Single β-strand conformations and handednessSingle β-strands tend to twist due to the innate chirality of natural amino acids. Using the established theoretical method15, our structural optimization for single strands showed that the handedness of single F3K strands was governed by the chirality of the aromatic residues, i.e., single LF3LK and LF3DK β-strands were left-handed twisted while DF3LK and DF3DK ones were right-handed, irrespective of the charged state of Lys4 (Fig. 1a–d and Supplementary Fig. 1a–d). This is in sharp contrast to their aliphatic counterparts I3K strands, where the handedness was dictated by the chirality of the C-terminal Lys residue. For example, single DI3LK and DI3DK strands were right- and left-handed twisted, respectively (Fig. 1e, f and Supplementary Fig. 1e, f). In contrast, single LI3DK and LI3LK β-strands were left- and right-handed twisted15. It is evident that DF3DK and DI3DK or LF3LK and LI3LK strands exhibited the opposite handedness at this stage.Fig. 1: Single-strand conformations, handedness, and intrastrand interactions.a–f Twisting directions of single β-strands for (a) LF3LK, (b) LF3DK, (c) DF3LK, (d) DF3DK, (e) DI3LK, and (f) DI3DK. g–i RDG isosurfaces of single DF3DK, DF3LK, and DI3DK β-strands, respectively. Atoms coloring scheme is: red, oxygen; blue, nitrogen; white, hydrogen, and gray, carbon. The two arrowed lines (from N- to C-terminus: blue and yellow) connecting potential H-bonding atoms on each side can define the twisting directions of the single strands. The blue, green, and red areas in the RDG isosurfaces represent attractive H-bonding, van der Waals interactions, and steric repulsion, respectively. When these peptides were positively charged via the side-chain protonation of Lys4, they showed the same twisting directions (Supplementary Fig. 1). Gradient isosurfaces of the other three peptide β-strands are given in Supplementary Fig. 2.To reveal the molecular explanation for this conformational difference, we performed the reduced density gradient (RDG) isosurface analysis. Such a method allows simultaneous analysis and visualization of various noncovalent interactions such as van der Waals interactions, H-bonds, and steric repulsion as real-space surfaces for molecular complexes16. Within the RDG isosurfaces, the blue, green, and red areas represent strong attractive H-bonding, weak van der Waals interactions, and strong steric repulsion, respectively16,17. We found that strong steric hindrance between the benzene ring of Phe3 and the local backbone (between Phe3 and Lys4), as denoted by a larger brown patch in the enlarged area of Fig. 1g or Supplementary Fig. 1g, repelled the C=O and N-H groups of Lys4 to shift downward for DF3DK and DF3LK or upward for LF3LK and LF3DK, irrespective of the chirality of Lys4 (Fig. 1g, h, and Supplementary Figs. 1g, h, 2). In contrast, there was a lack of such a strong steric hindrance between the isobutyl group of Ile3 and the local backbone for I3K, and instead, the orientation of the C=O and N-H groups of Lys4 was dictated by its long side chain (Fig. 1i and Supplementary Figs. 1i, 2).Handedness inversion induced by aromatic interactions in β-sheet assemblyBased on the above single-strand conformations, right-handed β-sheets were expected for LF3LK and LF3DK assembly, while left-handed ones for DF3LK and DF3DK. However, left-handed β-sheet nanofibrils were observed to be formed by the former two while right-handed twisted ones by the latter two in our experiments14. This is distinct from the self-assembly of I3K peptides, in which right- and left-handed β-strands eventually packed into left- and right-handed β-sheet nanofibrils11,15.To determine the mechanism underpinning such a discrepancy, we focused on β-strand dimers. As a fundamental structural motif of β-sheets and β-sheet assembly, dimers enable us to analyze interstrand interactions such as backbone H-bonding and side-chain interactions. The independent gradient model-based Hirshfeld partition (IGMH, 0.005 a.u.) was adopted to graphically describe these weak interactions17,18. Dimers were first constructed based on the single-strand conformations described in Fig. 1 or Supplementary