Peptoid nanosheets exhibit a new secondary-structure motif

A promising route to the synthesis of protein-mimetic materials that are capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers—structural relatives of biologically occurring polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation, can fold into defined structures through a combination of sequence-dependent interactions. However, the range of possible structures that are accessible to peptoids and other biological mimetics is unknown, and our ability to design protein-like architectures from these polymer classes is limited. Here we use molecular-dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially porous to water and ions. Moreover, their formation is enabled by the peptoids’ adoption of a secondary structure that is not seen in the natural world. This structure, a zigzag pattern that we call a Σ(‘sigma’)-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure, the Σ-sheet. The binary rotational-state motif of the Σ-strand is not seen in regular protein structures, which are usually built from one type of rotational state. We also show that the concept of building regular structures from multiple rotational states can be generalized beyond the peptoid nanosheet system.

A promising route to the synthesis of protein-mimetic materials that are capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers 1,2structural relatives of biologically occurring polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation 3 , can fold into defined structures through a combination of sequencedependent interactions [3][4][5][6][7][8] . However, the range of possible structures that are accessible to peptoids and other biological mimetics is unknown, and our ability to design protein-like architectures from these polymer classes is limited 9 . Here we use molecular-dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially porous to water and ions. Moreover, their formation is enabled by the peptoids' adoption of a secondary structure that is not seen in the natural world. This structure, a zigzag pattern that we call a S('sigma')-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure, the S-sheet. The binary rotational-state motif of the S-strand is not seen in regular protein structures, which are usually built from one type of rotational state. We also show that the concept of building regular structures from multiple rotational states can be generalized beyond the peptoid nanosheet system.
The peptoid nanosheet is a recently discovered, free-floating planar assembly that is only two molecules thick but that extends laterally for micrometres (Supplementary Figs 1, 2) 8, 10,11 . Nanosheets assemble from peptoids bearing alternating aromatic and charged sidechains (Fig. 1a) via compression at an air-water interface 8,10-12 . We find, through a combination of atomic-force microscopy (AFM; Supplementary  Fig. 3) 8,10,13 and powder X-ray diffraction (XRD) 8,10,11,13 , that nanosheets are bilayers, 3.0 6 0.3 nm (6s.d.) thick, in whose interior the aromatic sidechains are sequestered, and on whose surfaces the charged sidechains are presented. Optical microscopy shows nanosheets to be b ( roughly rectangular, many square micrometres in horizontal extent, and to have relatively straight edges ( Fig. 1a and Supplementary  Fig. 2b). XRD measurements in the plane of the bilayer show peaks at characteristic distances of 4.5 Å and 3.6 Å ( Supplementary Fig. 9), suggesting a high degree of order on the molecular scale. Direct observation of polymer chains in the nanosheet by transmission electron microscopy indicates a polymer-polymer parallel spacing of about 4.5 Å (ref. 8), in accordance with the 4.5-Å XRD peak.
To develop an atomistic model of peptoid nanosheets consistent with these observations, we used atomistic molecular-dynamics simulations in conjunction with our recently developed CHARMMbased 14 force field for peptoid backbones, MFTOID 15 (CHARMM, Chemistry at HARvard Molecular Mechanics; MFTOID, Molecular Foundry (MF) and Peptoid (TOID)). We surveyed a range of lowenergy nanosheet configurations ( Supplementary Fig. 4a) as starting points for molecular-dynamics simulations; here, we report the results of one such set of simulations (see Methods). Figure 1b and c show snapshots of a nanosheet patch, with periodic images displayed (for an image of the simulation box only, see Supplementary Fig. 4c) Supplementary Fig. 13). Each top and bottom panel (related by a double-headed arrow) show the same section and viewpoint, rendered in different ways. e, Water (green) encroaches at a pocket, suggesting that water channels might be engineered into nanosheets ( Supplementary Fig. 20). f, Backbone order. g, Aromatic disorder. Real-space measurements taken from simulation averages and inferred from scattering experiments (shown at the bottom) agree to within 1 Å .

