**3. Discussion**

The effect of side-chain length on lateral cross strand ion-pairing interactions between ammonium- and carboxylate-containing amino acids upon swapping the position of the charged amino acids was investigated. The fraction folded population for the HPTXaaZbb peptides was between 35% and 72% (Table 1). The extensive range of fraction folded population of the HPTXaaZbb peptides can be rationalized by the individual effects of the side-chain length of the ammonium- and carboxylate-containing at positions 4 and 9 on the hairpin formation, respectively, and the lateral cross strand Xaa4-Zbb9 interaction. In general, the fraction folded population of the HPTXaaZbb peptides for a given positively charged residue Xaa4 increased with increasing side-chain length of the negatively charged residue Zbb9 (except for peptide HPTDapAad; vide supra) (Table 1). This is consistent with the increased fraction folded hairpin population upon increasing the negatively charged residue side-chain length at position 9 for the HPTAlaZbb peptides [3]. In general, the fraction folded population of the HPTXaaZbb peptides for a given negatively charged residue Zbb9 decreased upon increasing the side-chain length of the positively charged residue Xaa4 (except for peptides HPTDapAad and HPTDabAad; vide supra) (Table 1). However, the fraction folded hairpin population for the HPTXaaAla peptides increased upon increasing the positively charged residue side-chain length at position 4 [3], suggesting the presence of cross strand Xaa4-Zbb9 interactions.

The two peptides with the highest fraction folded populations were HPTDapGlu (72 ± 3%) and HPTDapAsp (63 ± 1%). Similarly, the peptides with the same interacting residues, but the positions unswapped also exhibited the highest fraction folded populations in our previous study on HPTZbbXaa peptides (HPTGluDap: 63 ± 2%; HPTAspDap: 55 ± 3%) [22]. Nonetheless, the fraction folded populations of the HPTXaaZbb peptides with the charged residues swapped in this study (Table 1) were consistently higher compared to the corresponding unswapped HPTZbbXaa peptides in our previous study [22]. This is consistent with the higher fraction folded hairpin population for the HPTXaaAla peptides with the positively charged residue (Xaa) at position 4 compared to the corresponding HPTAlaXaa peptides with the positively charged residues (Xaa) at position 9 [3]. The change in fraction folded population upon swapping the residues in an interacting pair was consistent with studies on the protein G B1 domain [14] and a different hairpin system [19], which both showed a change in the stability of the host system upon swapping the position of interacting residues.

The largest difference in fraction folded population upon swapping was between the unswapped peptide HPTAadDab (26 ± 2%) [22] and the corresponding swapped peptide HPTDabAad (50 ± 1%). To gain further insight into this difference in the fraction folded population upon swapping, side-chain conformational analysis was performed on these two peptides by molecular mechanics calculations. The initial model was generated based on the solution structure of an analog of the parent YKL peptide (pdb code 1JY9 [46]). All possible combinations of low-energy side-chain dihedral angles (χ) for Aad and Dab were investigated. A combined total of 2916 conformations were minimized. The lowest energy conformation for the unswapped HPTAadDab exhibited higher energy (less negative energy, i.e., less stable) compared to that for the swapped HPTDabAad (Table 4), consistent with the fraction folded population for the two peptides. Conformations within 4 kcal/mol of the lowest energy conformer for each peptide were then examined (i.e., lowenergy conformations, Table 4) because room temperature can provide up to 4 kcal/mol of thermal energy. All but one low-energy conformation exhibited salt bridges between the charged residues at positions 4 and 9. There were more low-energy conformations for the unswapped HPTAadDab compared to the swapped HPTDabAad. The energy reflects the enthalpic component of the conformation, whereas the number of low-energy conformations reflects the entropic component of the folded form of the peptide. The

