be a safe value and can be used for all experiments.The ratio IA/IB also depends on the offset D of the rf carrier with respect to the exchanging 2 D spins, since decoupling becomes less efficient when the carrier is off-resonance.The ratio IA/IB has the smallest value when the carrier coincides with the chemical shift of the exchanging 2 D spins, i.e., when   (Fig.2).The heteronuclear scalar coupling constant 1 J( 15 N, 2 H) = 15.4Hz at pD 7.5 was determined experimentally from the doublet in the 2 H spectrum and corresponds to the expected value 1 J( 15 N, 2 H) = 1 J( 15 N, 1 H)  2 H)/ 1 H) with 1 J( 15 N, 1 H) = 98.6 Hz.
All experiments were performed at 14.1 T (600 MHz for 1 H, 151 MHz for 13 C, 92 MHz for 2 H, and -61 MHz for 15 N) using a Bruker Avance III spectrometer equipped with a cryogenically cooled TXI probe.The samples were prepared by dissolving 20 mM tryptophan (fully 13 C and 15 N enriched) in 100% D2O buffered with 20 mM citrate, acetate, Tris or phosphate buffer depending on the pH range.We determined kH in our earlier work 7 using 97% H2O and 3% D2O.The pH was adjusted by DCl or NaOD; the indicated pH values include corrections to take into account that the pH was measured in D2O with an electrode calibrated for H2O according to the following equation 20 pD = pHapparent + 0.4

Results and Discussion
For each pH and temperature, the exchange rates kD have been determined from three to seven ratios IA/IB of the signal intensities corresponding to six to fourteen experiments performed with variable numbers of π-pulses 2 < n < 8 in the CPMG trains, and different intervals, τ = 2.6, 5.3, 10.6 and 21.2 ms, but with the same total relaxation time 2τnCPMG.A minimum of two ratios IA/IB at different delays are required for an unambiguous determination of kD, since two rates fit a single IA/IB ratio.Figure 3 shows how this degeneracy is lifted by changing the inter-pulse delay 2τ in the CPMG pulse train.The pseudo first-order exchange rate constants were found to lie in a range 0 < kD < 40000 s -1 , depending on pH and temperature (Table 1).For each temperature the exchange rate kD was found to be slowest for pDmin 4.8.When the exchange rate kD is very low, one cannot neglect contributions due to the difference in relaxation rates of the in-phase 15 N coherence and other rates in the relaxation matrix of equation 6.From an earlier study of the exchange of indole protons, 7 we know that their exchange rate kH almost vanishes near pHmin.On the other hand, as can be seen in Table 1, the exchange rates kD do not vanish near pDmin.Moreover, if one neglects relaxation of deuterium, some apparent exchange rates are faster at lower temperatures, which is physically impossible.Hence, we incorporated a temperature-dependent quadrupolar relaxation rate RQ in Eq. ( 12) and subtracted it from the apparent exchange rates at all pD.The use of a single constant RQ to describe the effects of deuterium relaxation is rather naive.In particular for weak rf fields or large deuterium offsets, this assumption may lead to errors.We can calculate the relaxation rates of operator products containing terms such as Dz, (3Dz 2 -2E), Dx, Dy, (Dx 2 -Dy 2 ), (DyDz + DzDy) and (DxDz + DzDx). 21However, we have verified that under the conditions for which the rates of figure 4 were obtained, i.e., for strong rf fields and vanishing deuterium offsets, the exchange rates are barely affected if we assume that all deuterium terms have a common relaxation rate.The errors in the experimental ratios IA/IB were determined from standard deviations.The error propagation was further simulated by the Monte Carlo technique.The errors in the exchange rates kD were estimated from the curvature around the minima of  2 and found to lie in a range between 3 and 28%.
If the exchange rate constants kD are plotted as a function of pD on a logarithmic scale, one obtains a V-shaped curve that is characteristic of acid catalysis by D + ions and basic catalysis by OD - ions, the latter being more efficient (Fig. 4).In the cationic, zwitterionic and anionic forms of tryptophan, the exchange rates result from sums of acidic and basic contributions.The overall exchange rate constant kD can be written as: Where the rate RQ expresses contributions due to the quadrupolar deuterium relaxation to the decay of transverse 15 N magnetization.The indices D and OD represent the contributions of acidic and basic mechanisms (see below) for the cationic, zwitterionic and anionic forms of tryptophan, abbreviated by c, z, and a in Fig. 5.