Fig. 1, via parallel and anti-parallel arrangements. After structural optimization, the IGMH analysis indicated extensive interstrand π–π interactions within the most stable F3K dimers, indicated by the green regions between benzene rings, for the three interstrand contacting modes, namely FF (face-to-face), FB (face-to-back), and BB (back-to-back), as shown in Fig. 2 and Supplementary Fig. 3 for LF3LK and Supplementary Figs. 4,5 for DF3LK. The three modes are schematically depicted in Supplementary Fig. 6 for parallel and anti-parallel arrangements. Furthermore, interstrand π-π interactions were found to be stronger within the parallel dimers (left halves of Fig. 2 and Supplementary Figs. 3–5), as indicated by the larger green areas, compared to the anti-parallel dimers (right halves of Fig. 2 and Supplementary Figs. 3–5). For the FB contacting mode within the parallel dimer, there were three pairs of side-chain π-π stacking while only two pairs for the same mode within the anti-parallel dimer. Additionally, the side-chain π-π stacking for the parallel arrangements was parallel-displaced while T-shaped for the anti-parallel arrangements. These IGMH results suggested a high propensity of F3K β-strands for parallel arrangements upon packing, presumably driven by stronger side-chain π-π stacking interactions.Fig. 2: Dimer conformations, π-π stacking interactions between β-strands, and chiral inversion.IGMH analysis of π-π stacking interactions between β-strands within parallel and anti-parallel LF3LK dimers. These dimers were obtained after structural optimization, based on the single-strand conformations given in Fig. 1. Compared to the anti-parallel dimers, more extensive and stronger π-π stacking interactions were revealed within the parallel ones, as denoted by green patches in the IGMH isosurfaces. Importantly, chiral inversion of single strands only happened within the parallel dimers, irrespective of the contact modes between strands. Atoms coloring scheme is: red, oxygen; blue, nitrogen; white, hydrogen, and gray, carbon. The IGMH analysis for charged LF3LK dimers is given in Supplementary Fig. 3.To further determine which arrangement was preferable, we calculated the binding energies of the F3K dimers. In contrast, the DI3LK and DI3DK dimers were also included. Considering the three FB, FF, and BB contacting modes and the charged state of Lys4, 72 optimized dimer conformations were employed for such a calculation (Supplementary Table 1). For aliphatic I3K peptides, the dimers with anti-parallel arrangements always exhibited lower binding energies than the parallel ones, irrespective of their contacting modes (FF, FB, and BB) and charged states (neutral and positively charged). For aromatic F3K peptides, however, the dimers with parallel arrangements always displayed lower binding energies than the anti-parallel ones, even for the charged ones. Due to the possible electrostatic repulsive interactions between positively charged Lys4 side chains, the difference in the binding energy for F3K between the parallel and anti-parallel arrangements mostly decreased when the dimers were positively charged through the protonation of Lys4 side chains.Although it is generally perceived that the backbone H-bonding is slightly stronger for anti-parallel arrangements than parallel ones, we here demonstrated stronger parallel H-bonding interactions within F3K dimers, by using the core-valence bifurcation (CVB) index (refer to Supplementary Method 1 for the CVB index definition). Through the topological analysis of the electron localization function, the index can quantitively describe the H-bonding strength: the lower the CVB index is, the stronger the H-bond will be19. Except for the BB mode of DF3DK, all the parallel F3K dimers exhibited lower CVB indices after structural optimization than the anti-parallel ones for each contacting mode (Fig. 3). Such a result was virtually consistent with previous predictions for parallel β-sheets favorably formed by aromatic Phe residues20. We further verified that the parallel-displaced orientation of benzene rings within parallel arrangements led to the formation of aromatic ladders (Fig. 4, as discussed