Atomic Scale Structure of Self‐Assembled Lipidated Peptide Nanomaterials

β‐Peptides have great potential as novel biomaterials and therapeutic agents, due to their unique ability to self‐assemble into low dimensional nanostructures, and their resistance to enzymatic degradation in vivo. However, the self‐assembly mechanisms of β‐peptides, which possess increased flexibility due to the extra backbone methylene groups present within the constituent β‐amino acids, are not well understood due to inherent difficulties of observing their bottom‐up growth pathway experimentally. A computational approach is presented for the bottom‐up modelling of the self‐assembled lipidated β3‐peptides, from monomers, to oligomers, to supramolecular low‐dimensional nanostructures, in all‐atom detail. The approach is applied to elucidate the self‐assembly mechanisms of recently discovered, distinct structural morphologies of low dimensional nanomaterials, assembled from lipidated β3‐peptide monomers. The resultant structures of the nanobelts and the twisted fibrils are stable throughout subsequent unrestrained all‐atom molecular dynamics simulations, and these assemblies display good agreement with the structural features obtained from X‐ray fiber diffraction and atomic force microscopy data. This is the first reported, fully‐atomistic model of a lipidated β3‐peptide‐based nanomaterial, and the computational approach developed here, in combination with experimental fiber diffraction analysis and atomic force microscopy, will be useful in elucidating the atomic scale structure of self‐assembled peptide‐based and other supramolecular nanomaterials.


Introduction
[5] Small DOI: 10.1002/adma.2023111039][10] Additionally, peptide amphiphiles or lipidated peptides containing a hydrophobic lipid chain coupled to an oligopeptide sequence, to induce a secondary structure, self-assemble into a range of defined morphologies including nanofibers, [11][12][13][14][15][16] nanotubes, [11] twisted and helical ribbons, [17] micelles, [18] and nanotapes. [6]The most widely studied class of lipidated peptide consists of one alkyl tail that is generally attached to the N-terminus which can self-assemble in water resulting in nanostructures [12,[19][20][21][22][23][24] that are amenable to a wide range of bioactive ligands attached at the C-terminus. [11,25]nlike -peptides that have attracted most attention, [2,[26][27][28][29][30][31][32][33][34][35] the more recently discovered -peptide scaffolds are of particular interest because of their rapid selfassembly in water, resistance to proteolysis and mechanical stability. [36]39][40] -peptide scaffolds comprise exclusively of -amino acids.These amino acids are similar to -amino acids in that they contain an amino terminus and a carboxyl terminus.However, in -amino acids two carbon atoms separate these functional termini.-amino acids, with a specific side chain, can exist as the R or S isomers at either the  (C2) carbon or the  (C3) carbon.A  3 -peptide is made up of  3 -amino acids, which thus contains an additional methylene group for each amino acid within the backbone.The increased backbone flexibility imparted by the additional carbon atom of -peptides results in secondary structures and assemblies different to the naturally occurring -peptides. [36]e have previously shown that the N-acetylated  3 -tripeptides form helices with a near perfect pitch of three residues per turn, stabilized via six axially-oriented intermolecular hydrogen bonding interactions forming a cylindrical nanorod. [41,42]We have also shown this self-assembly to be persistent under a variety of conditions and meticulously investigated the role of the -amino acid side chains in the facial association of these self-assembled peptide nanorods, and in the formation of higher order structures. [43]-peptides are resistant to proteolytic degradation in biological systems, making them appealing for potential use in regenerative medicine and drug delivery, where long-term stabilization is required. [40]However, the specific interactions driving the self-assembly of -peptides are less understood compared to naturally occurring -peptides.Small  3 -peptide monomers are known to spontaneously form fibers of differing morphologies, depending on the  3 -amino acid sequence. [43]Specifically,  3 -peptides which self-assemble into hydrogels, by forming a homogeneous matrix of fibril-like structures, could potentially act as stabilized bio-scaffolds as a depot for localized long-term delivery of therapeutics in treating brain injuries and neurodegenerative diseases, [38,39] assisting with neural regeneration whilst reducing inflammation post-application of the hydrogel.A summary of the fibrous structures derived from -peptide self-assembly has been reported in a review by Kulkarni, et al. [36] While insights into fibrillar triple 14-helix structures formed by small tripeptides comprising N-acetyl capped  3 -amino acid sequence LIA have been obtained by complementing fiber diffraction data with molecular dynamics simulations, [41] the exact mechanisms of self-assembly and the arrangement of the -peptide units in supramolecular structures are still largely unknown.
Recently, a series of lipidated  3 -tripeptides reported by Habila et al. [43] were shown to form distinct supramolecular structures, depending on the positioning of the acyl chain within the  3 -tripeptide sequence.The lipidated supramolecular peptide assemblies comprised both well-structured and flexible regions, which introduces significant challenges for structural characterization by both experimental methods and computational modelling approaches.The incorporation of an alkyl chain within a self-assembling -peptide often results in a controlled selfassembly to form cylindrical nanofibers with uniform diameter, thereby expanding the potential of these materials. [11,13,44]nderstanding the interactions driving the self-assembly mechanisms and the resulting supramolecular structures of  3peptides is crucial to the design of novel biocompatible materials for specific applications.Computational methods have scope in complementing experimental approaches in guiding further de-velopments, and in understanding peptide self-assembly, by revealing the key interactions involved in the self-assembly process.Molecular dynamics (MD) is a tool that has been used to study peptide dynamics and self-assembly processes at different stages of progression.In our recent literature review, [45] we revealed that it can be challenging for "spontaneous" or "brute force" MD simulations to access the timescales on which the spontaneous self-assembly of biomolecules occurs, due to the sizeable energy barriers involved in solvation and desolvation of the intermediate aggregates in the self-assembly pathway.However, MD simulations of small self-assembled systems, comprised of random arrangements of the monomeric units into dimers or small oligomers are feasible, up to the microsecond timescale.By analyzing the structures observed through these simulations, insights into the mechanisms leading to the formation of the 2D and 3D supramolecular structures can be made, and their stability assessed, by regular MD simulation.One approach to expediting the crossing of energy barriers present during spontaneous peptide self-assembly is by combining enhanced sampling algorithms with classical MD simulations. [45]etadynamics (MetaD), [46][47][48] originally termed "Local Elevation", [49] is one such enhanced sampling method that can assist with the exploration of conformational space for biomolecules.With MetaD, movement through multidimensional phase space is described in terms of one or more variables (collective variables, or CVs), such as an interatomic distance, an angle or a dihedral angle within a molecular system, [50][51][52] the output from a principal component analysis (PCA), [53][54][55] or the number of contacts made between specific groups of atoms to make the biasing of phase space toward specific biological endpoints a function of the interactions made in a system. [56,57]The aim of CVs is to reduce the dimensionality of the atomic coordinates of the system, and represent the system free energy as a function of a small number of variables, describing as much of the real phase space of interest as possible.Metadynamics accelerates the crossing of energy barriers by adding biasing potentials along the chosen CV space at set time increments, to penalize the system for remaining in one place for too long.A detailed review of the MetaD and related enhanced sampling methods applied to study peptide self-assembly mechanisms can be found in reference. [45][60][61][62][63][64][65][66][67][68][69][70] Some specific examples include studies by Chrobak et al. [67] and Macchi et al., [65] who reported the application of MetaD methods to enhance the sampling of peptide dimerization, revealing insights into the initial stages of peptide self-assembly.Another report details the comprehensive structural sampling of low-order amylin peptide aggregates by use of MetaD methods. [56]The authors employed many MetaD CV parameters to define the self-assembly reaction pathway, highlighting that self-assembly is a complex and multidimensional process involving many competing interactions.However, to the best of our knowledge, there is no current study where the MetaD methods have been applied to simulate peptide self-assembly from the "bottom-up", starting from the monomeric units and progressing to supramolecular fibrillar aggregates, resulting in ordered fibrils on the nanometer length scale.In this work, we apply a combination of classical MD and MetaD methods to get insights into and understand the step-bystep mechanisms of formation of stable supramolecular structures from the lipidated  3 -peptide monomeric units.We report a systematic, bottom-up, atomistic modelling approach to study peptide self-assembly.Specifically, we implement the well-tempered MetaD (WT-MetaD) [71] method with multiple walkers [72] to sample the conformational space of octameric aggregates of R2-C12  3 -tripeptide carboxylic acid and its Cterminal amidated variant, that form different experimentally observed fiber morphologies (Table 1).By analyzing the structures sampled by the WT-MetaD simulations, we determine the seeds which may potentiate the different fiber morphologies and reveal putative supramolecular structures of the low dimensional materials formed by the acid and amide form of the lipidated  3peptides.We subsequently apply unbiased classical MD simulations to confirm the stability of the model, self-assembled peptide structures, and validate these models by comparison to experimental X-ray fiber diffraction and atomic force microscopy data.

