Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Oscillations, travelling fronts and patterns in a supramolecular system

Nature Nanotechnology volume 13, pages 1021–1027 (2018)Cite this article

Subjects

Abstract

Supramolecular polymers, such as microtubules, operate under non-equilibrium conditions to drive crucial functions in cells, such as motility, division and organelle transport1. In vivo and in vitro size oscillations of individual microtubules2,3 (dynamic instabilities) and collective oscillations4 have been observed. In addition, dynamic spatial structures, like waves and polygons, can form in non-stirred systems5. Here we describe an artificial supramolecular polymer made of a perylene diimide derivative that displays oscillations, travelling fronts and centimetre-scale self-organized patterns when pushed far from equilibrium by chemical fuels. Oscillations arise from a positive feedback due to nucleation–elongation–fragmentation, and a negative feedback due to size-dependent depolymerization. Travelling fronts and patterns form due to self-assembly induced density differences that cause system-wide convection. In our system, the species responsible for the nonlinear dynamics and those that self-assemble are one and the same. In contrast, other reported oscillating assemblies formed by vesicles6, micelles7 or particles8 rely on the combination of a known chemical oscillator and a stimuli-responsive system, either by communication through the solvent (for example, by changing pH7,8,9), or by anchoring one of the species covalently (for example, a Belousov–Zhabotinsky catalyst6,10). The design of self-oscillating supramolecular polymers and large-scale dissipative structures brings us closer to the creation of more life-like materials11 that respond to external stimuli similarly to living cells, or to creating artificial autonomous chemical robots12.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Kinetics of redox-fuelled PDI assembly and disassembly.
Fig. 2: Supramolecular oscillations.
Fig. 3: Supramolecular oscillator model.
Fig. 4: Supramolecular travelling fronts and patterns.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Alberts, B. et al. Molecular Biology of the Cell (Garland Science, New York, 2002).

  2. Valiron, O., Caudron, N. & Job, D. Microtubule dynamics. Cell. Mol. Life Sci. 58, 2069–2084 (2001).

    Article  CAS  Google Scholar 

  3. Mandelkow, E.-M. & Mandelkow, E. Microtubule oscillations. Cell Motil. Cytoskeleton 22, 235–244 (1992).

    Article  CAS  Google Scholar 

  4. Houchmandzadeh, B. & Vallade, M. Collective oscillations in microtubule growth. Phys. Rev. E 53, 6320–6324 (1996).

    Article  CAS  Google Scholar 

  5. Mandelkow, E., Mandelkow, E. M., Hotani, H., Hess, B. & Muller, S. C. Spatial patterns from oscillating microtubules. Science 246, 1291–1293 (1989).

    Article  CAS  Google Scholar 

  6. Tamate, R., Ueki, T., Shibayama, M. & Yoshida, R. Autonomous unimer–vesicle oscillation by totally synthetic diblock copolymers: effect of block length and polymer concentration on spatio-temporal structures. Soft Matter 13, 4559–4568 (2017).

    Article  CAS  Google Scholar 

  7. Lagzi, I., Wang, D., Kowalczyk, B. & Grzybowski, B. A. Vesicle-to-micelle oscillations and spatial patterns. Langmuir 26, 13770–13772 (2010).

    Article  CAS  Google Scholar 

  8. Lagzi, I., Kowalczyk, B., Wang, D. & Grzybowski, B. A. Nanoparticle oscillations and fronts. Angew. Chem. Int. Ed. 49, 8616–8619 (2010).

    Article  CAS  Google Scholar 

  9. Wang, G. et al. The non-equilibrium self-assembly of amphiphilic block copolymers driven by a pH oscillator. Colloids Surf. A 529, 808–814 (2017).

    Article  CAS  Google Scholar 

  10. Yoshida, R. Self-oscillating gels driven by the Belousov–Zhabotinsky reaction as novel smart materials. Adv. Mater. 22, 3463–3483 (2010).

