Impact of nucleic acid self-alignment in a strong magnetic field on the interpretation of indirect spin–spin interactions
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Heteronuclear and homonuclear direct (D) and indirect (J) spin–spin interactions are important sources of structural information about nucleic acids (NAs). The Hamiltonians for the D and J interactions have the same functional form; thus, the experimentally measured apparent spin–spin coupling constant corresponds to a sum of J and D. In biomolecular NMR studies, it is commonly presumed that the dipolar contributions to Js are effectively canceled due to random molecular tumbling. However, in strong magnetic fields, such as those employed for NMR analysis, the tumbling of NA fragments is anisotropic because the inherent magnetic susceptibility of NAs causes an interaction with the external magnetic field. This motional anisotropy is responsible for non-zero D contributions to Js. Here, we calculated the field-induced D contributions to 33 structurally relevant scalar coupling constants as a function of magnetic field strength, temperature and NA fragment size. We identified two classes of Js, namely 1JCH and 3JHH couplings, whose quantitative interpretation is notably biased by NA motional anisotropy. For these couplings, the magnetic field-induced dipolar contributions were found to exceed the typical experimental error in J-coupling determinations by a factor of two or more and to produce considerable over- or under-estimations of the J coupling-related torsion angles, especially at magnetic field strengths >12 T and for NA fragments longer than 12 bp. We show that if the non-zero D contributions to J are not properly accounted for, they might cause structural artifacts/bias in NA studies that use solution NMR spectroscopy.
KeywordsNucleic acid Self-alignment Magnetic susceptibility Scalar coupling Dipolar coupling Karplus equation
The major sources of structural information from NMR measurements of biomolecules in isotropic solution are nuclear Overhauser enhancements (NOEs), which provide information about short (<5 Å) inter-proton distances, and indirect spin–spin interactions that are characterized by scalar coupling constants (J), which provide information about torsion angles (Roberts 1993; Wijmenga and van Buuren 1998). In addition to these two sources, direct spin–spin interactions (D), known as (residual) dipolar couplings (RDCs), reveal the relative orientations of inter-nuclear vectors with respect to the direction of the external magnetic field. The direct spin–spin interactions can be measured under conditions where the studied molecules are at least partially aligned with respect to the magnetic field. The alignment typically requires supplementation of NMR buffers with some type of alignment media, such as bicelles, nonionic polymers, Pf1 bacteriophages, anisotropically compressed gels or covalent modifications of investigated molecules with paramagnetic tags (Bax and Tjandra 1997; Clore et al. 1998; Rückert and Otting 2000; Sass et al. 2000; Su et al. 2008; Tjandra and Bax 1997; Tycko et al. 2000; Wöhnert et al. 2003; Zweckstetter and Bax 2001).
For proteins, NMR structure determination is predominantly based on inter-proton NOEs. However, the structure determination of nucleic acids, particularly axially symmetric and elongated NA constructs, strongly depends on the use of direct and indirect spin–spin interactions due to the inherently low proton density and the absence of long-range contacts (Zhou et al. 1999).
