The interface required for chemical shift transfer (CST) is included within the FLYA algorithm used by ARTINA for chemical shift assignment (Schmidt and Güntert, 2012). The function of this algorithm has been described in detail by Schmidt and Güntert; in brief, a list of expected peaks is constructed from the protein of interest’s amino acid sequence, then this list is mapped to a list of measured peaks generated by manual or automated peak picking. The mapping is improved iteratively using global and local optimization methods (Bartels et al., 1997). This procedure is repeated for a series of replicates and the final output is determined as a majority consensus of these.

In order to initialize the assignment of expected peaks to measured peaks, the default procedure within FLYA uses statistics from the Biological Magnetic Resonance Data Bank (BMRB) (Hoch et al., 2023) to construct an initial “search space” for each expected peak, from which a measured peak is picked at random to assign it (Schmidt and Güntert, 2012). For each atom in a protein, this search space is defined by a statistical distribution parametrized by the mean and standard deviation of chemical shifts of the given atom type over all occurrences of its amino acid type within the BMRB. Due to the scale of the database and the high number of peaks in protein NMR spectra, this usually generates a large area containing also many incorrect possibilities for assignment, the center of which can deviate from the peak’s true position. By improving the initial search space for each atom, i.e., reducing its size and shifting its center closer to the true position, the accuracy of FLYA assignments can therefore be improved significantly (Bartels et al., 1996; Aeschbacher et al., 2013). The essence of the CST procedure relies on this concept, aiming to provide a better estimate of the peak’s true position and therefore also allowing for a smaller search space size (Figure 1A).

CST is performed as follows (Figure 1B): Given a source protein with a known assignment of chemical shifts and a target protein whose shifts have yet to be assigned, first a mapping of source atoms to target atoms must be defined. In the trivial case where source and target protein are identical in sequence, each source atom can simply be mapped to its copy in the target. However, this need not always be the case, and transfer of assignment data between different protein samples could also be highly beneficial in many cases. In this work, we compared pairs of distinct proteins by first performing a local pairwise sequence alignment tuned to produce large aligned sub-sequences between a small number of wide gaps (Supplementary Table S1). Each identical pair of amino acids in this alignment could then be used for CST. Aligned pairs of different amino acids and amino acids aligned to gaps were simply disregarded, falling back to FLYA’s default setting.

Based on this source-target mapping, new initial search spaces can be defined for each atom in the target protein, centered around the corresponding chemical shift in the source. Since this new center is likely to be more accurate, i.e., closer to the true position of the atom’s shift than the mean value obtained from BMRB, the search space’s width can then be reduced (higher precision), further facilitating its assignment.

The determined search space centers and sizes are then entered into FLYA as a list of mean values and standard deviations (“chemical shift statistics”), with the algorithm automatically applying the default BMRB-based search space for any atom not included.

When using FLYA as part of the ARTINA pipeline, automated visual analysis of each spectrum generates the experimental peaks to be used as input (Klukowski et al., 2022). For this work, execution was stopped after obtaining an assignment from FLYA. In practice, however, the output assignments can also be passed to the next stages of ARTINA, e.g., structure determination.

The dataset established for the training and testing of ARTINA models (Klukowski et al., 2022) was the source of raw NMR spectral data in this study. Since CST is most efficient if only a small number of spectra have to be measured for the target protein, we used a small subset of NMR spectra types from the ARTINA dataset, consisting only of the 2D HSQC ([¹H, ¹³C]-HSQC, [¹H, ¹⁵N]-HSQC) and 3D NOESY (¹³C-resolved [¹H, ¹H] NOESY, ¹⁵N-resolved [¹H, ¹H] NOESY) spectra. Unless specified otherwise, we used this small subset of spectra for a representative set of 15 proteins for all experiments in this work (Supplementary Table S2).