    Article  CAS  Google Scholar 

  11. Grzybowski, B. A. & Huck, W. T. S. The nanotechnology of life-inspired systems. Nat. Nanotech. 11, 585–592 (2016).

    Article  CAS  Google Scholar 

  12. Hess, H. & Ross, J. L. Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots. Chem. Soc. Rev. 46, 5570–5587 (2017).

    Article  CAS  Google Scholar 

  13. Leira-Iglesias, J., Sorrenti, A., Sato, A., Dunne, P. A. & Hermans, T. M. Supramolecular pathway selection of perylenediimides mediated by chemical fuels. Chem. Commun. 52, 9009–9012 (2016).

    Article  CAS  Google Scholar 

  14. Meisl, G. et al. Molecular mechanisms of protein aggregation from global fitting of kinetic models. Nat. Protocols 11, 252–272 (2016).

    Article  CAS  Google Scholar 

  15. Carnall, J. M. A. et al. Mechanosensitive self-replication driven by self-organization. Science 327, 1502–1506 (2010).

    Article  CAS  Google Scholar 

  16. Kondepudi, D. K. & Sabanayagam, C. Secondary nucleation that leads to chiral symmetry breaking in stirred crystallization. Chem. Phys. Lett. 217, 364–368 (1994).

    Article  CAS  Google Scholar 

  17. Ulery, B. D., Nair, L. S. & Laurencin, C. T. Biomedical applications of biodegradable polymers. J. Polym. Sci. B 49, 832–864 (2011).

    Article  CAS  Google Scholar 

  18. Scott, S. K. Oscillations, Waves, and Chaos in Chemical Kinetics (Oxford Univ. Press, Oxford, 1994).

  19. Sept, D., Limbach, H. J., Bolterauer, H. & Tuszynski, J. A. A chemical kinetics model for microtubule oscillations. J. Theor. Biol. 197, 77–88 (1999).

    Article  CAS  Google Scholar 

  20. Lange, G., Mandelkow, E.-M., Jagla, A. & Mandelkow, E. Tubulin oligomers and microtubule oscillations. Eur. J. Biochem. 178, 61–69 (1988).

    Article  CAS  Google Scholar 

  21. Cohen, S. I. A. et al. Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments. J. Chem. Phys. 135, 065105 (2011).

    Article  Google Scholar 

  22. Pojman, J. A. & Epstein, I. R. Convective effects on chemical waves. 1. Mechanisms and stability criteria. J. Phys. Chem. 94, 4966–4972 (1990).

    Article  CAS  Google Scholar 

  23. Epstein, I. R. & Pojman, J. A. An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (Oxford Univ. Press, Oxford, 1998).

  24. Nagypal, I., Bazsa, G. & Epstein, I. R. Gravity-induced anisotropies in chemical waves. J. Am. Chem. Soc. 108, 3635–3640 (1986).

    Article  CAS  Google Scholar 

  25. Tena-Solsona, M. et al. Non-equilibrium dissipative supramolecular materials with a tunable lifetime. Nat. Commun. 8, 15895 (2017).

    Article  CAS  Google Scholar 

  26. Maiti, S., Fortunati, I., Ferrante, C., Scrimin, P. & Prins, L. J. Dissipative self-assembly of vesicular nanoreactors. Nat. Chem. 8, 725–731 (2016).

    Article  CAS  Google Scholar 

  27. Mishra, A. et al. Biomimetic temporal self-assembly via fuel-driven controlled supramolecular polymerization. Nat. Commun. 9, 1295 (2018).

    Article  Google Scholar 

  28. Jalani, K., Dhiman, S., Jain, A. & George, S. J. Temporal switching of an amphiphilic self-assembly by a chemical fuel-driven conformational response. Chem. Sci 8, 6030–6036 (2017).

    Article  CAS  Google Scholar 

  29. Boekhoven, J., Hendriksen, W. E., Koper, G. J. M., Eelkema, R. & van Esch, J. H. Transient assembly of active materials fueled by a chemical reaction. Science 349, 1075–1079 (2015).

