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Investigating chiral morphogenesis of gold using generative cellular automata

Nature Materials (2024)Cite this article

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Abstract

Homochirality is an important feature in biological systems and occurs even in inorganic nanoparticles. However, the mechanism of chirality formation and the key steps during growth are not fully understood. Here we identify two distinguishable pathways from achiral to chiral morphologies in gold nanoparticles by training an artificial neural network of cellular automata according to experimental results. We find that the chirality is initially determined by the nature of the asymmetric growth along the boundaries of enantiomeric high-index planes. The deep learning-based interpretation of chiral morphogenesis provides a theoretical understanding but also allows us to predict an unprecedented crossover pathway and the resulting morphology.

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Fig. 1: The 432-symmetric chiral crystal growth and GCA.
Fig. 2: Training and morphogenesis transitions of two models, RDH3 and CBH1.
Fig. 3: Initial conditions and respective final morphologies of RDH3 and CBH1.
Fig. 4: Crystallographic analysis of RDH3 and CBH1.

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Data availability

All the data for reproduction of this study are available via Github at https://github.com/sangwonim/gca-chiral-morphogenesis. Additional data related to the paper are available from the corresponding authors upon reasonable request.

Code availability

The code for the GCA model is included in the Supplementary Information and available via Github at https://github.com/sangwonim/gca-chiral-morphogenesis and via Zenodo at https://doi.org/10.5281/zenodo.10872052 (ref. 47).

References

  1. Blackmond, D. G. Asymmetric autocatalysis and its implications for the origin of homochirality. Proc. Natl Acad. Sci. USA 101, 5732–5736 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Mann, S. Molecular recognition in biomineralization. Nature 332, 119–124 (1988).

    Article  CAS  Google Scholar 

  3. Lebreton, G. et al. Molecular to organismal chirality is induced by the conserved myosin 1D. Science 362, 949–952 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Tee, Y. H. et al. Cellular chirality arising from the self-organization of the actin cytoskeleton. Nat. Cell Biol. 17, 445–457 (2015).

    Article  CAS  PubMed  Google Scholar 

  5. Grande, C. & Patel, N. H. Nodal signalling is involved in left-right asymmetry in snails. Nature 457, 1007–1011 (2009).

    Article  CAS  PubMed  Google Scholar 

  6. Thitamadee, S., Tuchihara, K. & Hashimoto, T. Microtubule basis for left-handed helical growth in Arabidopsis. Nature 417, 193–196 (2002).

    Article  CAS  PubMed  Google Scholar 

  7. Sharma, V., Crne, M., Park, J. O. & Srinivasarao, M. Structural origin of circularly polarized iridescence in jeweled beetles. Science 325, 449–451 (2009).

    Article  CAS  PubMed  Google Scholar 

  8. Bouligand, Y. Twisted fibrous arrangements in biological materials and cholesteric mesophases. Tissue Cell 4, 189–217 (1972).

    Article  CAS  PubMed  Google Scholar 

  9. Orme, C. A. et al. Formation of chiral morphologies through selective binding of amino acids to calcite surface steps. Nature 411, 775–779 (2001).

    Article  CAS  PubMed  Google Scholar 

  10. Hazen, R. M. & Sholl, D. S. Chiral selection on inorganic crystalline surfaces. Nat. Mater. 2, 367–374 (2003).

    Article  CAS  PubMed  Google Scholar 

  11. Shukla, N. & Gellman, A. J. Chiral metal surfaces for enantioselective processes. Nat. Mater. 19, 939–945 (2020).

    Article  CAS  PubMed  Google Scholar 

  12. Im, S. W. et al. Chiral surface and geometry of metal nanocrystals. Adv. Mater. 32, 1905758 (2020).

    Article  CAS  Google Scholar 

  13. González-Rubio, G. et al. Micelle-directed chiral seeded growth on anisotropic gold nanocrystals. Science 368, 1472–1477 (2020).