In contrast to both NOEs and residual dipolar couplings, for which analytical relationships between the respective observable and geometry exist, the interpretation of scalar couplings typically relies on the quantitative relationship between the local geometry and the corresponding scalar coupling, established by means of (empirical) parameterization, i.e., by measurement of Js or calculation of Js using methods of quantum chemistry on a set of model molecules with known geometry. At present, approximately 33 distinct scalar coupling constants can be employed for the conformational analysis of nucleic acids. Specifically, the 3JH1′H2′, 3JH1′H2″, 3JH2′H3′, 3JH2″H3′, 3JH3′H4′, 3JH1′C3′, 3JH4′C2′, 3JH3′C1′, 3JH2′C4′, 2JH2′C1′, 2JH3′C2′, 2JH2′C3′, 2JH3′C4′, 1JH3′C3′, and 1JH2′C2′ couplings and their combinations are well established as good indicators of sugar conformations (Wijmenga and van Buuren 1998). Heteronuclear one-bond (1JC1′H1′) and three-bond scalar couplings, namely, 3JH1′C2/C4 and 3JH1′C6/C8, allow for the determination of the relative orientation of the base with respect to the sugar moiety via a description of the glycosidic torsion angle χ (Fonville et al. 2012; Ippel et al. 1996; Munzarova and Sklenar 2003; Trantirek et al. 2002). The use of scalar couplings is particularly important for the characterization of the phosphate backbone of NA, where the quantitative relations are established between the following: 3JC4′P, 3JH5′P, 3JH5″P, and 4JH4′P and the torsion angle β; 3JH4′H5′ and 3JH4′H5″ and the torsion angle γ; and 3JH3′P, 3JC2′P′, and 3JC4′P and the torsion angle ε (Roberts 1993; Wijmenga and van Buuren 1998). In addition to their quantitative interpretation in terms of the local structure, the scalar couplings can be used to identify the long-range structural features of nucleic acids. Non-zero values of the 1hJNH and 2hJNN scalar couplings can be used as direct experimental evidence of a hydrogen bond and as a reporter of the base-pairing pattern (Alkorta et al. 2008). Similarly, non-zero values of 3JPC and 2JPH across the P–O···H–C link report on the presence of specific structural features of nucleic acids, such as the turn-kink motif (Sychrovský et al. 2006).
Nevertheless, the interest in the self-alignment phenomenon was renewed with the availability of NMR spectrometers operating at high-magnetic field strengths, which provided sensitivity and resolution amiable to longer NA fragments (up to 40 bp). Between 2001 and 2004, several groups independently demonstrated that the magnetic susceptibility of nucleic acids is capable of producing sufficient self-alignment in dilute solutions of oligonucleotides of moderate lengths to measure the magnetic field-induced RDCs (fiRDCs) that can be employed for NA structural analysis (Al-Hashimi et al. 2001a, c; Bryce et al. 2004; Kung et al. 1995; van Buuren et al. 2004; Zhang et al. 2003). These works provided an important proof-of-concept and showed that RDCs can be obtained under conditions that do not perturb the studied system by the use of either additives (alignment media) or NA fragment paramagnetic tagging. However, the magnitudes of the RDCs obtained from the self-alignment were several times smaller than those routinely achievable using standard alignment media. The considerable relative errors in measuring small fiRDCs have a negative influence on the quality of NA structure refinement. This limitation and the fact that the determination of the fiRDC requires measurements at least two different magnetic field strengths are the primary reasons why NA self-alignment is not routinely used to characterize nucleic acid structure.
In the past, all studies have focused on the potential of NA self-alignment to measure fiRDCs in a non-invasive manner, and the self-alignment phenomenon has not been studied in detail with respect to the interpretation of scalar couplings. The direct (D) and indirect (J) spin–spin interactions have the same form of Hamiltonian, making them inseparable within a single NMR experiment; thus, the scalar coupled spectra should always be treated as spectra “contaminated” by the dipolar contributions. In some cases, this contamination can severely taint the structure determination process. The aim of this paper is to draw attention to the consequences of NA self-alignment on the interpretation of indirect spin–spin interactions in terms of NA structure and to identify problematic situations where the self-alignment might result in structural artifacts.
Materials and methods
Quantum chemical calculations
DFT calculations of magnetic susceptibilities were performed on each nucleic acid base (A, G, C, T, and U) using the B3LYP Exchange Correlation Functional (Becke 1993) as implemented in Gaussian 09, Revision A.02 (Frisch et al. 2009). The starting geometries of the five aforementioned nitrogenous bases correspond to idealized geometries of NA bases (Clowney et al. 1996). Subsequently added hydrogen atoms were optimized at the B3LYP/6-31G** level of theory and included the implicit solvent (CPCM) described within the polarizable continuum model (Miertuš et al. 1981; Miertus and Tomasi 1982). The ensuing GIAO calculations (Cheeseman et al. 1996; Wollinski et al. 1990) of the base χ magnetic susceptibility tensors were performed using the Pople triple-zeta-valence basis set 6-311++G(3df,3pd), with multiple polarizations used on all atoms (Ditchfield et al. 1971). The resulting computed nucleobase magnetic susceptibility tensors were expressed in the form of 3 × 3 symmetric matrix that is the sum of an isotropic (zeroth rank) and an anisotropic symmetrical (second rank) tensor.