Experimental
The specific peptide sequences and chemical structures used in this study are shown in Table 1.

Peptide Synthesis
The methods for peptide synthesis and purification are described in the supplementary information, Section S1.

Circular Dichroism (CD) Spectropolarimetry
Spectra were acquired using a JASCO J-815 spectrophotometer.The acquisition interval was between 190 and 260 nm with a data pitch of 0.5 nm, a continuous scanning mode at a speed of 50 nm min −1 with a response time of 2 s, and a band width of 1 nm.For all spectra, an average of 3 accumulations were used while keeping the temperature of the instrument and the cell constant at 20 °C by means of a Peltier module and a water-cooled system.A continuous flow of N 2 gas at 5 L min −1 was employed to purge the instrument of oxygen.Quartz cells with an optical path of 1 cm were used for all measurements.Data acquired in millidegrees (mdeg) was converted to ellipticity  (deg cm 2 dmol −1 ).

Atomic Force Microscopy (AFM) Imaging
AFM was performed on a Bruker Fastscan AFM with a Multimode head. 2 μL of a 0.125 mg mL −1 peptide solution in MilliQ water was placed on a freshly cleaved mica surface.The sample was air-dried and then blown with gentle stream of N 2 gas.Images were obtained via tapping mode with ScanAsist-Air silicon nitride cantilever (Bruker, Singapore) with a nominal spring constant of 0.4 N m −1 or for higher detail images with Fastscan-D SS (Bruker, Singapore) with a nominal spring constant of 0.25 N m −1 .Topographic, phase and amplitude images at a resolution of 512×512 were simultaneously obtained using scan frequency of 1 Hz with typical scan sizes of 5 μm x 5 μm and 1 μm x 1 μm.Images were processed with a sequence of plane fitting, offset flattening and a third-degree polynomial background subtraction using Gwyddion 2.55 (www.gwyddion.net)software.

Fiber Diffraction Analysis
3 -peptides (Table 1) were dissolved at 10 mg mL −1 in membrane filtered (2 μm pore size) distilled water and allowed to incubate at room temperature for 24 h.A droplet of about 10 μL of each solution was placed between two wax-filled capillary tubes arranged in a petri dish and the solution was allowed to dry overnight resulting in partially aligned fiber bundles.The samples were mounted on a goniometer head and diffraction data was collected using a Rigaku rotating anode X-ray source with a Saturn CCD detector, an exposure time of 30 or 60 s and specimen to detector distance of 50 and 100 mm respectively.Diffraction patterns were inspected using mosflm [73] and examined in detail using CLEARER. [74]Measurements were collected from the diffraction spacings using modules within CLEARER and comparisons were made between experimental and calculated diffraction patterns.The model structures generated from molecular modelling described below were uploaded to CLEARER and diffraction patterns were calculated utilizing the diffraction calculation module using unit cell parameters established from measurement of the diffraction signal positions.