    Article  PubMed  Google Scholar 

  14. Xu, L. et al. Enantiomer-dependent immunological response to chiral nanoparticles. Nature 601, 366–373 (2022).

    Article  CAS  PubMed  Google Scholar 

  15. Jiang, W. et al. Emergence of complexity in hierarchically organized chiral particles. Science 368, 642–648 (2020).

    Article  CAS  PubMed  Google Scholar 

  16. Kuzyk, A. et al. DNA-based self-assembly of chiral plasmonic nanostructures with tailored optical response. Nature 483, 311–314 (2012).

    Article  CAS  PubMed  Google Scholar 

  17. Yeom, J. et al. Chiromagnetic nanoparticles and gels. Science 359, 309–314 (2018).

    Article  CAS  PubMed  Google Scholar 

  18. Lee, H.-E. et al. Amino-acid- and peptide-directed synthesis of chiral plasmonic gold nanoparticles. Nature 556, 360–365 (2018).

    Article  CAS  PubMed  Google Scholar 

  19. Kim, R. M. et al. Enantioselective sensing by collective circular dichroism. Nature 612, 470–476 (2022).

    Article  CAS  PubMed  Google Scholar 

  20. Talapin, D. V., Rogach, A. L., Haase, M. & Weller, H. Evolution of an ensemble of nanoparticles in a colloidal solution: theoretical study. J. Phys. Chem. B 105, 12278–12285 (2001).

    Article  CAS  Google Scholar 

  21. Xiao, R.-F., Alexander, J. I. D. & Rosenberger, F. Morphological evolution of growing crystals: a Monte Carlo simulation. Phys. Rev. A 38, 2447–2456 (1988).

    Article  CAS  Google Scholar 

  22. Turner, C. H., Lei, Y. & Bao, Y. Modeling the atomistic growth behavior of gold nanoparticles in solution. Nanoscale 8, 9354–9365 (2016).

    Article  CAS  PubMed  Google Scholar 

  23. Müller, M. & Albe, K. Lattice Monte Carlo simulations of FePt nanoparticles: influence of size, composition, and surface segregation on order-disorder phenomena. Phys. Rev. B 72, 094203 (2005).

    Article  Google Scholar 

  24. Damasceno, P. F., Engel, M. & Glotzer, S. C. Predictive self-assembly of polyhedra into complex structures. Science 337, 453–457 (2012).

    Article  CAS  PubMed  Google Scholar 

  25. Zhang, D., Choi, C., Kim, J. & Kim, Y. M. Learning to generate 3D shapes with generative cellular automata. In 9th International Conference on Learning Representations (ICLR) (2021).

  26. Mordvintsev, A., Randazzo, E., Niklasson, E. & Levin, M. Growing neural cellular automata. Distill https://doi.org/10.23915/distill.00023 (2020).

  27. Von Neumann, J. & Burks, A. W. Theory of Self-Reproducing Automata (Univ. Illinois Press, 1966).

  28. Gardner, M. Mathematical games: the fantastic combinations of John Conway’s new solitaire game “life”. Sci. Am. 223, 120–123 (1970).

    Article  Google Scholar 

  29. Wootton, J. T. Local interactions predict large-scale pattern in empirically derived cellular automata. Nature 413, 841–844 (2001).

    Article  CAS  PubMed  Google Scholar 

  30. Manukyan, L., Montandon, S. A., Fofonjka, A., Smirnov, S. & Milinkovitch, M. C. A living mesoscopic cellular automaton made of skin scales. Nature 544, 173–179 (2017).

    Article  CAS  PubMed  Google Scholar 

  31. Kim, H. et al. γ-Glutamylcysteine- and cysteinylglycine-directed growth of chiral gold nanoparticles and their crystallographic analysis. Angew. Chem. Int. Ed. 59, 12976–12983 (2020).

