Design, Synthesis, Assembly, and Engineering of Peptoid Nanosheets.

Two-dimensional (2D) atomically defined organic nanomaterials are an important material class with broad applications. However, few general synthetic methods exist to produce such materials in high yields and to precisely functionalize them. One strategy to form ordered 2D organic nanomaterials is through the supramolecular assembly of sequence-defined synthetic polymers. Peptoids, one such class of polymer, are designable bioinspired heteropolymers whose main-chain length and monomer sequence can be precisely controlled. We have recently discovered that individual peptoid polymers with a simple sequence of alternating hydrophobic and ionic monomers can self-assemble into highly ordered, free-floating nanosheets. A detailed understanding of their molecular structure and supramolecular assembly dynamics provides a robust platform for the discovery of new classes of nanosheets with tunable properties and novel applications. In this Account, we discuss the discovery, characterization, assembly, molecular modeling, and functionalization of peptoid nanosheets. The fundamental properties of peptoid nanosheets, their mechanism of formation, and their application as robust scaffolds for molecular recognition and as templates for the growth of inorganic minerals have been probed by an arsenal of experimental characterization techniques (e.g., scanning probe, electron, and optical microscopy, X-ray diffraction, surface-selective vibrational spectroscopy, and surface tensiometry) and computational techniques (coarse-grained and atomistic modeling). Peptoid nanosheets are supramolecular assemblies of 16-42-mer chains that form molecular bilayers. They span tens of microns in lateral dimensions and freely float in water. Their component chains are highly ordered, with chains nearly fully extended and packed parallel to one another as a result of hydrophobic and electrostatic interactions. Nanosheets form via a novel interface-catalyzed monolayer collapse mechanism. Peptoid chains first assemble into a monolayer at either an air-water or oil-water interface, on which peptoid chains extend, order, and pack into a brick-like pattern. Upon mechanical compression of the interface, the monolayer buckles into stable bilayer structures. Recent work has focused on the design of nanosheets with tunable properties and functionality. They are readily engineerable, as functional monomers can be readily incorporated onto the nanosheet surface or into the interior. For example, functional hydrophilic "loops" have been displayed on the surfaces of nanosheets. These loops can interact with specific protein targets, serving as a potentially general platform for molecular recognition. Nanosheets can also bind metal ions and serve as 2D templates for mineral growth. Through our understanding of the formation mechanism, along with predicted features ascertained from molecular modeling, we aim to further design and synthesize nanosheets as robust protein mimetics with the potential for unprecedented functionality and stability.

Implicit-Solvent Coarse-Grained Simulation with a Fluctuating Interface Reveals a Molecular Mechanism for Peptoid Monolayer Buckling.

Peptoid polymers form extended two-dimensional nanostructures via an interface-mediated assembly process: the amphiphilic peptoids first adsorb to an air-water interface as a monolayer, then buckle and collapse into free-floating bilayer nanosheets when the interface is compressed. Here, we investigate the molecular mechanism of monolayer buckling by developing a method for incorporating interface fluctuations into an implicit-solvent coarse-grained model. Representing the interface with a triangular mesh controlled by surface tension and surfactant adsorption, we predict the direction of buckling for peptoids with a segregated arrangement of charged side chains and predict that peptoids with with an alternating charge pattern should buckle less easily than peptoids with a segregated charge pattern.

High-Resolution Coarse-Grained Modeling Using Oriented Coarse-Grained Sites.

We introduce a method to bring nearly atomistic resolution to coarse-grained models, and we apply the method to proteins. Using a small number of coarse-grained sites (about one per eight atoms) but assigning an independent three-dimensional orientation to each site, we preferentially integrate out stiff degrees of freedom (bond lengths and angles, as well as dihedral angles in rings) that are accurately approximated by their average values, while retaining soft degrees of freedom (unconstrained dihedral angles) mostly responsible for conformational variability. We demonstrate that our scheme retains nearly atomistic resolution by mapping all experimental protein configurations in the Protein Data Bank onto coarse-grained configurations and then analytically backmapping those configurations back to all-atom configurations. This roundtrip mapping throws away all information associated with the eliminated (stiff) degrees of freedom except for their average values, which we use to construct optimal backmapping functions. Despite the 4:1 reduction in the number of degrees of freedom, we find that heavy atoms move only 0.051 Å on average during the roundtrip mapping, while hydrogens move 0.179 Å on average, an unprecedented combination of efficiency and accuracy among coarse-grained protein models. We discuss the advantages of such a high-resolution model for parametrizing effective interactions and accurately calculating observables through direct or multiscale simulations.

Modeling sequence-specific polymers using anisotropic coarse-grained sites allows quantitative comparison with experiment.

Certain sequences of peptoid polymers (synthetic analogs of peptides) assemble into bilayer nanosheets via a nonequilibrium assembly pathway of adsorption, compression, and collapse at an air-water interface. As with other large-scale dynamic processes in biology and materials science, understanding the details of this supramolecular assembly process requires a modeling approach that captures behavior on a wide range of length and time scales, from those on which individual side chains fluctuate to those on which assemblies of polymers evolve. Here, we demonstrate that a new coarse-grained modeling approach is accurate and computationally efficient enough to do so. Our approach uses only a minimal number of coarse-grained sites but retains independently fluctuating orientational degrees of freedom for each site. These orientational degrees of freedom allow us to accurately parametrize both bonded and nonbonded interactions and to generate all-atom configurations with sufficient accuracy to perform atomic scattering calculations and to interface with all-atom simulations. We have used this approach to reproduce all available experimental X-ray scattering data (for stacked nanosheets and for peptoids adsorbed at air-water interfaces and in solution), in order to resolve the microscopic, real-space structures responsible for these Fourier-space features. By interfacing with all-atom simulations, we have also laid the foundation for future multiscale simulations of sequence-specific polymers that communicate in both directions across scales.

