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Flexible filaments buckle into helicoidal shapes in strong compressional flows

An Author Correction to this article was published on 27 August 2021

Abstract

The occurrence of coiled or helical morphologies is common in nature, from plant roots to DNA packaging into viral capsids, as well as in applications such as oil drilling processes. In many examples, chiral structures result from the buckling of a straight fibre either with intrinsic twist or to which end moments have been applied in addition to compression forces. Here, we elucidate a generic way to form regular helicoidal shapes from achiral straight filaments transported in viscous flows with free ends. Through a combination of experiments using fluorescently labelled actin filaments in microfluidic divergent flows and two distinct sets of numerical simulations, we demonstrate the robustness of helix formation. A nonlinear stability analysis is performed, and explains the emergence of such chiral structures from the nonlinear interaction of perpendicular planar buckling modes, an effect that solely requires a strong compressional flow, independent of the exact nature of the fibre or type of flow field. The fundamental mechanism for the uncovered morphological transition and characterization of the emerging conformations advance our understanding of several biological and industrial processes and can also be exploited for the controlled microfabrication of chiral objects.

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Fig. 1: Buckling conformations of Brownian filaments in compressional flow.
Fig. 2: Helical buckling of a non-Brownian filament.
Fig. 3: Stability analysis and rationale for helical shapes.
Fig. 4: Temporal dynamics and final helix radius.

Data availability

Source data for Figs. 1, 3 and 4 are provided with the paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The numerical codes used for the stability analysis and for simulations are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank R. Winkler for helping us appreciate the prevalence of helical shapes, as well as M. Shelley and E. Shaqfeh for illuminating discussions. We are grateful to G. Romet-Lemonne and A. Jégou for providing purified actin and to T. Darnige for help with the programming of the microscope stage. We also thank M. Oliveira and J. Fidalgo for help with the implementation of the optimized hyperbolic microchannel and filament tracking. A.L., B.C. and Y.L. acknowledge funding from the ERC Consolidator Grant PaDyFlow (Agreement 682367). D.S. acknowledges funding from a Paris Sciences Chair from ESPCI Paris. This work received the support of Institut Pierre-Gilles de Gennes (Équipement d’Excellence, ‘Investissements d’Avenir’, programme ANR-10-EQPX-34). J.L, R.C. and L.F. acknowledge funding from a Gulf of Mexico Research Initiative grant and from National Science Foundation grant no. DMS-1043626.

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Authors

Contributions

B.C. and D.S. performed the Brownian simulations, stability analysis and scaling theory. Y.L., O.d.R. and A.L. performed experiments. J.L., R.C. and L.F. performed non-Brownian simulations. All authors contributed to the analysis and interpretation of data and to the preparation of figures. B.C., D.S., A.L., O.d.R., Y.L. and L.F. wrote the paper.

Corresponding authors

Correspondence to Yanan Liu or David Saintillan.

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Supplementary information

Supplementary Information

Supplementary details of computational methods, stability analysis and scaling theory.

Supplementary Video 1

Experiment corresponding to the first row of Fig. 1a of the main text. See Supplementary Information for parameter values.

Supplementary Video 2

Experiment corresponding to the second row of Fig. 1a of the main text. See Supplementary Information for parameter values.

Supplementary Video 3

Experiment corresponding to the third row of Fig. 1a of the main text. See Supplementary Information for parameter values.

Supplementary Video 4

Experiment corresponding to the fourth row of Fig. 1a of the main text. See Supplementary Information for parameter values.

Supplementary Video 5

Brownian simulation corresponding to the fourth row of Fig. 1a of the main text. See Supplementary Information for parameter values.

Supplementary Video 6

Brownian simulation showing helical buckling of a weakly Brownian filament. See Supplementary Information for parameter values.

Supplementary Video 7

Non-Brownian simulation. The dot in the video shows the instantaneous position of the fibre centre of mass as it is transported by the flow. See Supplementary Information for parameter values.

Supplementary Video 8

Non-Brownian simulation. The dot in the video shows the instantaneous position of the fibre centre of mass as it is transported by the flow. See Supplementary Information for parameter values.

Supplementary Video 9

Video showing a numerical integration of the weakly nonlinear theory and illustrating how a helicoidal morphology emerges due to the interactions of unstable planar eigenmodes. See Supplementary Information for parameter values.

Source data

Source Data Fig. 1

Data for Fig. 1d,e.

Source Data Fig. 3

Data for Fig. 3a,b.

Source Data Fig. 4

Data for Fig. 4.

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Chakrabarti, B., Liu, Y., LaGrone, J. et al. Flexible filaments buckle into helicoidal shapes in strong compressional flows. Nat. Phys. 16, 689–694 (2020). https://doi.org/10.1038/s41567-020-0843-7

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