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Geometrical frustration yields fibre formation in self-assembly

Nature Physics volume 13, pages 1100–1104 (2017)Cite this article

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Abstract

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales1,2. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibres3,4. Beyond the diversity of molecular mechanisms involved5,6, we propose that fibres generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fibre formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibres form as well as for their metastable character.

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Figure 1: Frustration and adhesion compete to determine the morphology of aggregates of mismatched particles.
Figure 2: Polygon model of aggregation.
Figure 3: Aggregates resulting from our growth algorithm.
Figure 4: Fibre energy and structure.

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Acknowledgements

We thank R. Ball for a seminal conversation that inspired this work. We are also grateful to E. Efrati for his insights on the connection between frustration and intrinsic curvature, and for suggesting our initial fibre-forming realization using pentagons. We thank him and P. Ronceray for comments on the manuscript. This work was supported by grants from Université Paris-Sud’s Attractivité and CNRS’ PEPS-PTI programmes, Marie Curie Integration Grant PCIG12-GA-2012-334053, ‘Investissements d’Avenir’ LabEx PALM (ANR-10-LABX-0039-PALM), ANR grant ANR-15-CE13-0004-03 and ERC Starting Grant 677532. This work was also supported in part by the National Science Foundation’s MRSEC Program under Award Number DMR-1420709. ML’s group belongs to the CNRS consortium CellTiss.

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Authors and Affiliations

  1. LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

    Martin Lenz

  2. Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois, 60637, USA

    Thomas A. Witten

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  1. Martin Lenz
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  2. Thomas A. Witten
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M.L. and T.A.W. designed the research and wrote the manuscript. M.L. performed the research.

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Correspondence to Martin Lenz.

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Lenz, M., Witten, T. Geometrical frustration yields fibre formation in self-assembly. Nature Phys 13, 1100–1104 (2017). https://doi.org/10.1038/nphys4184

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