Bottom-Up Multistep Modelling of Self-Assembled Lipidated Peptide Materials
All-atom models of the peptide 1 and 2 assemblies were built from the bottom-up, via a multistep process involving molecular A) Schematic of "bottom-up" assembly of peptide-based fibrillar aggregates, starting from monomers (peptide 1 with a C-terminal carboxylate, depicted on the left and peptide 2 with a C-terminal amide illustrated on the right).This process progresses from monomers to oligomers and, finally, into superstructures that are consistent with experimental observations.B) Flow chart of the multistep procedure used to simulate the bottom-up assembly of -peptides 1 and 2. The detailed computational protocol is provided in Section S2 in the Supporting Information.For a more comprehensive visual representation of the models created at different stages of the multistep procedure, refer to Figures 2 and 3.
dynamics with the enhanced sampling procedures described below and in the Supporting Information.The process started from MD simulations of individual peptide monomers and progressed via enhanced sampling by the WT-MetaD method applied to higher oligomers (octamers).The dimer/trimer fragments extracted from the low-energy octameric aggregates sampled by WT-MetaD were used as putative seeds to potentiate periodic fibrillar assemblies.These small dimer/trimer seeds were extracted from the octameric systems to mimic the boundary effects of the fibrillar assembly, by eliminating the boundary interactions of the seeds with solvent.The dimer/trimer fragments were selected to maximize backbone hydrogen bonds, and to allow for near parallel lipid alignment within the selected fragment, to then enable the linear stacking of monomers, favourable for fibril formation in subsequent unbiased molecular dynamics simulations.The assembled periodic structures were subsequently subjected to relaxation by a systematic, classical MD simulation protocol, to ensure the stability of the assemblies formed, and obtain the structural details for experimental validation.A schematic of the proposed "bottom-up" self-assembly modelling approach is shown in Figure 1A, along with the multistep simulation workflow shown in Figure 1B, with each step outlined below.Complete details of the simulation workflow are described in Section S2 in the Supporting Information.

MD Simulations
MD simulations were performed using GROMACS-2020.3. [75]o parameterize the  3 -peptides, CHARMM-36M [76] compatible parameters were used. [77]Additional angular and dihedral terms specific to the amide linkage between the lipid and  3amino acid residues were obtained using the CHARMM-GUI webserver. [78,79]The system was solvated to a density of ≈1.0 g mL −1 with explicit TIP4P water (for all aqueous-state systems).The overall charge of the system was made neutral through the addition of sodium or chloride ions.Additional sodium and chloride ions were added to make a total salt buffer concentration of ≈150 × 10 −3 m, emulating physiological conditions.See Section S2 in the Supporting Information for further information.

Peptide Monomer MD Simulation
Classical MD simulations were performed of the solvated monomers of peptide 1 for 2 μs each, in triplicate, with randomized initial velocities.From the simulated ensemble a 2D free energy surface with respect to the peptide mainchain (backbone N, C, C, and O atoms, including oxygens in C-terminus) radius of gyration (r Gyr ) and the C-to N-terminal distance (CN dist ) was generated, and three low-energy (high population) clusters were observed (Figure S3, Supporting Information).The lowest energy cluster with the most extended structures, having maximum values of both r Gyr and CN dist , was identified.A representative structure was then extracted from this cluster (Figure S3, Supporting Information).This representative low energy extended backbone conformation of peptide 1 was selected for construction of the starting structure and the enhanced sampling simulations of both peptides 1 and 2 oligomers.

Fibril Seed Formation Via Peptide Octamer Sampling by WT-MetaD
All multiple walker, WT-MetaD simulations [71,72] were run for systems comprising 8 randomly orientated extended peptide monomers identified in the previous step, using GROMACS-2020.3 [75,80]with Plumed 2.6.2, [81]where the bias history was shared among three concurrently running replicates.The replicates for multiple walker WT-MetaD had randomized initial velocities and were generated using the equilibration phases described in the MD Simulations section (Supporting Information).The CVs biased in the WT-MetaD simulations were: (1) the number of contacts between the peptide backbone N and O atoms (the backbone hydrogen bonds), (2)   the number of contacts between the lipid carbon atoms (hydrophobic lipid interactions), and (3) the number of contacts between the Lys amino sidechain, NH 3 + and the Cterminal carboxylate for peptide 1 or amide group for peptide 2 (salt bridge interactions between Lys-3 and the C-terminus).See Section S2 of the Supporting Information for further information.

Analysis of the Free Energy Surfaces (FES) and Specific Interactions for Self-assembling Peptides
The FES of each WT-MetaD sampled self-assembling peptide system was generated by inversion of the biasing potentials applied in the predefined CV space.To determine the fibril seeds that can initiate or promote fibril self-assembly, clustering of structures in the FES was performed by analysis of the three biased CVs and also of additional unbiased CVs with MetaGUI, [82] using the WHAM algorithm. [83,84]The order parameters (Table 2) were selected to account for the phase space relevant to self-assembly.Specifically, CVs 1-6 describe all competing interactions occurring during peptide self-assembly, including backbone hydrogen bonds (CV1), lipid-lipid hydrophobic interactions (CV2), and the salt bridges that may form between the charged groups (CV3).CVs 4-6 are terms relating to the corresponding interactions made with water, while CVs 7 and 8 model the de-aggregation and orientation of the peptide units.Values of the cluster center coordinates are presented in Tables S4 and S5 in the Supporting Information.