side-chain conformational entropy contribution of the residues at positions 4 and 9 to the free energy of the folded form for the two peptides was calculated based on the Boltzmann distribution of the various low-energy conformations (Table 4). The more negative −TS reflected the higher side-chain conformational entropy in the folded form for the unswapped HPTAadDab compared to the swapped HPTDabAad, despite involving the same two potentially interacting residues. The conformation of the low-energy conformers was examined in detail. Each χ<sup>1</sup> dihedral was divided into three categories: gauche− (60◦ , g−), trans (180◦ , t), and gauche+ (300◦ , g+) [47,48]. The combination of the χ<sup>1</sup> dihedrals was represented in parentheses (Table 4, Figures S53 and S54), showing the conformation for the residue at position 4 followed by the conformation for the residue at position 9. For example, a conformation with t at position 4 and g+ at position 9 would be designated (t, g+). For the unswapped HPTAadDab, 8 of the 9 possible combinations were present (Table 4 and Figure S53), whereas only 4 of the 9 possible combinations were observed for the swapped HPTDabAad (Table 4 and Figure S54). Importantly, the majority of the low-energy conformations did not involve g− (for χ1) at either position in either peptide (68% for HPTAadDab, and 94% for HPTDabAad). This is most likely because the g− conformation is higher in energy compared to t and g+ [47,48], and the g− conformation would inherently point the side-chain away from the neighboring strand.

**Table 4.** Summary of the low-energy conformations from the side-chain conformational analysis of peptides HPTAadDab and HPTDabAad by molecular mechanics calculations.


<sup>1</sup> The number of conformations within 4 kcal/mol of the lowest energy conformer for each peptide. <sup>2</sup> The percentage of conformations within 4 kcal/mol of the lowest energy conformer with an Aad–Dab salt bridge, which is a hydrogen-bonded ion pair [49].

> More low-energy conformations were observed for the unswapped Aad4-Dab9 interaction compared to the swapped Dab9-Aad9 interaction (Table 4 and Figure 3). Apparently, the right-handed twist of the hairpin structure [11] raised the residue at position 4 and lowered the residue at position 9 (Figures 3 and 4). This "unleveled" relative positioning of the interacting residues resulted in more proper length matching for the Aad4-Dab9 interaction, enabling more low-energy conformations with the Aad4-Dab9 interaction and a higher proportion of the g− conformation in χ<sup>1</sup> (21 in 65, or 32%). For the swapped Dab4-Aad9 interaction, the unleveled relative positioning exacerbated the length difference between Dab4 and Aad9, leading to less low-energy conformations with the Dab4-Aad9 interaction and a relatively low proportion of the g− conformation in χ<sup>1</sup> (1 in 16, or 6%). This unleveled positioning created by the right-handed twist appeared to be one of the factors giving rise to the difference between the unswapped and swapped peptides.

− χ

− χ

**Figure 3.** The low-energy conformations from molecular mechanics calculations for peptides HPTAadDab and HPTDabAad. The backbone and DPro side-chain are shown in white. The residues at positions 4 and 9 are colored according to element: carbon in gray, oxygen in red, and nitrogen in blue. The other side-chains and all hydrogen atoms are omitted for clarity.

**Figure 4.** The chemical structure of HPTXaaZbb shown in perspective view, showing the consequence of the right-handed twist on a flat structure. The cartoon ribbon representation was generated from the solution structure of an analog of the parent YKL peptide using PyMOL (pdb code 1JY9 [46]).

The energetic contribution of lateral cross strand Xaa4-Zbb9 interactions to hairpin formation was determined by double mutant cycle analysis (Table 3). For the HPTXaaZbb swapped peptides in this study, the Dap4-Glu9 and Dap4-Asp9 interactions were most stabilizing (Table 3). Similarly, the Glu4-Dap9 and Asp4-Dap9 interactions were the most stabilizing in our previous study on the original unswapped HPTZbbXaa peptides [22]. This may be because shorter amino acids such as Dap and Asp are conformationally less flexible compared to amino acids with longer side-chains, leading to higher stabilizing lateral cross strand ion-pairing interactions due to less entropic penalty [22]. The mean conformational entropic penalty of one side-chain rotatable bond upon folding is 0.5 kcal/mol [50].

There is a dramatic decrease in fraction folded population and stabilizing side-chain interaction for peptides HPTDapAsp and HPTDapGlu upon increasing the Dap side-chain length by just one methylene to Dab (Tables 1 and 3). Increasing the side-chain length of Dap by one methylene to Dab would increase the electron-donating characteristics, decrease the electron-withdrawing characteristics from the backbone functionality, and thus decrease the cationic charge density on the ammonium group. This decrease in cationic charge density would decrease the electrostatic interaction with the negatively charged Asp and Glu, resulting in the decreased fraction folded population for peptides HPTDabGlu and HPTDabAsp compared to peptides HPTDapGlu and HPTDapAsp, respectively (Table 1 and Figure 3).

