Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Biomol NMR. Author manuscript; available in PMC 2010 June 1.
Published in final edited form as:
PMCID: PMC2782637

Empirical Correlation Between Protein Backbone 15N And 13C Secondary Chemical Shifts and its Application to Nitrogen Chemical Shift Re-referencing


The linear analysis of chemical shifts (LACS) has provided a robust method for identifying and correcting 13C chemical shift referencing problems in data from protein NMR spectroscopy. Unlike other approaches, LACS does not require prior knowledge of the three-dimensional structure or inference of the secondary structure of the protein. It also does not require extensive assignment of the NMR data. We report here a way of extending the LACS approach to 15N NMR data from proteins, so as to enable the detection and correction of inconsistencies in chemical shift referencing for this nucleus. The approach is based on our finding that the secondary 15N chemical shift of the backbone nitrogen atom of residue i is strongly correlated with the secondary chemical shift difference (experimental minus random coil) between the alpha and beta carbons of residue i-1. Thus once alpha and beta 13C chemical shifts are available (their difference is referencing error-free), the 15N referencing can be validated, and an appropriate offset correction can be derived. This approach can be implemented prior to a structure determination and can be used to analyze potential referencing problems in database data not associated with three-dimensional structure. Application of the LACS algorithm to the current BMRB protein chemical shift database, revealed that nearly 35% of the BMRB entries have δ15N values miss-referenced by over 0.7 ppm and over 25% of them have δ1HN values miss-referenced by over 0.12 ppm. One implication of the findings reported here is that a backbone 15N chemical shift provides a better indicator of the conformation of the preceding residue than of the residue itself.

The difference between the chemical shift (δ) of an amino acid and its random coil chemical shift (δcoil) is the secondary chemical shift (Δδ), which is widely used in protein secondary structure prediction (Wishart and Sykes 1994; Eghbalnia et al. 2005) and backbone dihedral angle constraint estimation (Cornilescu 1999). Values for Δδ13Cα, Δδ13Cβ, Δδ13C′, Δδ1Hα, Δδ1HN and Δδ15N assigned to a given residue generally are combined and used to estimate the secondary structure propensity of the residue or to derive geometrical constraints on the backbone torsion angles. Because chemical shift values are relative to a standard compound, the accuracy of such predictions depends critically on whether the chemical shift referencing is consistent and follows standard norms. The accuracy of back calculated chemical shifts from high-resolution protein structures is sufficiently accurate that it can be used to assay chemical shift referencing accuracy. By back calculating chemical shifts from proteins with high-resolution structures and comparing them to chemical shifts deposited in the BioMagResBank (BMRB) (Seavey et al. 1991; Ulrich et al. 2008), it was found that up to 20% of δ13C and 30% of δ15N were improperly referenced (RefDB) (Zhang et al. 2003). It is of importance also to detect and correct possible referencing errors in protein NMR data sets that are not associated with three-dimensional structures (more than 60% of the data sets in BMRB) (Wang and Wishart 2005). Approaches to this problem have been based either on secondary structure prediction tools (Wang and Wishart 2005; Marsh et al. 2006; Ginzinger et al. 2007) or on linear relationships between Δδ13Ciα,Δδ13Ciβ,Δδ13Ci, or Δδ1Hiα and (Δδ13CiαΔδ13Ciβ) (Wang et al. 2005). The latter approach, called LACS (linear analysis of chemical shifts) (Wang et al. 2005), utilizes “backbone geometry driven” linear correlations among chemical shifts themselves, instead of relying on secondary structure prediction. The performance of CheckShift (Ginzinger et al. 2007), the most recent approach based on predicted secondary structure, is claimed to equal that of LACS, under conditions of good secondary structure prediction accuracy. Whereas the initial LACS implementation (Wang et al. 2005) provided re-referencing only for δ13C (and δ1Hα), CheckShift can be used to determine re-referencing offsets also for δ15N.

We report here the extension of LACS to the re-referencing of δ15N (and δ1HN) chemical shifts. Whereas we earlier found linear relationships between Δδ13Ci (and Δδ1Hiα) and (Δδ13CiαΔδ13Ciβ), our recent statistical examination shows that linear relationships actually hold between Δδ15Ni (and Δδ1HiN) and (Δδ13Ci1αΔδ13Ci1β), where i is the residue whose chemical referencing is examined and i-1 is the index of the preceding residue. Correlations had been reported previously between Δδ15Ni (and Δδ1HiN) and øi and ψi-1 (Le and Oldfield 1994), and between øi and ψi and (Δδ13CiαΔδ13Ciβ) (Spera and Bax 1991; Wang et al. 2007).