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polymer backbones, and relative disorder in the aromatic and charged sidechains that are, respectively, internal and external to the bilayer ( Supplementary Figs 11 and 12). Individual peptoid chains maintain the brick-like arrangement that is favoured by the segregation of charged sidechains into positively and negatively charged blocks (Fig. 1a), in which gaps or 'pockets' between polymer termini alternate with the backbones' central portions, as one looks along the direction perpendicular to that of the polymer chains (Fig. 2b). As shown in Fig. 2c and Supplementary Fig. 12, backbone regions away from the pockets are the least dynamic portions of each peptoid, displaying a root-mean-squared fluctuation (RMSF) of #1 Å . The pocket-forming termini of each peptoid are more flexible than these interior regions, and are visibly less ordered (Fig. 2c, d and Supplementary Fig. 12), while the polymer sidechains are more flexible still. This hierarchy of flexibility is similar to that seen in proteins 16,17 . Figure 2e-g and Supplementary Fig. 8 show that the nanosheet thickness, interpolymer spacings and intersidechain spacings seen in our simulations lie within about an ångström of the mean characteristic distances seen in AFM and X-ray-scattering experiments 8,10,11 .
The range of nanosheet thicknesses measured by AFM, 2.7 nm to 3.3 nm ( Supplementary Fig. 3), is also reproduced in our simulations ( Supplementary Fig. 8). These comparisons allow us to assign physical features to experimental measurements, and to verify the accuracy of our simulations (see Supplementary Table 1).
This brick-like arrangement of backbones that allows polymers to alternate with pockets has important consequences for the stability of nanosheets as a function of peptoid length. As polymer length decreases, it should become less energetically favourable for each residue to form a nanosheet, because pockets-near which peptoids possess fewer favourable electrostatic and aromatic interactions-increase in number per unit area as polymer length decreases. Simulations indeed show that short polymers are not stable in nanosheet form. In Fig. 3, we report the results of simulations done using nanosheets built from polymers that are 4, 8, 12, 16, 20, 24 or 28 residues long. Polymers longer than 12 residues form stable nanosheets. Nanosheets built from 12-residue polymers show signs of instability and a decrease in order ( Fig. 3a-c) upon simulation, and nanosheets built from polymers shorter than 12 residues display an almost complete loss of structure within 40 ns of the start of the simu-  Fig. 18). Colouring backbones with respect to the backbone dihedral angle, w, makes clear that adjacent backbone monomers adopt opposed rotational states. This novel secondary structure, the S-strand, is discussed in Fig. 4. lation ( Fig. 3d and Supplementary Fig. 15). In accordance with our simulations, our experiments show that peptoids that are 12 or fewer residues in length do not form stable nanosheets ( Fig. 3e and Supplementary Figs 18 and 19). Our simulations suggest that this failure occurs because short-polymer nanosheets are unstable relative to disordered aggregates. Our simulations also suggest that if polymer connections are reinforced-for example, by head-to-tail cross-linking-this limitation could be overcome. When considering the design of nanosheets, the observation that interchain pockets are tolerated by polymers longer than a certain limit shows that pockets should be considered to be an integral part of the nanosheet structure. Simulations show that such pockets allow water to encroach on the aromatic centre of the bilayer (Fig. 2e and Supplementary Fig. 20b). This observation suggests that peptoid termini could be modified to create pockets able to bind specific small molecules, potentially permitting catalytic function. Furthermore, our simulations show that, if pockets on opposing leaves coincide, then nanosheets possess channels through which water can pass ( Supplementary  Fig. 20c), indicating the potential of nanosheets as selective membranes. Experimental work to test these predictions is under way.
The stability of extended, planar peptoid nanosheets is enabled by the polymers' linear, untwisted configurations. Our simulations reveal that this linearity results from the ability of sequential backbone residues to adopt one of two states, whose rotation about the backbone axis opposes and cancels each other. In Fig. 3d we have coloured these two rotational states red and blue. This building principle is distinct from that used by proteins: the backbones of protein secondary structures such as a-helices and b-sheets are defined primarily by a single rotational state.