    Article  CAS  Google Scholar 

  32. Cho, N. H. et al. Uniform chiral gap synthesis for high dissymmetry factor in single plasmonic gold nanoparticle. ACS Nano 14, 3595–3602 (2020).

    Article  CAS  PubMed  Google Scholar 

  33. Lee, H.-E. et al. Cysteine-encoded chirality evolution in plasmonic rhombic dodecahedral gold nanoparticles. Nat. Commun. 11, 263 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Zhang, N.-N., Sun, H.-R., Xue, Y., Peng, F. & Liu, K. Tuning the chiral morphology of gold nanoparticles with oligomeric gold–glutathione complexes. J. Phys. Chem. C 125, 10708–10715 (2021).

    Article  CAS  Google Scholar 

  35. Wang, S. et al. Helically grooved gold nanoarrows: controlled fabrication, superhelix, and transcribed chiroptical switching. CCS Chem. 3, 2473–2484 (2020).

    Article  Google Scholar 

  36. Ni, B. et al. Chiral seeded growth of gold nanorods into 4-fold twisted nanoparticles with plasmonic optical activity. Adv. Mater. 35, 2208299 (2022).

    Article  Google Scholar 

  37. Wang, H. et al. Selectively regulating the chiral morphology of amino acid-assisted chiral gold nanoparticles with circularly polarized light. ACS Appl. Mater. Interfaces 14, 3559–3567 (2022).

    Article  CAS  PubMed  Google Scholar 

  38. Graham, B., Engelcke, M. & Maaten, L. 3D semantic segmentation with submanifold sparse convolutional networks. In 2018 IEEE/CVF Computer Vision and Pattern Recognition (CVPR) 9224–9232 (2018).

  39. Bordes, F., Honari, S. & Vincent, P. Learning to generate samples from noise through infusion training. In 5th International Conference on Learning Representations (ICLR) (2017).

  40. Ahn, H.-Y., Lee, H.-E., Jin, K. & Nam, K. T. Extended gold nano-morphology diagram: synthesis of rhombic dodecahedra using CTAB and ascorbic acid. J. Mater. Chem. C 1, 6861–6868 (2013).

    Article  CAS  Google Scholar 

  41. Wu, H.-L. et al. A comparative study of gold nanocubes, octahedra, and rhombic dodecahedra as highly sensitive SERS substrates. Inorg. Chem. 50, 8106–8111 (2011).

    Article  CAS  PubMed  Google Scholar 

  42. Zhang, D., Choi, C., Park, I. & Kim, Y. M. Probabilistic implicit scene completion. In 10th International Conference on Learning Representations (ICLR) (2022).

  43. Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. In 33rd Conference on Neural Information Processing Systems (NeurIPS) (2019).

  44. Choy, C., Gwak, J. & Silvio, S. 4D Spatio-temporal ConvNets: Minkowski convolutional neural networks. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 3075–3084 (2019).

  45. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. In 3rd International Conference for Learning Representations (ICLR) (2015).

  46. Ronneberger, O., Fischer, P. & Brox, T. U-Net: convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015 234–241 (Springer, 2015).

  47. Im, S. W. & Zhang, D. Sangwonim/gca-chiral-morphogenesis: v1.0. Zenodo https://doi.org/10.5281/zenodo.10872052 (2024).

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Acknowledgements

This work is supported by the Defense Challengeable Future Technology Program of Agency for Defense Development, Republic of Korea (S.W.I., J.H.H., R.M.K. and K.T.N.); Korea Institute for Advancement of Technology (KIAT) grant P0019783 (S.W.I., J.H.H., R.M.K. and K.T.N.) funded by the Korean government (Ministry of Trade, Industry and Energy (MOTIE)); and the National Research Foundation of Korea (NRF) grant NRF-2020M3F7A1094300 (C.C. and Y.M.K.) funded by the Korean government (Ministry of Science and ICT (MSIT)). K.T.N. thanks the Institute of Engineering Research, Research Institute of Advanced Materials (RIAM) and SOFT Foundry Institute.

