Insights into biomolecular hydrogen bonds from hydrogen bond scalar couplings

Progress in Nuclear Magnetic Resonance Spectroscopy 45 (2004) 275–300 www.elsevier.com/locate/pnmrs

Insights into biomolecular hydrogen bonds from hydrogen bond scalar couplings Stephan Grzesieka,*, Florence Cordiera, Victor Jaravinea, Michael Barfieldb,*,1 a

Division of Structural Biology, Biozentrums, University of Basel, CH-4056 Basel, Switzerland b Department of Chemistry, University of Arizona, Tucson, AZ 85721, USA Received 16 June 2004

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 2. General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Overview of observed H-bond couplings and their magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Experimental correlations to proton chemical shift and H-bond geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Theoretical results from quantum-chemical and semi-empirical calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. DFT and ab initio results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Analysis of H-bond magnetization transfer by simple LCAO-MO, sum-over-states models . . . . . . . . . . . . . . . . . 2.3.3. Relation between hJ and dH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. H-bond dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Dependence on fast protein backbone motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Comparison to chemical exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Correlations to other NMR observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Electrostatic versus covalent character of H-bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Applications of H-bond couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Structure determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Nucleic acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. New NMR experiments based on H-bond magnetization transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Variations in H-bond geometry as detected by H-bond couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Detection of H-bond formation in peptide folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Ligand-induced strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Temperature-induced changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4. Comparison of native and A-state ubiquitin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5. H/D-isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

* Corresponding authors. Tel.: C41 61 267 2100; fax: C41 61 267 2109. E-mail addresses: [email protected] (S. Grzesiek), [email protected] (M. Barfield). 1 Tel.: C1 520 621 6348; fax: C1 520 621 8407. 0079-6565/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.pnmrs.2004.08.001

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4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Keywords: Hydrogen bond; Scalar coupling; Chemical shift; Secondary structure; Tertiary structure; Protein; Nucleic acid; NMR; Density functional theory

1. Introduction Despite their crucial role in the stabilization of biomolecular structures and their almost ubiquitous involvement in biomolecular reactions, such as enzymatic cleavage or ligand recognition, the detailed understanding of hydrogen bonding (H-bonding) in biomolecules in terms of energies, geometric preferences and dynamics, is still rather limited. What would be desirable is a technique that yields such information at high precision for all the individual H-bonds of a biomolecule. X-ray and neutron diffraction methods have made invaluable contributions to the present-day knowledge of biomolecular H-bonds [1,2]. Suffice it to mention the correct prediction of the H-bond networks in protein secondary structures based on the precise knowledge of the polypeptide backbone geometry [3] and the discovery of Watson– Crick base-pairing in the DNA double helix [4]. Detailed statistics on the heavy atom donor–acceptor geometries in proteins [5–7] have been compiled from the rapidly increasing number of entries in the RCSB Protein Data Bank. Yet, only the few available neutron diffraction structures [8] or the limited number of high to ultra-high resolution [9,10] X-ray structures of biomacromolecules define hydrogen atom positions within H-bonds without the use of fixed standard geometries. Only for these cases is it possible to have a reasonably precise description of the forces acting in individual H-bonds. A wealth of information on the energies in H-bonds has been provided by infrared (IR) spectroscopy for small molecules. In principle, IR spectroscopy can also resolve single H-bond vibrations in biomacromolecules by the use of difference methods. However, these methods need very specific isotope labeling schemes [11] such that the study of a larger number of H-bonds in a single biomacromolecule is impractical. Some of these difficulties are avoided in high-resolution NMR spectroscopy. This technique is being widely used to probe biomolecular H-bonds because of its ability to resolve individual H-bonding groups and because of the large effects of H-bonding on NMR observables such as chemical shifts, coupling constants, hydrogen exchange rates and fractionation factors [12]. The discovery that scalar couplings can be commonly observed across the H-bonds of regular secondary structure elements in nucleic acids [13,14] and proteins [15,16], as well as in a number of other H-bonds in biomolecules and smaller chemical compounds [17–20] has added another, very direct effect to this arsenal of individually observable H-bond parameters. The

couplings can be used to identify donor and acceptor groups in individual H-bonds from COSY experiments. Because of their strong dependence on H-bond distances and angles, the sizes of the couplings provide very sensitive measures of the H-bond geometries. The range of observable H-bond couplings (HBCs) and experiments for their detection in biomolecules have been the subject of earlier reviews [21–23]. The current review focuses on the contributions that experiments and quantumchemical calculations have made to the understanding of NMR H-bond parameters and other properties of biomolecular H-bonds. Specifically, we address the dependencies of HBCs on H-bond structural parameters and dynamics, the interrelation with other NMR parameters such as chemical shifts and other coupling constants, their use in biomolecular structure determination, and the detection of changes in H-bond geometries under changed biomolecular conditions.

2. General properties The original observations of the H-bond scalar couplings came as a surprise since scalar couplings had been usually associated with covalent bonds. However, it is now clear that across the H-bond, the same nucleus/electron/ nucleus magnetization transfer mechanisms are effective as within normal covalent bonds. Therefore, the same experiments for detection, quantification or magnetization transfer are applied to H-bond scalar couplings. Usually their size in biomacromolecules is determined most easily by quantitative J-correlation or spin-echo difference techniques [24], whereas the sign and magnitude can be determined from E.COSY experiments [25], if suitable passive nuclei are available. The most widely used experiments are based on the quantitative-J HNN-COSY [13,14] for the detection of h2JNN couplings2 in 15N–H/15N H-bonds and the long-range HNCO [15,16] for h3JNC 0 couplings in 15N–H/Oa13C H-bonds.

2 In the present work, we use the symbol hnJAB for trans H-bond scalar couplings between nuclei A and B in order to emphasize that one of the n bonds connecting the two nuclei in the chemical structure is actually an Hbond [14,22].

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Fig. 1. The most common H-bond couplings in biomolecules. Hydrogen, nitrogen, carbon, phosphorus, and fluorine symbols refer to 1H, 13C, 15N, 31 P, and 19F isotope nuclei, respectively. Scalar couplings are indicated in Hertz. An asterisk indicates that the sign of the coupling was not determined. (A) Donor and acceptor nitrogen. This situation arises in canonical Watson–Crick base pairs, but also in many unusual base pairs as well as in protein/nucleic acid and protein side chain contacts [13,14, 28–32,36,122,175,204,248,249]. The sign of both h1JHN and h2JNN was determined experimentally [14,27]. (B) Donor nitrogen and acceptor carbonyl. This situation arises in canonical protein backbone H-bonds, but also in nucleic acid base pairs as well as in contacts involving protein sidechains [15,16,33–35,250–252]. In agreement with theory [62], the sign of h3JNC 0 was determined experimentally as negative [33]. The sign of h2JHC 0 was observed experimentally as positive and negative [251], but is expected as positive from DFT/FPT calculations [44]. (C) Donor Ca and acceptor carbonyl in protein b-sheets. The positive sign of h3JCaC 0 is obtained from DFT calculations [58]. (D) Donor hydroxyl oxygen and acceptor nitrogen in RNA sugar/base contacts [253]. (E) Donor nitrogen and acceptor phosphate [107,254]. The negative sign of h2JHP and h3JNP is derived from DFT calculations [98]. (F) Donor hydroxyl oxygen and acceptor phosphate [254]. (G) Donor nitrogen and acceptor cysteine sulfur, which coordinates a metal ion (M) [17,255,256]. (H) Donor and acceptor are fluorine atoms. h1JHF is negative according to experimental and theoretical evidence, whereas h2JFF is positive according to experiments, but negative from theoretical estimates [19]. (I) Donor is fluorine and acceptor nitrogen [20].

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Watson–Crick base pairs [13,14], Hoogsteen base pairs [28], AA-mismatch base pairs and G4-tetrads or -hexads [29,30], histidine dimers [31], and arginine/guanosine H-bonds in protein–nuclei acid complexes [32]. Similarly, h3 JNC 0 couplings in N–H/OaC H-bonds (Fig. 1B) have a typical range of about K0.2 to wK1 Hz independent of whether they are detected in protein backbone to backbone [15,16,33], backbone to sidechain [33,34], sidechain to sidechain [35] as well as in nucleic acid base to base H-bonds [36]. At present, an absolute size of about 0.2 Hz seems to be the lower limit of scalar couplings that can be detected in biomacromolecules with reasonable effort. It is apparent from Fig. 1 that large HBCs in the size range of 1–10 Hz are only found in biomacromolecules, when nitrogen atoms, phosphate groups or sulfur atoms act as acceptors. The absence of such acceptors in protein backbone H-bonds and the consequently small size of the coupling constants limits their precise determination to smaller proteins, albeit backbone h3J NC 0 -correlations have been detected for proteins of up to 30 kDa molecular weight by the use of deuteration and TROSY techniques [37]. Theoretical studies [38–44] predict very strong electronic effects on oxygen atoms such as HBCs and chemical shift changes, when they act as H-bond donors or acceptors. Unfortunately, no oxygen isotopes exist that would make such effects detectable by high-resolution NMR. The strongest HBCs overall have been detected in small molecules with fluorine donor or acceptor atoms [19,20], where the size of h1J and h2J couplings is in the range of 20–150 Hz (Fig. 1H and I). Fig. 1 lists HBCs for only the most common situations in biomacromolecules. Others have been observed such as h4JNN [45] in guanosine quartets, h3JHCa [46] in protein backbones, h2 JH2H3 in Watson–Crick A–U base pairs [47], as well as h4Jpp [48,49] or h2JHH and h3JHH [18,50] in small H-bonding molecules. 2.2. Experimental correlations to proton chemical shift and H-bond geometry

2.1. Overview of observed H-bond couplings and their magnitudes Fig. 1 shows the most common hydrogen bond types in biological macromolecules, for which HBCs have been detected so far. From this experimental work, but also from theoretical calculations [26,27], it is evident that the type of the covalently bound neighbors of H-bond donors and acceptors only has a limited influence on the size of the couplings. This can be seen for example from h2JNN couplings in N–H/N H-bonds, which connect 15N-donor and acceptor nuclei (Fig. 1A). The h2JNN coupling constants usually lie in the range 6–11 Hz regardless of the exact chemical nature of the surrounding moieties. Examples include h2J NN in the canonical U/T/A and G/C

A strong correlation between the size of the H-bond coupling, the chemical shift of the H-bonding proton and the H-bond geometry was found already in the early observations [13,15]. In general, strong couplings correspond to high-frequency (downfield) proton shifts and short donor–acceptor distances. This is evident for H-bonds in the two proteins ubiquitin and protein G (Fig. 2A, filled circles), which show a relationship of the form h3

J NC 0 Z 0:261 Hz=ppm !dHN C 1:742 Hz ðr Z 0:87Þ (1a)

after a ring current correction has been applied to the amide proton chemical shift dHN. The correlation is