Molecular anisotropy of magnetic susceptibility
Experimental validation of the reconstruction approach based on nucleobase-specific magnetic susceptibilities can be found in Bryce et al. (2004).
Results and discussion
Unlike the RDCs induced by orienting media that are evaluated by comparing the spectra measured in isotropic and orienting solutions, the magnetic field-induced dipolar couplings can never be completely switched off. If not taken into account, the fiRDCs might become a source of systematic errors. To identify the scalar couplings whose quantitative interpretation is potentially biased by NA self-alignment we simulated the magnetic field-induced dipolar contributions to all currently used J-coupling constants for NA structural analysis as a function of the strength of the external magnetic field (9.4, 11.8, 22.3, and 28.1 T), the temperature (278, 293, and 308 K), and the length of the NA fragment (12, 24, and 36 bp) for the two most common nucleic acid motifs, namely A-DNA (A-RNA) and B-DNA. For 15 of 33 calculated Js, the magnetic field-induced RDC contributions were found to exceed the typical experimental error in J-coupling determinations by a factor of two or more (Tjandra et al. 1996; Wang and Bax 1996; Yao et al. 2009). These J couplings are potential sources of interpretational bias, and they can be formally divided into two different categories: (1) 1JCH and (2) 3JHH. The effect of self-alignment on the quantitative interpretation of these J couplings in terms of structure was analyzed in detail (vide infra). For a complete overview of the simulated RDC contributions, see Supplementary Information—Tables S2 and S3.
Effect of self-alignment on the interpretation of 1JCH
For other structurally important 1JCHs, such as 1JC3′H3′ and 1JC2′H2′ that provide information about the conformation of the sugar ring or 1JH5′C5′ and 1JH5″C5′, which are used for stereospecific assignment of the H5′ and H5″ resonances, the situation is analogous to the 1JC1′H1′. In general, the absolute values of the corresponding fiRDCs increase with increasing magnetic field strength as well as with increasing nucleic acid fragment sizes (Supplementary Information—Tables S2 and S3). The interpretation of 1JC3′H3′ and 1JC2′H2′ is based on the observation that for N-type sugars, the 1JC2′H2′ and the 1JC3′H3′ values are approximately 8 Hz higher and lower, respectively, than their values in S-type sugars (Ippel et al. 1996). For 1JC2′H2′ and 1JC3′H3′ in both N-type and S-type sugars, the corresponding fiRDCs are significant, and they have comparable magnitudes and signs (Supplementary Information—Tables S2 and S3). Consequently, the fiRDCs for those Js do not change their relative differences and do not affect their structural interpretation. The situation with the fi1DC5′H5′/H5″ demonstrates that fiRDC might even, in certain cases, facilitate the NA structure determination process. The 1JH5′C5′ and 1JH5″C5′ values are being used for the stereospecific assignment of H5′ and H5″. The assignment is based on fact that 1JH5′C5′ is generally larger than 1JH5″C5′ (Ippel et al. 1996). The presence of the fi1DC5′H5′ and fi1DC5′H5″ contributions makes the difference between the 1JH5′C5′ and 1JH5″C5′ values even more pronounced because the absolute magnitudes of fi1DH5′C5′ and fi1DH5″C5′ are comparable, whereas their signs differ (Supplementary Information—Tables S2 and S3). Taken together, these results show the following: For fi1DC1′H1′, disregarding the dipolar contribution is always connected with interpretational bias. In contrast, the fiRDC contributions to 1JC3′H3′ and 1JC2′H2′ as well as those to 1JH5′C5′ and 1JH5″C5′ is not expected to impair the corresponding apparent 1JC–Hs interpretation.