Fibril Seed Extraction
To generate fibril seeds for use in the simulations of the fibrillar peptide self-assembly, representative structures of each octamer cluster from the WT-MetaD trajectories were taken from the ensemble of structures; see details in the Supporting Information.The processed representative structures with the most locally ordered peptides (shown by orange-colored carbon atoms, Figures 2A and 3A) were selected as fibril seeds for subsequent MD simulations of the periodic fibrillar assemblies.The boundary peptides (grey) in the oligomer were required to mimic a peptide crowd environment for the central seed (orange in Figures 2A and 3A), and to allow for favourable lipid-lipid interactions and orientations.Subsequent simulations of protofibril formation were then performed with the replicate seeds in proximity within the periodic cell thus mimicking the peptide boundary effects.This approach enabled us to mimic the effects of environment on fibril seed evolution, which is one of the current computational challenges in simulating peptide self-assembly. [45]

Fibril Assembly, Fibril Elongation/Growth, and Fibril Equilibration
The representative structures from clusters identified by WT-MetaD simulations were selected if they contained specific peptide motifs to be used as seeds in the subsequent periodic fibrillar assembly simulations via equilibration protocols 1-3 (Figure 1 and Tables S1-S3, Supporting Information).Specifically, peptide arrangements that allowed for stacked backbone hydrogen bonding and projection of the lipid chains towards the center of the construct were considered as putative seeds for fibril assembly (Figures 2A and 3A).A trimer fragment for peptide 1 and a dimer fragment for peptide 2, both with aligned adjacent peptide backbones (conducive to subsequent stacking along the fiber axis) were identified and extracted from their respective minimum energy octamer clusters as sampled by metadynamics.These fibril seeds were replicated and rotated/translated to allow for stacking of the lipid groups in a parallel arrangement.The individual seeds were separated by ≈1 nm within a periodic cell to ensure sufficient freedom for subsequent relaxation (Figures 2B,C  and 3B).The periodic structures were then equilibrated via the multistep process described in detail in the Supporting Information (Section S2, Supporting Information), resulting in the assembled proto-fibrillar structures shown in Figure 2D,E for peptide 1, and Figures 3C for peptide 2. Using the fibril elongation/growth protocol, extended 3D periodic fibril models were produced as shown in Figure 2F,G (peptide 1) and Figure 3D (peptide 2).

MD Simulations of the Assembled Periodic Fibrillar Structures
Unbiased spontaneous MD simulations were performed on the extended 3D periodic assembled peptide fibril models to equilibrate the formed structures and compare with the experimental fiber diffraction measurements (Figures 2H and 3E).

Fiber Characterization by AFM Imaging and Fiber Diffraction
Morphology of the fibers formed by peptides 1 and 2 were analysed by AFM (Figure 4A,C; Figures S8-S11, Supporting Information).Peptide 1 formed nanobelts while peptide 2 formed twisted fibrils, indicating that the C-terminal amidation of 1 caused this morphology switch and altered the assembly behavior.Closer examination of the nanobelts formed by peptide 1 revealed the presence of stacked layers.The heights of these layers were measured at two different sites with three repeats at each site and found to be in the range of 2.5-3.0 nm (Figure S12, Supporting Information).X-ray fiber diffraction (XFD) data revealed a well-ordered pattern for peptide 1, indicating a high degree of structural order arising from the fibers (Figure 4B).XFD patterns showed a series of high-angle diffraction signals on the meridian arising from the repeat distances along the fiber axis.Sharp diffraction signals also appear on the equator of the pattern which arise from the packing and organization of the lateral interactions between molecules.Major key signals appear at 0.47; 0.46; 0.45; 0.43 nm on the meridian.Major, strong, sharp equatorial signals were observed at 0.23; 0.16; 1.2; and 0.98 nm.
X-ray fiber diffraction from partially aligned R2-C12 amide (peptide 2) also showed a well oriented pattern, with well-defined meridional and equatorial orientation (Figure 4D).Major signals appeared at 0.49 nm on the meridian with 0.45 nm offmeridionals, with peaks at 1.73 and 1.14 nm on the equator.Comparison of the diffraction data from the free acid (peptide 1) with the amide (peptide 2) showed that the free acid form had a series of very sharp reflections (Figure 4B), likely to have arisen from the well-ordered semicrystalline packing.In contrast, the XFD pattern from the amide form suggests a more helical nature, with clear, strong off-meridional signals.These patterns are consistent with the observations from AFM, showing the nanobelts for peptide 1 versus the narrow filaments formed by peptide 2.

All-atom Theoretical Models of the Self-Assembled Peptide Fibers: Bottom-Up Modelling from Peptide Monomers to Fiber Seeds to 3D Periodic Extended Fibrillar Structures
Classical and enhanced sampling MD simulation methods were applied to study the self-assembly of peptides 1 and 2 and assist with the atomic-scale resolution of their fibrillar aggregates.Following the protocols described above, we present the peptide fiber structures in all-atom details, simulated from the "bottomup", from individual monomers through small clusters (seeds) to periodic fiber aggregates.Different resultant structure morphologies were obtained for the bottom-up assemblies of the R2-C12 carboxylate peptides (peptide 1) and their amidated variants (peptide 2).A flat, almost rectangular-prismed structure was formed by peptide 1, with lipids extended and facing the core of the tape-like assemblies, stabilized by the outer-facing polar and salt-bridge interactions.These rectangular/flat structures were conducive to the lateral stacking of peptide 1 along the "flat" faces (Figure 2E-H).By contrast, a flexible, cylindrical fiber was produced by simulations of the peptide 2 assembly (Figure 3C).Due to the curved edges of the peptide 2 fibers (Figure 3C-E) lateral stacking appears sterically hindered, affording the twisted fibril morphology.As with peptide 1, peptide 2 lipids tend to orientate towards the core of the assembled structure.These results demonstrate that C-terminal amidation of peptide 1 to produce peptide 2, leads to a different mode of selfassembled morphology, as was also observed by AFM and XFD (Figure 4).