Protein rotational states are quantified by their backbone dihedral angles, traditionally denoted w and y, and conventionally described by a Ramachandran plot 18 . As shown in Fig. 4a-d, regular chiral protein structures such as the a-helix and b-sheet correspond roughly to a single location, i, on the Ramachandran plot 18 . In contrast, stable nanosheets are composed of peptoids whose backbone states occupy two specific regions of the Ramachandran plot (Fig. 4f), labelled i and j. Chains whose adjacent residues alternate between these two states remain linear. A snapshot of three backbone segments (Fig. 4e) emphasizes this alternating motif. We call this motif the S-strand, because its linear, twist-free nature derives from the combination, or sum ('S'), of its two rotational states (and because the resulting polymer 'snakes' back and forth). In principle one could have a S-strand built from any two opposed rotational states. However, density functional theory calculations show that the particular rotational states observed in our atomistic simulations are the lowest-energy S-type arrangement for isolated polymers (Fig. 4g and Supplementary Figs 23-26). This comparison provides additional confidence in the accuracy of the MFTOID force-field simulations, and confirms that the basic rotational tendency of an isolated peptoid backbone 15 (Fig. 4h) is preserved by the sidechain-sidechain interactions established within the nanosheet (Fig. 4f).

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The S-strand motif is protein-like in its regularity, but is different from protein secondary structures in important ways: it is a molecular motif that permits planar assemblies of macroscopic extent; it is stabilized for reasons other than hydrogen bonding; and it is built from two (not one) rotational states. The closest comparable secondary structures in proteins, b-sheets, are unable to maintain macroscopic flatness owing to a propeller-like twist in the shape of each strand (although fibril-like protein assemblies can be of considerable size 19 and can be combined to form structures of macroscopic extent 20 ). The S-sheet therefore represents a complement to the basic building blocks of the protein world. To replicate the S-sheet assembly using other polymers, one therefore needs two things: molecular rotational properties that give rise to symmetry about the diagonal of the Ramachandran plot (Fig. 4f), and sidechain sequence patterning that promotes these conformations within a desired assembly.
The principle underlying the stability of the S-strand and the peptoid nanosheet is that regular secondary structures can be built from more than one rotational state-that is, from more than one point on the Ramachandran plot. This principle immediately suggests the possibility of a large set of novel secondary structures, some of which are shown in Fig. 5. The potential applications of this set of structures go beyond those of the nanosheet system-the S-strand is but one member of this set-and may include the formation of novel folded structures and assemblies. Since the 1950s, the literature on protein secondary structure has focused on the idea of building with one type of rotational state 18 , to make 'single-point' Ramachandran structures. We propose that building higher-order, multi-point secondary structures might greatly expand the repertoire of folded polymeric building blocks. Figure 5d provides guidelines for backbone design. It may also help to characterize structurally the rapidly growing family of solid-state peptoid polymer crystals 21 . Such crystals consist largely of extended polymer conformations that so far have eluded characterization at atomic resolution; the extended backbones seen in Fig. 5d are candidate conformations. More generally, the new building principle that we have identified, combined with the ability to encode into peptoids a defined sequence of chemically diverse monomers, offers a way to create new structured polymers through combinatorial design.
Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

METHODS
Experimental nanosheet synthesis. Block-charge peptoids of lengths L 5 4, 8, 12, 16 or 28 residues were synthesized and purified using automated solid-phase synthesis 3 . For L $ 12 residues ( Supplementary Fig. 18d-f) and L . 12 residues (Fig. 3e), peptoids were present at a concentration of 20 mM in 10 mM Tris buffer, pH 8.0. Peptoid nanosheets of length L # 12 were absent at this concentration ( Supplementary Fig. 18d), perhaps because not enough polymer adsorbed to the air-water interface (see discussions following Supplementary Fig. 18d); therefore we attempted to produce L # 12 nanosheets at higher concentrations ( Fig. 3e and Supplementary Fig. 18a-c). Peptoids of length L 5 12 were present at a concentration of 1 mM ( Supplementary Fig. 18c), of length L 5 8 at 22 mM (Supplementary Fig. 18b), and of length L 5 4 at 41 mM ( Supplementary Fig. 18a), all in 10 mM Tris buffer, pH 8.0. Sheets were prepared by agitation via the vial-rocking method 10 . To test whether the peptoids were adsorbing to the air-water interfacea prerequisite to assembly-we obtained surface tension data for the L 5 4, 8 and 12 peptoids via the pendant drop method (see discussions following Supplementary Fig. 18) 24 . Nanosheet yield analysis by optical microscopy. Identical volumes were removed from each sample and applied to a thin agarose-gel slice to allow imaging for Fig. 3e and Supplementary Fig. 18 (ref. 25).
