¹⁵N transverse relaxation measurements for the characterization of µs–ms dynamics are deteriorated by the deuterium isotope effect on ¹⁵N resulting from solvent exchange

Abstract

¹⁵N R₂ relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide—water exchange can severely skew Hahn-echo based ¹⁵N R₂ relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the ¹⁵N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent ¹⁵N R₂ rate constants—which should not be mistaken with protein inherent chemical exchange contributions, R_ex, to ¹⁵N R₂. For measurements of ¹⁵N R₂ rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D₂O molar fraction in the sample buffer, as low as 1%, or the use of an external D₂O reference along with a modified ¹⁵N R₂ Hahn-echo based experiment. This combination allows for the measurement of R_ex contributions to ¹⁵N R₂ originating from conformational exchange in a time window from µs to ms.

Introduction

Proteins are inherently dynamic systems with motions that cover a several orders of magnitude wide time scale from femtosecond to more than seconds (Mittermaier and Kay 2009; Palmer 2015). Such dynamics may be local, concerted, correlated or of anti-correlated nature (Salvi et al. 2012; Pelupessy et al. 2003; Fenwick et al. 2011; Vogeli et al. 2014; Vogeli and Yao 2009). Nuclear magnetic resonance spectroscopy (NMR) is one of the major methods to study protein dynamics. A plethora of NMR experiments have been and are further being developed to elucidate protein motions (Palmer 2015, 2004; Vogeli et al. 2014; Mittermaier and Kay 2006; Vallurupalli et al. 2012; Lange et al. 2008; Fawzi et al. 2011; Charlier et al. 2016, 2013). One of the standard experiments are ¹⁵N R₁, R₂ relaxation measurements and the ¹⁵N NOE experiment for the detection of the rotational correlation time of the molecule under study as well as local fast dynamics at a residue-specific resolution (i.e. for each ¹⁵N–¹H moiety along the amino acid sequence) (Kay et al. 1989; Farrow et al. 1994). These measurements have been complemented with more sophisticated experiments and analyses to obtain also intermediate and slow time scale information from µs up to ms. This includes the ¹⁵N CPMG- or ¹⁵N R_1ρ based relaxation dispersion experiments (Loria et al. 1999; Mulder et al. 2001), CEST or DEST measurements (Vallurupalli et al. 2012; Fawzi et al. 2011) and alternatively ¹³C methyl relaxation measurements covering protein side-chain dynamics (Kiteyski-LeBlanc et al. 2018; Tugarinov and Kay 2005). Towards a more comprehensive picture of dynamics, residual-dipolar couplings (Lange et al. 2008; Tolman et al. 2001; Peti et al. 2002), cross-correlated relaxation (Pelupessy et al. 2003; Vogeli and Yao 2009; Vogeli 2017), paramagnetic relaxation enhancement (PRE) (Pintacuda and Otting 2002; Iwahara and Clore 2006; Xu et al. 2008) and eNOE-based (Vogeli et al. 2014, 2012) data have been acquired and can be used in combination with molecular dynamics simulation (Showalter and Bruschweiler 2007; Markwick et al. 2009) or ensemble averaging (Fenwick et al. 2011; Lange et al. 2008; Vogeli et al. 2012; Bouvignies et al. 2005; Lindorff-Larsen et al. 2005) and chemical-shift based structural ensemble prediction (Camilloni and Vendruscolo 2012; Kannan et al. 2014; Case 2013).

For the investigation of µs–ms dynamics, ¹⁵N R₂ measurements are among the most frequently used experiments. The ¹⁵N R₂ rate constant, which describes the decay of ¹⁵N transverse magnetization as measured, e.g. in a Hahn-echo experiment, has an exchange contribution, R_ex, due to conformational and chemical exchange that modulates the ¹⁵N chemical shift tensor (Luginbuhl and Wuthrich 2002; Cavanagh et al. 2007) that adds to the R_2,0 auto-relaxation rate constant: R₂ = R_2,0 + R_ex.

It is probably surprising that the presented work identifies a systematic error in several ¹⁵N R₂ relaxation measurements for the characterization of µs-ms dynamics that deteriorates the dynamics analysis of proteins and in particular intrinsically disordered proteins (IDP) and protein loops when measured under physiological conditions (i.e. pH ~ 7.4 and at a temperature of ~ 37 °C). The identified culprit is the fast exchange of the amide protons with water and simultaneously with the internal reference substance, D₂O, resulting in an exchange contribution induced by the deuterium-induced isotope shift of ¹⁵N, that becomes particularly acute at physiological pH and temperatures. We exemplify this effect using Hahn-echo based ¹⁵N R₂ measurements that do not suppress exchange contributions and CPMG relaxation dispersion measurements on α-synuclein, which is an IDP associated to Parkinson’s disease, as well as the PDZ2 domain of human phosphatase and provide a straightforward solution (i.e. the use of a very low D₂O molar fraction, as low as 1%, or, alternatively, the use of an external D₂O lock and the appropriate pulse sequence).

Materials and methods

Protein expression and purification

Acetylated α-synuclein was expressed using co-expression of the N-terminal acetyltransferase B (NatB) complex and the α-synuclein plasmid (pRK172), as described earlier (Johnson et al. 2010). Expression and purification were performed as described earlier (Huang et al. 2005), with some modification. Briefly, after transformation, colonies containing both plasmids (NatB and pRK172) were grown at 37 °C in 10 ml Lysogeny Broth (LB) medium overnight and were then transferred into 1 L of LB media. After reaching an OD₆₀₀ of around 0.5, cells were harvested by centrifugation and resuspended into 1 L M9 minimal media containing ¹⁵NH₄Cl and grown till an OD₆₀₀ of 1.0 was reached. Protein expression was carried out overnight at 37 °C, after induction with 1 mM IPTG. Cells were harvested by centrifugation and α-synuclein, present in the periplasm, were purified using ion exchange chromatography and hydrophobic interaction chromatography as described earlier (Campioni et al. 2014).

