Research ArticleCHEMICAL PHYSICS

Inward growth by nucleation: Multiscale self-assembly of ordered membranes

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Science Advances  29 Jun 2018:
Vol. 4, no. 6, eaat1817
DOI: 10.1126/sciadv.aat1817
  • Fig. 1 Self-assembly of β-CD and SDS into concentric hollow microtubes, lamellar phases, or polyhedral capsids.

    (A) In solution, the hydrophobic tail of the SDS molecule will preferentially reside in the hydrophobic pocket of two stacked β-CD molecules, creating a compact unit, the [SDS@2β-CD] complex (16). Above 40°C, the complexes are soluble in water. Below this temperature, the complexes spontaneously form bilayers that self-assemble into polyhedral capsids, multiwalled microtubes, or lamellar phases depending on the concentration. Below 3 weight % (wt %), no superstructures are observed. The process is thermoreversible, as discussed in the Supplementary Materials. Above the melting temperature, the structures disassemble back into the individual complexes (1618). (B) Yang et al. (19) showed that the complexes are organized in-plane in a rhombic lattice, showing that the formation of these rhombic bilayers is a logical consequence of the sevenfold symmetry of the β-CD molecule. The structure optimizes the alignment of in-plane hydrogen bonds between the cyclodextrins. (C) Confocal microscopy image of [SDS@2β-CD] microtubes, stained with Nile red fluorescent dye. Scale bar, 5 μm.

  • Fig. 2 Time evolution of SAXS profiles.

    A 10 wt % hot solution of SDS@2β-CD was rapidly quenched to room temperature. Intensity is plotted as a function of scattering vector Embedded Image where λ is the wavelength of the incident x-rays and θ as the scattering angle. The initial scattering intensity corresponds to the form factor of the [SDS@2β-CD] complex in solution. After an initial waiting time, the structure almost simultaneously appears at all length scales. Data from two sample-to-detector distances were appended and partially binned to average out the noisy tail of the low-q measurements at the start of the experiment.

  • Fig. 3 Ultrasmall-angle scattering experiments.

    (A) SAXS profiles of a subset of a typical experiment, showing the many oscillations in the intermediate states of self-assembly, together with a profile during the later stages of self-assembly. Even before the emergence of oscillations, the scattering profiles show a slope at very small angles, indicating large-scale density fluctuations. (B) Fits of selected SAXS profiles to a model of hollow cylinders (23). The shallow amplitude is likely caused by a convolution with the detector point-spread function, combined with a comparatively short but highly polydisperse cylinder length. (C) Integrated SAXS profiles multiplied by a power of q, showing the appearance and shift of oscillations due to the radius of the microtubes. (D) Average cylinder radius 〈r〉 and thickness 〈δ〉 from fits to the simplified expression in Eq. 1. To aid the fit, the average radius of the previous five profiles was given as the starting point for the fit of each successive curve. The shaded area denotes the extent of the 95% confidence interval. (E) Time evolution of the Porod invariant Q, for comparison. The Porod invariant was calculated by integration over the accessible q range only.

  • Fig. 4 Inward growth is a nucleation process.

    (A) Time evolution of the average central microtube radius 〈r〉 for different [SDS@2β-CD] concentrations. (B) The logarithm of t0/s scales linearly with the reciprocal of the logarithm of c/c*, as predicted by classical nucleation theory for a disc-shaped critical nucleus. Moreover, when the average microtube radius is plotted in (C) as a function of log tA × log c/c*, all the data collapse onto a single curve. (D) The thickness 〈δ〉 of the (multi-)wall shows a typical square-root scaling with the Porod invariant Q over the later part of the experiment. The shaded areas in (A) and (C) denote the extent of the 95% confidence intervals.

  • Fig. 5 Proposed mechanism for the microtube formation.

    (A) [SDS@2β-CD] complexes in solution nucleate into (B) ordered bilayers, governed by directional hydrogen bonding with their neighbors. (C) When the bilayer reaches a certain size, it becomes advantageous to close the ring, gaining bond free energy at the cost of bending free energy. (D) Because nucleation and growth are not separated, new bilayers keep nucleating, both inside and outside preexisting tubes. (E) Bilayers that nucleated outside preexisting tubes form new tubes. Bilayers that nucleated inside preexisting tubes are restricted in their size and form concentric inner cylinders. (F) Because of the large amount of material that is accommodated in the bilayers in a limited space, a dense packing of concentric cylinders is obtained. The cylinders are consequently deformed in a slightly hexagonal form (27). Evidence for this deformation is given in fig. S2.

  • Fig. 6 Tracing the interbilayer separation.

    (A) Integrated SAXS profiles recorded after temperature quench, multiplied by a power of q to compensate for the apparent q−2 decay. The asterisk denotes the presence of an iso-scattering point. Time evolution of (B) the average spacing 〈d〉 calculated from the peak positions in (A), and (C) the Porod invariant Q, given by integrating I(q) × q2 over the full q range. The Porod invariant is proportional to the amount of (structured) material (28). The spacing between the bilayers appears first at approximately 18 nm and shifts slowly to higher values. In the final sample, on the order of 10 concentric cylinders are present. (D) Static SAXS profiles of preassembled [SDS@2β-CD] complexes. When plotted as a function of concentration in (E), the interbilayer distance 〈d〉 scales with the expected c−1 in the concentration regime where the structure is lamellar. In the tubular concentration regime, the interbilayer spacing scales with Embedded Image.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaat1817/DC1

    Supplementary Text

    fig. S1. Optical microscopy during self-assembly.

    fig. S2. Melting of microtubes follows reverse process.

    fig. S3. Competition between bond formation and bending energy.

    fig. S4. Chiral pitch of cylinders.

    fig. S5. Influence of salt on the interbilayer separation.

    fig. S6. Form factor fitting.

    Reference (41)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Optical microscopy during self-assembly.
    • fig. S2. Melting of microtubes follows reverse process.
    • fig. S3. Competition between bond formation and bending energy.
    • fig. S4. Chiral pitch of cylinders.
    • fig. S5. Influence of salt on the interbilayer separation.
    • fig. S6. Form factor fitting.
    • Reference (41)

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