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Morphology selection via geometric frustration in chiral filament bundles

Nature Materials volume 15, pages 727–732 (2016)Cite this article

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Abstract

In assemblies, the geometric frustration of a locally preferred packing motif leads to anomalous behaviours, from self-limiting growth to defects in the ground state1. Here, we demonstrate that geometric frustration selects the equilibrium morphology of cohesive bundles of chiral filaments, an assembly motif critical to a broad range of biological and synthetic nanomaterials. Frustration of inter-filament spacing leads to optimal shapes of self-twisting bundles that break the symmetries of packing and of the underlying inter-filament forces, paralleling a morphological instability in spherical two-dimensional crystals2,3,4. Equilibrium bundle morphology is controlled by a parameter that characterizes the relative costs of filament bending and the straining of cohesive bonds between filaments. This parameter delineates the boundaries between stable, isotropic cylindrical bundles and anisotropic, twisted-tape bundles. We also show how the mechanical and interaction properties of constituent amyloid fibrils may be extracted from the mesoscale dimensions of the anisotropic bundles that they form.

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Figure 1: Twisted bundle morphology and geometric frustration.
Figure 2: Continuum theory of size and morphology selection.
Figure 3: Discrete-filament simulations of twisted bundles.
Figure 4: Morphology selection of amyloid fibres.

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Acknowledgements

Support for this research by was provided through NSF CAREER grant DMR 09-55760 and a fellowship from the Alfred P. Sloan Foundation (D.M.H., I.R.B. and G.M.G.), through NSF-CMMI 08-56262, USDA-NIFA #2010-65504-20429, NSF-EEC 11-56645, and the Virginia Tech Institute for Critical Technology and Applied Science (J.R.B.). Numerical simulations were performed on the UMass Shared Cluster at the Massachusetts Green High Performance Computing Center. The authors are grateful for valuable discussions with A. Dinsmore and input on this manuscript from N. Menon, P. Ziherl, H. Hagan and A. Gopinathan.

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Authors and Affiliations

  1. Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA

    Douglas M. Hall, Isaac R. Bruss & Gregory M. Grason

  2. Department of Biological Systems Engineering and Macromolecules and Interfaces Institute, Virginia Tech, Blacksburg, Virginia 24061, USA

    Justin R. Barone

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  1. Douglas M. Hall
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  2. Isaac R. Bruss
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  3. Justin R. Barone
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  4. Gregory M. Grason
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Contributions

G.M.G. developed the continuum theory and its application to anisotropic bundle morphology. D.M.H., I.R.B. and G.M.G. developed the simulation approach to anisotropic bundle morphologies. D.M.H. carried out and analysed simulations. J.R.B. performed SEM analysis of mesoscale amyloid fibre morphologies. D.M.H. and G.M.G. applied continuum theory predictions to experimental data. All authors contributed to the writing of the manuscript.

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Correspondence to Gregory M. Grason.

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Hall, D., Bruss, I., Barone, J. et al. Morphology selection via geometric frustration in chiral filament bundles. Nature Mater 15, 727–732 (2016). https://doi.org/10.1038/nmat4598

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