Detailed Theoretical and Experimental Characterization of Self-Assembled Peptide Nanomaterials
The supramolecular nanostructures produced by MD simulations are in broad agreement with both XFD and AFM data.The peptide 1 XFD pattern showed more equatorial spacings and the spacings were less diffused compared to peptide 2 (Figures 4B  and 4D).The only sharp signal from the diffraction data of peptide 2 was at 0.49 nm on the meridian, which suggests a regular stacking along the fiber axis.These patterns observed by fiber diffraction data support the MD simulations results, whereby the peptide acid (peptide 1) organizes to form more ordered architecture (Figures 2 and 5A) while the amide (peptide 2) forms cylindrical fibers (Figures 3 and 5B).The CD spectra for both peptides (1 and 2) (Figures S13 and S14, Supporting Information) show that while peptide 1 has a robust secondary structure, peptide 2 does not have a defined secondary structure in solution.Fiber diffraction data and AFM images are therefore in good agreement with our modelling, where each method demonstrates that peptide 1 orients in a well-ordered semicrystalline packing, forming defined nanobelt morphology, a consequence of the secondary structure and salt-bridge interactions, while pep-tide 2 appears to be more dynamic and flexible.The CD spectrum matches well with the hairpin structure reported in the literature and complements the -peptide 1 conformation within the minimum structural unit used for XFD prediction (Figure 7). [85,86]The MD simulation results of the equilibrated fibrils were also consistent with AFM, where peptide 1 was observed as laterally associated belt/tape like assemblies (Figure 4A), reminiscent of the equilibrated structure seen in Figure 5A.By comparison, cylindrical, twisted fibril morphologies were observed by AFM for peptide 2 (Figure 4C), congruent with the MD simulation structures (Figure 5B).
The sharp diffraction signals of the XFD pattern from peptide 1 flat nanobelts suggest semicrystalline packing within the diffraction sample while the broader diffraction peaks from peptide 2 twisted fibrils indicate a more dynamic/flexible organization, consistent with the modelled peptide assemblies.This finding is demonstrated by the RMSD measurements (Figure S7, Supporting Information) within the simulated equilibrated ensembles of the fibrillar peptide nanostructures (Figure 5).To ensure the reliability of our proposed all-atom structural models of the peptide nanostructures we subjected the protofibrils to six replicate spontaneous MD simulations with randomized initial velocities.The peptide 1 structural model converged to ≈0.19 nm RMSD from the initial structure, with consistent results in all six replicates (Figure S7A,D, Supporting Information).The RMSD plots of the peptide 2 assembly are shown in Figure S7B,C,E,F in the Supporting Information.Generally, both strand 1 and 2 of peptide 2 converged to 0.8 to 1.3 nm RMSD from the initial structure, respectively, indicating significantly more dynamic behavior for peptide 2 compared to 1. Therefore, semicrystalline packing obtained for peptide 1 by simulations was consistent with the fiber diffraction experiments (Figure 4B).Similarly, the dynamic be-havior of the simulated peptide 2 nanostructures is consistent with the lack of sharp peaks observed by XFD pattern (Figure 4D).
To relate the theoretical simulations of peptides 1 and 2 nanostructures more closely to the experimental observations, we generated plots of different functional group atom density profiles along the plane perpendicular to the fiber axes (Figure 6).As expected, for the fibers of 1 and 2, the polar portions faced outward while the hydrophobic lipid groups aggregated towards the core of the structures.The peptide 1 flat nanobelt model represents a single layer of flat nanobelts.From the MD simulations, residual water trapped within the solid fiber was observed predominantly between the repeat layers at the unit cell interface, intercalated with the polar or charged backbone and sidechain atoms.The experimentally observed repeat layering for the peptide 1 nanobelts of approximately 2.5-3.0 nm (see height profiles in Figure S12 in the Supporting Information), and the peak observed in the XFD pattern at ≈3.3 nm (Figure 4B), was consistent with the density plots generated from the MD simulations.Specifically, the lipid moieties of peptide 1 extend ≈3 nm along the x-axis.Furthermore, one layer of the flat nanobelt structure was found to span approximately 4 nm, as evaluated by the distance between the backbone atoms of the adjacent leaflets (Figure 6A).These distances of 3-4 nm from MD simulation analysis are within the experimental errors of both the AFM and XFD experiments.
Atom density profiles obtained from the MD simulated ensemble of peptide 2 twisted fibrils were also consistent with the (limited) data available from the XFD pattern for this more dynamic assembly.Two fibril strands of peptide 2 were simu-lated side-by-side (Figure 3), affording two density distributions (Figure 6B).The peak density values for the backbone heavy atoms of the neighboring strands are ≈1.9 nm apart, with this separation distance being in good agreement with the peak of 1.73 nm observed in the XFD pattern of peptide 2 twisted fibrils (Figure 4D).To further validate the model structure of peptide 1, we simulated XFD patterns to compare with experimental XFD data (Figure 7).A single layer from the model was extracted and CLEARER [74] was used to calculate the diffraction pattern from a model structure in a unit cell 4.0 × 2.4 × 0.5 nm a = b = g = 90°, which allowed suitable packing of the molecules to generate an idealized structural model which was highly repeating.CLEARER imposes cylindrical symmetry to produce a simulated diffraction pattern (Figure 7C) which can be compared to the experimental data.The comparison shows an excellent match for meridional signals complementing the experimentally observed doublet at 0.46-0.47nm and a weak signal at 0.45 nm which arise from the organization of the stacked layers along the fiber axis.Off meridionals appear to match at 0.43-0.44nm.Equatorial signal positions are dominated by the packing between the molecules perpendicular to the fiber axis but modulated by the organization of the sidechains, and relative intensities will be affected by the sidechain orientations.Comparison of the simulated and experimental data shows a strong low angle signal at 2.40 nm which correlates with the peptide layers, matching the experimentally observed signal at 2.35 nm.Additionally, the predicted signal at 1.56 nm matches the experimental signal at 1.57 nm.Signals also appear in the simulated pattern at 1.29 and 1.20 nm.At wider angles, signals become more difficult to measure accurately, but overall there is a sound agreement between both the experimental and theoretical XFD data.

