Collagen-Inspired Self-Assembly of Twisted Filaments

Collagen consists of three peptides twisted together through a periodic array of hydrogen bonds. Here we use this as inspiration to find design rules for programmed specific interactions for self-assembling synthetic collagenlike triple helices, starting from disordered configurations. The assembly generically nucleates defects in the triple helix, the characteristics of which can be manipulated by spatially varying the enthalpy of helix formation. Defect formation slows assembly, evoking kinetic pathologies that have been observed to mutations in the primary collagen amino acid sequence. The controlled formation and interaction between defects gives a route for hierarchical self-assembly of bundles of twisted filaments.

Figure 1

Robust twisted filaments from a collagen-inspired scheme (a) Schematic showing three collagen peptides, and the network of hydrogen bonds that hold them together. We create an analogous network of bonds in our self-assembly schematic below, where each polymer is colored based on the different sequences of three stickers (A, B, and C) on the polymer. (b) Initial condition and final configuration for a simulation showing successful self-assembly of a collagenlike triple helix, based on the schematic in (a). (c) Disordered configurations almost universally lead to a variety of loops and rackets lacking a triple-helical geometry. (d) Schematic showing the maximal alphabet version of our self-assembly scheme, where each folding unit is comprised of a unique set of stickers. Crosstalk is prevented between different folding units, and helix formation robustly occurs.

Figure 2

Dependencies of helix geometry on material parameters. (a) Pitch of the helix, as a function of the aspect ratio of the folding unit, defined as the ratio of the length of the sticky section of each folding unit and the length of each folding unit. The pitch generally increases as a function of aspect ratio, as can be seen from the snapshots taken from simulations at specific values of the aspect ratio. (b) The correlation of the helix handednessas a function of distance along the filament. Length is measured in units of the repeats of the pattern. Decay is mediated by the presence of chiral defects where two strands switch their positions relative to the third strand, as shown in the inset of the simulation snapshot. The reason strand switching corresponds to changes in chirality is illustrated in the schematic. (c) Average radius of the helix, as a function of distance from the nucleation site. Successful assembly of a helical ground state implies a constant, small radius over the entire length of the bundle. (d) Chirality of the filament as a function of chiral bias. Increasing the bias for right-handed configurations shifts the average chirality towards 1. (e) Decay in the correlation of chirality along the filament.

Figure 3

Localization and kinetics of defects. (a) Radius of the helix along the filament (solid line). Sticker strength along the filament (dotted line). The peak in average radius indicates local unbinding in the region of lower sticker strength, as shown in the simulation snapshot. Inset: comparison of the helix radius of regions in simulations with bubble defects to similar regions in simulations without bubble defects. For regions before the defect (dotted line), there is no change in the progression of folding. For regions after the defect (solid line) there is an initial delay in folding. (b) Defect formation probability along the filament, as measured by the fraction of simulations in which the folding unit three units ahead of the indicated position is of the opposite sign of the folding unit at the indicated position (solid line). Chiral bias as a function of distance along the filament (dotted line). The two peaks (solid line) correspond to the boundaries of the right-handed segment of the helix (dotted line). (c) Defect formation probability (solid line) and bending stiffness (dotted line) along the filament. The peak (solid line) indicates that defects form across mechanically weaker regions with higher probability.