To evaluate CST with experimental data, we investigated sequence homology between proteins in the ARTINA dataset (Klukowski et al., 2022) (Supplementary Table S2) and both RefDB (Zhang et al., 2003) and BMRB using sequence alignment parameters specified in Supplementary Table S1. As sequence alignment scores had no upper bound, they were normalized by the score of aligning each protein to itself. If the homolog protein was found in both RefDB and BMRB, preference was given to RefDB. We refer to the protein from the ARTINA dataset as the target and from RefDB/BMRB as the source protein.

All pairs with normalized sequence alignment score above 80% were selected for chemical shift alignment. In this step we propagated information from the sequence alignment into the source chemical shift list. This was indispensable as differences between the source and target sequences, such as insertion or deletion, require appropriate reindexing of chemical shifts in the source before applying CST to the target.

Subsequently, each shift in the aligned source list was compared with the corresponding target shift. An aligned shift was considered “correct” if it was within a given tolerance from the target position (0.03 ppm for ¹H, 0.4 ppm for ¹³C/¹⁵N). Then, we calculated the “fraction of correct aligned shifts” for each pair of source/target homologous proteins, which is defined as the ratio of correct aligned shifts to total shifts in the aligned list.

In this experiment, we used protein pairs with a fraction of correct aligned shifts greater than or equal to 50%. Combining with the requirement of >80% sequence alignment score, we identified 12 source-target pairs for which experimental spectra were available in the ARTINA benchmark. These pairs corresponded to 9 distinct target proteins (Supplementary Figure S2, Supplementary Table S3).

To investigate the impact of complementary input (chemical shift list of the source protein) on the accuracy of the chemical shift assignment of the target protein, we first evaluated the baseline performance of de novo automated assignments of target proteins, without any transfer information (Supplementary Figure S1).

Subsequently, we ran the chemical shift transfer in an idealized setting, where each target protein’s own chemical shift list was passed as the transfer source. This corresponds to the scenario, unlikely in practice, in which the chemical shifts do not change between the source and target proteins, or that the input shift list for CST is equal to the expected output. It is important to note that FLYA still uses peak lists prepared for a minimal set of experimental spectra ([¹H, ¹³C]-HSQC, [¹H, ¹⁵N]-HSQC, ¹³C-resolved [¹H, ¹H] NOESY, ¹⁵N-resolved [¹H, ¹H] NOESY) to perform chemical shift transfer. Therefore, it cannot simply copy the input shifts to the output, and some chemical shifts cannot be assigned due to missing signals in the input data. However, this experimental setting represents the best possible initial search space positions for FLYA, and therefore can be used to estimate an upper bound for CST accuracy. In this case, the width of each search space was set to 0.04 ppm for ¹H nuclei and 0.4 ppm for ¹³C and ¹⁵N nuclei.

As expected, we observed a significant improvement in chemical shift accuracy by 23.5 percentage points (pp) in the idealized reference case, as compared to de novo assignment, where no complementary input was used. The average assignment accuracy of 68.8% for 15 proteins used in the de novo experiment increased to 92.3% using CST (Supplementary Figure S1). The fact that FLYA was unable to attain 100% accuracy in these reference experiments was likely mainly due to the minimal set of spectra used (Supplementary Table S2).

In both reference experiments (Supplementary Figure S1) the assignment errors had a tendency to accumulate in side-chains (90.6% accuracy with CST, 66.3% without), leaving the accuracy of the backbone assignment above the average (95.3% accuracy with CST, 73.4% without)—a result consistent with previous studies of FLYA (Schmidt and Güntert, 2012) and ARTINA (Klukowski et al., 2022).

Another notable observation is that the availability of source chemical shifts affects the variance of the output accuracy. In de novo experiments, the discrepancy between the most and least accurately assigned proteins is 34.9 pp, compared to only 13.8 pp in the idealized CST case.

Overall, the experiments we have conducted, ranging from scenarios with minimal to maximal information available for chemical shift transfer, indicate that source protein information provides useful guidance for the combinatorial optimization that reduces the ambiguity of the assignment, resulting in fewer errors and enhancing the overall reliability of protein assignment.

