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Investigating chiral morphogenesis of gold using generative cellular automata


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 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 and via Zenodo at (ref. 47).


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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

Authors and Affiliations



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.

Peer review

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).

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