The PDZ2 domain from human phosphatase (hPTP1E) was encoded into a pET21 expression system with a T7 promoter and Histidine tag. Expression and purification were performed as described earlier (Gianni et al. 2005), with some modifications. After transformation, a single colony was inoculated overnight in 10 ml LB medium at 37 °C and then transferred into 1 L M9 minimal media containing ¹⁵NH₄Cl and grown till an OD₆₀₀ of 0.5 was reached. Protein expression was induced by adding 1 mM IPTG and cells were harvested by centrifugation after 5 h. A Ni-affinity column (HisTrap FF) was used for purification of protein and the histidine-tag was cleaved with Human Rhinovirus 3C (HRV 3C) followed by another Ni-affinity column purification step.

NMR Measurements

NMR spectra were recorded with 500 µM of ¹⁵N-labeled acetylated α-synuclein dissolved in 20 mM Tris (pH 7.4) and 100 mM NaCl, unless indicated differently. Spectra of ¹⁵N-labeled PDZ domain, dissolved in 50 mM sodium phosphate buffer (pH 8.0) and 150 mM NaCl, were recorded at an experimental temperature of 303 K. ¹⁵N TROSY- ${R}_{2}^{\beta }$ rate constants were measured by applying the NMR experiment described earlier (Lakomek et al. 2013). ¹⁵N R₂ experiments, applying proton decoupling during the relaxation delay period (Cavanagh et al. 2007), were recorded using the pulse sequence described in Fig. 1. For proton decoupling, waltz64 with an RF amplitude of 2.5 kHz was applied. ¹⁵N R_1ρ rate constants were recorded using the NMR experiment described in (Lakomek et al. 2012). CPMG-based ¹⁵N R₂ rate constants were determined using a proton-decoupled CPMG experiment, similar to the one described by Yuwen et al. (2014), however using waltz64 with an RF amplitude of 2.5 kHz for proton decoupling rather than DIPSI2. ¹⁵N R₂ rate constants were measured for the two CPMG frequencies, 20 Hz and 100 Hz. All NMR experiments were performed on a Bruker 600 MHz Avance III HD spectrometer equipped with cryogenic probe. Spectral dimensions were Ω(¹H) x Ω(¹⁵N) = 14.014 ppm × 35 ppm. 512 complex points were recorded in the direct dimension (¹H) and 80 complex points in the indirect dimension (¹⁵N), resulting in an acquisition time of 60.08 ms in the direct and 37.5 ms in the indirect dimension, respectively. The ¹H carrier was set to 4.7 ppm and the ¹⁵N carrier to 118 ppm, respectively. The magnetization decay was recorded using four different relaxation decay periods, in an inter-leaved manner (Lakomek et al. 2012). For α-synuclein, R₂ relaxation delays were set to 0 ms, 200 ms, 100 ms, and 50 ms and for the ¹⁵N R_1ρ experiments, delays were set to 1 ms, 120 ms, 60 ms, and 20 ms, respectively. The spin-lock RF field strength in the ⁵N R_1ρ measurement was set to 2 kHz. For experiments using the ¹⁵N TROSY-${R}_{2}^{\beta }$ sequence decay periods differed slightly; at pH 7.4 and at a temperature of 303 K or 283 K delays were 0, 100, 50, and 20 ms. Spectral intensities for the different decay periods were recorded in an inter-leaved manner, 16 scans were recorded for each decay period. The total experimental time was 4.75 h. For the PDZ domain, relaxation delays were set to 0 ms, 50 ms, 30 ms, and 10 ms. For the CPMG experiments, a fixed relaxation delay of 200 ms was used. Relaxation data where recorded for two different CPMG frequencies, 100 Hz and 20 Hz by adjusting the number of 180° (N) pulses and the inter-pulse delay accordingly.

Fig. 1

Pulse scheme for the ¹⁵N R₂ relaxation (Hahn-echo) experiment. ¹H magnetization is transferred to ¹⁵N in-phase magnetization via a refocused INEPT transfer. After a z-filter, a Hahn echo (Δ − 180–(N) − Δ) with the variable relaxation delay Δ is performed. ¹H decoupling during the Hahn echo minimizes the evolution of the anti-phase term during the relaxation period. Echo/ anti-echo encoding for quadrature detection is performed prior to the t₁ evolution period. Narrow rectangles indicate hard 90° pulses and broader rectangles hard 180° pulses. The rectangular ¹H pulses marked—x are low power 90° pulses (1.2 ms at 600 MHz); shaped low power ¹H pulses (1.9 ms) correspond to the center lobe of a (sinx)/x function, all serving to return the water magnetization to z prior to detection (Pervushin et al. 1998). For application to samples that also are enriched in ¹³C: durations of ¹³C pulses (all 180°) are equal to $\frac{\sqrt{3}}{2\varOmega }$ (47.4 µs at 600 MHz), where Ω is the frequency difference between ¹³C^α and ¹³C′. Delay durations are δ = 2.65 ms and ε corresponds to the duration of the decoding gradient G₄ (60.8 µs; the slight offset (ε/2) relative to the ¹⁵N 180° pulse enables insertion of the decoding gradient G₄, without introducing a linear phase error in the ¹H dimension. Gradients: G₀ (1000 µs; 21 G/cm), G₁ (2650 µs; 0.7 G/cm), G₂ (2550 µs; 1.4 G/cm), G₃ (500 µs; 42 G/cm), G₄ (1000 µs; 7 G/cm), G₅ (300 µs; -23 G/cm), G₆ (300 µs; 7 G/cm), G₇ (1000 µs; 35 G/cm) and G₈ (60.8 µs; 23 G/cm) are sine-bell shaped. Phase cycling: φ₁ = 8(y), 8(-y); φ₂ = y; and φ₃ = y, x, − y, − x, − y, − x ,y ,x; φ₄ = y; φ₅ = y and φ_rec = y, − x, − y, x, − y, x, y, − x, − y, x, y, − x, y, − x, − y, x. Quadrature detection is implemented using the Rance-Kay echo/anti-echo scheme (Kay et al. 1992), with the polarity of gradients G₅ and—G₅ inverted, and φ₃ = y, − x, − y, x, − y, − x, y, x, φ₄ = − y and φ₅ = − y for the second FID generated for each quadrature pair. The relaxation decay of ¹⁵N (in-phase) coherence is sampled at different delay durations Δ in an inter-leaved manner

