Curvature Instability in a Chiral Amphiphile Self-Assembly

We present the first experimental evidence for the morphological transition from twisted to helical ribbons in amphiphile aggregates. This transition, from structures possessing negative Gaussian curvature to helically curved structures, is shown to be directly linked to ribbon width. Time-resolved cryotransmission electron microscopy images of a peptidomimetic amphiphile further capture the dynamic transformation between the two geometries along a single ribbon unit. Quantitative analysis indicates that both ribbon width and pitch grow with ribbon maturation, maintaining a constant ratio.

Figure 1

Schematic of a typical cryo-TEM specimen and the corresponding image. Specimen thickness ranges between 80 and 150 nm. The right panel displays twisted ribbons (a), helical ribbons (b), and nanotubes (c), together with their appearance in the projected images, and the corresponding Gaussian (left) and bending (right) curvatures.

Figure 2

Temporal and structural evolution of ${\mathrm{C}}_{12}\mathrm{\text{−}}{\beta }_{12}$ assembly. (a) Molecular structure of ${\mathrm{C}}_{12}\mathrm{\text{−}}{\beta }_{12}$. (b) Qualitative description of the time-dependent evolution of structures (width and morphology): Twisted ribbons populate the solution after overnight incubation as shown in (c), helical ribbons form following aging for 4 weeks as shown in (d), and nanotubes form after $\approx 4\mathrm{months}$ (not shown). The black arrows in (c) follow the nodes of constant pitch along one narrow twisted ribbon, while the white arrows mark the larger pitch of another, wider ribbon of the same geometry. The red asterisk and arrows mark one helical ribbon existing in the field of twisted ribbons. The dashed lines in (d) are located left and below 2 neighboring helical ribbon captured at different stages of their development towards closed nanotubes. Each line follows 2 pitch lengths (complete turns). Note that the two molecular complexes have different diameter as well as different pitch. $\mathrm{\text{Bar}}=100\mathrm{nm}$.

Figure 3

Morphology transition in ${\mathrm{C}}_{12}\mathrm{\text{−}}{\beta }_{12}$ solutions. Upper panel: Statistical analysis of the variations of ribbon pitch with ribbon width. Note that $p$ varies linearly with $w$ for the two classes. The majority of structures ($>92\%$) are grouped in class I; these create narrow twisted ribbons at early time points, which transition into helices as ribbons get wider ($w$ $\mathrm{\text{transition}}=30\pm 4\mathrm{nm}$) with aging. Class II structures are characterized by a longer pitch (smaller $w/p$); these assemblies remain twisted over the entire study period. Lower panel: Cryo-TEM image showing a ribbon that becomes wider along its length, concurrently transitioning from twisted (white arrows) to helical (black arrows). $\mathrm{\text{Bar}}=25\mathrm{nm}$.

Figure 4

Cryo-TEM images showing ribbons undergoing strong orientational fluctuations at regions where curvature changes from twisted (white arrows) to helical (black arrows) ribbons. $\mathrm{\text{Bar}}=100$ (a),(b) and 50 nm (c),(d). S in (a) and (b) marks the support film. (d) is a section of (c), shown at twice the magnification.