below). Such a well-ordered packing mode was most likely to greatly alleviate the potential intermolecular steric hindrance, thereby constituting the main drive for the formation of stronger H-bonding interaction between parallel backbones. In contrast, there was a lack of aromatic ladders for anti-parallel arrangements (Supplementary Fig. 7).Fig. 3: CVB indices of F3K β-sheet dimers.Each dimer has six conformations that are differentiated by parallel and anti-parallel arrangements and three contacting modes. For each dimer conformation, the index shown was the average value of the indices of all interstrand H-bonds.Fig. 4: Parallel LF3LK dimers and pentamer.a Parallel LF3LK dimers with FF, FB, and BB contacting modes. Yellow and blue colors are used to distinguish the two molecules. b Parallel LF3LK pentamer containing one FF, one BB, and two FB modes, in which two side-chain aromatic ladders were formed along the long axis of the β-sheet. Atoms coloring scheme is: red, oxygen; blue, nitrogen; white, hydrogen, and gray, carbon.The most striking finding with the dimers was that chiral inversion occurred for single β-strands for all the parallel arrangements (FF, FB, and BB). For example, LF3LK β-strands turned into right-handed ones (left halves of Fig. 2 and Supplementary Fig. 3) and DF3LK β-strands converted into left-handed ones (left halves of Supplementary Figs. 4, 5). In contrast, there was no chiral inversion within all the anti-parallel dimers. For example, LF3LK and DF3LK β-strands adopting anti-parallel arrangements remained left- and right-handedness, respectively (right halves of Fig. 2 and Supplementary Figs. 3–5). This chiral inversion within the parallel dimers was indeed driven by the parallel-displaced contacts between side-chain benzene rings (Fig. 4a). Such a contacting mode of benzene rings not only caused stronger π-π stacking but also strengthened H-bonding between backbones via decreasing intermolecular steric hindrance, as described above. As a result, the parallel dimers with chiral inversion exhibited lower binding energies (Supplementary Table 1) and were thus thermodynamically favored, compared to the anti-parallel ones in which the strand handedness remained unchanged (Supplementary Fig. 7a).Based on the optimized dimers (parallel, Fig. 4a; anti-parallel, Supplementary Fig. 7a), the Kabsch algorithm was then applied to construct assemblies at higher structural levels along the H-bonding direction. This method enables the best alignment of β-strands within their assemblies, by calculating the optimal rotation matrix that minimizes the root mean squared deviation (RMSD) between two paired sets of points (backbone H-bonding donors and acceptors)21. Pentamers featuring a repeat of one FF, one BB, and two FB modes were constructed (Supplementary Fig. 8). After structural optimization, two aromatic ladders were clearly formed with the parallel pentamer along the H-bonding direction (Fig. 4b) while there was no such an ordered aromatic ladder for the anti-parallel pentamer (Supplementary Fig. 7b). These aromatic ladders between β-strands were reminiscent of the Phe zipper interaction between β-sheets, which was formed via their facial complementarity22. Further packing of the optimized pentamers along the H-bonding direction via the Kabsch algorithm gave rise to long β-sheets. After structural optimization using a semiempirical QC method, GFN0-xTB23, parallel β-sheets exhibited left-twisted spirals for LF3LK and LF3DK and right-twisted spirals for DF3LK and DF3DK (Fig. 5a). At much higher structural level, lateral stacking of these left- and right-handed β-sheets will inevitably result in the formation of fibrils with left- and right-handedness, respectively, in good line with our experimental observations (Fig. 5b). Because no chiral inversion occurred for single strands within anti-parallel arrangements, anti-parallel β-sheets would exhibit right-twisted spirals for LF3LK and LF3DK and left-twisted spirals for DF3LK and DF3DK, thus contradicting our experimental observations and excluding the possibility of these microscopic structures.Fig. 5: Handedness of multi-stranded β-sheets and nanofibrils.a Multi-stranded