Measuring distances by single-angle X-ray scattering and AFM. Nanosheet thicknesses were calculated via AFM 8,10,13 . We obtained AFM images of dry nanosheets deposited on a mica substrate in ambient air. Other distances, such as intrapolymer spacings ( Fig. 2 and Supplementary Fig. 8), were obtained via XRD 8,10,11,13 . XRD data also show a peak corresponding to the thickness of the nanosheet. Molecular-dynamics protocol. We surveyed a range of low-energy nanosheet configurations ( Supplementary Fig. 4a) as starting points for molecular-dynamics simulations. To conduct this survey we built 28-residue polymers into monolayers in a brick-like arrangement, and joined two identical opposing monolayers to form a bilayer ( Supplementary Fig. 4a). The brick arrangement is suggested by simple electrostatic considerations, because peptoids' charged sidechains are segregated into positive and negative blocks along each chain 11 (Fig. 1a). The computational search space so defined possesses six degrees of freedom, described by distances between polymers within the same layer and between monolayers ( Supplementary  Fig. 4a). We calculated energies (in implicit water) for a large number of these parameter sets, and chose six low-energy versions on which to focus ( Supplementary Fig. 4b). Each nanosheet version was then explicitly solvated and relaxed in a sequence of protocols (see Supplementary Fig. 4d), before undergoing constant-pressure molecular-dynamics simulation using a leap-frog integrator (a commonly used second-order numerical method for integrating equations of motion) with a 1-fs timestep. Each of the six low-energy versions of the nanosheet was seen to be stable for over 50 ns of molecular-dynamics simulation at standard temperature and pressure; that is, each had ceased to evolve (structural snapshots for each simulation are available in Supplementary Information), and did not dissolve or convert to a different structure ( Supplementary Fig. 5). (In contrast, high-energy initial configurations did not yield stable structures.) These simulations reveal that, in the region of the energy minimum dictated by charged sidechains 11 , there exists a rugged free-energy landscape with a range of near-degenerate nanosheet structures. Biomolecules, by contrast, often possess clear free-energy minima [26][27][28][29][30] .
Our simulations represent periodically replicated patches of nanosheets of approximate dimensions 60 nm 3 18 nm, and so do not address the nature of nanosheet order on the micrometre scale. Given that nanosheets are produced by a far-from-equilibrium mechanical protocol 10 , and given the stability of all six nanosheet versions in our simulations, it is possible that extended nanosheets consist of a patchwork of different types of stable local order. Nonetheless, each of the six low-energy nanosheet versions displays molecular features consistent with experiments ( Supplementary Fig. 8), from which we infer that substantial portions of nanosheets display locally the atomic-scale features seen in our simulations. In the main text, for brevity, we present results from one particular nanosheet version, number 5.
Supplementary Figure 4 describes our generation of the six molecular-dynamics starting configurations. Molecular-dynamics simulations were done using the CHARMM software package 14 . Aside from the initial set-up, all nanosheet series were simulated using a leap-frog integration algorithm with a 1-fs timestep. Simulations were performed in the isothermal-isobaric (NPT, for constant particle number, pressure and temperature) ensemble at 300 K and 1 atmospheric pressure, in an orthorhombic periodic box in which the three orthogonal box dimensions were allowed to vary independently. The Hoover algorithm was used to maintain constant pressure 31 . Hydrogen bonds were constrained using the SHAKE protocol 32 . Particle-mesh Ewald summation was used to evaluate longrange electrostatic interactions, with a real-space cut-off of 12 Å , a sixth-order cubic spline, and a k value (width of the Gaussian distribution) of 0.34. Van der Waals interactions were calculated up to a distance of 12 Å , with a smoothing function applied from 10 Å to 12 Å .