The random coil chemical shift difference (δ13Ccoilαδ13Ccoilβ) of each residue type, statistically derived from our maximum entropy analysis (Wang et al. 2007) and consistent with experimental observations (Wishart et al. 1995), was used to calculate (Δδ13CiαΔδ13Ciβ). Δδ15Ncoil for each residue type X was taken from the experimental data for the hexapeptide Gly-Gly-X-Ala-Gly-Gly, with the neighboring effect of X on Δδ15Ncoil of Ala corrected by using data provided in the same report (Wishart et al. 1995). Neighboring effects of X on Gly also have been determined experimentally from data on shorter peptides Gly-Gly-X-Gly-Gly (Schwarzinger 2001), and the corrections derived from the two sets of data are similar. Nearest neighbor corrections also have been derived statistically from database information (Wang and Jardetzky 2002), but these values are less consistent with experiment, probably because they were based on limited data. Ideally, neighboring effects should be measured from all 400 Gly-Gly-X-Y-Gly-Gly hexapeptides. Lacking this information, we made the simplifying assumption that the effect of X on Δδ15Ncoil of other residue types is the same as it is on Ala.

A different set of random coil chemical shifts, determined at pH of 2.3 for short peptides Gly-Gly-X-Gly-Gly (Schwarzinger et al. 2000), which takes account the significant changes in the (δ13Ccoilαδ13Ccoilβ) values of Asp and Glu near and below their side chain pKa values (3.8 for Asp, and 4.1 for Glu), has been used for proteins at pH < 4.

For each BMRB entry, a robust fitting procedure (Wang et al. 2005) was used to linearly fit Δδ15Ni with (Δδ13CiαΔδ13Ciβ) or (Δδ13Ci1αΔδ13Ci1β). The distributions of the fitted slopes are shown in Figure 1. The mean values (slopes) of these two distributions show that Δδ15Ni is statistically four times more sensitive to (Δδ13Ci1αΔδ13Ci1β) (Gaussian distribution N(−0.4, 0.20)) than to (Δδ13CiαΔδ13Ciβ) (Gaussian distribution N(−0.1, 0.22)). The mean slope for the fit to (Δδ13Ci1αΔδ13Ci1β) was −0.4, whereas the mean slope for the fit to (Δδ13CiαΔδ13Ciβ) was −0.1. The fact that the latter value is close to zero indicates that Δδ15Ni is unrelated statistically to the intra-residue values (Δδ13CiαΔδ13Ciβ).

Figure 1
Comparison of the distributions of the fitted slopes for Δδ15Ni with (Δδ13Ci1αΔδ13Ci1β) and (Δδ13CiαΔδ13Ciβ ...

Fitting of Δδ1HiN with (Δδ13Ci1αΔδ13Ci1β) yielded slopes with distribution N(−0.07, 0.046), and fitting of Δδ1HiN with (Δδ13CiαΔδ13Ciβ) yielded N(−0.02, 0.034). These values show the similar trends but are five times smaller, owing to the smaller scale of δΔ1HN. However, the root mean square errors of the inter and intra-residue secondary chemical shifts fittings are indistinguishable (data not shown), which indicates that the correlation is very weak and explains why the slopes are so different among proteins.

The variation of the fitted slopes comes from the different amino acid content, the different α, β structure content of these proteins, and variability of the available chemical shift data. In order to deal with such variations, we developed the following procedure for checking the referencing of δ15N for a protein on the basis of the available set of NMR chemical shift data.

  1. Calculate the carbon secondary chemical shift difference, (Δδ13Ci1αΔδ13Ci1β) and the nearest-neighbor corrected nitrogen secondary chemical shifts, δΔ15Ni.
  2. Use the robust fitting procedure, which reduces effects of outlier points to fit δΔ15Ni with (Δδ13Ci1αΔδ13Ci1β), to derive the slope k and intercept b:
  3. If k is close to the expected mean (0.4±0.1), report −b as the reference offset.
  4. If k is outside the range (0.4±0.1), and if the data are insufficient for slope determination or if the distribution of chemical shifts along x-axis suggests that the protein is unfolded or contains only helix or sheet, then use a bounded slope (k within 0.4±0.05) in least square linear fitting Δδ15Ni with (Δδ13Ci1αΔδ13Ci1β) to re-estimate b. Report −b as the reference offset. The criterion for insufficient data is when the total number of chemical shift pairs available (Ntotal = number of (Δδ13Ci1αΔδ13Ci1β), Δδ15Ni) values) is fewer than 66 (arbitrary number). The criterion for poor distribution of chemical shifts is when fewer than 15% of the total number of chemical shift pairs (Ntotal) have ((Δδ13Ci1αΔδ13Ci1β)<2)or((Δδ13Ci1αΔδ13Ci1β)>2).
  5. If k is outside the range (0.4±0.1), and sufficient data of good distribution are available (neither of the two above criteria are met), then report −b determined in step 3 as the reference offset.