parallel β-sheets for LF3LK, LF3DK, DF3LK, and DF3DK and anti-parallel β-sheets for DI3LK and DI3DK after structural optimizations. Atoms coloring scheme is: red, oxygen; blue, nitrogen; white, hydrogen, and gray, carbon. b Nanofibrils formed by the six peptides and their handedness. Scale bars, 20 nm.In contrast, there was no chiral inversion for I3K strands when packing into dimers, regardless of parallel and anti-parallel arrangements (Supplementary Fig. 9). The underlying mechanism was due to the lack of side-chain aromatic rings in I3K peptides, although Ile has similar hydrophobicity and β-sheet forming propensity to Phe24,25. As a consequence, the hydrophobic collapse of Ile side chains cannot provide a high orientation and a highly ordered side-chain packing, thus being unable to reverse the handedness of single strands upon packing into dimers and higher-order structures such as β-sheets and nanofibrils.Handedness evolution with other amphiphilic aromatic peptidesWe extended our investigation on all L-form Fmoc-FFy and Fmoc-FWy peptides9. Although the right-handedness of Fmoc-FWy nanofibers was proposed to be mainly caused by the intermolecular steric hindrance between bulky Trp side chains, the relationship between suprastructure handedness and aromatic interactions remains elusive.Consistent with LF3LK, our simulations indicated that single strands of Fmoc-FFy and Fmoc-FWy twisted in a left-handed direction (Fig. 6a, b, with Fmoc-FFR and Fmoc-FWR as the examples). When packing into β-sheet structures, these strands tended to adopt parallel arrangements within a β-sheet, imposed by the π-π inter-locking of Fmoc groups between adjacent β-sheets26,27. Upon forming dimers, chiral inversion happened for single β-strands within the optimized Fmoc-FFR dimeric structure (from left-handedness to right-handedness), in which the side-chain benzene rings adopted a parallel-displaced orientation and thus resulted in strong π-π stacking interactions (Fig. 6c), similar to LF3LK and LF3DK. In our simulations, we deliberately constructed parallel Fmoc-FFR dimers without chiral inversion for single strands (Fig. 6d). The dimeric structure formed at the initial stage of structural optimization exhibited weaker side-chain π-π stacking interactions. Afterward, this structure rapidly converted into the structure shown in Fig. 6c, accompanied by the chiral inversion of single strands, again exhibiting a thermodynamically favorable chiral inversion. As expected, the optimized dimers containing right-handed strands further evolved into left-handed β-sheets (Fig. 6g), as demonstrated by the Kabsch algorithm, and these left-handed β-sheets would eventually associate into left-handed helical nanofibers, consistent with experimental observations (Fig. 6i).Fig. 6: Handedness evolution for Fmoc-FFR and Fmoc-FWR.a, b Single β-strands. c–f Dimers. g, h Multi-stranded β-sheets. i, j Self-assembled β-sheet nanofibrils observed from experiments. Note that chiral inversion for single Fmoc-FFR strands occurred upon dimerization and further assembly, while it was not the case for Fmoc-FWR. Atoms coloring scheme is: red, oxygen; blue, nitrogen; white, hydrogen, and gray, carbon. Scale bars, 20 nm.In contrast, Fmoc-FWR β-strands remained left-handedness within the optimized dimeric structure (Fig. 6f), that is, no chiral inversion. More importantly, both benzene and indole rings were parallel-displaced in such a dimeric conformation, and there were strong π-π stacking interactions between the two strands, as denoted by the magenta arrow. The subsequent packing of the dimers along the H-bonding direction led to the formation of right-handed β-sheets (Fig. 6h), which would further associate into right-handed helical nanofibers (Fig. 6j). Similarly, we also constructed parallel Fmoc-FWR dimers with chiral inversion for single strands (from left-handed to right-handed). At the initial stage of our structural optimization, however, there was marked steric repulsion between two indole rings, making them less contact within such a structure (as indicated by the black arrow in Fig. 6e). At the final stage of structural optimization, the dimeric β-sheet structure collapsed.