To characterize ARTINA-CST under more realistic conditions, we carried out over 1,000 automated chemical shift transfers with 15 proteins using the test examples described in sections 2.3.1 and 2.3.2.

In the first series of experiments, a variable fraction of atoms was selected at random for perturbation (20%, 50% and 100%), as described in section 2.3.1, imitating a variable degree of discrepancies between known source chemical shifts and the target protein. Perturbed chemical shifts were used as input for the ARTINA-CST procedure together with 4 NMR spectra of the target protein ([¹H, ¹³C]-HSQC, [¹H, ¹⁵N]-HSQC, ¹³C-resolved [¹H, ¹H] NOESY, ¹⁵N-resolved [¹H, ¹H] NOESY). ARTINA-CST automatically extracted cross-peak positions from experimental data and combined them with the corresponding perturbed shift list, yielding the assignment of the target protein. This result was compared with de novo ARTINA assignment, which involved the same procedure, but without the perturbed chemical shift list as input.

The use of CST turned out to be highly beneficial in all three experimental settings (20%, 50% and 100% shift perturbation) and for almost all proteins included in the study. The relative improvement in assignment accuracy is depicted in Figures 3A–C by the ratio between the accuracy of the chemical shift assignment with the CST procedure and with the de novo approach, with a value of 1.0 corresponding to a neutral effect of CST.

As expected, the value of the ratio depends on the parameters c and p of the test generation procedure (section 2.3.1). In the least challenging setting (Figure 3A), the scaling factor ( c = 0.2 ) largely restricts chemical shift deviations between source and target chemical shift list. As the chemical shift values in the source and target shift lists lie in close proximity, even for perturbed atoms, the CST transfer procedure yields similar performance regardless of the number of atoms perturbed, demonstrating a 1.36-fold relative improvement on average as compared to the de novo runs.

When the scaling coefficient was set to a moderately higher value ( c = 0.5 ), the effect of the larger of chemical shift perturbations on the overall CST accuracy was apparent (Figure 3B), with the relative improvement averaged over all proteins varying between 1.37 and 1.29 for 0% and 100% perturbed chemical shifts respectively. Finally, the strongest perturbation ( c = 1.0 , Figure 3C) result in a further decrease in CST accuracy, as compared with previous settings (Figures 3A, B), but preserving strong positive impact (1.37-fold–1.23-fold improvement) relative to de novo calculations.

Subsequently, we repeated the above experiment using structure-based perturbations (section 2.3.2) instead of random ones. The results for these assignments show a strong resemblance to those for the fully randomized perturbations (Figures 3D–F), including correlation between CST accuracy and c , p parameters of the test example preparation procedure. The points with 0% perturbations correspond to the idealized case, as described in section 3.1.

Overall, we identified no major changes in the performance of the algorithm that depend on the spatial distribution of the chemical shift perturbation, and in both experimental settings the number of perturbations and corresponding variance were the primary factors affecting the accuracy of the procedure.

For individual cases, we observed a particularly large improvement in the assignment obtained with the CST procedure. For instance, the C-terminal NlpC/P60 domain of lipoprotein Spr from Escherichia coli [PDB 2K1G (Aramini et al., 2008)], showed poor performance in de novo chemical shift assignment (48.3% accuracy), compared to 94.7% obtained in the idealized case of CST (Figure 3).

Even in the experimental setting with the strongest perturbation (standard deviation equal to BMRB standard deviation and perturbations applied to all shifts, which resulted in the large majority of shifts being moved significantly from their original positions), the fraction of correct assignments for this protein was raised by 20.4 pp upon application of the CST procedure. In all other cases the positive impact of the chemical shift transfer was even stronger (30.8–49.8 pp improvement, depending on the experimental setting).

The primary reason for such improvements was the ability of the CST method to resolve chemical shifts in the proximity of the dynamic loop of residues 16–32, 79–81, 90–93, 99–101, long positively charged side chains (37.3% without CST vs. 91.5% with idealized CST) and aromatics (54.9% vs. 93.7%).