    Article  CAS  Google Scholar 

  30. Scott, S. K. Chemical Chaos (Clarendon, Oxford, 1993).

  31. Hammele, M. & Zimmermann, W. Modeling oscillatory microtubule polymerization. Phys. Rev. E 67, 021903 (2003).

    Article  Google Scholar 

  32. Nicolis, G. & Prigogine, I. Self-Organization in Nonequilibrium Systems (Wiley, Hoboken, 1977).

  33. Zhang, Y., Tsitkov, S. & Hess, H. Complex dynamics in a two-enzyme reaction network with substrate competition. Nat. Catal. 1, 276–281 (2018).

    Article  Google Scholar 

  34. Orlova, T. et al. Revolving supramolecular chiral structures powered by light in nanomotor-doped liquid crystals. Nat. Nanotech. 13, 304–308 (2018).

    Article  CAS  Google Scholar 

  35. Gelebart, A. H. et al. Making waves in a photoactive polymer film. Nature 546, 632–636 (2017).

    Article  CAS  Google Scholar 

  36. Sorrenti, A., Leira-Iglesias, J., Markvoort, A. J., de Greef, T. F. A. & Hermans, T. M. Non-equilibrium supramolecular polymerization. Chem. Soc. Rev. 46, 5476–5490 (2017).

    Article  CAS  Google Scholar 

  37. Sorrenti, A., Leira-Iglesias, J., Sato, A. & Hermans, T. M. Non-equilibrium steady states in supramolecular polymerization. Nat. Commun. 8, 15899 (2017).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Region Alsace, University of Strasbourg Institute for Advanced Study (USIAS), LabEx grant ‘Suproscill’ (CSC-THE-17) and ERC-2017-STG ‘Life-Cycle’ (757910). M.S. acknowledges an STSM from the CMST COST Action CM1304 Emergence and Evolution of Complex Chemical Systems. We acknowledge T. Ebbesen, C. Genet and M. Seidel for help with the IR-SLS.

Author information

Authors and Affiliations

  1. University of Strasbourg, CNRS, ISIS UMR 7006, Strasbourg, France

    Jorge Leira-Iglesias, Alessandra Tassoni, Takuji Adachi & Thomas M. Hermans

  2. Non-linearity and Complexity Research Group, Systems Analytics Research Institute, Engineering and Applied Science, Aston University, Birmingham, UK

    Michael Stich

Authors
  1. Jorge Leira-Iglesias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandra Tassoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takuji Adachi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Stich
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Thomas M. Hermans
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.L.-I. and T.M.H. designed and performed the experiments, and analysed the data. J.L.-I. performed the synthesis. A.T. performed the static and dynamic light scattering experiments. A.T. and T.A. developed the IR-SLS experiments and interpreted the results. J.L.-I., A.T. and T.A. carried out the IR-SLS experiments. M.S. and T.M.H. performed the modelling and interpretation of the results. J.L.-I. and T.M.H. wrote the paper. All the authors discussed the results and commented on the manuscript. T.M.H. conceived the overall project and supervised the research.

Corresponding author

Correspondence to Thomas M. Hermans.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Supplementary Information

Supplementary Sections 1–7 and Supplementary Figures 1–17

Supplementary Video 1

Supramolecular oscillations in a semi-batch reactor

Supplementary Video 2

Propagating front of supramolecular assemblies

Supplementary Video 3

The propagating front induces large scale in-plane convection

Supplementary Video 4

Control experiment. Seeded front versus non-seeded region

Supplementary Video 5

An outward propagating oxidation front induces flow-alignment of PDIassem

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leira-Iglesias, J., Tassoni, A., Adachi, T. et al. Oscillations, travelling fronts and patterns in a supramolecular system. Nature Nanotech 13, 1021–1027 (2018). https://doi.org/10.1038/s41565-018-0270-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-018-0270-4

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing