Bicontinuous cubic phases in biological and artificial self-assembled systems

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  • ReceivedNov 19, 2019
  • AcceptedJan 28, 2020
  • PublishedFeb 28, 2020



the National Natural Science Foundation of China(21922304,21873072,31670841)

Shanghai Rising-Star Program(17QA1401700)

Wenzhou Institute

University of Chinese Academy of Sciences(WIUCASQD2019005)


This work was supported by the National Natural Science Foundation of China (21922304, 21873072 and 31670841), Shanghai Rising-Star Program (17QA1401700) and Wenzhou Institute, University of Chinese Academy of Sciences (WIUCASQD2019005).

Interest statement

The authors declare that they have no conflict of interest.

Contributions statement

Han L and Deng Y proposed the topic and outline of the manuscript. The manuscript was originally drafted by Cui C, and further enriched by Han L and Deng Y. All the co-authors contributed to the discussion and refinement of the manuscript.

Author information

Congcong Cui received his Bachelor degree from Henan Normal University and Master degree from Yunnan Normal University. Currently, he is a research assistant in Tongji University. His research interest is focused on mesostructured materials and biomineralizations.

Yuru Deng received her undergraduate degree from Kaohsiung Medical University and PhD degree from State University of New York, USA. She did her postdoctoral training at Wadsworth Centre (NY), investigating Cubic Membrane (CM) nanostructures. She was an assistant professor at National University of Singapore (2002–2013) and is currently a Senior Research Associate at Wenzhou Institute, University of Chinese Academy of Sciences. She is internationally recognized as a pioneer in CM research, an emerging field in biomedicine and nano-technology.

Lu Han received his undergraduate degree from Shanghai Jiao Tong University. He completed his PhD work in 2011 at Shanghai Jiao Tong University and at Stockholm University in 2010. He joined Shanghai Jiao Tong University as an assistant professor in 2011 and became an associate professor in 2013. He moved to Tongji University as a professor in 2017. His current research focuses on synthesis and characterization of mesostructured materials, biomineralizations, and structural analyses by transmission electron microscopy.


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  • Figure 1

    Schematic diagram of the molecule packing in biological cubic membranes and the self-assembly of block copolymers.

  • Figure 2

    (a) Isolated mitochondria from 7-day starved amoeba Chaos carolinense revealed by TEM. (b) SEM micrograph showing the intact outer surfaces of the isolated mitochondria. Reproduced with permission from Ref. [71]. Copyright 2014, Springer-Verlag Wien. (c) SARS-CoV-induced cubic membranes in Vero cell. Reproduced under the terms of the CC BY 4.0 License [74]. Copyright 2004, The Authors. (d) 3D model of gyroid surfaces.

  • Figure 3

    (a1) TEM images of mitochondria with multilayer cubic membranes in a tree shrew cone photoreceptor cell. (a2) 3D model of 12-layered G surfaces and (a3) the corresponding 2D projection map. The TEM image exactly matches the 2D simulated projection. Reproduced with permission from Ref. [75], Copyright 1987, Springer-Verlagl and Ref. [54], Copyright 2009, Elsevier. (b1) Photograph of T. opisena. (b2) Optical micrograph of the green ventral wing area. (b3) SEM image of SG crystallites. Reproduced under the terms of the CC BY 4.0 License [76]. Copyright 2017, The Authors. (c1) Photograph of the weevil L. augustus. (c2) Optical micrograph of individual scales attached to the exoskeleton of L. augustus. (c3) Cross-sectioned SEM image of a region of a scale of L. augustus. Reproduced with permission from Ref. [11]. Copyright 2008, American Physical Society.

  • Figure 4

    The phase diagram for linear AB diblock copolymers with theoretical calculation by (a) self-consistent mean-field theory and (b) experimental results for PI-PS. Phases are labeled lamellar (L, LAM), hexagonal cylinders (H, HEX), bicontinuous Ia-3d cubic (Ia-3d), body-centered cubic (bcc) spheres (Im-3m), close-packed spheres (CPS), hexagonally perforated layers (HPL), and disordered (DIS). Reproduced with permission from Ref. [24], Copyright 2006, American Chemical Society and Ref. [104], Copyright 1995, American Chemical Society.

  • Figure 5

    (a) Schematic diagram of the core-shell bicontinuous SDD structure formed by microphase separation with a mixture of solvents. TEOS: tetraethylorthosilicate. (b) Optical micrograph of the sample showing the structural color from purple to blue. (c) SEM and (d, e) TEM images with different orientations, showing two sets of hollow diamond frameworks adhering to each other. Reproduced with permission from Ref. [139], Copyright 2018, Wiley-VCH, and Ref. [38], Copyright 2014, The American Chemical Society.

  • Figure 6

    (a) Synthetic phase diagram of polyisoprene-b-poly(ethylene oxide) (PI-PEO) and inorganic components (in weight fractions). White areas are marked as different structures. A schematic of the phase of pure PI-PEO is shown at the bottom. Reproduced with permission from Ref. [163]. Copyright 2009, American Chemical Society. (b) Synthetic phase diagram of the structure of macroporous silica based on the PEO-PS-PtBA polymer system (in volume fractions). Different points represent different structures: from normal-phase (oil in water) cage-type (n-C, black), normal-phase 2D hexagonal (n-H, purple), and lamellar (L, pink) to unique inverse-phase (water in oil) hyperbolic-surface (i-HS) structures, including the shifted double-diamond (i-SDD, red), single-gyroid (i-SG, dark green), and shifted double-primitive (i-SDP, blue), inverse-phase 2D hexagonal (i-H, orange) and inverse-phase micellar (i-M, reseda). Reproduced with permission from Ref. [40]. Copyright 2018, American Chemical Society.

  • Figure 7

    (a) SEM image of the intergrown structure of SDP and SDD. (b) Skeletal graph representing the centers of the channel for P to D networks according to SEM observations. Reproduced with permission from Ref. [39]. Copyright 2017, Wiley-VCH. (c) SEM images of the intergrown structure of DD and SG. (d) Schematic drawings of the structural relationships between the original DD and SG. Reproduced with permission from Ref. [41]. Copyright 2016, American Chemical Society.

  • Figure 8

    Structural transformations in biological membranes and artificial self-assembled systems. (a) ER in sebocytes of primates. Reproduced with permission from Ref. [197]. Copyright 1974, The Williams & Wilkin Co. (b) SG structure in macroporous silica scaffolds. Intergrown/transformation between tubular and cubic structures in biological membranes (c) [198] and macroporous silica (d), respectively. Reproduced with permission from Ref. [198]. Copyright 1974, Wiley-VCH. The tubular and cubic membranes are connected by a sparse lamellar structure. They have almost the same transition patterns and behaviors in both systems. The SEM image in (d) has a stronger 3D effect and can show more details. (Images of b and d are provided by Lu Han.)


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