As described in section 2.4, we used pairs of homologous proteins identified in RefDB/BMRB and the ARTINA benchmark of NMR spectra to assess the performance of the chemical shift transfer in fully experimental setting. In this procedure, the chemical shift list deposited in RefDB/BMRB was regarded as source, and four NMR spectra ([¹H, ¹³C]-HSQC, [¹H, ¹⁵N]-HSQC, ¹³C-resolved [¹H, ¹H] NOESY, ¹⁵N-resolved [¹H, ¹H] NOESY) were used by ARTINA-CST as input for the transfer procedure to the target system. In this experiment all cross-peaks in the abovementioned spectra were identified automatically by deep neural network models included in the ARTINA visual spectrum analysis layer. As in the previous experiments, we performed for each target protein additional de novo assignments to assess the relative performance of the CST procedure.

The results show an overall mean improvement by CST over de novo assignment of 7.4% (0.0%–14.4%) in the chemical shift assignment accuracy of all shifts and 9.7% (1.2%–23.9%) for the backbone NH groups (Figure 4). Out of 12 homolog pairs, the impact of CST was positive both for all shifts and NH groups in 11 cases. Only in one case (2JVD) the impact of CST was neutral for all shifts and positive for NH groups.

ARTINA-CST has a single parameter, c CST , which corresponds to the level of shift perturbation one expects to observe when transferring chemical shift assignments from the source to the target protein. It plays the same role as the scaling factor c for the synthetic data preparation in section 2.3.1, indicating the fraction of BMRB variance in individual shifts we expect to observe in a particular dataset. In this experiment, c CST was set to 1.0, indicating lack of a prior assumption about the variance of the distribution (i.e., we expect the chemical shifts in the target protein to deviate from the source the same way the individual shifts deposited in the BMRB database deviate from their mean value). Despite this conservative assumption, ARTINA-CST still yielded a substantial improvement in the chemical shift assignment accuracy, as compared with de novo assignment. Specific tuning of the expected perturbation parameter is expected to result in further improvement of the ARTINA-CST performance, as it provides weak constraints on the initial search-space for individual chemical shifts.

In a second series of experiments, we therefore carried out chemical shift transfers between the 12 homolog pairs using different values of the expected perturbations, c CST = 0.10, 0.15, 0.20, 0.25, 0.50, 1.00, as well as with fixed-size search spaces of 0.09 ppm for ¹H and 1.2 ppm for ¹³C/¹⁵N shifts that are independent of BMRB shift distributions. The results indicate that decreasing the size of the initial search space proved effective to increase ARTINA-CST accuracy (Figure 5). For each automated chemical shift assignment in this experiment, we calculated the ratio between the accuracies of CST-based and de novo assignment. With the lack of prior assumptions about the variance of chemical shifts ( c CST = 1.0 ), ARTINA-CST achieved 10% median improvement over de novo assignment, for which no information from the homologous protein was used. As the value of the expected perturbation parameter c CST decreased, the overall performance of the method increased and saturated at about 26% for c CST ∈ 0.1 , 0.25 . As two reference experiments, we evaluated the accuracy of chemical shift transfer with fixed tolerances (green box, Figure 5) and with an idealistic optimal reference, where the information about target chemical shifts is assumed to be known (upper bound accuracy) (blue box, Figure 5).

Chemical shift transfer impacts full assignment and amide N/H assignment in similar way (Figure 5). For c CST = 1.0, the relative median increase in assignment accuracy is 11%. The quality of the solution increases with decreasing expected perturbation coefficient, saturating at 20% for c CST ∈ 0.1 , 0.25 . The relative improvement for amide groups is smaller compared to all shifts, because the generally higher accuracy of NH shift assignments in de novo experiments leaves smaller room for improvements (68.0% and 77.2% accuracy for all shifts and NH groups respectively).