Simulations reported in the main text were performed in a solution consisting of water, the nanosheet's counterions, and potassium chloride at a concentration of 10 mM. We also carried out a series of independent simulations of the version 5 nanosheet, in which potassium chloride concentrations were set to 0.1 mM, 1 mM, 50 mM and 100 mM (Supplementary Fig. 14). These simulations verified that simulated nanosheet structures do not change markedly over the range of salt concentrations used in our experiments 8,10,11 . Computational X-ray scattering. We calculated scattering spectra at wavevector q using the expression where the sum runs over all atoms, f j is the atomic scattering factor for atom j and r j is the position of atom j. Equation (1) assumes that electrons are localized at atomic sites. We let f j equal the atomic number, an approximation that is nearly exact at the experimental X-ray energies of 11 keV (ref. 33). The values of q were discretized so as to be commensurate with the periodic box.
Experimental in-plane X-ray-scattering spectra were taken by allowing nanosheets to dry on a Kapton grid, stacking the sheets on top of each other to produce a sample with a uniform orientation 12 . The absence of lamellar peaks when the X-ray beam was fired 'face-on' into the stack confirmed that the nanosheet normals were uniformly oriented parallel to the grid normal. However, the radially averaged signal indicated that various sheets and/or domains existed within the beamline, as expected given that the beam cross-section (120 mm 3 800 mm) is greater than the typical nanosheet size (20 mm 3 20 mm). To compare with these in-plane, radially averaged spectra, we radially averaged the simulated scattering spectra (equation (1)) in the xy plane of the nanosheet, I(q xy )~I(q) h i q z~0 , ffiffiffiffiffiffiffiffiffiffi q 2 x zq 2 y p~q xy . Finally, these intensities (I(q xy )) were normalized by the expected intensity of an equivalent ideal gas (I IG (q xy )), which is discussed in Supplementary Fig. 17. Direct measurements. While X-ray scattering is useful for comparing simulation to experiment, direct measurements of some features (for example, polymer y-padding, nearest neighbour N-N spacing, bilayer thickness) provide additional information with regards to distances and distributions. Supplementary Fig. 7 and its associated text discusses those measurements and how they are calculated, while Supplementary Fig. 8 compares experimental observations to those metrics. Measurement of order in the bilayer. For each peptoid (Fig. 3a), we designate the position of the backbone nitrogen of the ith residue to be r i . A simple measure of order is the angle h backbone,x between each peptoid backbone and the x axis h backbone,x~c os {1 (r last {r second ) :x r last {r second j j ð2Þ a-Helical and b-sheet segments from proteins. A structure database was obtained from the Structural Classification of Proteins (SCOPe; release 2.03) that contains proteins with no more than 40% sequence identity with each other (http://scop. berkeley.edu/downloads/pdbstyle/pdbstyle-sel-gs-bib-40-2.03.tgz). a-Helical and b-sheet segments were identified using the DSSP (Define Secondary Structure of Proteins) algorithm 34 . (w, y) pairs were obtained for all residues within a-helical and b-sheet segments, which contributed towards the histograms in Fig. 4b, d, respectively. Quantum mechanics calculations. Density functional theory was used to assess the low-energy structures available to a peptoid backbone consisting of two alternating sets of dihedral angles (w, y). B3LYP and M05-2X were the two functionals used to calculate the energies of a configuration. B3LYP is a commonly used and widely applicable functional 35 , and M05-2X is a newer functional that accounts for dispersion forces 22 . Gaussian 09 (C.01) was used for density functional theory calculations 23 . For each peptoid model, the alternating pattern is defined by the numbers A and B (Fig. 4h), where adjacent (w, y) pairs take the values (2A, B) and (2B, A). A and B were constrained to range from 50u to 180u in steps of 10 u.
Molecules were optimized at the HF/6-31G* level of theory 36