Seminar with Gerd Schröder-Turk – University of Copenhagen

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Seminar with Gerd Schröder-Turk

Labyrinth-like nanostructures in plant cells and insect

Senior Lecturer in Mathematics and Statistics at Murdoch University, Perth, Australia, Gerd Schröder-Turk, Dr. habil., will visit CPSC on 21 December to give the talk Labyrinth-like nanostructures in plant cells and insects - speculations on formation mechanisms and function.

Bicontinuous geometries are fascinating structures that are characterised by spatially extended highly-ordered arrangements on the nanoscale. Allan Schoen’s Gyroid minimal surface is in many ways the ideal archetype of these geometries, being a surface that divides space into two identical domains, each of which is an ordered maze-like infinite labyrinth.

For the Gyroid and all other bicontinuous forms, the characteristic defining feature is that all components –the lipid membranes, the aqueous channels, the inner-cellullar and the extra-cellular components– all ‘percolate’ throughout space, i.e., they allow macroscopic and fast transport. This is for example evident in the diffusion constants of the ‘inverse cubic’ lipid/water bicontinuous phases which is orders of magnitude faster than in other lipid/water phases such as micelles or lamellae.

Butterfly Gyroid nanostructure in solid chitin.

Bicontinuous phases are found in synthetic systems, from lipid/water mixtures, to copolymeric plastics and mesoporous silicates. Our understanding of how they form, and the applications they afford (drug delivery agents, nanoengineering templates, photonics), is developing fast.

However, bicontinuous phases are also found widely in biology, in membrane systems (prolamellar body, ER, golgi, etc), biopolymeric nanostructures (insect photonic crystals) to biomineralised materials (e.g. sea urchin calcite skeleton). Nature squarely outperforms synthetic bicontinuous materials, in terms of control over symmetry, length scale, topology, epitaxial relationships, and many other aspects relating to the structure formation process. Unfortunately, our understanding of both how and why nature forms biocontinuous materials is nowhere near as well developed for the synthetic case.

Prolamellar body in maize (images from [1;2]).

In this talk, I will first review the bicontinuous gyroid structure, using the occurrence as a photonic crystal in green butterflies as an example. I will review aspects of the biological formation mechanism [3] as well as of the geometric argument that gyroids form by virtue of providing minimal heterogeneity [4]. To lighten things up a bit, examples of the sparkling reflections produced by photonic effects will be shown (‘Structural Coloration – color without pigments’, [5]).

Then I will switch to the question of why bicontinuous geometries form in prolamellar bodies in plant cells. I will in particular address two questions:

1. Formation: Interestingly, the prolamellar body forms what is called an 'unbalanced' biocontinuous form, that is, a structure where the two aqueous channels are not of the same volume. As far as I know, the PLB is the only example of this happening in the biological or chemical world(technically speaking, the membrane has the symmetry group of the single diamond, rather than of the double diamond).

Also, the PLB forms an interesting array of bicontinuous symmetries, including the Wurtzite form which has not been reported elsewhere. I will explore, if geometric arguments derived from the ‘unbalanced’ nature can explain why these unconventional symmetries prevail in the PLB (technically, this is the question of constant-mean-curvature membranes as opposed to minimal-surface-membranes)

2. Function: It is unclear if the highly-ordered form of the PLB has a function beyond the transport-related advantages of bicontinuous geometries (in fact, the ocurrence of many other disordered variants suggests that maybe it does not). Given the photonic properties of many insect bicontinuous structures and given the dominant role of light in the conversion from PLB to the chloroplast, it seems plausible to investigate potential photonic properties of the PLB geometries - Thomas Landh already alluded to such possibilities.

Sadly, the length scales of the PLB structures are too small to give optical effects in the visible (or the relevant) range of the spectrum of light. I will show that this remains the case even when anisotropic dielectric properties due to the membrane-like nature are considered.

I am a material geometer, and proudly so, but largely an ignorant when it comes to the biological and bio-chemical properties of plant cells. I am excited about presenting this talk at the Copenhagen Plant Science Centre, and look forward to being challenged about my geometry-focused world-view of the nanoscale by the people who really know plant cells.

Dr. Schröder-Turk received his PhD in Physical Sciences from the Australian National University. In 2013, he was awarded a Habilitation degree (Dr. rer. nat. habil.) in Physics from the Friedrich-Alexander Universität Erlangen-Nürnberg and won the 2014 Emmy-Noether Prize for outstanding habilitation thesis.

Time: 21 December 2016, 13:00-14:00

Place: Thorvaldsensvej 40, 1871 Frederiksberg C, room K117 & M117.

[1] Selstam et al., "Structural organization of prolamellar bodies (PLB) isolated from Zea Mays", Biochimica et Biophysia Acta, 1768, 2007.
[2] Gunning B, "Membrane geometry of 'open' prolamellar bodies", Protoplasma, 215, 2001.
[3] B. Winter et al., "Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi", Proceedings of the National Academy of Sciences 112(42), 12911-12916 (2015) - see references therein.
[4] Schröder-Turk et al., "Polycontinuous geometries for inverse surfactant phases with more than two aqueous network domains", Faraday Discussions 161, 215-247 (2013).
[5] S.T. Hyde and G.E. Schröder, "Novel surfactant mesostructural topologies: between lamellae and columnar (hexagonal) forms", Curr. Opin. Colloid Interf. Sci. 8, 5-14 (2003).
[5] M. Saba, et al., "Absence of circular polarization in reflections of butterfly wing scales with chiral Gyroid structure", Materials Today: Proceedings 1, 193-208 (2014).