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been established for nucleic acid (Fig. 2B) [13,28], where the correlation h2

h2

J NN couplings

JNN Z 1:27 Hz=ppm !dHN K 9:6 Hz ðr Z 0:86Þ

(1b)

h2

holds. JNN values in A–T/A–U base pairs are in the range of 7–9 Hz, whereas G–C base pairs have smaller h2JNN values of 6–7 Hz. Correspondingly, N/N distances, on ˚ shorter in crystallographic average, are by about 0.1 A ˚ ) than in G–C base structures of A–T/A–U base pairs (2.82 A ˚ ) [13]. pairs (2.92 A Due to the correlation with the chemical shift, the dependence of HBCs on the H-bond geometry is not surprising, since it is well established that both isotropic [51–55] and anisotropic chemical shifts [56,57] of the H-bonding proton depend strongly on H-bond donor–acceptor distances. Fig. 3 shows this correlation between the proton chemical shift and the proton–oxygen distance dHO in early work of Wagner, Pardi and Wu¨thrich [51]. A dependence of the type
3 dHO3 K 2:3 DdHN =ppm Z 19:2 A

Fig. 2. Relation between H-bond coupling and chemical shift of the H-bonding proton. (A) Proteins: correlation between h3JNC 0 couplings and amide proton chemical shifts in human ubiquitin and protein G. Open and filled circles correspond to amide proton chemical shifts before and after ring-current correction, respectively. The solid line depicts a linear fit using the ring-current corrected shifts (see text). The inset shows a histogram of observed h3JNC 0 couplings in a-helical (open bars) and b-sheet (filled bars) conformations. (B) Nucleic acids: correlation between h2JNN couplings and the imino proton chemical shifts in Watson–Crick and Hoogsteen base pairs of an intramolecular DNA-triplex. The solid line depicts a linear fit to the data (see text). Adapted from Ref. [28].

masked to some extent without such a correction (Fig. 2A, open symbols, rZ0.82). Thus for lower precision structures or for mobile protein surfaces, where the positions of the aromatic sidechains are less well defined such that the ring current correction cannot be calculated accurately, it is difficult to identify the true effect of H-bonding on the proton chemical shift. In addition to this chemical shift correlation, h3JNC 0 in proteins depends strongly on the secondary structure (Fig. 2A, inset) [15]. For the two proteins ubiquitin and protein G, the average h3JNC 0 for H-bonds in b-sheet regions is K0.53G0.15 Hz, whereas a-helical H-bonds have a weaker average h3JNC 0 of K0.36G0.18 Hz. As average crystallographic N/O distances in b-sheet H˚ ) are about 0.1 A ˚ shorter than in a-helical bonds (2.91 A ˚ H-bonds (2.99 A) [5], this indicates that the couplings are stronger for shorter H-bond lengths. Similar correlations between the magnitude of H-bond J-coupling, proton chemical shift and structure have

Fig. 3. Relation between H-bond distance and chemical shift of the H-bonding proton. Plot of the chemical shifts for the amide protons in BPTI and for the Ca protons in the antiparallel b-sheets (indicated by squares) of this protein vs. their distance from the nearest oxygen atom. Dd is the observed chemical shift at 50 8C and pH 3.5 minus the corresponding random-coil and ring-current shifts. Only those Ca protons were considered ˚ of an oxygen atom. The solid and dashed lines that are within 3.5 A represent the best fits according to the inverse cubic distance dependencies given in the text. Reprinted with permission from Ref. [51].

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was found for the ring current corrected deviations of the amide proton chemical shifts from their random coil values. A similar correlation, K3
3 dHO DdHa =ppm Z 19:6 A K 0:7;

holds for the chemical shifts of 1Ha nuclei that are in proximity to carbonyl oxygens (Fig. 3). Such conformations are usually found in b-sheets and the correlation expresses the fact that Ha resonances in b-sheets are often easy to identify from their pronounced high-frequency (down-field) shifts. It is interesting to note that also for such Ca–H/OaC conformations H-bonds couplings of the type h3JCaC 0 can be observed (Fig. 1C and see below) [58]. The distance dependence of the h3JNC 0 couplings has been analyzed in detail by Bax and co-workers [33] for ˚ resolution crystallographic protein G, for which a 1.1 A structure [59] is available (Fig. 4). The data were fitted to a correlation of the form h3


JNC 0 Z K5:9 !104 Hz expðK4dNO =AÞG0:09 Hz


ln½Kh3 JNC0 =ð5:9 !104 HzÞ dNO Z K0:25 A

(2a) (2b)

where an exponential dependence on the nitrogen–oxygen distance (dNO) was assumed due to the exponential radial dependence of atomic orbitals. An analysis of h3JNC 0 data for the Escherichia coli cold-shock protein A confirmed the validity of Eqs. (2a) and (2b) and showed that the agreement ˚ resolution is considerably better with coordinates of a 1.2 A X-ray structure of a homologous protein than with the

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˚ X-ray structure of the same coordinates from the 2.0 A protein [60]. For the high-resolution structure of protein G, the deviations of h3JNC 0 couplings from a pure distance dependence (Fig. 4) are clearly larger than the experimental errors, which can be as low as 0.02 Hz for small proteins [61]. Three different sources are expected to contribute to these deviations: (1) true inaccuracies in the crystallographic model of the structure, (2) the angular dependence of the HBCs, and (3) the averaging over different conformations due to the internal dynamics of proteins. The importance of structural inaccuracies may be grasped from the exponential distance dependence given by Eqs. (2a) and (2b), which can be approximated as
Dh3 JNC0 =h3 JNC 0 DdNO Z K0:25 A

(2c)

for small variations DdNO and Dh3JNC. Thus a deviation of ˚ in dNO corresponds to a relative change of 40% in 0.1 A h3 JNC 0 . Inaccuracies of this order are not unexpected for the ˚ resolution crystallographic structure of protein G 1.1 A (1IGD) with typical backbone heavy atom B-factors of ˚ 2 (BZ8p2Dr2). In addition, true differences about 5 A between the solid state and the solution form of the protein may also be non-negligible. Currently, the number of observations of experimental HBCs is not sufficient for a systematic test of angular dependencies. Also with respect to H-bond dynamics, the experimental data (discussed below) are rather limited and do not show strong trends. The deepest insights into both phenomena have been obtained from theoretical calculations where the H-bond geometry can be varied systematically and the influence of dynamics can be simulated. A description of these results will be given in the next sections. 2.3. Theoretical results from quantum-chemical and semi-empirical calculations

Fig. 4. Correlation between the observed h3JNC 0 values and H-bond lengths in protein G, averaged over three crystal structures (1IGD, 2IGD, and 1PGB), to which protons were added with X-PLOR, assuming ˚ . The curve is the best fit exponential, K5.9!10 4 rNH Z1.02 A ˚ . Open circles exp(K4RNO) Hz, where RNO is the H-bond length in A correspond to side-chain carboxyl groups, H-bonded to backbone amides, and were not used in the fit. Reprinted with permission from Ref. [33].

Since, analogous to other scalar couplings, H-bond couplings are transmitted via the electrons [19,28,62], an understanding of the relevant electronic interactions should provide important information on the behavior of electronic wavefunctions within H-bonds as well as on their geometric arrangements and dynamics. According to Ramsey [63], four contributions to the nuclear spin Hamiltonian are generally considered to be important for electron-mediated nuclear spin–spin couplings [64–68]. These are the paramagnetic spin-orbit (PSO), the diamagnetic spin-orbit (DSO), the spin dipolar (SD), and the Fermi contact (FC) terms. Besides coupling constants involving fluorine, the FC terms are often the most important. The couplings across the canonical biomolecular H-bonds are no exception to this rule. For example, when all four terms were considered, the FC contributions accounted for more than 94% of the total computed values of h2JNN, 1JNH, and h3JNC 0 in N–H/N or N–H/OaC [44,62] H-bond models. A satisfactory

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analysis of the Fermi contact contributions requires a precise description of electron correlation effects. This can be achieved via multiconfiguration interaction [69–73], many body perturbation theory [74], equations of motion (EOM, formally equivalent to time-dependent Hartree– Fock) [75–77], second order polarization propagator coupled cluster [78,79], and EOM coupled cluster [80], or density functional theory (DFT) [81–85] methods. The DFT methods offer the advantage of computational times roughly equivalent to Hartree–Fock methods, but with the inclusion of the electron correlation effects. Thus, the calculations are quick and can be extended to larger molecules. Additionally, in our experience DFT geometry optimizations give results comparable to second order Møller–Plesset corrections (MP2) with the same basis set. DFT calculations can be performed on larger systems such as DNA triplexes [27]. An effective method for computing FC contributions to scalar coupling for low-Z elements makes use of a combination of DFT and finite perturbation theory (FPT) [86–89] methods. Most of the magnetic shielding calculations are also based on DFT methods in combination with the gauge including atomic orbital (GIAO) method performed at the same level of theory [27,28,90–92]. A large number of recent computational studies using DFT and ab initio MO methods have reproduced the size and trends of the observed coupling constants in the imino-group H-bonds of nucleic base pairs, in the amide to carbonyl and amide to phosphate H-bonds of proteins and their complexes as well as in smaller molecules [19,20,26–28,48,50,62,92–104]. 2.3.1. DFT and ab initio results 2.3.1.1. N–H/N H–bonds. Computed results for h2JNN in N–H/N H–bonds demonstrate an approximately exponential dependence on the N–N distance [27,28,94,97,105] (Fig. 5A). With the exception of charged base pairs, the calculated values are almost independent of nucleic acid base pair type. In complete agreement with experimental h2 JNN values of 6–8 Hz for A–T and G–C pairs in duplex

DNA [14], the DFT-derived h2JNN couplings range from 7.5 ˚ found in DNA to 6 Hz for N–N distances of 2.8–2.9 A crystal structures [13]. Also in agreement with the experimental correlation between imino proton chemical shifts and h2JNN (Fig. 2B), calculated imino proton (1HN) shifts show a similar exponential distance dependence as the h2 JNN couplings (Fig. 5B). In contrast, the h1JHN couplings have a more complicated behavior (Fig. 5C). A distinct maximum at small positive values is found for uncharged ˚ . This base pairs at N–N distances around w2.8 A reproduces the experimentally observed small positive h1 JHN values in DNA duplexes [14]. At N–N distances ˚ , the DFT calculations predict a shorter than w2.6 A crossing to strongly negative h1JHN values, which can be explained by the fact that for very short N–N distances the H-bond becomes symmetric, and H-bond h1JHN and covalent 1JNH couplings become indistinguishable (see below). Angular dependencies of h2JNN couplings in N–H/ N bonds have been investigated by Del Bene, Cremer, Limbach, Malkin, Pervushin, Wasylishen and coworkers [94,97,101,105,106]. The couplings depend strongly on the direction of the acceptor lone pair relative to the donor N–H moiety [101,105] such that linear arrangements show maximal h2JNN values. A weaker dependence is found on the N–H/N angle [94,97,106], where bent configurations appear to yield stronger couplings. 2.3.1.2. N–H/OaC H-bonds. A variety of angles and distances characterize the exact geometry of N–H/OaC H-bonds in proteins. In Fig. 6A, the N–H/OaC H-bond geometry is defined by the H/O distance, rHO, the two internal angles q1h:N–H/O and q2h:H/OaC and the dihedral angle rh:H/OaC–N 0 , measured about the OaC bond. The DFT/FPT calculations of this situation on small dipeptide fragments demonstrate an approximately exponential decay with donor–acceptor distance rHO, a strong dependence on the angle q2 (Fig. 6B), and weaker dependencies on the angles q1 and r (Fig. 6C) [62,92,93]. A simple feature of these angular dependencies is that straight N–H/O and H/OaC angles correspond to the strongest

Fig. 5. DFT/FPT Fermi contact contributions to trans H-bonding coupling constants and DFT/GIAO isotropic imino 1HN chemical shifts plotted versus interresidue separations rNN in N–H/N H-bonds of Watson–Crick G–C and A–T and Hoogsteen T$A and CC$A base pairs. (A) h2JNN (B) d1HN, (C) h1JHN. Adapted from Ref. [27].