The software Sparky 3.115 (T. D. Goddard and D. G. Kneller, SPARKY 3, University of California, San Francisco, USA) and Bruker Topspin 3.5pl7 (Bruker, Inc., Billerica, MA, USA) were used for analyzing the spectra and extracting the rate constants.

NMR spectra recorded on samples containing D₂O in the sample buffer were measured using a regular Shigemi tube (Sigma-Aldrich, Merck KGaA, Darmstadt, Germany). For samples without D₂O in the sample buffer, D₂O was added as an external reference using a Wilmad coaxial insert (stem length 50 mm, 2 mm diameter) and the sample was kept in a thin wall 5 mm NMR tube (Wilmad NMR tubes, 5 mm diam., precision, Sigma-Aldrich, Merck KGaA, Darmstadt, Germany). The coaxial insert containing D₂O was inserted into the 5 mm thin-wall NMR tube containing the sample.

Simulation of CPMG relaxation dispersion curves

CPMG relaxation dispersion curves were calculated using the formula:

$${R_{ex}}=~{p_H}{p_D}\Delta\omega^{2}{k_{ex}}/\left[ {k_{{ex}}^{2}+~{{\left( {p{{_{H}^{2}}\Delta\omega^4}+144{/_{CP}}} \right)}^{1/2}}} \right]$$

(1)

as described in (Palmer et al. 2001; Ishima and Torchia 1999), with the basic CPMG element τ_CP/2 − 180° − τ_CP/2. The inter-pulse delay τ_CP relates to the CPMG frequency ν_CPMG via ν_CPMG = 1/(2τ_CP). Τhe chemical shift difference induced by the deuterium isotope effect is $\Delta \delta ({\text{N}})=687 \pm 35$ ppb (Tugarinov 2014) which amounts to ca. Δω = 250 rad s⁻¹ and Δω/2π = 40 Hz at a magnetic field strength of 14.1 T (corresponding to a proton Larmor frequency of 600 MHz) and k_ex is equal to the assumed amide solvent exchange rate constant (see Results section for derivation); p_D is the population of deuterium in the sample buffer (e.g. 0.1 for 10% D₂O) and p_H the population of H₂O in the sample buffer.

Results

Pulse sequence for the measurement of ¹⁵N R₂ relaxation

The average backbone amide exchange rate constant shows a strong pH dependence, with a minimum around pH 3 (10⁻¹/min at 298 K) and a tenfold increase for each pH unit (Wagner and Wuthrich 1979; Dempsey 2001), resulting in ca. 10² / min at pH 6 (298 K) and roughly 10³ / min at pH 7.4 (298 K). Indeed, for α-synuclein at 288 K, measured amide solvent exchange rates varied between 2 and 20 s⁻¹ for different residues at low salt concentration (20 mM) and between 10 s⁻¹ and 80 s⁻¹ for high salt concentrations (300 mM) (Croke et al. 2008). With the emphasis to measure ¹⁵N relaxation of α-synuclein at physiological conditions including physiological temperature (i.e. 303 K) we have therefore selected an NMR pulse sequence that measures the transverse relaxation of ¹⁵N in-phase coherence, with proton decoupling applied during the relaxation period to alleviate the impact of exchange of the ¹⁵N–¹H moiety with water. By that, evolution into anti-phase N_x/yH_z coherence is minimized (Fig. 1). This is different from e.g. ¹⁵N TROSY- ${R}_{2}^{\beta }$ experiments using a Hahn-echo based pulse sequence element (Fig. S1) (Lakomek et al. 2013; Wang et al. 2003). Because if anti-phase N_x/yH_z coherence is present or evolves during the Hahn-echo relaxation delay in presence of amide exchange, amide exchange will lead to decorrelation of two spin-order (Skrynnikov and Ernst 1999). This loss of the N_x/yH_z coherence will lead to an artificial extra relaxation contribution to the measured ¹⁵N R_2, rate constant as illustrated in Fig. S2 (this artificial extra relaxation contribution is denoted R_ex,amide in Fig. S2).