Further lengthening the positively charged residue Dab in HPTDabGlu and HPTDabAsp did not alter the fraction folded population or the Xaa4-Zbb9 interaction as drastically as the change upon lengthening Dap to Dab. The longer side-chains are more flexible, and therefore, more energy would be needed to confine the side-chain conformation to enable the cross strand ion-pairing interaction. This would decrease the overall energetic contribution of the cross strand ion-pairing interaction for residues with longer side-chains. However, as the side-chain length of the positively charged residue Xaa4 increases, the fraction folded population of HPTXaaAla peptide increases [3]. As such, this increase in hairpin formation (due to the positively charged residue Xaa) compensates for the increase in the side-chain entropic penalty for the longer side-chains to form a cross strand ion-pairing interaction, leading to less drastic changes in the fraction folded population.

In general, the interaction free energy became less stabilizing with increasing sidechain length of the positively charged residue Xaa4 for a given negatively charged residue Zbb9 (except for Dap4-Aad9) in the swapped HPTXaaZbb peptides in this study (Table 3). The same general trend was also observed in our previous study on the original unswapped HPTZbbXaa peptides, but with less stabilizing lateral cross strand interactions between residues at positions 4 and 9 [22]. This difference in interaction energy could be due to the difference in the relative placement of the residues at position 9 on the C-terminal strand and position 4 on the N-terminal strand (Figure 4, vide infra), stemming from the inherent right-handed twist of sheet structures [28].

The Xaa4-Asp9 interactions were more stabilizing compared to the corresponding Xaa4-Glu9 and Xaa4-Aad9 interactions for a given Xaa4 (Table 3). This is perhaps the result of the relative positioning of Xaa4 and Zbb9. The right-handed twist of the hairpin structure [11] lowers Zbb9 and raises Xaa4 (Figure 4). For Xaa4 to interact with Zbb9, the ammonium group on Xaa4 and the carboxylate group on Zbb9 need to be close to one another. Apparently, length matching is critical for lateral cross strand interactions [22,23]. Since the carboxylate group on Zbb9 is inherently longer than the ammonium group on Xaa4, the shorter Asp9 would be more well suited to interact with Xaa4 (especially shorter residues) compared to the longer Glu9 and Aad9 due to the "unleveled" relative positioning of the residues created by the right-handed twist (Figure 4). In comparison, interactions between the longer Glu9 (and Aad9) and Xaa4 would be weaker compared to the corresponding Xaa4-Asp9 interactions. Furthermore, the Xaa4-Asp9 interaction would be more stabilizing because of the need to pay less of an entropic penalty to confine the short Asp9 side-chain conformation to enable the Xaa4-Asp9 interaction compared to the longer Glu and Aad. For the original unswapped HPTZbbXaa peptides [22], there is no general trend among the Asp4-Xaa9, Glu4-Xaa9, and Aad4-Xaa9 interactions for a given Xaa9 residue. This may be because the unleveled relative positioning created by the right-handed twist facilitates the length matching, bringing the inherently shorter ammonium functionality closer to the inherently longer carboxylate functionality. These results are consistent with the studies on cross-strand interactions in the protein G B1 domain [14], showing that swapping the amino acid positions in lateral cross-strand interactions changed the interaction energy. Overall, our results suggest that there is an orientation preference for lateral cross strand interactions to stabilize sheet systems, despite the apparent symmetry of lateral cross strand interactions based on statistical studies [24].

The Dap4-Aad9 and Lys4-Aad9 interactions were less stabilizing compared to the Dab4-Aad9 and Orn4-Aad9 interactions if one disregards the error bars. The low stabilization of the Lys4-Aad9 interaction may be due to the conformationally more flexible

Lys side-chain, leading to the need to pay a higher entropic penalty to confine the long Lys and Aad side-chains to enable the Lys4-Aad9 interaction. The low stabilization of the Dap4-Aad9 interaction may be due to the length discrepancy between Dap and Aad, which is further magnified by the unleveled relative placement of residues at positions 4 and 9 resulting from the right-handed twist. Importantly, the combination of unleveled relative placement of the interacting functional groups and difference in entropic penalty necessary to form the lateral cross-strand interaction resulted in the observed trends and the effects upon swapping interacting residues.