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the geometric dependencies for the DFT/FPT-calculated h3 JNC 0 couplings were parameterized [92] to good approximation by h3


!fcos2 q2 J NC 0 Z K366 Hz expðK3:2rHO =AÞ K sin2 q2 ½0:47 cos2 r C 0:70 cos r C 0:11g

(3)

where the weak dependence on the N–H/O angle q1 has been neglected. A further neglect of the dependence on the dihedral angle r, which is weak for sufficiently straight H/OaC angles q2, yielded the correlation h3

2
J NC 0 Z K360 Hz expðK3:2rHO =AÞcos q2 C 0:04 Hz

(4)

˚ K1 in Eqs. (3) and The exponential decay constant of 3.2 A ˚ K1 in (4) is in reasonable agreement with the value of 4 A Eqs. (2a) and (2b) derived from a fit of experimental data neglecting any angular dependencies. It is interesting to observe that the slightly smaller theoretical decay constant coincides with the finding that short N–H/OaC H-bonds in proteins usually adopt straighter N–H/O and H/OaC angles than longer H-bonds [5,7]. Thus the neglect of the angular attenuation of h3JNC 0 in the fit of Eqs. (2a) and (2b) may have led to a slight overestimation of the distance decay. When experimentally measured h3JNC 0 couplings in proteins are compared to h3JNC 0 values from DFT/FPT calculations using peptide fragments of the corresponding protein structures, reasonable, albeit not perfect agreement is usually obtained [92,93] (Fig. 7). As shown recently [108], a considerable part of the remaining differences between observed and calculated values can be explained by the internal dynamics of proteins (see below). Fig. 6. Geometric dependence of h3JNC 0 couplings. (A) Diagram of a formamide dimer depicting the designations of internuclear distances and angles: H-bond distance rHO, internal angles q1h:N–H/O and q2h:H/OaC, and dihedral angle rh:H/OaC–N 0 , measured about the OaC bond. (B) DFT/FPT results for h3JNC 0 in formamide dimers plotted versus q2 in the range 120–2408 with rHOZ1.8 (triangles), 2.0 (squares), ˚ (circles). The dimers were constrained to the plane (rZ1808; and 2.2 A q1Z1808). The lines are plots of the results from Eq. (3) for the three values of rHO. (C) DFT/FPT results as in (B) for h3JNC 0 in formamide dimers. Filled circles show a variation of q1 with q2 fixed at 1808, r at 1808, and rHO at ˚ , respectively. Filled diamonds show a variation of r with q1 fixed at 2.0 A ˚ , respectively. Adapted from Ref. [92]. 1808, q2 at 1808, and rHO at 2.0 A

couplings. In the analogous N–H/OaP H-bonds, similar predictions hold [98] and agree with experimentally determined h3JNP values that are strongest (K4 to K5 Hz) for nearly straight H/OaP angles, but drop to values weaker than K0.35 Hz for angles smaller than 1268 [107]. Guided by insights from a linear combination of atomic orbitals/sum-over-states (LCAO/SOS) analysis (see below),

Fig. 7. The DFT/FPT data for h3JNC 0 in the 34 formamide dimers extracted from protein G plotted versus the experimental data. The solid line corresponds to the linear regression h3JNC 0 (DFT/FPT)Z1.12 h3JNC 0 (expt) K0.05 Hz. Reprinted with permission from Ref. [92].

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2.3.2. Analysis of H-bond magnetization transfer by simple LCAO-MO, sum-over-states models The electron densities derived from the DFT calculations per se provide no information about the parts of the electronic wavefunctions, which are relevant for the scalar magnetization transfer, and thus give no physical insight into the transfer mechanism. Various types of analyses have been introduced to dissect the obtained electron density functions into more meaningful entities such as atoms in molecules (AIM) [109], natural bond orbitals (NBO) [110,111], and the decomposition of J into orbital contributions using orbital currents and partial spin polarization (J-OC-PSP) [44]. Another approach is the direct, model-independent visualization of coupling pathways using real-space functions based on coupling energy and coupling electron deformations densities [112,113]. While all these methods have their specific advantages and disadvantages, the success of scalar couplings (in comparison, for example with chemical shifts) to provide meaningful conformational information depends crucially on the availability of simple expressions relating coupling constants to internal and dihedral angles and bond distances. In this respect, semi-empirical valence bond and molecular orbital (MO) methods [64,65] have been particularly helpful for gaining physical insights and establishing simple geometric correlations both in covalently bonded and in H-bonded systems. The main conclusions of such an analysis of scalar couplings across N–H/N [27] and N–H/OaC [92] H-bonds are briefly examined in the following sections. 2.3.2.1. N–H/N H-bonds. In the delocalized MO model of Pople and Santry [114,115], the Fermi contact contribution to the nuclear spin–spin coupling constant JAB between nuclei A and B is given by JAB Z

16 2 hme gA gB hajdðrA ÞjaihbjdðrB Þjbipab 9

(5)

where me is the Bohr magneton, eh/(4p mec), a and b are atomic or hybrid orbitals centered on nuclei A and B, and d(rA) and d(rB) are Dirac d-functions evaluated at A and B, respectively. The quantity pab is the mutual atom–atom polarizability as defined by Coulson and Longuet–Higgins [116,117] X X cia cib cja cjb pab Z 4 (6) 3i K 3j i;occ j;unocc where cia and cjb, for example, denote the coefficients of orbital a and b in the ith occupied and jth unoccupied MOs, respectively. The summations run over occupied and unoccupied MOs with corresponding energies 3i and 3j. Thus, in this simple MO analysis, the Fermi contact contribution to the nuclear coupling is proportional to an electronic part defined in terms of orbital coefficients and energies.

Fig. 8. A simple model used to describe nuclear spin–spin coupling in the N–H/N 0 hydrogen-bonding region. The hybrid orbital t centered on N is directed toward the 1s atomic orbital h on H, and t 0 denotes a hybrid orbital on N 0 . The bs are resonance integrals associated with different pairs of orbitals.

In order to obtain explicit expressions from Eqs. (5) and (6) for the trans H-bond couplings, a variational method was used in a simple three-orbital representation of an H–N/N 0 nucleic acid fragment [27]. This simple model depicted in Fig. 8 consists of two sp2 hybrid orbitals t and t 0 on N and N 0 , respectively, and of the 1s atomic orbital h on hydrogen. The interactions between these three orbitals are described via the resonance integrals b, b 0 , and b 00 . The coefficients appropriate to Eq. (6) appear in the MOs as linear combination of these orbitals ck Z ckt t C ckh h C ckt 0 t 0

(7)

where the index k denotes the different occupied and unoccupied MOs. With the usual approximations including the neglect of the resonance integral b 00 in Fig. 8, MO energies and coefficients of the MO wavefunctions can be obtained analytically from the 3!3 secular determinant of the electronic interaction Hamiltonian [118]. Using these wavefunctions, the mutual atom–atom polarizabilities (Eq. 6) for the three types of couplings (h2JNN 0 , 1JNH and h1 JHN 0 ) in the hydrogen bonding region are   b2 b 02 ðah K at Þ2 (8) ptt 0 Z K 3 2 3C 2 2r ðb C b 02 Þ b C b 02 pth Z

b2 2r 3

b 02 2r 3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi with rZ b2 C b 02 C ðah K at Þ2 =4 and where ah and at denote Coulomb integrals. A number of general insights can be deduced from Eq. (8). First, the expressions for both ptt 0 and pht 0 contain the squares of the resonance integral b 0 as a factor. If the overlapping region between two orbitals is not too large, resonance integrals can be approximated as proportional to overlap integrals. Thus for a weak N–H/N 0 H-bond, where b 0 /b, both ptt 0 and pht 0 are proportional to the square of the pht 0 Z

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Fig. 9. Semiempirical MO results for nuclear spin–spin coupling constants h2 JNN 0 , h1JHN 0 and 1JNH in N–H/N 0 plotted as a function of b 0 /b. Coupling ˚ , rHN 0 O3.5 A ˚ and at b 0 /bZ constants at b 0 /bZ0 correspond to rNHZ1.04 A ˚ . Adapted from Ref. [27]. 1, rNHZrHN 0 Z1.04 A

wavefunction overlap S(h;t 0 ) between the hydrogen 1s orbital and the sp2-orbital of the acceptor N 0 . The scalar couplings are proportional to the atom–atom polarizabilities (Eq. (5)), and so the h2JNN 0 and h1JHN 0 couplings should also be proportional to the square of this overlap. As atomic orbitals decay exponentially at larger distances, the square of the overlap also decays exponentially. This leads to the approximate exponential distance dependence of H-bond scalar couplings. Second, since the overlap will decrease when the direction of the H/N 0 vector deviates from the direction of the acceptor sp2 lone pair, there should be an approximate cos2-dependence on the respective angle. This is observed in DFT calculations [101,105]. Third, the model is symmetric with respect to the nitrogen donor and acceptor atoms N and N 0 . Accordingly, Eq. (8) shows this symmetry with regard to an interchange of b4b 0 and pth4pht 0 . This means that covalent 1JNH and H-bond h1JHN 0 become indistinguishable for the symmetric situation, where bZb 0 . Fourth, since all three mutual atom–atom polarizabilities in Eq. (8) have positive signs and 15N and 1H have magnetogyric ratios of opposite sign, Eq. (5) predicts a positive sign for h2JNN 0 and negative signs for both 1JNH and h1JHN 0 . In Fig. 9, h2JNN 0 ,h1JHN 0 and 1JNH based on Eqs. (5) and (8), are plotted as a function of the ratio b 0 /b using estimated values of the ah and at Coulomb and the b resonance integrals [27]. As b 0 /b approaches zero, the directly bonded coupling 1JNH has its maximum absolute value and the trans H-bonding coupling constants h2JNN 0 and h1JHN 0 vanish. 1 JNH decreases in magnitude as the hydrogen approaches N 0 , and becomes equal to h1JHN 0 for b 0 /bZ1 corresponding to the hydrogen at the midpoint of a symmetric hydrogen bond (see also Fig. 5C and the respective discussion). In the limit b 0 2/b2 and (ahKat)2/b2, the mutual atom–

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Fig. 10. Schematic diagram showing representative hybrid and atomic orbitals in the formamide dimer depicted in Fig. 6A. For simplicity, each second-row atom has a set of three (trigonal) hybrid-type orbitals (HTOs). Only one of these HTOs is depicted for N and N 0 . Of particular interest here are the 1s atomic orbital h of the donor hydrogen and the HTOs o1–o3 on the acceptor oxygen. The 2pp atomic orbitals on O and C perpendicular to the plane are not depicted. Adapted from Ref. [92].