Physical Chemistry Chemical Physics Accepted Manuscript
This journal is © The Royal Society of Chemistry 2015 Phys.Chem.Chem.Phys | 5 Please do not adjust margins Please do not adjust margins The mole fractions fc, fz and fa of the cationic, zwitterionic and anionic forms of tryptophan are: = (1 + 10 pD−p a1 + 10 2D−p a1 −p a2 ) −1   = (1 + 10 −pD+p a1 + 10 pD− a2 ) −1   = (1 + 10 −pD+p a2 + 10 −2pD+p a1 +p a2 ) −1 (13) Where [D + ] = 10 −pD , [OD − ] =   10 pD .The auto-ionization constant   of D2O depends on the temperature. 23In H2O and at 25°C, p a1 = 2.46 for the protonation of the carboxyl group, while p a2 = 9.41 corresponds to the protonation of the amine group.In D2O at 25°C, we have determined that p a1 = 2.60 and p a2 = 10.05. 24he variation of p a with temperature 23 has been taken into account.Figure 4 and Table 2 show the results of the fitting of the exchange rate constants kD to Eq. ( 12), which allows one to obtain the catalytic rate constants for the contributions of acid and basic mechanisms for each of the three forms c, z, and a.The basic contribution of the cationic form and the acidic contribution of the anionic form are masked by other terms and can be neglected.
The activation energy Ea of the transition state provides a measure of the strength of N-D or N-H bonds. 25The activation energy Ea is defined by the Arrhenius equation where A is an empirical pre-exponential "frequency factor", R the universal gas constant, T the temperature and k the exchange rate.
The dependence of Ea on pH or pD for H-H and D-D exchange processes and the activation energies and pre-exponential frequency factors are shown in Table 3 for protons and in Table 4 for deuterium.
One can speak of a kinetic isotope effect when the exchange rate is affected by isotopic substitution. 26In the present case, we compare the exchange rates of indole protons in tryptophan with H2O on the one hand, and analogous exchange rates of indole deuterons with D2O on the other.The kinetic isotope effect is defined as the ratio of rate constants kH/kD.The change in exchange rates results from differences in the vibrational frequencies of the N-H or N-D bonds formed between 15 N and 1 H or 2 D. 27,28,29 Deuterium will lead to a lower vibrational frequency because of its heavier mass (lower zero-point energy).If the zero-point energy is lower, more energy is needed to break an N-D bond than to break an N-H bond, so that the rate of the exchange will be slower.Moreover, one expects Ea to be larger for deuterium.The results in Table 3 and 4 do not support this conclusion, but if one assumes the same preexponential frequency factor for H and D, the Ea is indeed larger for the heavier isotope.Please do not adjust margins Please do not adjust margins Fig. 6 shows exchange rates kD and kH at 300 K.For acid catalyzed exchange, kD/kH > 2.5 because D3O + is a stronger acid than H3O + .For base catalyzed exchange, kD/kH < 1.However, to compare the difference between catalysis by OH -and OD -, we need to take into account the difference of the ionization constants: p  (D 2 O) = 14.95 and p  (H 2 O) = 13.99 at 25°C .Fig. 7 shows the base-catalyzed exchange rate constants kD and kH as a function of pOH or pOD.The exchange rates kD are slightly lower than kH, giving the approximate kinetic isotope effects: kH/kD = 2.2 ± 0.3, 2.3 ± 0.3 and 2.1 ± 0.3 at 300 K, 310 K and 320 K respectively (Fig. 7.) These values result from averages of the exchange rate constants for the zwitterionic and anionic forms (Table 5).
In Table 5 the KIE is defined as k H i /k D i for acid catalysis or as k OH i /k OD i for base catalysis, where i = c, z, and a stand for the cationic, zwitterionic, and anionic forms of tryptophan in solution, with the heaviest isotope always in the denominator.If tunneling can be neglected, the KIE depends on the nature of the transition state.The maximum isotope effect for N-H bonds is kH/kD ≈ 9, assuming that the bond is completely broken in the transition state (TS).The KIE can be reduced if the bonds are not completely broken in the TS.The KIE can be close to 1 if the TS is very similar to the reactant (N-D bond nearly unaffected) or very similar to the product (N-D bond almost completely broken).
The experimental ratio  OH  / OD  is near its maximum when pH > pKa2, which suggests that the N-D bond is broken in the rate-limiting step and that the deuteron is half-way between the donor and the acceptor.However the ratio  OH  / OD  ≈ 1 suggests that the N-D bond is either only slightly or almost completely broken in the TS.The protonation of the amine withdraws electron density and increases the acidity of the H N group which favors the formation of the anionic form.This explains why  OH  / OH  > 1 and  OD  / OD  > 1.For the acidcatalyzed exchange constants, we observe an inverse kinetic isotope effect.This can happen when the degree of hybridization of the reactant is lower than that of the reaction center in the TS during the rate-limiting step.
The mechanisms for proton or deuteron exchange have been thoroughly reviewed. 30,31,32Englander 30 and his collaborators pointed out that the rate of the exchange of protons attached to nitrogen depends on the ability to form hydrogen-bonded complexes in the transition state involving the donor (tryptophan) and the acceptor (D2O or OD -).This occurs in three steps: (i) encounter of the donor and the acceptor, (ii) formation of the transition state involving the donor and acceptor, and (iii) cleavage of the N-D bond.The mechanism of acid-catalyzed exchange consists of the addition onto the nitrogen of a D + ion from the solvent, followed by removal of D + by D2O (Fig. 8).The mechanism of the base-catalyzed reaction involves removing the indole deuterium to create the conjugate base, which then abstracts a D + from D2O to regenerate the indole (Fig. 9).Table 5. Kinetic isotope effects (KIE)  H / D for the exchange rate constants of each of the three forms of tryptophan in solution: c (cationic), z (zwitterionic), and a (anionic).Altogether we can say that the rate-limiting step in the basecatalyzed mechanism is the removal of the proton or deuteron from the nitrogen.On the other hand, for the acid-catalyzed mechanism, is the donation of a proton or deuteron by H3O + respectively D3O + .Finally, the curves of log kD vs. pD and of log kH vs. pH show a combination of specific base catalysis at high pH, and a specific acid catalysis at low pH, which becomes more important at higher temperatures.

