2.2.2. Similarity Metrics of Δδ

Each peak in a 2D 1H-13C NMR spectrum has three dimensions, including peak intensity and 1H and 13C chemical shifts, all of which are sensitive to protein HOS. Previous spectral comparisons on insulin [38] and filgrastim [26] 2D spectra have applied PCA for similarity evaluation, which took into account all spectral variables from the three dimensions (two frequencies and intensity) for comparison. However, no similarity metrics were derived. The filgrastim 1H-15N spectral comparison established a combined chemical shift difference (CCSD) metric of 8 ppb [26]. The chemical shift comparison was repeated here for the 48 methyl peaks between Lantus® and Basaglar®. For each brand the inter-lot averaged chemical shift values were used as DP specific δ. The differences of chemical shift (Δδ) between the two DPs were plotted along both 1H and 13C axis (Figure 4A,B). The maximum 1H Δδ was 3.4 ppb identified in the Leu-d peak. The maximum 13C Δδ was −13 ppb identified in the Leu-j peak. When a 10% larger difference is permitted in the maximum Δδ, similarity metrics with rounded values of 4 and 15 ppb for the 1H and 13C chemical shifts, respectively, can be proposed. These metrics are on par with the previous CCSD metric of 8 ppb [26] or 4 ppb [41], which was a normalized Δδ value from both the 1H and 15N axes.

**Figure 4.** The chemical shift and relative peak height difference between insulin glargine drug products of Lantus® and Basaglar®. The 1H (**A**) and 13C (**B**) chemical shift difference and the relative peak heights (**C**) were plotted along the labeled peaks of Figure 3B.
