Twisting of Charged Nanoribbons to Helicoids Driven by Electrostatics

Conformal order and Poincaré-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes

Understanding the organization of matter under the long-range electrostatic force is a fundamental problem in multiple fields. In this work, based on the electrically charged tethered membrane model, we reveal regular structures underlying the lowest-energy states of inhomogeneously stretched planar lattices by a combination of numerical simulation and analytical geometric analysis. Specifically we show the conformal order characterized by the preserved bond angle in the lattice deformation and reveal the Poincaré-Klein mapping underlying the electrostatics-driven inhomogeneity. The discovery of the Poincaré-Klein mapping, which connects the Poincaré disk and the Klein disk for the hyperbolic plane, implies the connection of long-range electrostatic force and hyperbolic geometry. We also discuss lattices with patterned charges of opposite signs for modulating in-plane inhomogeneity and even creating 3D shapes, which may have a connection to metamaterials design. This work suggests the geometric analysis as a promising approach for elucidating the organization of matter under the long-range force.

Molecular Insight into the β-Sheet Twist and Related Morphology of Self-Assembled Peptide Amphiphile Ribbons

Self-assembly of high-aspect-ratio filaments containing β-sheets has attracted much attention due to potential use in bioengineering and biomedicine. However, precisely predicting the assembled morphologies remains a grand challenge because of insufficient understanding of the self-assembly process. We employed an atomistic model to study the self-assembly of peptide amphiphiles (PAs) containing valine-glutamic acid (VE) dimeric repeats. By changing of the sequence length, the assembly morphology changes from flat ribbon to left-handed twisted ribbon, implying a relationship between β-sheet twist and strength of interstrand hydrogen bonds. The calculations are used to quantify this relationship including both magnitude and sign of the ribbon twist angle. Interestingly, a change in chirality is observed when we introduce the RGD epitope into the C-terminal of VE repeats, suggesting arginine and glycine's role in suppressing right-handed β-sheet formation. This study provides insight into the relationship between β-sheet twist and self-assembled nanostructures including a possible design rule for PA self-assembly.

Control of Peptide Amphiphile Supramolecular Nanostructures by Isosteric Replacements

Supramolecular nanostructures with tunable properties can have applications in medicine, pharmacy, and biotechnology. In this work, we show that the self-assembly behavior of peptide amphiphiles (PAs) can be effectively tuned by replacing the carboxylic acids exposed to the aqueous media with isosteres, functionalities that share key physical or chemical properties with another chemical group. Transmission electron microscopy, atomic force microscopy, and small-angle X-ray scattering studies indicated that the nanostructure's morphologies are responsive to the ionization states of the side chains, which are related to their pK_a values. Circular dichroism studies revealed the effect of the isosteres on the internal arrangement of the nanostructures. The interactions between diverse surfaces and the nanostructures and the effect of salt concentration and temperature were assessed to further understand the properties of these self-assembled systems. These results indicate that isosteric replacements allow the pH control of supramolecular morphology by manipulating the pK_a of the charged groups located on the nanostructure's surface. Theoretical studies were performed to understand the morphological transitions that the nanostructures underwent in response to pH changes, suggesting that the transitions result from alterations in the Coulomb forces between PA molecules. This work provides a strategy for designing biomaterials that can maintain or change behaviors based on the pH differences found within cells and tissues.