atom polarizability ptt 0 is three times pht 0 (Eq. (8)). This implies that the electronic features associated with the h2 JNN 0 coupling should be three times that for the h1JHN 0 coupling. Additionally in Eq. (5), the nitrogen s-electron density htjd(rN)jti is almost 19 times larger than for hydrogen (htjd(rN)jti/hsjd(rH)jsiZ18.7). Both factors more than compensate for the smaller 15N magnetogyric ratio (gN/gHZK0.10) and explain the larger magnitudes observed for h2JNN 0 as compared to h1JHN 0 . Thus, most of the trends in the DFT and experimental magnitudes can be rationalized by this LCAO/SOS analysis. However, the negative sign for h1JHN 0 over the entire range of the parameter b 0 is an error of this simple model. 2.3.2.2. N–H/OZC H-bonds. A similar LCAO/SOS analysis was carried out for the case of h3JNC 0 scalar couplings across N–H/OaC H-bonds [92]. Depicted in Fig. 10 for an N–H/OaC–N 0 moiety are those orbitals which are relevant to this discussion. For simplicity, the classical hydrogen bonding geometry is assumed with trigonal hybridization at the N, O, and C atoms. One of the hybrid type orbitals (HTOs) on N is directed to the 1s atomic orbital (AO) h of the donor hydrogen atom. In addition to the three trigonal sp2 HTOs on the acceptor oxygen atom O, there is a 2pp AO (not depicted) perpendicular to the plane. The HTO o1 forms the OaC s-bond with c1 on C while o2 and o3 designate the oxygen lone pair orbitals. Similar to the discussion on the N–H/N H-bond, the Pople–Santry formalism implies a quadratic dependence of the coupling constants on the overlap integrals in the N–H/OaC H-bond. Because of their proximity, the most important overlap integrals should involve the donor hydrogen atom and the acceptor oxygen orbitals. Using the geometric parameterization of Fig. 6A, the overlap integrals between the donor hydrogen and the acceptor oxygen

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orbitals assume simple geometric dependencies on the H/ OaC angle q2 and the H/OaC–N 0 dihedral angle r: pffiffiffi pffiffiffi Sðh;o1 ÞZ½Sðh;sO ÞC 2 cosq2 Sðh;psO Þ= 3 pffiffiffi pffiffiffi pffiffiffi Sðh;o2ÞZ½Sðh;sO ÞCð 3 cosrsinq2 Kcosq2 ÞSðh;psO Þ= 2= 3 pffiffiffi pffiffiffi pffiffiffi Sðh;o3ÞZ½Sðh;sO ÞKð 3 cosrsinq2 Ccosq2 ÞSðh;psO Þ= 2= 3 Sðh;ppO ÞZsinrsinq2 Sðh;psO Þ ð9Þ where sO, psO, and ppO are 2s and 2p AOs on oxygen, with psO in the direction of the OaC bond and ppO perpendicular to the plane. The most important Fermi contact contributions to the H-bond scalar coupling are expected to result from the overlap integral S(h;o1), since it involves bonds that have non-vanishing density at the coupled nuclei, e.g. the donor n–h and acceptor o1–c1 s-bonds in Fig. 10. The quadratic dependence on S(h;o1) implies that h3JNC 0 should show a cos2q2 dependence on the H/OaC angle, as well as an exponential dependence on rHO, which is implicit in the square of the atomic overlap integrals S(h;sO) and S(h;psO). This is indeed what is approximately found in the DFT calculations shown in Fig. 6B and the resulting parameterization in Eq. (4). In addition to this direct interaction, overlap of the hydrogen with the oxygen lone pairs o2 and o3 can lead to higher-order perturbation contributions to h3JNC 0 . In many H-bonding situations the donor hydrogen will interact very effectively with these lone pairs, and the latter by angularly independent interactions with o1, c1, c2, and c3. As a consequence, indirect contributions to h3JNC 0 arising from the overlaps S(h;o2) and S(h;o3) should depend on both r and q2 in Eq. (9). The parameterization of the DFT results in Eq. (3) takes this into account and shows that the additional angular dependence on r is particularly important for bent H/OaC arrangements, where the direct overlap S(h;o1) is small (e.g. as q2/908). 2.3.3. Relation between hJ and dH From a theoretical point of view, the ubiquitous correlation of trans-H bond coupling constants and proton chemical shifts is surprising, because the differences and the complexity of the mathematical expressions for scalar coupling and nuclear shielding preclude a rigorous connection between the two parameters. In the Ramsey formulation [119] magnetic shielding is the sum of diamagnetic sd and paramagnetic sp terms. The second order perturbation expression of sp includes a sum over the manifold of excited singlet states. The LCAO-MO analysis of these second order expressions gives summations over the occupied and unoccupied MOs and a quadruple sum over the atomic orbitals and the associated integrals. Moreover, the gauge origin dependence of magnetic shielding requires techniques such as gauge including atomic orbitals (GIAO) or individual gauge for localized (molecular) orbitals (IGLO) [91]. In contrast, the dominant Fermi contact terms for scalar

coupling yield a sum over the triplet state manifold in second order perturbation theory (Eqs. (5) and (6)). These FC terms are much simpler than the expressions for paramagnetic shielding, because the Dirac d-functions (e.g. in Eq. (5)) remove the quadruple summation over the atomic orbitals and the resulting integrals only involve s-type orbitals. Thus overall, the mathematical expressions for scalar FC coupling and shielding are very different, and it is hard to single out a particular term that would explain the experimental correlation between scalar coupling and 1H chemical shifts. As the experimental couplings and chemical shifts cover only a limited range, the observed linear correlations may be an approximation of a more complicated behavior. Indeed, it should be noted that in the DFT/FPT analysis of N–H/OaC H-bonds [92], the h3JNC 0 couplings follow a distance ˚ K1 rHO) (Eq. (4)), dependence of the form exp(K3.2 A 1 N ˚ K1 rHO) whereas the H chemical shifts have an exp(K2.0 A dependence. As the typically observed HBCs correspond to H/O distances within a rather small range of about ˚ , deviations from a linear distance dependence 1.8–2.1 A are not very pronounced for both exponentials. 2.4. H-bond dynamics 2.4.1. Dependence on fast protein backbone motions It is obvious that the experimentally observed HBCs represent time averages over the motions of H-bonds up to a time that is determined by the inverse of the coupling constants and the total time used for magnetization transfer, i.e. about 0.1–1 s. Recently, Sattler and co-workers [108] demonstrated that a significant part of the deviations between predicted and experimentally observed HBCs in proteins can be explained by fast protein backbone motions. The time dependence of H-bond geometries of the SMN Tudor domain, a 55-amino acid protein, was derived from 200-ps trajectories of molecular dynamics simulations. The values of h3JNC 0 were obtained from DFT/FPT calculations every 0.5-ps interval and then averaged over the entire trajectory. The improvement in the prediction of H-bond J-couplings is dramatic (Fig. 11): whereas RMS deviations of 0.35 or 0.19 Hz were obtained from DFT/FPT calculations based on the static X-ray or the lowest energy NMR structures, respectively, the rms deviation between experiment and the dynamically averaged prediction drops to only 0.04 Hz. This result clearly proves the highly dynamic nature of the H-bond network in proteins. Thus, the dynamics of H-bond geometry needs to be taken into account for any accurate prediction of HBCs and presumably also of any other physicochemical parameter that is related to the local backbone geometry. 2.4.2. Comparison to chemical exchange Classically, the dynamical behavior of biomacromolecular H-bonds is probed by the determination of hydrogen exchange (HX) rates with solvent [120], where the opening of the H-bond is usually assumed as a necessary condition

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Fig. 11. Experimental and calculated h3JNC 0 coupling constants in the SMN Tudor domain. The filled circles represent DFT/FPT predicted h3JNC 0 values averaged over a 200-ps MD trajectory. Open squares (triangles) denote h3JNC 0 predicted by DFT/FPT based on the SMN Tudor domain Xray (NMR) structure. Squares and triangles are connected by vertical lines to indicate the structural uncertainty. Adapted from Ref. [108].

for exchange. In studies on nucleic acids [36] and proteins [60,61,121], no particular correlation could be detected between the experimentally determined HX rates and the size of the H-bond J-couplings. A striking example is the temperature behavior of backbone H-bonds E64/Q2 and V17/M1 in ubiquitin [61] (Fig. 12), which are located at the ends of ubiquitin’s b5–b1–b2 b-sheet (Fig. 19). Over the temperature range from 5 to 65 8C, the h3JNC 0 couplings for both H-bonds weaken monotonically by 0.1–0.2 Hz and the 1 N H chemical shifts decrease monotonically by 0.2–0.3 ppm. As expected intuitively, the exchange rate for the amide hydrogen of residue E64 increases from 0.2 sK1 at 25 8C to 2.2 sK1 at 55 8C due to the thermal destabilization of the structure. In strong contrast, the exchange rate for V17 decreases from 0.8 to 0.3 sK1 over the same temperature range. This behavior was explained by a rearrangement of the ubiquitin structure at higher temperatures such that the amide of V17 becomes more protected by surrounding hydrophobic sidechains [61]. Apparently in this situation, the local weakening of H-bonds, as evidenced by the reduction of h3JNC 0 H-bond couplings, is not the limiting factor for the HX mechanism. Besides HX exchange with solvent, line broadening by conformational exchange gives further evidence for the dynamical behavior of H-bonding groups. For example, this is the case for guanosine amino protons, which are generally observed as very broad resonances due to intermediately fast rotations around the C–N bond. Also for this type of exchange, only a moderate reduction of h2JNN from w7 to w6 Hz was observed within the amino N–H/N H-bonds in guanosine quartets [36]. A similar observation was made for A–U base pairs in a dynamical region of an RNA structure, where the uridine imino proton (H3) resonances are

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Fig. 12. Comparison between temperature-induced changes in H-bond couplings and amide hydrogen exchange (HX) rates for residues E64 and V17 in human ubiquitin. (A) Temperature dependence of h3JNC 0 amide proton chemical shifts, and HX rates. (B) Selected regions of the water exchange HSQC experiment [257] at 25 and 55 8C showing the increased HX at higher temperature for E64, but the decreased HX for V17. The top rows (reference) show the sum of two subspectra with inverted or noninverted water magnetization during the water–1H/1HN mixing period. This represents the amount of non-exchanged 1HN magnetization. The bottom rows (exchange) show the difference of the two subspectra, representing the amount of exchanged water magnetization. Adapted from Ref. [61].