Effect of self-alignment on the interpretation of 3JHH
2/3/4JCH and 2/3/4JHP fiRDC
In the process of J coupling interpretation the errors from fiRDCs, which are the subject of the present study, will add to the other known errors such as those due to neglect of J averaging by internal motion and those due to passive spin-relaxation, referred to as spin-flip(s) (Harbison 1993; Bruschweiler and Case 1994; Vogeli et al. 2008). The spin-flip phenomenon comes for the interference between J-coupling and cross-relaxation and its primary effect is reduction in apparent J. As the effect of spin flip is indirectly proportional to T1, the respective error is most significant for small NA fragments (studied at low magnetic fields) and decreases rapidly with the molecular size (particularly when studied at high magnetic fields). For example, the error in 3JHH coupling due to spin-flip reaches up to 1 Hz for 12–14 bp NA fragment while the corresponding error will be smaller than 0.1 Hz for 36 bp NA fragment (Harbison 1993). Similarly to the error due to spin flip, the averaging of J by internal motion leads to reduction in apparent J. For structured parts of NA, the errors due to the neglect of motional J averaging are expected to be smaller than 1 Hz (Bruschweiler and Case 1994; Trantirek et al. 2002; Vokacova et al. 2009). Altogether, the neglect of fiRDC contribution appears to be one of the most significant sources of bias in quantitative interpretation of J couplings, especially for medium to larger size nucleotides studied in high magnetic fields.
The fiRDCs can serve as both an important source of information on the structure and dynamics as well as, if not properly accounted for, a source of structural artifacts/bias in the solution NMR spectroscopy of nucleic acids. Although the usefulness of the fiRDCs for the structural characterization of nucleic acids and their complexes was demonstrated by number of studies (Al-Hashimi 2013; Al-Hashimi et al. 2001b; Zhang and Al-Hashimi 2008), the contributions from fiRDCs to apparent J couplings are among the current most overlooked sources of artifacts in the structure determination of nucleic acids. With recent advances in NMR instrumentation as well as in the automation of the nucleic acid structure determination process, NMR spectroscopy is becoming accessible to a growing community of non-expert users employing pre-programmed “black-box” routines for the interpretation of acquired primary NMR data. The corrections for the fiRDCs are not routinely implemented in the current generation of programs for automated nucleic acid structure determination; thus, an unquestioning use of these programs might adversely affect the quality of NA structures derived from solution NMR data. The situation is expected to worsen in the future with the upcoming generations of NMR spectrometers operating at magnetic fields of up to 28 T, where the fiRDC contributions to apparent J couplings will in many cases become comparable to or even exceed the modulation of the J couplings due to the local conformation. At the currently commonly available magnetic fields (11–17 T), disregarding the fiRDC contributions when interpreting J couplings could in principle be tolerated for the production of low-resolution structural models based on semi-quantitative NMR data; however, properly accounting for fiRDCs appears to be essential for the production of precise and accurate nucleic acid structures. Moreover, accounting for fiRDC contributions is particularly important in applications involving empirical (re)-parameterizations of Karplus equations. Studies that correlate experimental J couplings with the J couplings from quantum chemical calculations, especially studies aiming at benchmarking the calculation methods, must pay particular attention to the fiRDC-induced contamination of J.
This work was supported by the Czech Science Foundation (13-28310S, 13-27676S, 16-10504S), by the Grant M200551205 from Academy of Sciences of the Czech Republic, R&D development grant from INSTRUCT and the Project “CEITEC” (CZ.105/1.100/02.0068). LT was supported by a career development grant from the European Organization for Molecular Biology (IG2535) and an ECOPOD grant from the Marie-Curie Re-integration program.
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