*2.2. β-Hairpin Structure Characterization by NMR*

The peptides were analyzed by <sup>1</sup>H–1H homonuclear two-dimensional solution NMR spectroscopy, including double-quantum filtered-correlated spectroscopy (DQF-COSY) [33], total correlation spectroscopy (TOCSY) [34], and rotating-frame nuclear Overhauser effect

*β*

β

α

β

spectroscopy (ROESY) [35] at 298 K. Sequence-specific assignment of all peptides was performed based on the TOCSY and ROESY spectra (Tables S1–S36) [36]. For a given Xaa4- Zbb9 pair, the chemical shift dispersion of the peptides followed the trend HPTFXaaZbb > HPTXaaZbb > HPTUXaaZbb (Tables S1–S36). Since the higher the fraction folded population, the higher the chemical shift dispersion [37], this trend is consistent with the intended designs of the peptides. −

The β structure of the experimental and fully folded reference peptides was confirmed by the chemical shift deviations of the Hα signals, the <sup>3</sup> JHN<sup>α</sup> spin–spin coupling constants, and the NOE cross-peaks. The Hα chemical shift deviation (∆δHα) is the difference between the Hα signal for the residue of interest and the corresponding random coil Hα signal [38]. In this study, the fully unfolded reference peptides were considered to be random coil [11,22,23,26]. A positive ∆δHα value suggests an extended β-sheet conformation [38,39]. The ∆δHα values of the residues Thr2 through Val5 and Orn8 through Leu11 for the experimental HPTXaaZbb peptides and the fully folded reference HPTFXaaZbb peptides were positive (Figure 2, Figures S1 and S2), suggesting an extended β-strand conformation for these residues. This is consistent with the intended design. In general, the ∆δHα values for the residues in the strand regions (residues 2–5 and residues 8–11) of the fully folded reference peptides were more positive compared to those for the corresponding experimental peptides (Figure 2, Figures S1 and S2), suggesting that the fully folded reference peptides were more well folded than the corresponding experimental peptides. The ∆δHα values of the terminal residues Arg1 and Gln12 for the experimental peptides were near zero (Figure 2, Figures S1 and S2), most likely due to end fraying effects [21]. The ∆δHα values for Gly7 were negative or mostly close to zero (Figure 2, Figures S1 and S2), consistent with turn formation [12]. α <sup>α</sup> α Δδ α α Δδ α β Δδ α Δδ α Δδ α Δδ α

Δδ α **Figure 2.** The chemical shift deviation (∆δHα) for the residues in peptides HPTFLysGlu (**a**) and HPTLysGlu (**b**).

α α β α α The DQF-COSY spectra were used to determine the <sup>3</sup> JHN<sup>α</sup> spin–spin coupling constants for each residue in the peptides (Tables S37–S45) [33,40]. The <sup>3</sup> JHN<sup>α</sup> coupling constants of the residues in the fully folded reference HPTFXaaZbb peptides showed values higher than 7 Hz (Tables S43–S45), consistent with a β-hairpin structure [36,41]. The experimental HPTXaaZbb peptides also exhibited <sup>3</sup> JHN<sup>α</sup> coupling constants higher than 7 Hz, but slightly lower <sup>3</sup> JHN<sup>α</sup> values compared to those for the fully folded reference HPTFXaaZbb peptides (Tables S37–S39 and S43–S45). This suggested that the experimental HPTXaaZbb peptides may not be as well folded as the fully folded reference HPTFXaaZbb peptides. For the unfolded reference HPTUXaaZbb peptides, some residues exhibited 3 JHN<sup>α</sup> values near or less than 7 Hz (Tables S40–S42), suggesting that these peptides may not be as well folded as the experimental HPTXaaZbb peptides or the fully folded reference HPTFXaaZbb peptides.

The NOE cross-peaks in the ROESY spectra included sequential, intra-residues, medium-range, and long-range NOEs with a number of cross strand Hα–Hα, Hα–HN,

HN–HN correlations (Figures S3–S50). All sequential Hα–HN NOE correlations in every strand for all peptides were observed (Figures S39–S50), consistent with β-strand formation [42,43]. In addition, the lack of dαN(*i*, *i* + n) (*n* = 2,3,4) and dNN(*i*, *i* + n) (*n* = 1, 2) patterns rules out the formation of other secondary structures (Figures S39–S50) [42,43]. A network of cross strand side-chain-side-chain NOEs between residues on the two βstrands was observed for the experimental peptides HPTXaaZbb and fully folded reference peptides HPTFXaaZbb (Figures S3−S38), consistent with β-hairpin formation for these peptides. Long-range NOE cross-peaks between Thr2 and Xaa9 were observed for most of the experimental HPTXaaZbb peptides and fully folded reference HPTFXaaZbb peptides (Figures S3−S38), consistent with a right-handed twist [11,27,28]. The number of cross-peaks in the ROESY spectra followed the general trend HPTFXaaZbb > HPTXaaZbb > HPTUXaaZbb (Figures S3−S38), consistent with the intended fraction folded population for our designs [3,22,23].