Author information

Author notes

  1. These authors contributed equally: Sang Won Im, Dongsu Zhang.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Seoul National University, Seoul, Korea

    Sang Won Im, Jeong Hyun Han, Ryeong Myeong Kim & Ki Tae Nam

  2. Institute of New Media and Communications, Seoul National University, Seoul, Korea

    Dongsu Zhang & Young Min Kim

  3. Department of Electrical and Computer Engineering, Seoul National University, Seoul, Korea

    Changwoon Choi & Young Min Kim

Authors
  1. Sang Won Im
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Contributions

K.T.N. and Y.M.K. conceived the project. S.W.I. and D.Z. designed the experiments and implemented the GCA model. D.Z. and C.C. developed the GCA model. S.W.I., J.H.H. and R.M.K. synthesized and characterized the nanoparticles. J.H.H. conducted the FDTD simulations. S.W.I., D.Z., Y.M.K. and K.T.N. wrote the manuscript with contributions from all authors. Y.M.K. guided the numerical simulations. K.T.N. guided all aspects of the work.

Corresponding authors

Correspondence to Young Min Kim or Ki Tae Nam.

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The authors declare no competing interests.

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Peer review information

Nature Materials thanks Qian Chen, Zhifeng Huang and Jianping Xie for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 432 helicoid morphologies depending on sequences of an amino acid and peptides, and seed morphologies.

SEM images of 432 helicoids synthesized using a, Cys, b, Glu-Cys, c, Cys-Gly, d, Glu-Cys-Gly as chiral amino acid or peptide. (Scale bar: 200 nm) *Cys was injected after 20 min of cube seed growth.

Extended Data Fig. 2 Morphogenesis processes of 432 helicoids.

432 helicoids with different growth time were observed by SEM. (Scale bar: 200 nm) Each 432 helicoid start from a 20-30 nm low-Miller-index-faceted seed and evolves to a high-Miller-index-faceted intermediate morphology. Depending on the seed morphologies and peptide sequences, the chiral intermediates and final chiral features were determined.

Extended Data Fig. 3 Predicted \(4/m\bar{3}2/m\)- and 432-symmetric crystal morphologies.

a, Each crystal is assumed to be composed of one type of surface Miller index. A morphology of a crystal is determined by the orientation of red-indicated facet. Therefore, crystal morphologies can be corresponded to the stereographic projection of this facet. The type of morphology is distinguished by convexity, flatness, or concavity of three elementary edges connecting 〈100〉, 〈111〉, 〈110〉 vertices. b, Chiral morphologies are predicted by breaking mirror symmetry between adjacent facets of 7 different high-Miller-index-faceted morphologies that is theoretically predicted. Depending on the convexity or concavity of the edges, different chiral features appear.

Extended Data Fig. 4 Experimental confirmation of the crossover between RDH3 and CBH1 pathways.

a, Schematic description of growth pathways and crossovers discovered from GCA. Solid lines indicate possible pathways of RDH3, CBH1, and crossover from RDH3 to CBH1. Dotted line indicates impossible crossover from CBH1 to RDH3 b, H3 intermediate after growth in GSH-containing solution for 30 min. c, H3 after growth in GSH-containing solution for 120 min. d, H3 intermediate was injected to Cys-containing solution. H1 morphology with the chiral edge structure was obtained. e, H1 intermediate after growth in Cys-containing solution for 30 min. f, H1 after growth in Cys-containing solution for 120 min. g, H1 intermediate was injected to GSH- containing solution, but H1 morphology was remained. (Scale bar: 200 nm).

Supplementary information

Supplementary Information

Supplementary Figs. 1–14 and text.

Supplementary Code 1

Code for GCA.

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Im, S.W., Zhang, D., Han, J.H. et al. Investigating chiral morphogenesis of gold using generative cellular automata. Nat. Mater. (2024). https://doi.org/10.1038/s41563-024-01889-x

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