Analysis of Interatomic Interactions in the Fibril Assemblies
To probe the specific interatomic interactions driving the selfassembly of peptides 1 and 2 and the observed morphology switch, we extracted the specific interaction distances from the atomic pair radial distribution functions (RDF), obtained from the ensemble of structures generated by MD simulations (Figures 8 and 9).The peak (location and height) in an atom pair distance distribution plot calculated using RDF is related to the probability of a specific interaction occurring at a particular distance separating the pair of atoms, relative to an ideal gas.
For the RDF plot of the backbone nitrogen and oxygen atoms, peaks were observed for interatom distances of d 1 = 0.23 nm, d 2 = 0.29 nm and d 3 = 0.42 nm (Figure 8A,E), where d 1 is the distance between the backbone nitrogen and oxygen atoms within the same peptide backbone amide; d 2 is the interatom distance between adjacently stacked peptide backbone nitrogen and oxygen atoms; and d 3 is the distance between the C-terminal carboxylate oxygen and the adjacent peptide backbone amide nitrogens.The presence of clearly defined RDF peaks representing intra-and intermolecular contacts of the backbone nitrogen and oxygen atoms suggests persistent peptide backbone interactions of all monomers within the nanobelt structure.The RDF results demonstrate that peptide monomer stacking via backbone hydrogen bonding can be suggested as a driving force for formation of the flat nanobelt assemblies observed for peptide 1.Further, the salt bridges formed between the C-terminal carboxylate oxygen and the protonated lysine amino group of an adjacent monomer facilitated the self-assembly and stability of the peptide 1 nanobelts.The interactions between the carboxylate oxygen and the lysine amino nitrogen were evidenced by a broad RDF peak at d 4 = 0.27 nm (Figure 8B), corresponding to the salt bridge between adjacently stacked monomers within the same fibril strand (Figure 8F).Broader peaks in Figure 8B   to a charge-assisted hydrogen bond between the nitrogen atoms of the lysine amino groups and the adjacent backbone oxygen atoms, at d 6 = 0.28 nm (Figure 8C), indicating the lysine amino groups made transient interactions with the peptide backbone, potentially while transitioning between intra-and interstrand salt bridges (Figure 8F).The RDF plot of the lipid carbon atom interaction distances is shown in Figure 8D.The broad, not clearly defined pair distribution around 0.48-0.52nm indicates that the lipids tend to aggregate, making nonspecific but persistent hydrophobic interactions.As observed from the MD trajectories, the lipid groups of peptide 1 tend to self-orientate towards the core of the assembled structure, and exist primarily in an extended conformation, forming "rectangular prism" fibril tape structures.
RDF analysis was also performed on the structural ensemble formed by peptide 2, to gauge for differences in the specific interactions driving the assembly of the original and amidated peptides.From the six replicate MD simulations of peptide 2 RDF plots were generated (Figure 9) to determine the key interac-tions contributing to its assembly.The interatomic interaction pairs driving the self-assembly of peptide 1 were analyzed for the peptide 2 systems, and the RDF plots showed both lower and broader peaks, than in the respective RDF plots of the peptide 1 construct (Figure 8).These results suggest that the key interactions driving the amidated peptide assembly were weaker and less defined than in the original peptide systems.Specifically, in Figure 9A, we show the RDF plot of backbone hydrogen bonding distances obtained from the 6 replicate MD simulations of the peptide 2 construct.Distances d 7 , d 8 , d 9 , and d 10 relate to specific backbone nitrogen-oxygen pairs (hydrogen bonds) separated by 0.29, 0.42, 0.47, and 0.55 nm, respectively.The MD simulations showed backbone hydrogen bonding in the peptide 2 twisted fibril to be more dynamic than in the flat nanobelt structure of peptide 1, as reflected by the presence of four peaks in Figure 9A compared with the two peaks in Figure 8A.Backbone hydrogen bonds tended to break and reform across the backbone throughout simulations of the peptide 2 construct, manifesting in the appearance of peaks at d 9 and d 10 which are not present for peptide 1.Notably, with respect to the effect of C-terminal amidation on its interactions with the lysine amino group, the peak at d 11 = 0.39 nm corresponds to the distance between the C-terminal amide oxygen and the lysine amino nitrogen (Figure 9B,F).Interestingly, this interaction distance (d 11 ) was comparable to the peptide 1 C-terminal carboxylate oxygen and the lysine amino nitrogen pair interaction distance, d 4 = 0.27 nm (Figures 8B and 9F).However, the marked reduction in the d 11 peak height relative to the d 4 peak height (Figures 8B and 9B), demonstrates a significant weakening of the C-terminal oxygen to lysine amine interaction upon C-terminal amidation.Further, the peptide 2 pair interactions at distances d 12 and d 13 represent states where the absent C-terminal amide to lysine interaction is "replaced" by the lysine residue to backbone hydrogen bonding interactions.Additionally, there was an increase in peak height for the lysine amine to backbone oxygen interactions for peptide 2 relative to peptide 1 (d 14 in Figure 9C relative to d 6 in Figure 8C).Generally, it was observed that while the C-terminal amide to ly-sine interactions were often broken (as shown by d 12 and d 13 in Figure 9B), there was a commensurate increase in the specific and nonspecific interactions of lysine amine to backbone oxygen in peptide 2 aggregate systems (Figure 9C).This mobility of the lysine amine relative to the backbone further demonstrates the weakening of the C-terminal amide to lysine interaction in peptide 2 relative to the C-terminal carboxylate interaction with the lysine amine in peptide 1.Non-specific lipid carbon interactions were shielded by solvent-exposed outer hydrophilic groups (i.e., the peptide backbones) of both the peptide 1 nanobelts and the peptide 2 twisted fibrils (Figures 8D and 9D).
These results suggest that the morphology switch from flat nanobelts to twisted fibrils was most likely caused by the replacement of the salt bridge interactions between the lysine amine and C-terminal carboxylate in peptide 1, with the lysine amine to Cterminal amide interactions in peptide 2. The simulated structures revealed that C-terminal carboxylate to lysine amine salt bridge interactions (Figure 8B vs Figure 9B) in the peptide 1 nanobelts provide stabilizing architecture for the backbone hydrogen bonding interactions (Figure 8A vs Figure 9A), therefore reducing the availability of the lysine amine to interact with the backbone oxygen atoms via charge-assisted hydrogen bonding (Figure 8C vs Figure 9C).Due to amidation of the C-terminus, no salt bridges can form in peptide 2, thus removing the scaffolding architecture stabilizing the peptide 1 backbone hydrogen bonds.In the peptide 2 assembly we observed the capacity of the backbone hydrogen bonds to continuously reform, resulting in a more dynamic hydrogen bonding network for peptide 2 (Figure 8A compared with Figure 9A) caused by the weakening of the C-terminal interactions with the lysine amine relative to peptide 1 (Figure 8B compared with Figure 9B).The increased lability of the lysine amine in peptide 2 enables peptide 2 to form additional interactions with the backbone oxygen atoms (Figure 8C compared with Figure 9C) which leads to the twisting of the fiber observed in the MD simulations and experimentally.
These results demonstrate the capacity of atomistic simulation methods to resolve and explain the structures formed by self-assembled peptide biomaterials, even where the atomic coordinates of the assemblies are not experimentally available.Inspired by the distinct morphology differences in the nanomaterials formed by self-assembling lipidated  3 -peptides caused by a single point mutation (amidation) of the C-terminus, we have shown that the bottom-up assembly of peptide-based fibrillar aggregates can be modelled in all-atom details, starting from monomers, toward oligomers and, finally, into superstructures that are consistent with experimental findings.