In Fig. 1, a TROSY-based and Hahn-echo based ¹⁵N R₂ experiment is shown that avoids this bias introduced by amide exchange. In details, anti-phase ¹⁵N magnetization generated after the first INEPT transfer is transferred further to in-phase ¹⁵N magnetization in the second step of the re-focused INEPT transfer (b). Therefore, at the beginning of the relaxation period, N_x in-phase magnetization is present. After a z-filter (c), in-phase N_x magnetization is subject to transverse ¹⁵N R₂ relaxation during the Hahn-echo element. Importantly, the generation of anti-phase magnetization is minimized by ¹H decoupling (d). After a second z-filter (e), gradient as well as phase-cycling based echo/anti-echo encoding is achieved prior to t₁ evolution. After t₁ evolution (f), N_x/yH^β coherence is transferred to H_x/yN^β coherence during a TROSY-read out scheme, opening this pulse sequence also for large systems (Pervushin et al. 1997) (g), which then evolves during acquisition. Further, ¹⁵N magnetization, transferred from ¹H during the TROSY read-out scheme is destroyed by a 90° pulse on ¹⁵N (h) (Lakomek et al. 2012; Favier and Brutscher 2011). Note that in this experiment, ¹⁵N R_2,0 auto-relaxation (plus R_ex contribution) and therefore the average of fast and slowly relaxing NH doublet components is measured rather than the decay of the slowly relaxing N_x/yH^β line, which is measured in the ¹⁵N TROSY-${R}_{2}^{\beta }$experiment (Lakomek et al. 2013). The relevance of selecting a ¹⁵N-inphase-based pulse sequence becomes apparent when comparing the ¹⁵N relaxation rate constants measured for the intrinsically disordered protein α-synuclein using the pulse sequence of Fig. 1 compared to those measured using the ¹⁵N TROSY-${R}_{2}^{\beta }$experiment (Lakomek et al. 2013) (see Fig. S3).

¹⁵N R₂ relaxation contribution by the deuterium isotope effect

Measuring ¹⁵N relaxation of α-synuclein at physiological conditions (i.e. pH 7.4 and 303 K) using the pulse sequence shown in Fig. 1, we noticed a variation of extracted rate constants, depending on the D₂O molar fraction in the sample buffer. This is demonstrated in Fig. 2, for which ¹⁵N R₂ rate constants of α-synuclein were measured in 4%, 10%, and 50% D₂O, respectively. The apparent rate constants measured are significantly elevated with increased D₂O, apart from C-terminal residues 110–140 that do not show any significant increase, due to exchange protection through hydrogen bond formation of acidic-side chains with amide groups (Khare et al. 1999).

Fig. 2

D₂O-dependent ¹⁵N relaxation rate constants. ¹⁵N R₂ rate constants of ¹⁵N-labeled α-synuclein, measured using the pulse sequence shown in Fig. 1 and in the presence of (A) 4% (black), 10% D₂O (red), or 50% D₂O (blue). The experimental temperature was 303 K and the pH was 7.4. The increase of the relaxation rates with increase of D₂O identifies D₂O as a culprit for ¹⁵N transverse relaxation measurements

This finding points to a R_ex contribution because of the deuterium isotope effect that modulates the ¹⁵N chemical shift tensor due to exchange between protons and deuterons in the amide group at an exchange rate constant, k_ex, which is equal to the solvent exchange rate constant (Henry et al. 1987). This can be seen as follows: The residue-specific k_ex is the sum of the forward and backward pseudo first order reaction rate constant, k_HD and k_DH, respectively, where k_HD is the product of the amide solvent exchange rate constant, k_NH, describing the exchange of amide protons with water, and the likelihood that an exchange to a deuteron takes place instead of a proton, which is equal to the population of D₂O in the sample buffer, p_D: ${k}_{HD}= {k}_{NH}\times {p}_{D}$. Vice versa, the rate constant for the backward reaction is ${k}_{DH}= {k}_{ND}\times {p}_{H}$ where p_H is the population of H₂O in the sample buffer and k_ND the exchange of the amide deuterium with water. It is assumed that k_ND = k_NH (Connelly et al. 1993). This yields:

$${k_{ex}}=~{k_{HD}}+~{k_{DH}}=~{k_{NH}}\left( {{p_D}+~{p_H}} \right)={k_{NH}}~$$

(2)

Figure 3 illustrates the described process.

Fig. 3

Chemical exchange between and amide N–H and N–D moiety changes the resonance frequency of the ¹⁵N nucleus by changing the chemical shift tensor via the deuterium isotope effect. In equilibrium, the rate constant that describes the conversion from N–H to N–D is described by the solvent amide exchange rate multiplied with the population of D₂O in the sample buffer. The backward reaction from N–D to N–H is described by the solvent amide exchange rate times the population of H₂O in the sample buffer. It is thereby assumed that the exchange of the amide deuterium with water is equal to the exchange of an amide proton with water (Connelly et al. 1993)

The exchange rate constant describing the modulation of the chemical shift tensor can also be obtained from a kinetic derivation as we shall see:

$$NH + D_{2} O\xrightarrow{{k_{{HD}}^{{\left( 2 \right)}} }}ND + HDO$$

(3a)

$$ND + H_{2} O\xrightarrow{{k_{{DH}}^{{\left( 2 \right)}} }}NH + HDO$$

(3b)

Equations (3a) and (3b) are of pseudo first order, since both the H₂O and D₂O molar fractions are much higher than the protein molar fraction in water. Therefore, we obtain:

$$NH\xrightarrow{{k_{{HD}}^{{\left( 2 \right)}} \left[ {D_{2} O} \right]}}ND$$

(4a)

$$ND\xrightarrow{{k_{{DH}}^{{\left( 2 \right)}} \left[ {H_{2} O} \right]}}NH$$

(4b)

with the pseudo first order rate constants:

$${k_{HD}}=k_{{HD}}^{{\left( 2 \right)}}~\left[ {{D_2}O} \right]=k_{{HD}}^{{\left( 2 \right)}}~{\left[ {{H_2}O} \right]_0}~ \times ~{p_D}=~{k_{NH}}~ \times ~{p_D}$$

(5a)

and

$${k_{DH}}=k_{{DH}}^{{\left( 2 \right)}}~\left[ {{H_2}O} \right]=k_{{DH}}^{{\left( 2 \right)}}~{\left[ {{H_2}O} \right]_0}~ \times ~{p_H}=~{k_{NH}}~ \times ~{p_H}~$$

(5b)

where ${\left[{H}_{2}O\right]}_{0}$ is the molar fraction of H₂O in the sample buffer in the absence of D₂O; p_D is the population of D₂O and p_H is the population of H₂O in the sample buffer, resulting in an actual molar fraction $\left[{H}_{2}O\right]= {\left[{H}_{2}O\right]}_{0} \times {p}_{H}$ of H₂O and $\left[{D}_{2}O\right]= {\left[{H}_{2}O\right]}_{0} \times {p}_{D}$ of D₂O in the sample buffer. (Note that for low molar fractions of D₂O, actually HDO is present in the sample buffer which has twice the molar fraction as D₂O. However, the likelihood of an exchange from NH to ND is only half in the presence of HDO compared to D₂O. Both pre-factors cancel out such that the final pseudo first order rate constant is the same. We therefore use the simplified description involving D₂O).

For the rate equation describing the time evolution of the molar fraction of the amide group $\left[NH\right]$ we obtain:

$$\frac{d}{dt} \left[NH\right]= - {k}_{HD} \left[NH\right]+ {k}_{DH} \left[ND\right]$$

(6)

Solving the linear differential equation and using the initial condition [NH] (t = 0) = [NH]₀ and [ND] (t = 0) = 0, as only ¹⁵N bound to protons is present after the refocused INEPT and start of the relaxation period, yields:

$$\left[ {NH} \right]\left( t \right)=~\left( {{k_{HD}}~{{[NH]}_0}~{e^{ - ~\left( {{k_{HD}}+~{k_{DH}}} \right)t}}+~{k_{DH}}~{{[NH]}_0}~} \right)/\left( {{k_{HD}}+~{k_{DH}}} \right)$$

(7a)

Using the relations described in Eq. (5a, 5b) this yields:

$$\left[ {NH} \right]\left( t \right)=~\left( {{k_{NH}}~~{p_D}~{{[NH]}_0}~{e^{ - {k_{NH}}~\left( {{p_D}+~{p_H}} \right)t}}+~{k_{NH}}~{p_H}~{{[NH]}_0}~} \right)/\left( {{k_{NH}}~\left( {{p_D}+~{p_H}} \right)} \right)$$

(7b)

which further simplifies with ${p}_{D}$ to

$$\left[ {NH} \right]\left( t \right)=~\left( {~{p_D}~~{e^{ - {k_{NH}}~t}}+{p_H}~} \right){[NH]_0}$$

(7b)

an thus ${k}_{ex}= {k}_{NH}$. That means that the chemical shift tensor gets modulated at the amide solvent exchange rate.

Τhe chemical shift difference induced by the deuterium isotope effect is $\varDelta {\updelta }\left(\text{N}\right)=687\pm 35$ ppb (Tugarinov 2014) which amounts to ca. Δω = 250 rad s⁻¹ and Δω/2π = 40 Hz at a magnetic field strength of 14.1 T (corresponding to a proton Larmor frequency of 600 MHz). With an amide exchange rate constant, k_ex, in the range between 10 and 100 s⁻¹ at pH 7.4 and 303 K, the exchange process is neither in the fast exchange limit, Δω $\ll$ k, nor in the slow exchange limit, Δω $\gg k$, but rather on an intermediate timescale. To estimate the exchange contribution on ¹⁵N R₂ as a result of solvent exchange in the sample buffer, the following formula was used:

$${R}_{ex}\approx \frac{{p}_{a}{p}_{b}{k}_{ex}}{1+{\left(\frac{{k}_{ex}}{\varDelta \omega }\right)}^{2}}$$

(8)

as described in (Millet et al. 2000). For 4% D₂O, described by p_a = 0.96 and p_b = 0.04, Eq. (8) yields R_ex = 3.31 s⁻¹ for k_ex = 100 s^− 1, R_ex = 0.38 s^− 1 for k_ex = 10 s^− 1 and R_ex = 0.04 s^− 1 for k_ex = 1 s^− 1. While for 50% D₂O R_ex = 21.55 s^− 1 for k_ex= 100 s^− 1, R_ex = 2.5 s^− 1 for k_ex= 10 s^− 1 and R_ex = 0.25 s^− 1 for k_ex= 1 s^− 1 are estimated. Please note Eq. (8) is strictly speaking no longer fulfilled in the latter case because p_a =p_b = 0.5 but can be used to get approximate values. Furthermore, effects like a different dipolar coupling interaction for ¹⁵N–D versus ¹⁵N–H or the quadrupole moment of the deuteron have not been taken into consideration.

Nonetheless, with this rough estimate, an idea on the order of magnitude of the exchange contribution caused by the deuterium isotope effect modulating the ¹⁵N chemical shift tensor as a result of chemical exchange between amide protons and deuterons is obtained. It is in good agreement with the experimentally observed D₂O dependency of the ¹⁵N R₂. There is an additional loss mechanism by solvent exchange from a ¹⁵N–¹H moiety to ¹⁵N–D moiety during the relaxation delay making the latter moiety impossible to detect by ¹H acquisition (Kim et al. 2013). This effect sales linear with the D₂O concentration and can explain partly the observed increase in ¹⁵N R₂ rate constants for the sample containing 50% D₂O. As deuterium is not decoupled during the relaxation period, also ¹⁵N-D anti-phase magnetization will evolve during the relaxation period and contribute by scalar relaxation of the second kind. This effect also scales linear with the D₂O concentration in the sample buffer; further an¹⁵N–H spin pair will show a higher ¹⁵N R₂ rate constant than a ¹⁵N-D spin pair (Vasos et al. 2006; Xu et al. 2005). Scalar relaxation of the second kind induced by the exchange of amide protons can also be an additional loss mechanism in Hahn-echo based ¹⁵N R₂ measurements (Kateb et al. 2007), however we did not observe any significant differences when changing the RF amplitude of the waltz64 ¹H decoupling scheme from 2.5 kHz to 6 kHz (Fig. S4).

The use of an external deuterium lock for ¹⁵N R₂ relaxation measurements

The findings discussed above request ¹⁵N relaxation R₂ measurements in absence of D₂O in the sample buffer. This is achieved by using a coaxial insert by Wilmad comprising D₂O inserted into a 5 mm thin-wall NMR tube containing the ¹⁵N-labeled α-synuclein in its D₂O-free buffer. The external D₂O reference is added by inserting a 2 mm capillary which leads to a loss of 16% effective sample volume for a 5 mm NMR tube. No line broadening as result of potential B₀ inhomogeneity was observed, however the quality of water suppression was slightly worse and the spectral noise increased slightly.

This approach allows for ¹⁵N relaxation measurements using external D₂O as a lock substance. Figure 4 shows a comparison of the Hahn-echo based ¹⁵N R_2, relaxation rate constants of α-synuclein in presence of 4% D₂O and in the absence of any D₂O in the sample buffer, at two temperatures 283 K and 303 K. Interestingly, while rate constants at pH 7.4 and 283 K vary little (Fig. 4a), at 303 K rate constants measured in the absence of D₂O are systematically lower than in the presence of only 4% of D₂O, with the exception of the last ~ 30 residues (Fig. 4b). Similar observations have been made with a D₂O-free sample that lacked an external locking substance and was thus measured without locking the magnetic field (data not shown).

Fig. 4

The importance of using a D₂O molar fraction as low as 1% or an external deuterium lock for the measurement of Hahn-echo based ¹⁵N relaxation rates of ¹⁵N-labeled α-synuclein: ¹⁵N relaxation rates in the absence of D₂O versus a D₂O content of 4% and 1% in the sample buffer. Hahn-echo based ¹⁵N R₂ rate constants of α-synuclein measured with the pulse sequence shown in Fig. 1. Rate constants measured in the presence of 4% D₂O (black) are compared to those measured without D₂O (light blue) in the sample buffer at pH 7.4 and temperatures of a 283 K and b 303 K (using an external deuterium lock). When using a D₂O molar fraction of 1% (red), even at 303 K the effect is small

The effect of sample internal D₂O on the ¹⁵N R₂ relaxation measurements on the folded protein domain PDZ2

To illustrate that the documented deuterium exchange effects are visible not only for IDPs as illustrated above for α-synuclein, relaxation measurements on the ¹⁵N-labeled PDZ2 domain of human phosphatase (Gianni et al. 2005) were performed at pH 8.0 and a temperature of 303 K. The impact of the presence of D₂O in the sample buffer on the measured Hahn-echo based ¹⁵N R₂ rate constants for the PDZ2 domain is illustrated in Fig. 5. Some residues in loop regions (i.e. Asn16, Gly19, Gly24, Gly25, Gly34, Gly50, and Gly63) show a systematic increase in the ¹⁵N R₂ rate constants when measured in the presence of only 4% D₂O in the sample buffer compared to the sample without any D₂O in the sample buffer, using an external D₂O reference. Glycine residues appear thereby to be overrepresented which is attributed to their overall fast intrinsic amide-water exchange (Bai et al. 1993).

Fig. 5

domain (PDB ID: 3PDZ) shown in a ribbon representation

Impact of D₂O on the Hahn-echo based ¹⁵N R₂ rate constants of the globular domain PDZ2. a ¹⁵N R₂ relaxation rates using the pulse sequence of Fig. 1 were measured on the PDZ2 domain of human phosphatase (Gianni et al. 2005) in the presence of 4% D₂O (black) and absence of D₂O (blue) in the buffer. In the latter case, a sample-external D₂O inside an insert was used for locking the magnetic field. The influence of D₂O is pronounced for a few residues in loops (i.e. Asn16, Gly19, Gly24, Gly25, Gly34, Gly50, and Gly63) with a strong overrepresentation of glycine residues attributed to their overall fast intrinsic amide-water exchange. b The residues for which the relaxation was altered by the absence of D₂O are highlighted in blue on the structure of PDZ2

The impact of internal D₂O on CPMG-based relaxation dispersion experiments

Because of the significant R_ex contribution on the measured Hahn-echo based ¹⁵N R₂ rate constant caused by D₂O in the sample buffer, we simulated the anticipated R_ex contributions in a CPMG relaxation dispersion experiment. At pH 7.4 and 25 °C (298 K), for solvent-exposed residues the amide exchange rate will assume values in the order of k_NH = 10 s⁻¹ to k_NH = 100 s⁻¹, (Croke et al. 2008) depending on the extend of solvent exposure of the respective residue. Calculations for different amounts of D₂O in the sample buffer (1%, 4% and 10%) are shown in Fig. 6. As illustrated in Fig. 6a, in the presence of 10% D₂O for a residue showing fast amide exchange with = 100 s⁻¹ the R_ex contribution due to D₂O in the sample buffer is present at CPMG frequencies less than 100 s⁻¹, but is significantly reduced for CPMG frequencies ν_cpmg > 100 s⁻¹, and fully averaged out for a CPMG frequency ν_cpmg = 500 s⁻¹. The observed effects scales approximately linearly with the amount of D₂O in the sample buffer (Fig. 6a). However, even for a D₂O molar fraction as low as 1%, the maximum R_ex contribution goes up to 1 s⁻¹ (at low CPMG frequencies with ν_cpmg < 100 s⁻¹). While this may be negligible for the structured part of a large globular protein with an R₂ rate constants of e.g. 50 s⁻¹, it amounts to an error of 50% for an IDP with a rate constant of e.g. 2 s⁻¹. For an amide exchange rate constant of k_NH < 10 s^− 1, the effect is reduced by approximately ten-fold and therefore less critical for only low amounts of D₂O in the sample buffer (Fig. 6b). Overall, the R_ex contribution roughly scales linearly with the percentage of D₂O in the sample buffer and the given amide exchange rate constant k_NH. Therefore, at lower pH < 6.5 and temperatures around or below room temperature, where the amide exchange rate will usually be less than k_NH < 10 s^− 1, at 1% of D₂O in the sample buffer the R_ex contribution by D₂O can be safely ignored. When approaching physiological pH and temperature however, the amide exchange rate constants for many residues can approach values of 100 s^− 1 (Croke et al. 2008). Then, for ν_cpmg < 100 s^− 1 the R_ex contribution by D₂O in the sample buffer can add a significant systematic error on measured R₂ relaxation dispersion profiles of IDPs that have low R_2,0 auto-relaxation constants.

Fig. 6

Simulated CPMG relaxation dispersion curves in presence of different amounts of D₂O in the sample buffer. The R_ex contribution to ¹⁵N R₂ is shown as a function of the applied CPMG frequency, with ν_cpmg = 1/(2 τ_cp) and τ_cpmg/2 − 180˚ (N) − τ_cpmg/2 constituting the basic CPMG block. Data are shown for an amide exchange rate constant of a k_NH = 100 s^− 1 and 10% (blue), 4% (red) and 1% (yellow) D₂O in the sample buffer as well as for amide exchange rate constant of b k_NH = 10 s^− 1 and 10% (blue), 4% (red) and 1% (yellow) D₂O in the sample buffer. See “Materials and Methods” for further details.

We have tested the impact of D₂O in sample buffer on the extracted CPMG-based ¹⁵N R₂ rate constants experimentally with α-synuclein. Indeed, at a CPMG frequency of 100 Hz, the exchange contribution induced by D₂O appears to be reduced substantially. However, at a low CPMG frequency of 20 Hz we observe substantial R_ex contributions, leading to increased ¹⁵N R₂ rate constants in the presence of 10% D₂O (Fig. 7).

Fig. 7

Impact of D₂O on CPMG-based ¹⁵N R₂ rate constants of α-synuclein with weak CPMG frequencies (i.e. 20 Hz and 100 Hz). CPMG-based ¹⁵N R₂ rate constants of α-synuclein were measured at pH 7.4 and at 303 K in the presence of 10% D₂O (black), 1% D₂O (red) and in the absence of D₂O in the sample buffer (light blue). The CPMG frequency was a 20 Hz and b 100 Hz

Finally, we measured also standard ¹⁵N R_1ρ relaxation measurements (Lakomek et al. 2012) with a spin-lock RF amplitude of 2 kHz on α-synuclein (pH 7.4, 303 K). As expected, when comparing ¹⁵N R_1ρ rate constants in the presence of 10% D₂O and absence of D₂O in the sample buffer, we observe only little differences, which is attributed to the loss of measurable magnetization from the exchange to a N-D moiety during the relaxation delays (Fig. 8).

Fig. 8

Little impact of D₂O on ¹⁵N R_1ρ rate constants of α-synuclein under a spin-lock frequency (i.e. 2 kHz). ¹⁵N R_1ρ rate constants for α-synuclein (pH 7.4, 303 K) were measured using a spin-lock RF amplitude of 2 kHz in absence (blue) and presence (black) of 10% D₂O

Therefore, the R_ex contribution induced by D₂O in the sample buffer appears to be suppressed for a standard ¹⁵N R_1ρ experiment employing a spin-lock RF amplitude of 2 kHz.

Discussion

The presented data shows that at near physiological pH (i.e. pH 7.4) and physiological temperatures of 30–37 °C, solvent exchange of the amide protons with deuterium in the sample buffer can impact Hahn-echo based ¹⁵N R₂ measurements significantly due to the deuterium isotope effect even at low molar fraction of D₂O in the sample buffer (as low as 4%). This effect is pronounced for several loop residues in the folded protein domain PDZ2 but is most prominent in the intrinsically disordered protein α-synuclein. As many IDPs show very low ¹⁵N R₂ rate constants (< 5 s⁻¹) due to their high intrinsic flexibility, even a small systematic artifactual R_ex contribution of e.g. 1 s^− 1 can lead to a large error in the data. Therefore, for Hahn-echo based ¹⁵N R₂ measurements the use of only a very low D₂O molar fraction in the sample buffer, as low as 1%, is necessary or, alternatively, the use of an external D₂O lock using a coaxial capillary insert.

Since IDPs form a large part of the human proteome (30–40%) and play an essential role in cellular signaling and regulation of many biomolecular interactions (Tompa 2002; Wright and Dyson 1999, 2015), over the last two decades solution-state NMR provided important insights to characterize secondary structure propensity, conformational space (Abyzov et al. 2016; Salvi et al. 2017) and non-local and local dynamics of IDPs using mainly ¹⁵N CPMG based relaxation dispersion experiments (Kay et al. 1989; Farrow et al. 1994; Loria et al. 1999; Mulder et al. 2001; Wright and Dyson 2015; Salvi et al. 2017; Sugase et al. 2007; Rezaei-Ghaleh et al. 2012; Maltsev et al. 2013; Bah et al. 2015; Zweckstetter 2016; Delaforge et al. 2018; Kurzbach et al. 2015; Lakomek et al. 2016; Schneider et al. 2015; Arai et al. 2015; Charlier et al. 2017). Several experimental strategies have been designed to allow the recording of ¹H-¹⁵N correlation spectra (Lopez et al. 2016; Yuwen and Skrynnikov 2014) and CPMG relaxation experiments of IDPs under physiological conditions and obviate the influence of amide exchange (Yuwen et al. 2014; Kim et al. 2013a, b), but the adverse impact of D₂O through the isotope effect has to our knowledge escaped attention. At physiological pH and near physiological temperatures, we observed a substantial R_ex contribution induced by D₂O in the sample buffer that is not suppressed for a low CPMG frequency of 20 kHz. That finding is in agreement with simulated data that predict a substantial contribution for CPMG frequencies < 100 Hz. At a CPMG frequency of 100 Hz the R_ex contribution induced by D₂O in the sample buffer appears however suppressed, in agreement between experimental and simulated data.