broadened beyond detection. In this case, h2JNN is also reduced by only about 1 Hz and the U–N3–H3/N1–A correlations were clearly observable by an adenosine H2-detected HNN-COSY experiment [122]. An explanation for these phenomena must be that open states of the H-bonds are not significantly populated even in the presence of such motions. Since the COSY experiments measure only the ensemble average of electron mediated magnetization transfer across the H-bond, the H-bond coupling values will not be affected very strongly provided that the average population of closed H-bonds is still high. 2.5. Correlations to other NMR observables H-bond couplings are not only correlated to the chemical shift of the H-bonding hydrogen nucleus, but also to a number of other NMR observables. Thus in N–H/N H-bonds of nucleic acid base pairs, the chemical shift of the 15N donor nucleus (typically between 140 and 160 ppm) increases with increasing strength of the h2JNN coupling, i.e. decreasing donor–acceptor distance, whereas the shift of the 15N-acceptor nucleus (typically between 190 and 230 ppm) decreases [27]. Similarly, the strength of the normal one-bond coupling 1JNH decreases with increasing h2JNN according to a linear correlation of the

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form 1JNHZ0.80!h2JNNK92.9 Hz [28]. These trends are understandable, since with decreasing N–N distances, the N–H/N H-bonds become more symmetric and the distinction between donor and acceptor disappears (see above). Thus donor and acceptor chemical shifts as well as the covalent one-bond 1JNH and H-bond h1JHN couplings converge to, respectively, similar values in the symmetric situation. An especially interesting correlation in proteins between h3 JNC 0 and the size of the covalent peptide group 1JNC 0 coupling was found by Juranic, Macura and co-workers [123–125]. The 1JNC 0 couplings are known to depend on secondary structure [126]. 1JNC 0 values are about K15 Hz in both a-helical and b-sheet conformations, whereas 1JNC 0 is stronger (more negative) in turn configurations. Due to their large size, these couplings are readily measurable also in larger proteins. The correlation between 1JNC 0 and h3JNC 0 (Fig. 13) can be described as [123]: 1

JNC0 ðk; k K 1Þ C 2:74 h3 JNC 0 ðk; mÞ K 0:88 h3 JNC 0 ðn; k K 1Þ C 15:6 Hz Z 0

(10)

where k, m, n indicate the residue numbers of the respective N and C 0 nuclei. According to Eq. (10) the weakening of the h3JNC 0 (k, m) coupling between residue k and m corresponds to a strengthening of the 1JNC 0 (k,kK1) coupling between residue k and kK1. This anti-correlation was ascribed to a competition for s-electron density at the position of the nitrogen nucleus k, which is necessary for efficient magnetization transfer by the Fermi contact mechanism for both couplings. Eq. (10) indicates that there is also a correlation between the h3JNC 0 (n,kK1) and h3JNC 0 (k,m) values of the two H-bonds (Nn–H/OaCkK1 and Nk–H/OaCm) that

originate from the same peptide group. An increase in one h3JNC 0 coupling leads to an increase in the other. This correlation is a clear manifestation of the polarizability of the peptide group, which leads to co-operative formation of H-bond networks in biomacromolecules [1]. As a consequence, connected H-bonds are stronger than isolated H-bonds. Indeed, such cooperatively connected H-bond networks could be identified from the combined analysis of 1 JNC 0 and h3JNC 0 couplings [124,125] as well as by detection of correlated changes in h3JNC 0 couplings which occur when a ligand binds to a protein [127] (see below). A special case of a connected H-bond network is commonly found in b-sheets, where the a-hydrogen of a residue preceding an H-bonding amide nitrogen is itself in H-bonding distance to the carbonyl oxygen H-bond acceptor of the amide nitrogen (Fig. 14). For such Ca–Ha/OaC configurations, the Ha chemical shift depends strongly on the Ha/O distance as shown in Fig. 3. Also for this situation, H-bond h3JCaC 0 -correlations between the 13Ca donor and the 13C nucleus of the carbonyl acceptor was determined recently [58]. Due to the geometry of these bifurcated HN/O/Ha H-bonds, an inverse correlation exists between the respective Ha/O and HN/O distances [128] (Fig. 14A). This can also be established very clearly by NMR from a comparison of the size of h3JCaC 0 and h3JNC 0 couplings, which connect Ca and N to the same carbonyl acceptor (Fig. 14B). The anti-correlation is statistically very significant (rZ0.99) and suggests a strongly correlated motion of the entire Ha–Ca–(CO)–N–H double-donor group relative to the carbonyl acceptor. 2.6. Electrostatic versus covalent character of H-bonds The observation of H-bond scalar couplings by NMR [13,14,19] and of anisotropy in the Compton scattering

Fig. 13. Linear correlation between 1JNC 0 and h3JNC 0 observed in ubiquitin. The data are plotted according to the expression 2.74 h3 JNC0 ðk; mÞZK1 JNC0 ðk; kC 1ÞC 0:88 h3 JNC0 ðn; kK 1ÞK 15:6 Hz derived from Eq. (10). The designation of residue numbers (k, n, m) and coupling constants is indicated on the right. The unusual behavior of residue F4 was explained by an unusual hydrogen bond of the carbonyl of residue I3 to the T14 hydroxyl group. Two points (dashed symbols) are from the reverse turns, and their placement in the plot is tentative. Adapted from Ref. [123].

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Fig. 14. Anti-correlation of strengths of Ca–Ha/OaC and N–HN/OaC H-bonds sharing the same carbonyl acceptor in protein G. (A) Ha/O/HN/O distance anti-correlation according to the X-ray structure 1IGD. Observed Ca–Ha/OaC correlations are indicated by filled circles. (B) h3JCaC 0 /h3JNC 0 anti˚ ; h3 JCaC0 Z 0:53 h3 JNC0 C 0:51 Hz: correlation. Data are labeled by the acceptor residue. Solid lines represent linear regressions: dOHAZK1.30 dOHNC4.96 A Adapted from Ref. [58].

profile of ordinary ice [129] have refueled discussions about Pauling’s original idea of a partially covalent nature of H-bonds [130,131] in a number of related news articles [132–136] as well as in the scientific literature. For the Compton experiment, it was shown subsequently that the anisotropy can be explained by a repulsive superimposition of molecular orbitals [137–139], which involves charge transfer from the acceptor to the donor [140]. For H-bond couplings on the other hand, most of the controversies seem to reflect confusion about the definition of covalency and the physical basis of the electronic magnetization transfer mechanism. Because the Fermi contact term often dominates, the observation of H-bond couplings implies a correlation between s-electron spins in the vicinity of coupled nuclei on both sides of the hydrogen bridge. However, this correlation per se does not necessarily indicate an attractive contribution to the total H-bond energy or a covalent character of the hydrogen bond. Many studies using NMR parameters to interpret the nature of H-bonds argue from properties computed from the ground state wavefunctions. However, this may be a questionable assumption, because the FC terms depend not only on the ground state but also on the triplet states, which enter the second order perturbation expression [63,114,141,142]. A ground state description is used in the extensive literature on the relationship between scalar couplings and many types of bond orders. Bond orders are closely associated with electron correlation features, which are of critical importance for the FC contributions. For example, a valence bond (VB) order description was introduced [64,143–145] to better understand mechanisms of coupling and explicit expressions were given for the direct and indirect contributions in terms of fragment bond orders. As applied to h3JNC 0 for example, such descriptions lead to dependencies on orbital interactions which are completely analogous to those in the LCAO/SOS method described above. A series of papers by Limbach and coworkers [19,20,94, 146] makes use of an empirical VB bond order model and an LCAO-MO analysis to interpret trans H-bond couplings in simple A–H/B systems. It is shown that various H-bond

properties such as coupling constants, chemical shifts and isotope effects can be approximated by products of empirical valence bond orders [94]. These authors [19,94] suggest that the overlap between the hydrogen s-orbital and orbitals on A and B leads to the substantial A,B coupling and provides evidence for a covalent nature of the H-bonds. They also note that failure to observe H/B couplings in some systems could be caused by a cancellation of terms with opposite sign rather than implying that the interaction is inherently electrostatic. An extensive analysis of the nature of H-bonds based on the ground state electron densities in protein H-bonds was carried out by Arnold and Oldfield [109]. These authors analyzed h3JNC 0 -couplings and 1HN chemical shifts in terms of Bader’s atoms-in-molecules (AIM) theory [147]. A good correlation was found between experimental h3JNC 0 data for protein G and AIM local energy densities. The 1HN chemical shifts also correlate with local energy densities, and especially in the region between ca. 7–12 ppm, the correlations of h3JNC 0 and d(1HN) with kinetic energy densities are very similar. For typical protein H-bonds with 1HN chemical shifts less than 12 ppm, the analysis of the energy densities at the bond critical point indicates that the h3JNC 0 couplings involve non-covalent interactions between the donor H and the acceptor O. A clear relation was found between the mutual penetration of non-bonding van der Waals shells and the magnitude of h3JNC 0 . For proton chemical shifts larger than about 12 ppm, partial covalent character (as defined by the energy densities at the bond critical point) begins to develop, which turns into a fully covalent shared-electron interaction above 20 ppm. Such strong chemical shifts are observable in low-barrier hydrogen bonds, which are postulated as transition states with significant covalent character in various enzyme catalytic events [148–151]. Wilkins and colleagues used the natural bond order (NBO) method [111,152] to analyze mechanisms for h2JNN and h1JHN scalar coupling in a DNA A–T base pair [110]. This analysis dissects the Fermi contact terms from the DFT/FPT calculations into contributions classified as Lewis (individual orbital contributions corresponding to the

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natural Lewis structure of the molecule), delocalization (resulting from pairwise donor–acceptor interactions), and residual repolarization (corresponding to correlation-like interactions). From this analysis the authors also note that an H-bond need not be covalent for finite scalar coupling, but they conclude that covalent character is an important factor for coupling in nucleic acid base pairs. Thus the steric repulsive interaction between the acceptor lone pair and the donor N–H s-bond is outweighed by the attractive hyperconjugative delocalization energy arising from the donation of electron density from the lone pair into the antibonding N–H s*-orbital. This mechanism provides a net stabilization of 8 kcal/mol. This theme is expanded in a subsequent NBO study [42] on the correlation between scalar couplings and H-bond stabilization energies for O/N–H/O/N H-bonds. Good linear correlations can be established between the total molecular interaction energy dE, the hyperconjugative delocalization energy as well as the h2JO/N–O/N couplings. For N–H/N H-bonds, the total H-bond stabilization dE can be calculated from h2JNN as dE/ (kcal/mol)Zh2JNN 1.09 HzK1K1.29. Thus a typical 7 Hz h2 JNN value corresponds to a total H-bond energy of 6.3 kcal/mol. Tuttle et al. [44] have also performed a detailed analysis of the NMR spin–spin coupling mechanism across H-bonds in proteins using the J-OC-PSP method [153,154]. These authors conclude that the coupling in protein N–H/OaC H-bonds (as modeled using formamide dimers) involves three effects: a dominant electrostatic effect, which is followed by steric exchange interactions, and least important are covalent effects associated with transfer of electronic charge. Electric field effects are expected to be largest for linear H/OaC arrangements in conformity with the largest magnitudes for h3JNC 0 . A covalent contribution is also observed as defined by charge transfer from an oxygen lone pair into the antibonding N–H s*-orbital. This covalent contribution increases with bending of the H-bond and ˚ and :H/OaC amounts to maximally 15% at rOHZ1.9 A (q2)Z1208. Pecul et al. [38] have used ab initio methods to define and calculate ground state complexation energies, scalar couplings and shielding constants for a series of simple, H-bonded dimers (X–H/Y). They find that the isotropic and anisotropic shielding constants of the proton engaged in the H-bond and the h1JHY and h2JXY couplings correlate well with the binding energy in spite of the diversity of the complexes under investigation. Del Bene, Bartlett and co-workers have also performed a series of extensive, ab initio studies of two-bond trans H-bond couplings [26,39, 155–157]. No correlation was found between the magnitude of the trans HBC and bond polarity, the absence of which was taken as an indication for covalent character [157]. To summarize, it might be said that the ‘covalent’ versus ‘ionic’ controversy really hinges on the exact definition of covalency. From the NBO analysis of the N–H/N [42,110] and J-OC-PSP analysis of the N–H/OaC H-bonds [44], it

seems clear that charge transfer occurs from the acceptor lone-pair to the donor antibonding X–H s*-orbital and that this transfer contributes to the stability of the H-bond. The exact size of this stabilizing contribution and of the total H-bond energy depends on the donor–acceptor geometry and increases for shorter distances. As the H-bond coupling size and the chemical shift of the H-bonding proton have similar (but not exactly identical) geometric dependencies, there is a correlation between all these quantities. Clearly, for very short H-bonds a fully covalent shared-electron character is expected, whereas for the typical H-bonds in the backbone of proteins or in nucleic acid base pairs the covalent contribution should only be on the order of few percent. As expressed in a discussion by Del Bene, Bartlett and co-workers [157], the mere observation of H-bond couplings is not a proof of any covalent character, but certainly, it does not exclude covalency either.