In cases where only partial backbone chemical shift values are available, or where the protein is unfolded or contains only α- or β-structure (smaller dispersion of data along the x-dimension), factors other than backbone geometry might dominate the dispersion of δ15N. In these cases, restriction of the slope (as defined in step 4) improves the accuracy of offset estimation (along the y-dimension). The arbitrary numbers are introduced here for lack of a “true” reference offset; otherwise it is possible that the offset values could be optimized by use of a machine learning method.

Figure 2 shows the agreement among LACS, RefDB, and CheckShift for δ15N offsets. The offsets detected by LACS have a standard deviation of 0.39 ppm with those from CheckShift and a standard deviation of 0.62 ppm with those from RefDB. The same procedure was used to fit Δδ1HiN with (Δδ13Ci1αΔδ13Ci1β) (k bounded at −0.07±0.01 for step 4); in this case, the offsets detected by LACS show a standard deviation of 0.11 ppm with those from RefDB. Thus, by using the newly observed linearity between δ15Ni, Δδ1HiN and (Δδ13Ci1αΔδ13Ci1β) LACS can give precise offset estimations for both δ1HN and δ15N.

Figure 2
Comparison of the offsets (ppm) estimated by LACS, CheckShift and RefDB.

Overall, LACS values showed better agreement to CheckShift than to RefDB, whose offsets are based on chemical shifts back-calculated from high-resolution structures. This result may reflect the fact that δ15N values are difficult to estimate accurately from structure. However, analysis by LACS and CheckShift of the chemical shift data from a few BMRB entries yielded very poor agreement. These outliers, which were excluded from Figure 2, are listed in Table 1, along with available reference offsets predicted by RefDB. In cases where all three values were available, the LACS values were closer to the RefDB values than to the CheckShift values. Because the RefDB values are associated with three-dimensional structures, this result suggests that LACS may lead to fewer large re-referencing errors than CheckShift. Considering the deviations among LACS, CheckShift, and RefDB, we suggest that experimental δ15N or δ1HN values should be re-referenced if and only if the offsets predicted by LACS for δ15N are > 0.7 ppm or for δ1HN are >0.12 ppm. This approach should reduce the chance of introducing systematic errors when re-referencing a large set of proteins. However, for a single protein, users should always examine the LACS plot to check for possible miss-assignments, uneven distribution of chemical shifts along the x axis, and/or insufficient data.

Table 1
List of BMRB entries that CheckShift and LACS predict significantly different δ15N reference offsets.

An advantage of LACS is that it can be applied even in cases where the backbone chemical shifts are partially assigned; this makes LACS more widely applicable than other approaches. We used the algorithm to examine possible referencing problems in the current BMRB protein chemical shift database. The results suggest that nearly 35% of the BMRB entries have δ15N values miss-referenced by over 0.7 ppm and over 25% of them have δ1HNvalues miss-referenced by over 0.12 ppm.

Previous studies showed that Δδ15Ni and Δδ1HiN are correlated with øi and ψi-1 (Le and Oldfield 1994). The results reported here imply that ψi-1 plays a more important role than øi on Δδ15Ni and Δδ1HiN. Therefore, this study not only extends the LACS approach for re-referencing to δ15N and δ1HN but also suggests that Δδ15Ni and Δδ1HiN values should be used as indicators of conformation the i-1-th residue rather than the i-th. Furthermore, it has also been shown that Δδ15Ni can be predicted from øi, ψi-1 and χ1 (Wang and Jardetzky 2004). Omission of χ1 and øi in our linear regression analysis might be responsible for the dispersion of Δδ15Ni around the fitted line. Conversely, it might be possible to derive χ1 and øi constraints after extracting the backbone effect (where the linearity holds). However, studies of this kind currently are greatly hindered by the limited amount of protein chemical shift data associated with three-dimensional structures.

The standalone executable application for using LACS to determine all backbone chemical shift reference offsets can be downloaded from or from BMRB (

Supplementary Material

Fig. S1-S8


This work is a continuation of the LACS re-referencing tool development supported by NIH grants P41 RR02301 and 1U54 GM074901 to J.L.M.