For standard ¹⁵N R₂ measurements (aiming at the investigation of ps-ns dynamics), employing a CPMG frequency of at least 100 Hz as well as proton decoupling (Kim et al. 2013a, b; Yuwen et al. 2014) (to counteract the adverse effect of amide exchange), the effect is however reduced substantially and will not lead to an artificial increase of the ¹⁵N R₂ rate constants. Also, in standard ¹⁵N R_1ρ experiments that spin-lock ¹⁵N transverse magnetization, deuterium isotope effects will be suppressed, as long as the spin-lock RF amplitude, given in frequency units, is significantly faster than the amide exchange rate constants—which is usually the case, e.g. for an RF amplitude of 2 kHz and an amide exchange rate in the order of 100 s^− 1.

Therefore, the discussed effect is uncritical for standard ¹⁵N R₂ experiments that aim at characterizing ns-ps dynamics and therefore suppress R_ex contributions by spin-lock fields with high RF amplitude in the case of R_1ρ measurements or high CPMG frequencies in the case of ¹⁵N CPMG-based ¹⁵N R₂ experiments. But it is important for standard ¹⁵N R₂ experiments that aim at the quantification of R_ex contributions due to conformational dynamics on a µs-ms timescale, such as Hahn-echo based ¹⁵N R₂ experiments or the more popular CPMG-based ¹⁵N R₂ relaxation dispersion experiments. (For both experiments it is important to employ proton decoupling during the relaxation period such as suggested by (Kim et al. 2013a, b) and (Yuwen et al. 2014) to counteract adverse effects of amide exchange.) The deuterium induced R_ex contribution is less critical for globular proteins with higher ¹⁵N R₂ rate constants and in the presence of large R_ex effects due to conformational dynamics, in the order of, e.g. 10 s^− 1. But it can become very critical for the interpretation of CPMG-based relaxation dispersion curves or Hahn-echo based ¹⁵N R₂ experiments of intrinsically disordered proteins (IDPs) that are characterized by low ¹⁵N R₂ rate constants (in the order of a few s^− 1) and where even a small R_ex contribution in the order of e.g. 0.5 s^− 1 or more can add to the ¹⁵N R₂ rate constant substantially.

Indeed, for CPMG-based relaxation dispersion experiments the CPMG frequency for the first, low frequency data points, can be lower than the solvent-exchange rate, depending on the settings for the minimal frequency of the CPMG block in relaxation dispersion experiments, and thus exchange with deuterons in the sample buffer may adversely affect the accuracy of the extracted results and may lead to artificial R_ex effects, which originate from deuterium exchange and a modulation of the ¹⁵N chemical shift tensor through the deuterium isotope effect rather than conformational dynamics. For Hahn-echo based ¹⁵N R₂ measurements, that do not suppress but detect all R_ex contributions, R_ex contributions caused by the deuterium isotope effect are never suppressed and therefore most severe. For high precision CPMG-based relaxation measurements as well as Hahn-echo based ¹⁵N R₂ experiments that aim at the quantification of µs-ms dynamics, we therefore recommend also the use of a very low D₂O content, as low as 1%, or, alternatively, the use of an external deuterium reference, which is easily possible using commercially available NMR tube inserts. This is most critical for IDPs or very flexible loop region in globular proteins that are characterized by low ¹⁵N R₂ rate constants.

Conclusion

The determination of the ¹⁵N R₂ relaxation rate constants is a standard NMR experiment in the evaluation of the dynamics of proteins, including both folded and intrinsically disordered protein entities. While measurements at low pH (< 6.5) or low temperatures (< 10 °C) are usually uncritical because of low solvent amide exchange rates, at physiological pH and temperatures, effects related to solvent amide exchange can lead to artifactual R_ex contributions.

The presented results show that the presence of D₂O > 1% in the sample buffer can deteriorate the accuracy of the rates constants measured using a Hahn-echo based ¹⁵N R₂ experiments and also for low CPMG-frequency data points (< 100 Hz) in CPMG relaxation dispersion experiments. For CMPG frequencies > 100 Hz as well as for ¹⁵N R_1ρ experiments that apply a high-power spin-lock RF amplitude, of e.g. 2 kHz, the modulation of the ¹⁵N chemical shift tensor by deuterium isotope effect due to amide exchange between N-H and N-D is suppressed and will not lead to artificial R_ex contributions, even in the presence of larger amounts of D₂O in the sample buffer. Therefore, the discussed effect is uncritical for standard ¹⁵N R₂ experiments that aim at the characterization of ps-ns dynamics. For Hahn-echo based ¹⁵N R₂ measurement or CPMG-based ¹⁵N R₂ relaxation dispersion experiments at near physiological conditions that aim at the characterization of µs-ms dynamics, we however recommend the use of a very low D₂O content in the sample buffer, as low as 1% molar fraction or, alternatively, the use of an external deuterium reference. This applies both to in vitro or in-cell NMR experiments (Hansel et al. 2014; Reckel et al. 2007; Luchinat et al. 2014; Plitzko et al. 2017; Lippens et al. 2018; Theillet et al. 2016) and is most important for intrinsically disordered proteins that are characterized by low ¹⁵N R₂ rate constants and where even small R_ex contributions can lead to large changes in the measured ¹⁵N R₂ rate constant.