3. Applications of H-bond couplings 3.1. Structure determination The magnetization transfer by H-bond scalar couplings offers the possibility to identify directly the H-bond partner in a COSY experiment, such as the HNN-COSY for h2JNN correlations [13,14] or the long-range quantitative HNCO for h3JNC 0 correlations [15,16]. Clearly, the complicated process of NMR structure determination of biomacromolecules can benefit from this unambiguous detection of the macromolecular H-bond network. As the h2JNN coupling constants are larger and easier to detect than the h3JNC 0 couplings, the impact of this technique has been stronger for nucleic acid than for protein structure determination. 3.1.1. Nucleic acids The unequivocal establishment of canonical Watson–Crick base pairing [13,14] by h2JNN correlations across N–H/N H-bonds has become widespread in the determination of classical nucleic acid stem or stem-loop structures [158–173]. However, an especially high potential appears in the determination of H-bond networks involving unusual base pairs in more complicated nucleic acid structures such as higher-order triads to heptads [174]. It was shown initially [28,175] that correlations from U/T–15N3 or G1–15N1 to 15N7 nuclei across the N–H/N H-bonds of GA mismatch, Hoogsteen and reverse Hoogsteen base pairs are detectable by the simple HNN-COSY experiment. Meanwhile pulse sequences have been improved for the sensitive detection of HBCs in many other unusual base pairs. Most notable is the optimization for detection in the absence of directly observable H-bonded protons [30,122,176,177], for 15 N/15N H-bond partners with wide chemical shift separation [29,36], by the quenching of scalar relaxation [178], in the presence of overlap [179], or the detection of N–H/

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Fig. 15. H(CN)N(H) spectrum of the tetrameric DNA quadruplex d(GCGGAGGAT) containing a hexad A$(G$G$G$G)$A and the two tetrads G$G$G$G and G$C$G$C. The H8(G,u2):N2(G, u1), H8(G, u2):N4(C, u1), and H8(A, u2):N2(G, u1) cross peaks identify NH2/N7 hydrogen bonds within the tetrad and hexad motifs (shown above with the correlated nuclei indicated with gray circles) in the absence of detectable amino protons. The magnetization transfer pathway is indicated at bottom right. Two intranucleotide cross peaks, H2(A5/A8, u2):N6(A5/A8, u1), are also observed. Reprinted with permission from Ref. [194].

OaC H-bonds in nucleic acids by h3JNC 0 [36] and h4JNN [45] correlations. These techniques have found a number of applications in the unequivocal determination of unusual base pairing schemes [180–183]. In particular, Majumdar, Patel and colleagues have contributed enormously to the effort to obtain structural information on higher-order nucleic acids from H-bond scalar couplings. These workers have given many examples of complicated nucleic acid structures that are based on J-coupling detected H-bond networks [32,184–192]. Some of this work has been reviewed recently [193,194], and Fig. 15 shows an exceptionally striking illustration of the detection of the H-bond network in a DNA hexad, where all amino group N–H/N H-bonds were detected in a two-dimensional H–(C–N/H)–N relay experiment. A further application that should be mentioned in this context is the combination of J-detected RNA H-bond networks with a residual dipolar coupling based approach to fast assignment and structure determination in RNA structural genomics projects [195,196]. 3.1.2. Proteins In spite of the small size of h3JNC 0 couplings, the sensitivity of the long-range HNCO experiment is usually sufficient for the detection of backbone H-bond networks in

small to medium-sized proteins at millimolar concentration especially when deuteration and TROSY-techniques at higher fields are being used [37]. When such long-range HNCO H-bond correlations are detectable, the assignment is usually unique due to the excellent dispersion of resonances that results from the strong variation of both 13C 0 and 15N chemical shifts as a function of H-bond geometry [197]. A number of recent structure determinations have used h3JNC 0 - and also side-chain h2 JNN-based approaches for the unambiguous identification of H-bond networks in proteins [198–209]. Thus for example, H-bonds involving the sidechains of active site residues in superoxide dismutase [203] and in chorismate mutase [204] were detected by HBCs, which were hitherto unobserved in the respective X-ray structures. An attempt was also made for the direct determination of a complete structure based solely on the h3JNC 0 -detected H-bonds and on secondary chemical shifts of the small 64-residue a/b protein chymotrypsin inhibitor 2 [210]. This information was sufficient to generate structures that are as ˚ backbone RMSD from the crystal structure. close as 1.0 A However, the fold was not uniquely defined and several possible solutions were generated. Nevertheless, the correct fold could then be identified by knowledge-based scoring functions derived from structural databases.

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3.2. New NMR experiments based on H-bond magnetization transfer Besides the normal high-resolution NMR experiments for H-bond detection and quantification, a number of other experiments have been proposed, which provide additional structural and dynamical information based on the possibility of scalar transfer between donor and acceptor groups. Thus, H-bond lengths and local dynamics were characterized from cross-correlated relaxation experiments involving 15 N donor and acceptor multi-quantum coherences [211–213] and by the simultaneous detection of 15N donor and acceptor longitudinal relaxation rates [214]. The lengths of H-bonds have also been determined to very good accuracy by a comparison of one-bond 15Ndonor–1H and 1 H/15Nacceptor residual dipolar couplings [215], where transfer to the 15N acceptor was obtained by h2JNN. A further remarkable achievement is the detection of h2JNN correlations not only in the liquid, but also in the solid state by CP-MAS experiments [216,217]. 3.3. Variations in H-bond geometry as detected by H-bond couplings By their strong dependence on the H-bond geometry, the H-bond scalar couplings are one of the most sensitive parameters available to characterize subtle structural re-arrangements, which occur under changed conditions in biomacromolecules. A number of recent investigations have used the size of the h3JNC 0 couplings in proteins to monitor such changes in detail. Because the coupling constants are small, usually concentrations in the range of several millimolar and perdeuteration are required to obtain sufficiently precise data (reproducibility !0.02 Hz) even for small (!w10 kDa), well-behaved proteins [61,127]. Pressure variations up to 2000 bar were investigated by Gronenborn, Akasaka and coworkers for the protein G [218]. As monitored by h3JNC 0 the H-bond strength was found to increase in peripheral regions and to decrease in the protein center. Unfortunately sensitivity was severely limited in this investigation by the small (20 ml) volume of the pressure cell. Two studies have addressed the question of whether the variation of specific properties in homologous proteins can be correlated with patterns in the detected h3JNC 0 couplings. Thus Markley and coworkers [121] observed that mutants of the sweet protein brazzein exhibit distinct changes in h3JNC 0 detected H-bond patterns, which correlate with a variation in sweetness. All ‘sweet’ variants show the same h3JNC 0 correlations, whereas the ‘non-sweet’ variants lacked an H-bond in the center of the a-helix and a second one in the center of the b-sheet. The extent and strength of h3JNC 0 detected H-bond networks in hyperthermophile and mesophile rubredoxin analogues were compared by Prestegard and coworkers [219]. Despite a 83% sequence homology and a low RMSD for the backbone heavy atoms in the crystalline state, subtle, but definite changes

were identified in the detailed hydrogen-bonding patterns. The mesophile protein shows an increased number of hydrogen bonds in its secondary structure elements, whereas the hyperthermophile exhibits an overall strengthening of N– H/OaC hydrogen bonds in the loops involved at the metal binding site as well as evidence for an additional N–H/ S(Cys) hydrogen bond. The data suggest that the particular NMR hydrogen bond pattern found in the hyperthermophile leads to an increased stabilization at the metal binding pocket. In the following, we describe in more detail some of the efforts to follow changes in H-bonds by H-bond scalar couplings during peptide folding, ligand binding, thermal unfolding, chemical destabilization and hydrogen/deuterium exchange. 3.3.1. Detection of H-bond formation in peptide folding The first 20 residues of Ribonuclease A are known as the S-peptide and provide a model system for the study of peptide folding [220]. It is largely unfolded in aqueous solution, whereas the addition of trifluoroethanol (TFE) induces an a-helical structure that is very similar to the structure of the equivalent N-terminal part of the full Ribonuclease A [221]. In order to monitor the transition of the H-bonds from the unfolded to the folded state, h3JNC 0 correlations were followed in long-range HNCO experiments over a range of TFE concentrations from 0 to 90% [222]. Fig. 16A shows small regions of these long-range HNCO spectra that comprise a-helical NH(i)/OaC(iK4) corre0 0 lations for 0 residues F10 HN –A6C , E11HN –A7 C , and R12HN–A8C . Clearly, the individual H-bond correlations become stronger with increasing TFE concentration. For0 example, the cross peak corresponding to the R12HN–A8C H-bond is invisible in the spectrum at 10% TFE (marked by a dotted circle) and gradually increases in intensity for TFE concentrations of 20–90%. The variation in intensity is the result of a change in the ensemble average of the individual hydrogen bonds. Apparently, at low TFE concentrations, the individual backbone hydrogen bonds are only weakly populated such that the h3JNC 0 couplings are weak and the cross peak intensities are small. At higher concentrations of TFE, cross peaks corresponding to a-helical hydrogen bonds can be observed for a larger number of residues. Consistent with the close correlation between HBCs and amide proton chemical shifts (Fig. 2A), the HNCO crosspeaks also shift strongly towards high proton frequencies. At 60% TFE, sequential a-helical H-bond J-connectivities can be established for all amide hydrogens of residues A6 to M15. However, at and beyond the putative helix stop signal D16 no intramolecular backbone H-bonds are detected even at 90% TFE. A quantitative analysis of the individual h3JNC 0 coupling values yields a detailed picture of the folding transition. At the different TFE concentrations, the Hbonds of the S-peptide undergo a change from open to closed conformations. Since only single resonances are

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experiment correspond to time (and ensemble) averages over the different conformations. Since the exponential distance dependence of h3JNC 0 is very steep (Eqs. (2a) and (2b)), it can be assumed that in this mixture of conformations, mostly fully formed H-bonds contribute to the long-range HNCO cross peak intensities. An average value of K0.38 Hz was found for h3JNC 0 constants in ahelical H-bonds of (fully folded) ubiquitin [15]. Thus, to a first approximation one can assume that the population pi of an individual closed H-bond i in the S-peptide is given as jh3JNC 0 j/0.38 Hz Fig. 16B shows these individual H-bond populations pi as a function of residue number. The individual populations can be compared quantitatively to predictions of the Zimm–Bragg [223] and Lifson–Roig [224,225] theories of the coil to a-helix transition. The form of the measured population profile is close to the bell-shaped profile expected from these theories (Fig. 16B). The formation of the helix is co-operative. Once nucleation is achieved in the center (around residue E11), helix propagation is facile and progresses from this point towards the peptide ends. The h3JNC 0 NMR data provide residuelevel information about this process and corroborate the theoretical predictions.