Conclusion
While peptide self-assembly has been demonstrated as a powerful bottom-up approach to the fabrication of new biocompatible nanomaterials, and a significant number of peptide-based biomaterials have been produced; including peptide amphiphiles, experimentally consistent fully-atomistic models of peptide-based materials are scarce.This deficiency hinders the understanding of their assembly mechanisms and molecular architecture, which is due to the inherent complexities of examining the multiple time and length scales of the self-assembly process both experimentally and computationally, especially at the lowest -nano -end of the time and length scales.Therefore, the determination of high-resolution atomically-resolved structures for a selfassembled nanomaterial would revolutionize our ability to custom design new materials through informed structure-based design rules for modulating biological interactions at the molecular level.
We have reported a systematic bottom-up approach for modelling the self-assembly of  3 -peptide foldamers using metadynamics to enhance the sampling of the initial stages of the seed formation from monomers and oligomers.From multiple walker, well-tempered metadynamics simulations of octameric peptide systems, where the bias used was a function of interactions driving the self-assembly, we proposed initial fibril seed structures that enabled the construction of stable supramolecular peptide morphologies in agreement with experimental fiber diffraction analysis and AFM imaging.Using the developed equilibration protocols, we were able to simulate the self-assembled flat nanobelt structure of the lipidated  3 -tripeptide R2-C12 (pep-tide 1: Ac-AX(Lau)K-OH), which remained stable throughout unbiased MD simulation and agreed well with the experimental data.Using the same equilibration protocols for the R2-C12 amidated peptide (peptide 2: Ac-AX(Lau)K-NH 2 ), we were able to simulate its assembly into the twisted fibril morphology.From analysis of the key interactions driving the self-assembly of both morphologies, specifically, the backbone hydrogen bonds, lysine interactions with the C-terminus and backbone oxygens, and the lipid-lipid hydrophobic interactions, we found that the saltbridges formed between the R2-C12 lysine amine and the Cterminal carboxylate are key drivers to the flat nanobelt formation.These salt-bridges stabilize the hydrogen bonding interactions formed between the stacked monomeric units of R2-C12, providing a scaffolding architecture through which nanobeltlike fibril structures can form.Removal of this salt-bridge by Cterminal amidation of R2-C12 weakens the scaffolding support for backbone hydrogen bonds, leading to more flexible, twisted fibril formation.The curved edges of the twisted fibril strands are less conducive to tight packing than the flat nanobelts formed by R2-C12, thus explaining the morphology switch for the amidated R2-C12 system.All theoretical structural models formed by this bottom-up self-assembly protocol were in good agreement with the AFM observed structures and fiber diffraction data.The methods developed here will be generally applicable to studying the self-assembly of novel peptide superstructures, in their original or functionalized forms, and should be especially powerful in cases where the atomic coordinates of the assemblies are not experimentally resolvable, and/or experimental information is limited.
is a  3 -homoAla residue replacing the methyl R-group with a methylene amide linkage to the alkyl chain;b) Peptide functionalities likely to drive the self-assembly shown with yellow for the lipid chain, blue for the lysine amino group and red for the C-terminal groups.

Figure 1 .
Figure1.A) Schematic of "bottom-up" assembly of peptide-based fibrillar aggregates, starting from monomers (peptide 1 with a C-terminal carboxylate, depicted on the left and peptide 2 with a C-terminal amide illustrated on the right).This process progresses from monomers to oligomers and, finally, into superstructures that are consistent with experimental observations.B) Flow chart of the multistep procedure used to simulate the bottom-up assembly of -peptides 1 and 2. The detailed computational protocol is provided in Section S2 in the Supporting Information.For a more comprehensive visual representation of the models created at different stages of the multistep procedure, refer to Figures2 and 3.