Conclusions
We have adapted our method that was originally designed for measuring fast H-H exchange rates kH to the study of D-D exchange rates k.In tryptophan in aqueous solution over a range of pH, respectively pD, the kinetic isotope effect, defined as the ratio kH/kD between the H-H and D-D exchange rates, was determined at several temperatures.The dependence of the activation energies on pH, provides new insight into the mechanisms of the exchange processes.The results agree with the mechanisms discussed by Englander et al. 30

Figure 2 .
Figure 2. (Top) Experimental ratio IA/IB as a function of the amplitude ν1 D of the rf field applied to the deuterium spins recorded at pD 7.7 and T = 300 K with τ = 10.6 ms and nCPMG = 2. (Bottom) Experimental ratio IA/IB as a function of the offset Ω D of the carrier frequency with respect to the deuterium resonance for pD 9.4, T = 300 K, τ = 10.6 ms, and nCPMG = 2.The lines correspond to Eqs. 9 (top) and 6 (bottom).For the blue lines, we have assumed that different operator products involving deuterium terms have distinct quadrupolar relaxation rates that depend on the spectral density.For the green lines, we have assumed that all deuterium terms have the same relaxation rate.For strong on-resonance rf fields, as we have used for the determination of exchange rates, the ratios IA/IB do not change significantly if one assumes a single or several distinct relaxation rates.

Figure 4 .
Figure 4. Exchange rate constants kD as a function of pD over the temperature range 290 < T < 320 K. Solid lines result from fits to Eq. (12).

Figure 5 .
Figure 5. Tryptophan exists in three forms c (cationic), z (zwitterionic) and a (anionic), with mole fractions fc, fz and fa that depend on pD.

Figure 7 .Figure 6 . 7
Figure 7. Base catalyzed exchange rates kD and kH as a function of pOH or pOD at different temperatures

Figure 8 .
Figure 8. Acid-catalyzed mechanism of exchange.The transition state is shown in brackets.

Table 1 .
Pseudo first-order exchange rate constants kD [s -1 ] as a function of temperature and pD.

Table 3 .
Activation energies Ea and pre-exponential frequency factors A for the indole proton H N in tryptophan.

Table 4 .
Activation energies Ea and pre-exponential frequency factors A for the indole deuterium D N in tryptophan.The activation energies and the pre-exponential factors are strongly correlated.

Table 2 .
Exchange rate constants kD and kH [s-1 ] 7a) Proton exchange rates were not measured at these temperatures.7PhysicalChemistryChemical Physics Accepted ManuscriptThis journal is © The Royal Society of Chemistry 2015