Fig. 16. Observation of TFE-induced folding of the S-peptide by h3JNC 0 correlations. The sequence of the peptide is shown on the top. Boxed residues have a-helical h3JNiC 0 iK4 correlations at high TFE-concentrations. (A) Small sections of the long-range HNCO spectra (14.1 T) recorded on the S-peptide at 10, 20, 30, 45, 60 and 90% (v/v) TFE. Trans-H-bond correlations (h3JNC 0 ) are marked by the residue number of the HN group followed by the residue number of the acceptor carbonyl. The cross peak 0 corresponding to the R12HN–A8C H-bond is invisible in the spectrum at 10% TFE and marked by a dotted circle. (B) Fit of the Lifson–Roig model to experimental H-bond populations piZjh3JNC 0 j/0.38 Hz for different TFE concentrations. Measured data points are indicated by squares. Data corresponding to the fit of the Lifson–Roig theory with different average values of the H-bond weight w (1.37, 1.45, 1.54, 1.63, 1.67, and 1.77) are represented by continuous lines. Adapted from Ref. [222].

observed for all the nuclei of the S-peptide, the exchange between the different conformations is fast on the time scale of the chemical shifts (wmilliseconds). Therefore h3 JNC 0 values derived from the long-range HNCO

3.3.2. Ligand-induced strain The question whether ligand binding to a protein causes detectable changes in h3JNC 0 couplings was addressed in a study on the chicken c-Src SH3 domain [127]. This protein binds to the peptidic ligand RLP2 consisting of residues RALPPLPRY. The size of the h3JNC 0 correlations in the SH3 domain was determined in the presence and absence of the RLP2 peptide. The SH3/RLP2 binding interaction induces changes in h3JNC 0 values for a number of H-bonds, which clearly exceed the experimental reproducibility (Fig. 17A). The observed changes are highly correlated with regard to their location in the structure (Fig. 17B). For example, the changes in h3JNC 0 values indicate that ligand binding weakens many H-bonds between strands b3 and b4 and between strands b1 and b5. The most pronounced change occurs for the H-bond S55/D38, which becomes undetectable after ligand binding (Fig. 17A). Conversely, the H-bonds between strands b1, b2, and b3 become stronger for residues I31 and N33, which are located towards the C-terminus of strand b2. These changes can be rationalized by an induced fit mechanism in which hydrogen bonds across the protein participate in a compensatory response to forces imparted at the protein-ligand interface. Upon binding, the two leucineproline segments of the ligand (L3/P4 and L6/P7) intercalate between the three aromatic side chains of Y11, Y57, and W39 that protrude at the SH3 surface from strands b1, b5, and b3. This intercalation acts like a wedge between sheets b1/b5 and b3/b4 and induces a weakening of the H-bonds, which connect the respective b-strands. Translated into an H-bond lengthening by Eqs. (2a) and (2b), the detected

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Fig. 17. Ligand-induced strain in the hydrogen bonds of the c-Src SH3 domain detected by changes in the h3JNC 0 coupling constants. (A) Measured h3JNC 0 values and corresponding NO distances. The h3JNC 0 values measured for free (open circles) and RLP2-bound (filled circles) SH3 are plotted as a function of donor residue. Error bars correspond to statistical errors from repeated experiments. The scale on the right side of the plot is obtained from the exponential relationship of Eq. (2a) and reflects the corresponding distance between the N and O atoms in the H-bond. Secondary structural elements are mapped across the top. A trans-H-bond scalar coupling was not observed for residue S55 in the RLP2-bound form of SH3. The gray bar at this residue reflects an upper limit for the possible value of jh3JNC 0 j. (B) Propagation of strain across the SH3 5-stranded b-sheet is illustrated by a two-dimensional schematic diagram of changes in H-bond length. In order to visualize the H-bond network and protein ligand-interactions more clearly, the area within the dashed box is repeated in the upper part of the figure. Double-sided arrows indicate an increase, inward-pointing arrows a decrease, and dashed lines no change in H-bond length. Propagation of changes in H-bond length occurs via a domino-like mechanism through H-bond networks, where change of one peptide plane orientation alters the orientations of other peptide planes within the same network. The H-bonds in these connected networks are highlighted by gray boxes. Adapted from Ref. [127].

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changes in h3JNC 0 values correspond to an increase of the ˚. N–O distances of 0.02–0.12 A A second phenomenon is evident from the analysis of the changes in h3JNC 0 . The changes are not only correlated along the direction of b-strands, but also along H-bond networks connecting peptide planes across the entire b-sheet (Fig. 17B). This observation seems not surprising, since the repositioning of one peptide plane should influence the orientation of adjacent peptide planes in the H-bond network due to the attractive H-bond forces. Hence, the structural rearrangement at the protein-ligand interface is propagated in a domino-like effect through networks formed by H-bonded peptide planes. This is in complete agreement with the cooperative nature of H-bond formation detected by X-ray and neutron diffraction techniques [1] and the co-operativity of H-bond networks deduced from the combined analysis of h3JNC 0 and 1JNC 0 coupling constants [123–125]. 3.3.3. Temperature-induced changes The temperature-dependence of h2JNN couplings has been investigated for Watson–Crick base pairs in short DNA duplexes [226] and a 22-nucleotide RNA hairpin [227]. For base pairs in regular stem regions, the limited data of both studies are very similar and show a decrease of 0.5–0.8 Hz from the regular h2JNN values around 7 Hz for a temperature increase of 40 K. An about three-times stronger decrease was observed for a Watson–Crick UA base pair next to a non-canonical GU pair [227]. Thus the thermal expansion of H-bonds in nucleic acids is clearly detectable from the weakening of the h2JNN couplings. An extensive study on the temperature-dependence of HBCs in proteins and of many other NMR parameters describing H-bond properties was carried out for human ubiquitin [61]. A plot of the h3JNC 0 scalar couplings measured for temperatures from 5 to 65 8C is shown in Fig. 18. As for the nucleic acids, the temperature increase

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induces a decrease in the absolute size of H-bond coupling constants. Assuming a sole exponential dependence on the H-bond distance according to Eqs. (2a) and (2b), the derivative of ln jh3JNC 0 j with respect to temperature should be a measure of the linear thermal expansion coefficient ðaL Z rK1 NO vrNO =vTÞ of the hydrogen bond. Assuming an ˚ , aL can be estimated as average rNO value of 3.0 A aL zK

1 vlnjh3 JNC0 j 12 vT

(11)

Using this expression and slopes vlnjh3JNC 0 j/vT calculated from a linear regression of the data in Fig. 18, the average linear expansion coefficient aL amounts to (1.7G0.2)!10K4 KK1 for all backbone H-bonds observed in ubiquitin. No significant differences in aL were found for alpha-helical or beta-sheet conformations. The linear thermal expansion coefficient for H-bonds agrees remarkably well with values of (5.2G0.5)!10K4 KK1 for the volume expansion coefficient aV Z VK1 vV=vT z3aL for staphylococcal nuclease [228] and av values in the range of 5–6!10K4 KK1 for five other proteins [229]. Thus the entire protein and the H-bonds expand at the same rate, whereas thermal expansion coefficients for covalent bonds are orders of magnitude smaller, e.g. aL (diamond)Z1.2! 10K6 KK1 [230]. This is consistent with the notion that the thermal expansion of proteins is mostly due to the weakening of non-covalent chain–chain contacts such as H-bond and sidechain to sidechain interactions. It is also interesting to note that the relative changes of h3JNC 0 couplings in proteins (2!10K3 KK1) are very similar to the changes of h2JNN couplings in nucleic acids (w0.6/7/ 40 KZ2!10K3 KK1). As both couplings show very similar exponential distance dependencies (Figs. 4 and 5), this indicates that H-bonds in nucleic acids and proteins have a very similar thermal expansion behavior. A residue-specific analysis of the h3JNC 0 couplings in ubiquitin reveals that not all hydrogen bonds are affected to

Fig. 18. Temperature dependence of h3JNC 0 coupling constants in human ubiquitin versus amino acid sequence. For each H-bond, h3JNC 0 couplings are depicted in equidistant spacing from left to right for the five temperatures 5, 25, 45, 55, and 65 8C. Data are plotted on a logarithmic scale. Error bars correspond to rms deviations of separate experiments. Corresponding secondary structure elements are shown at the top. Reprinted with permission from Ref. [61].

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the trends of h3JNC 0 couplings and hydrogen exchange rates coincide and give definite evidence of the particular thermal instability of this region in ubiquitin. The instability can be rationalized by the fact that the N-terminal part of strand b5 is only H-bonded on one side, i.e. towards b1, and is not stabilized by any secondary or tertiary interactions towards the other side (Fig. 19). Breaking of the b5/b1 H-bonds isolates the b1/b2 hairpin to a large extent from the rest of the ubiquitin structure. Indeed the b1/b2 hairpin can exist as an autonomous unit without tertiary contacts in the A-state of ubiquitin (see below) as well as in peptides consisting of only the first 17 or 35 ubiquitin residues [231,232]. This example shows that the differential analysis of the NMR H-bond parameters can lead to verifiable conclusions on the folding and stability of entire proteins.