Crystallization and arrest mechanisms of model colloids.

We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong interactions. Arrested states are characterized by the formation of networks of face-sharing tetrahedra that can be detected by a local common neighbor analysis.

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.

Ion-specific control of the self-assembly dynamics of a nanostructured protein lattice.

Self-assembling proteins offer a potential means of creating nanostructures with complex structure and function. However, using self-assembly to create nanostructures with long-range order whose size is tunable is challenging, because the kinetics and thermodynamics of protein interactions depend sensitively on solution conditions. Here we systematically investigate the impact of varying solution conditions on the self-assembly of SbpA, a surface-layer protein from Lysinibacillus sphaericus that forms two-dimensional nanosheets. Using high-throughput light scattering measurements, we mapped out diagrams that reveal the relative yield of self-assembly of nanosheets over a wide range of concentrations of SbpA and Ca(2+). These diagrams revealed a localized region of optimum yield of nanosheets at intermediate Ca(2+) concentration. Replacement of Mg(2+) or Ba(2+) for Ca(2+) indicates that Ca(2+) acts both as a specific ion that is required to induce self-assembly and as a general divalent cation. In addition, we use competitive titration experiments to find that 5 Ca(2+) bind to SbpA with an affinity of 67.1 ± 0.3 µM. Finally, we show via modeling that nanosheet assembly occurs by growth from a negligibly small critical nucleus. We also chart the dynamics of nanosheet size over a variety of conditions. Our results demonstrate control of the dynamics and size of the self-assembly of a nanostructured lattice, the constituents of which are one of a class of building blocks able to form novel hybrid nanomaterials.

Structure-determining step in the hierarchical assembly of peptoid nanosheets.

Organic two-dimensional nanomaterials are of growing importance, yet few general synthetic methods exist to produce them in high yields and to precisely functionalize them. We previously developed an efficient hierarchical supramolecular assembly route to peptoid bilayer nanosheets, where the organization of biomimetic polymer sequences is catalyzed by an air-water interface. Here we determine at which stages of assembly the nanoscale and atomic-scale order appear. We used X-ray scattering, grazing incidence X-ray scattering at the air-water interface, electron diffraction, and a recently developed computational coarse-grained peptoid model to probe the molecular ordering at various stages of assembly. We found that lateral packing and organization of the chains occurs during the formation of a peptoid monolayer, prior to its collapse into a bilayer. Identifying the structure-determining step enables strategies to influence nanosheet order, to predict and optimize production yields, and to further engineer this class of material. More generally, our results provide a guide for using fluid interfaces to catalytically assemble 2D nanomaterials.

Competing thermodynamic and dynamic factors select molecular assemblies on a gold surface.

Controlling the self-assembly of surface-adsorbed molecules into nanostructures requires understanding physical mechanisms that act across multiple length and time scales. By combining scanning tunneling microscopy with hierarchical ab initio and statistical mechanical modeling of 1,4-substituted benzenediamine (BDA) molecules adsorbed on a gold (111) surface, we demonstrate that apparently simple nanostructures are selected by a subtle competition of thermodynamics and dynamics. Of the collection of possible BDA nanostructures mechanically stabilized by hydrogen bonding, the interplay of intermolecular forces, surface modulation, and assembly dynamics select at low temperature a particular subset: low free energy oriented linear chains of monomers and high free energy branched chains.

Ratio of effective temperature to pressure controls the mobility of sheared hard spheres.

Using molecular dynamics simulations, we calculate fluctuations and responses for steadily sheared hard spheres over a wide range of packing fractions φ and shear strain rates γ[over ̇], using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature T(eff) that is equal to or larger than the kinetic temperature T(kin). We find a crossover in the relationship between the relaxation time τ and the the nondimensionalized effective temperature T(eff)/pσ(3), where p is the pressure and σ is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies τ ̇γ∝exp(-cpσ(3)/T(eff)), where c depends weakly on φ, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on T(eff)/pσ(3) as it depends on T(kin)/pσ(3) in equilibrium. This regime includes both near-equilibrium conditions where T(eff)≃T(kin) and far-from-equilibrium conditions where T(eff)≠T(kin). We discuss the implications of our results for systems with soft repulsive interactions.

Universal jamming phase diagram in the hard-sphere limit.

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature T, packing fraction ϕ or pressure p, and applied shear stress Σ. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities T/pσ³, pσ³/ε, and Σ/p, where T is the temperature, p is the pressure, Σ is the stress, σ is the sphere diameter, ε is the interaction energy scale, and m is the sphere mass. We demonstrate that the phase diagram is universal at low pσ³/ε; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are nondimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.

Equivalence of glass transition and colloidal glass transition in the hard-sphere limit.

We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation.

Activated dynamics and effective temperature in a steady state sheared glass.

We conduct nonequilibrium molecular dynamics simulations to measure the shear stress sigma, the average inherent structure energy E{IS}, and the effective temperature T{eff} of a sheared model glass as a function of bath temperature T and shear strain rate gamma. For T above the glass transition temperature T0, the rheology approaches a Newtonian limit and T{eff}-->T as gamma-->0, while for T