Supplementary materials Figures showing plots of Δδ15Ni vs. (Δδ13CiαΔδ13Ciβ) and Δδ15Ni (Δδ13Ci1αΔδ13Ci1β) for the BMRB entries listed in Table 1. Based on the calculation of Mahalanois distance, possible outliers (far away from majority of the points) have been removed prior to applying the robust fitting procedure.


  • Cornilescu G, Delaglio F, Bax A. Protein backbone angle restraints from searching a database for chemical shift and sequence homology. J Biomol NMR. 1999;13:289–302. [PubMed]
  • Eghbalnia HR, Wang L, Bahrami A, Assadi A, Markley JL. Protein energetic conformational analysis from NMR chemical shifts (PECAN) and its use in determining secondary structural elements. J Biomol NMR. 2005;32:71–81. [PubMed]
  • Ginzinger SW, Gerick F, Coles M, Heun V. CheckShift: automatic correction of inconsistent chemical shift referencing. J Biomol NMR. 2007;39:223–227. [PubMed]
  • Le H, Oldfield E. Correlation between nitrogen-15 nuclear magnetic resonance chemical shifts in proteins and secondary structure. J Biomol NMR. 1994;4:341–348. [PubMed]
  • Marsh JA, Singh VK, Jia Z, Forman-Kay JD. Sensitivity of secondary structure propensities to sequence differences between alpha- and gamma-synuclein: implications for fibrillation. Protein Science. 2006;15:2795–2804. [PubMed]
  • Schwarzinger S, Kroon GJ, Foss TR, Wright PE, Dyson HJ. Random coil chemical shifts in acidic 8 M urea: implementation of random coil shift data in NMRView. J Biomol NMR. 2000;18:43–48. [PubMed]
  • Schwarzinger S, Kroon GJ, Foss TR, Chung J, Wright PE, Dyson HJ. Sequence-dependent correction of random coil NMR chemical shifts. J Am Chem Soc. 2001;123:2970–2978. [PubMed]
  • Seavey BR, Farr EA, Westler W, Markley JL. A relational database for sequence-specific protein NMR data. J Biomol NMR. 1991;1:217–236. [PubMed]
  • Spera S, Bax A. Empirical Correlation Between Protein Backbone Conformation and C and C 13C Nuclear Magnetic Resonance Chemical Shifts. J Am Chem Soc. 1991;113:5490–5492.
  • Ulrich EL, Akutsu H, Doreleijers JF, Harano Y, Ioannidis YE, Lin J, Livny M, Mading S, Maziuk D, Miller Z, Nakatani E, Schulte CF, Tolmie DE, Wenger RK, Yao H, Markley JL. BioMagResBank, Nucleic Acids Res. 2008;36:D402–D408. [PMC free article] [PubMed]
  • Wang L, Eghbalnia HR, Bahrami A, Markley JL. Linear analysis of carbon-13 chemical shift differences and its application to the detection and correction of errors in referencing and spin system identifications. J Biomol NMR. 2005;32:13–22. [PubMed]
  • Wang L, Eghbalnia HR, Markley JL. Nearest-neighbor effects on backbone alpha and beta carbon chemical shifts in proteins. J Biomol NMR. 2007;39:247–257. [PubMed]
  • Wang Y, Jardetzky O. Investigation of the neighboring residue effects on protein chemical shifts. J Am Chem Soc. 2002;124:14075–14084. [PubMed]
  • Wang Y, Jardetzky O. Predicting 15N chemical shifts in proteins using the residue-specific individual shielding surfaces from phi, psi(i-1), and chi1 torsion angles. J Biomol NMR. 2004;28:327–340. [PubMed]
  • Wang Y, Wishart DS. A simple method to adjust inconsistently referenced 13C and 15N chemical shift assignments of proteins. J Biomol NMR. 2005;31:143–148. [PubMed]
  • Wishart DS, Bigam CG, Holm A, Hodges RS, Sykes SD. 1H, 13C and 15N random coil NMR chemical shifts of the common amino acids. I. Investigations of nearest-neighbor effects. J Biomol NMR. 1995;5:67–81. [PubMed]
  • Wishart DS, Sykes BD. The 13C chemical-shift index: a simple method for the identification of protein secondary structure using 13C chemical-shift data. J Biomol NMR. 1994;4:171–180. [PubMed]
  • Zhang HY, Neal S, Wishart DS. RefDB: a database of uniformly referenced protein chemical shifts. J Biomol NMR. 2003;25:173–195. [PubMed]