Fig. 19. Ubiquitin’s secondary structure topology and backbone H-bonds as observed by h3JNC 0 correlations. The H-bonds are depicted by a dotted line between the amide proton donor (filled hexagon) and the oxygen acceptor 0 (open hexagon). The double-sided arrow highlights the E64HN–Q2C h3 H-bond, for which the strongest temperature-induced changes in JNC0 are observed (see text). Adapted from Ref. [61].

the same extent by the thermal expansion. Thus specific regions can be identified that are the least thermostable. This is the case for the N-terminal region in the vicinity of the H-bond E64/Q2 connecting strands b5 and b1 (Figs. 18 and 19). On an absolute scale, the decrease in h3 JNC 0 by 0.17 Hz for this H-bond is the largest of all observed H-bonds over the temperature range from 5 to 65 8C (Fig. 18). The strong temperature effect on the H-bond E64/Q2 is also evident from a very strong increase in the amide proton exchange rate (Fig. 12) from 0.2 to 2.2 sK1 for the temperature change from 25 to 55 8C. Thus in this case,

3.3.4. Comparison of native and A-state ubiquitin Further details on the stability and interplay of ubiquitin’s secondary structure elements were obtained from a quantitative study of the H-bond network in ubiquitin’s A-state and a comparison to the native state [233]. Under A-state conditions (60% methanol, 40% H2O, pH 2) ubiquitin adopts a stable, partially folded structure, which differs substantially from the native state [234,235]. The structural changes are clearly detectable by h3JNC 0 correlations (Fig. 20). In the native state (Fig. 20A), the H-bond network corresponds to a five-stranded b-sheet and a single a-helix. In the A-state (Fig. 20B), the H-bond connectivities of the first anti-parallel b-sheet b1/b2 and of the a-helix are conserved, whereas all the H-bond correlations for residue 39–72 are of the type NH(i)/ OaC(iK4) and indicate that the C-terminal part changes into one long a-helical structure. This is consistent with an earlier analysis [235] based on heteronuclear chemical shifts and short- to medium-range NOEs. This analysis also

Fig. 20. Comparison between H-bonds detected in the native and A-state of ubiquitin. Two-dimensional maps representing the detected h3JNC 0 scalar correlations (filled diamonds) are shown for the native (A) and A-state (B). Secondary structure elements are indicated on the top and sides. (C) Sketch of the A-state structure with the independent secondary structure elements sheet b1/b2, helix a, and helix a 0 . These elements have no tertiary contacts and are connected by flexible linkers under A-state conditions (40% H2O, 60% CD3OH, pH 2). Adapted from Refs. [233, 235].

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Fig. 21. Comparison of h3JNC 0 constants and 1HN chemical shifts in the conserved a-helix of ubiquitin’s native (open circles) and A-state (filled diamonds). Filled diamonds connected to dotted lines indicate upper limits for jh3JNC 0 j in cases where no H-bond cross peaks could be detected. The backbone and H-bond structure of ubiquitin’s alpha helix (ball and stick) in the native state is shown on the right. H-bonds are shown as dark cylinders for strong h3JNC 0 values and as light cylinders for weak h3JNC 0 values. Weak h3JNC 0 values are found for H-bonds located at the exterior face of the helix. Adapted from Ref. [61,233].

showed that the A-state’s three secondary structure elements, i.e. b-sheet b1/b2 and helices a and a 0 , have no tertiary contacts and are connected by flexible linkers (Fig. 20C). It is revealing to compare the sizes of h3JNC 0 and the amide proton chemical shifts for both states of ubiquitin. Overall the number of detected H-bonds increases from 29 in the native state to 39 in the A-state. However, the h3JNC 0 values also become more uniform and their average size decreases from K0.50 to K0.27 Hz. Similar trends are visible for the chemical shifts. This is consistent with a more uniform and also more flexible structure in the A-state. One example of this behavior is shown for the conserved, amphipathic helix a in Fig. 21. In native ubiquitin (open symbols), very strong couplings (K0.4 to K0.7 Hz), associated with strong proton downfield shifts, are found for H-bonds K27/I23, I30/V26, Q31/K27 and E34/ I30. These H-bonds are located on the face of the a-helix that is directed towards the hydrophobic core (Fig. 21, right). Respectively, weaker couplings (K0.2 to K0.3 Hz) and lower frequency (upfield) proton chemical shifts are observed for H-bonds located at the exterior, water-exposed face of the helix. This pattern leads to strong periodicities over three to four residues in the h3JNC 0 values and 1HN chemical shifts. Such periodicities in the 1HN chemical shifts are often observed for amphipathic helices [54,55] and were postulated to result from different H-bond lengths on opposing helix sides [54]. The close correlation between 1HN shifts and h3JNC 0 indeed proves that the H-bonds of ubiquitin’s a-helix are shorter on the interior

side and that the helix is bent around the hydrophobic core by about 98 [61]. In strong contrast to the native state, no such strong periodicities are observed in the A-state and both h3JNC 0 and 1HN shifts are considerably reduced (Fig. 21, filled symbols). Thus in the A-state, the H-bonds have comparable strengths across the entire helix and the helix bend is released. Apparently, the change from the strongly asymmetric hydrophobic/hydrophilic contacts on both helix sides in the native state to the homogenous methanol/water environment in the A-state leads to a straight and symmetric helix structure. 3.3.5. H/D-isotope effects As a final example of a differential investigation on H-bond coupling constants, we mention the effect of 1H/2H exchange of the H-bonding hydrogen nucleus. The structural effects of isotopic exchange are commonly described in terms of changes in bond vibrations. The lower zero-point vibrational energy of deuterated compounds together with the anharmonicities of bond potentials leads to a shortening of covalent D–X bonds on the order of a few hundredths of an Angstrom as compared to H–X bonds [146,236]. This phenomenon is clearly observable in NMR as a chemical shift change of neighboring nuclei, e.g. the well-described one-bond isotope shift of the X-nucleus [236,237]. For H-bonds the shortening of the covalent bond length upon deuteration is usually accompanied by a comparable change of the donor–acceptor distance. A lengthening of the donor–acceptor distance upon deuteration is known as the classical Ubbelohde effect [146,238,239], which has been

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HBCs upon deuteration is of similar order (5–10%) in proteins and nucleic acids. In addition, the 1HN/2HN exchange also increases the absolute size of 1JNC 0 couplings in proteins by 0.25G0.07 Hz and increases the shieldings of the peptide group 15N and 13C 0 nuclei by about 0.65 and 0.08 ppm, respectively. These isotope effects are consistent with a reduction of H-bond donor–acceptor overlap, a shortening of the covalent N-hydrogen bond length and a consequent increase of electron density around the nitrogen nucleus. It is difficult to determine the exact differences of H-bond heavy atom donor–acceptor distances from the isotope effects on H-bond couplings, because the couplings report primarily on the hydrogen-acceptor orbital overlap and the 1HN/2HN exchange influences both the covalent N–H and the H/acceptor lengths. However, the observed reductions in the H-bond couplings are not inconsistent with an expected increase of the H/acceptor lengths on the order ˚ , that is based both on the observed increase of 0.04–0.06 A donor–acceptor distances in small molecule X-ray structures and a reduction of the N-hydrogen bond length of ˚ upon deuteration [243]. about 0.02–0.03 A Even though the Ubbelohde effects are small, their energetic importance should not be underestimated. Using a simple estimate of the Coulomb energy, an increase by ˚ in N–O and a decrease by 0.03 A ˚ in N–H distances 0.03 A 1 N 2 N due to H / H exchange, would destabilize a protein backbone H-bond by 22 cal/mol [243]. Therefore, deuteration of all H-bonds in a protein should lead to considerable differences in the total internal energy and is expected to contribute to the observed destabilization in D2O [244,245]. Fig. 22. Effect of 1H/2H exchange on h2JNN and h3JNC 0 in biomacromolecules. (A) 15N3 signals of thymidine in selectively 15N-labelled d(CGCGAATTCGCG)2 recorded at 14.1 T showing the splitting by h2 JNN to the adenosine 15N1-acceptor in H2O and D2O. Adapted from Ref. [226]. (B) Comparison of h3JNC 0 values obtained for deuterated (D2O) and protonated (H2O) backbone H-bonds in human ubiquitin. The dashed line corresponds to an average offset hh3JNC 0 (H2O)–h3JNC 0 (D2O)i of K0.03 Hz. Adapted from Ref. [243].

observed in many X-ray crystallographic studies of small molecules, e.g. [238,240]. However, gas-phase studies show that also shortening of the donor–acceptor distance can occur due to a coupling of bending and stretching modes [241,242]. Very little is known about such Ubbelohde effects in biomacromolecules. Due to their dependence on the donor–acceptor overlap, H-bond couplings should be sensitive to such effects. A study on a limited number of H-bonds in selectively labeled double-stranded DNA reported the reduction of H-bond h2JNN (w7 Hz) couplings after H2O/D2O solvent exchange [226] by about 0.3–0.4 Hz (Fig. 22A). A recent study on the effect of the deuteration of protein backbone H-bonds [243] showed that 1HN/2HN exchange also decreases the absolute size of h3JNC 0 on average by 0.03G0.03 Hz (Fig. 22B). Thus, the relative change of

4. Conclusion This review covers the various theoretical and experimental insights into biomolecular H-bonds in biomacromolecules that were obtained from H-bond scalar couplings during the last few years. A detailed understanding of geometric factors that determine the size of couplings, chemical shifts and bond energies has been achieved by quantum-chemical methods. Consistent with experimental results, linear geometries and short donor–acceptor distances correspond to the strongest couplings. Much of this can be rationalized by simple LCAO/SOS models, which explain the couplings from a dominant contribution of the overlap between the hydrogen and the acceptor orbitals. It is clear that there is no simple one-to-one relation between H-bond couplings and H-bond energies. However, for the common biomolecular N–H/N and N–H/OaC H-bonds in nucleic acids and proteins, larger absolute size couplings usually correspond to larger bond energies. The observation of the H-bond couplings alone is not a sufficient condition for a covalent character of H-bonds, since repulsive interactions can also lead to electron correlation and scalar couplings [17,246].

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Nevertheless, for the common biomolecular H-bonds, small parts of the attractive forces and of the couplings seem to result from charge transfer of the acceptor lone pair to the anti-bonding s*-orbital of the donor group. These contributions could be called covalent. Although this controversy of electrostatic vs. partially covalent character is essentially a semantic one, the charge transfer and deviations from simple electrostatics could have implications for the correct parameterization of H-bonds in molecular dynamics force fields. Enhancements, like the inclusion of fluctuating charges [247] may need to be considered to model charge transfer and H-bond polarization. A number of practical applications have arisen from the possibility of achieving H-bond-mediated scalar magnetization transfer. Chiefly, these are the unambiguous detection of H-bond networks in nucleic acids and to a lesser extent in proteins for structure determination. Other applications include the creation of multi-quantum coherences across H-bonds for relaxation and weak alignment studies. A crucial question is whether H-bond couplings have given new insights into the forces that hold macromolecules together. The couplings have revealed details of the formation of individual H-bonds during protein folding and have made it possible to quantify changes in H-bond networks as a result of ligand binding and under variations of pressure, temperature, and other parameters. A very fundamental result is that H-bond couplings can only be predicted accurately when the time-dependent variations of H-bond geometry resulting from the dynamics of biomolecules are taken into account [108]. Apparently, the H-bond geometries of static structures do not describe H-bonding truthfully. A further essential aspect is H-bond cooperativity. The co-operativity is evident from the correlation of the coupling size across H-bond networks and from the correlated changes of the couplings under perturbations. Thus the highly dynamic and cooperative character of the canonical H-bonds in biomacromolecules is directly and individually observable by H-bond couplings.

Acknowledgements We gratefully acknowledge our collaborators Drs Andrei Alexandrescu, Andrew Dingley, Juli Feigon, Linda Nicholson for their enthusiasm and support. We also would like to thank Drs Ad Bax, Rafael Bru¨schweiler, Daniel Ha¨ussinger, Bertil Halle, Burkhart Luy, Sebastian Meier, Markus Meuwly and many other colleagues who have contributed by many valuable suggestions and critical comments. This work was supported by SNF grant 3100-061757.00.

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