Thomas K. Haxton

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.

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<T0, sigma approaches a yield stress and T{eff} approaches a limiting value near T0. In the shear-dominated regime at high T, high gamma or at low T, we find that sigma and E{IS} each collapse onto a single curve as a function of T{eff}. This indicates that T{eff} is controlling behavior in this regime.

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.

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.

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.

Mapping the glassy dynamics of soft spheres onto hard-sphere behavior

We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition.

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 Ca2+. These diagrams revealed a localized region of optimum yield of nanosheets at intermediate Ca2+ concentration. Replacement of Mg2+ or Ba2+ for Ca2+ indicates that Ca2+ 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 Ca2+ 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.

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.

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.

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.