Figure 2 .
Figure 2. The bottom up self-assembly of peptide 1.The peptides are shown in a stick representation with red oxygen, blue nitrogen and white hydrogen atom colors.Only polar hydrogen atoms are shown.For periodic systems the unit cell is shown as a blue transparent box.A) Different orientations of exemplar peptide 1 structure from the energetically favorable octamer cluster obtained by the WT-MetaD simulation.Most ordered monomers within the octamer selected as fibril seeds are shown with orange carbon atoms, disordered monomers at the phase boundary between peptide and water shown with light grey carbon atoms.B-E) Structures representing the starting and end points of Equilibration Protocols 1-3 for the self-assembly of peptide 1.Backbone carbon, lipid carbon, nitrogen, oxygen, and polar hydrogen atoms are shown with a dark grey, yellow, blue, red, and white stick representation.Where relevant, trapped water molecules within the solid state are shown as an aqua blue surface.Ordered construct from the cluster shown as B) Front view and C) Top view.Equilibrated fibril seed shown as D) Front view and E) Top view.Vertically extended fibril strand produced by stacking of the previously equilibrated fibril seed shown as F) Front view and G) Top view.This elongated fibril strand is replicated three times laterally.H) Flat nanobelts produced post-MD equilibration.

Figure 3 .
Figure 3.The bottom up self-assembly of peptide 2. A) Different views of the cluster representative from the WT-MetaD simulation of peptide 2. Ordered monomers to act as fibril seeds are shown with orange carbon atoms, disordered monomers at the phase boundary between peptide and water have light grey carbon atoms.B-E) Structures representing the starting and end points of Equilibration Protocols 1-3 for the self-assembly of peptide 2.unit cell is shown as a blue, rectangular prism.Backbone carbon, lipid carbon, nitrogen, oxygen, and polar hydrogen atoms are shown with a grey, yellow, blue, red, and white stick representation.B) The initial assembly.Front view of ordered construct from the cluster fragment.C) Front view of the assembled, twisted fibril protofiber.D) Front view of the protofibril, extended vertically to afford two fibril strands.E) Equilibrated twisted fibrillar structure.

Figure 4 .
Figure 4. A) AFM images of the flat nanobelts formed by 1. B) Fiber diffraction pattern of peptide 1.C) AFM images of the twisted fibrils formed by 2. D) Fiber diffraction pattern of peptide 2.

Figure 5 .
Figure 5. Bottom-up constructed periodic all-atom models of fibrillar lipidated peptide nanomaterials.Lipid carbon atoms are colored yellow, peptide backbone carbons are shown in two shades of grey for peptides 1 and 2, while nitrogen and oxygen atoms are shown in blue and red, respectively.A) 3D periodic model of the peptide 1 flat nanobelts, with trapped water shown as a transparent aqua surface.B) Similar representation of peptide 2 twisted fibrils.

Figure 6 .
Figure 6.Atom density profiles showing distribution of functional groups within the modelled peptide nanostructures, with average normalized density values obtained from the MD simulated ensembles of A) peptide 1 flat nanobelts and B) twisted fibrils formed by peptide 2.

Figure 7 .
Figure 7. Predicted versus experimental fiber diffraction of peptide 1.A) Top view, and B) Front view of the minimum structural unit for XFD prediction is shown as a solid stick representation within the unit cell (blue rectangular prism).Backbone carbon, lipid carbon, nitrogen, oxygen, and polar hydrogen atoms are shown with a grey, yellow, blue, red, and white stick representation.Repeat units are shown to illustrate stacked fibril units and are given a semi-transparent representation.C) The fiber diffraction pattern calculated with CLEARER, using the minimum structural unit from MD simulations, and shown with a white background.Actual XFD data of the peptide 1 flat nanobelts has a grey background.
at d 4 and d 5 indicate flexibility/mobility in the lysine amine relative to the C-terminal carboxylate.Another RDF peak was observed corresponding

Figure 8 .
Figure 8. Specific interactions occurring within the fibrils via RDF obtained from the final assembly of peptide 1.Structures are shown with main peptide chain colored in grey carbon, blue nitrogen, red oxygen and white hydrogen atoms, while the acyl atoms are colored in yellow.Only polar hydrogen atoms are shown.All RDF plots are labelled with key interaction distances, d x , where d is distance and x is a label for that distance.The RDF plots included are of: A) key backbone hydrogen bond distances (backbone oxygen to nitrogen distances); B) the C-terminal carboxylate oxygen to lysine amino nitrogen salt bridge distances; C) peptide backbone oxygen to lysine amino nitrogen distances; D) carbon-carbon distances from the monomer 1 lipid group to the lipid groups of monomers 2-144.The persistent interactions identified by the RDFs are shown as insets representing; E) backbone hydrogen bonds and F) salt bridge formations between lysine and carboxylate groups.

Figure 9 .
Figure 9. Specific interactions occurring within the fibrils via RDF obtained from the final assembly of peptide 2. For clarity, all structures are shown with grey carbon, blue nitrogen, red oxygen, and white hydrogen atoms.Only polar hydrogen atoms are shown.Labelling of distances, d, is congruent with Figure 8. Plots of RDF are shown of: A) backbone oxygen to nitrogen pairs (key hydrogen bond distances); B) C-terminal amide oxygen to the lysine amino nitrogen; C) peptide backbone oxygen to the lysine amino nitrogen.D) lipid groups carbon-carbon pairs.Equivalent structural distances are shown for: E) backbone hydrogen bonding distances; F) C-terminal oxygen to the lysine amino nitrogen atoms; G) backbone oxygen to the lysine amino nitrogen atoms.

Table 1 .
3-peptide systems studied in this work, and morphologies formed by the monomeric units.

Table 2 .
List of collective variables (CVs) used for clustering.MetaD simulations and clustering were performed with the biased CVs.Unbiased CVs were only used for clustering of the WT-MetaD ensemble; b) As defined by Equation S1 (Section S2) in the Supporting Information;c) Not Applicable.The radius of gyration originates from the center of mass of all atoms involved and is not defined by Equation S1 in the Supporting Information; d) Radius of gyration of the specific groups within the peptide aggregate.