ORCID Profile
0000-0001-7964-683X
Current Organisations
Murdoch University
,
Universität Potsdam
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Publisher: AIP Publishing
Date: 21-12-2020
DOI: 10.1063/5.0029301
Abstract: The quantizer problem is a tessellation optimization problem where point configurations are identified such that the Voronoi cells minimize the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd’s algorithm [M. A. Klatt et al. Nat. Commun. 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the “Voronoi liquid” by Ruscher, Baschnagel, and Farago [Europhys. Lett. 112, 66003 (2015)]. Here, we investigate the cooling behavior of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallizes from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench), the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a body-centered cubic ordered structure. This result is in line with the geometric intuition that the geometric Lloyd’s algorithm corresponds to a type of fast quench.
Publisher: Oxford University Press (OUP)
Date: 18-10-2021
Abstract: Bicontinuous membranes in cell organelles epitomize nature’s ability to create complex functional nanostructures. Like their synthetic counterparts, these membranes are characterized by continuous membrane sheets draped onto topologically complex saddle-shaped surfaces with a periodic network-like structure. Their structure sizes, (around 50–500 nm), and fluid nature make transmission electron microscopy (TEM) the analysis method of choice to decipher their nanostructural features. Here we present a tool, Surface Projection Image Recognition Environment (SPIRE), to identify bicontinuous structures from TEM sections through interactive identification by comparison to mathematical “nodal surface” models. The prolamellar body (PLB) of plant etioplasts is a bicontinuous membrane structure with a key physiological role in chloroplast biogenesis. However, the determination of its spatial structural features has been held back by the lack of tools enabling the identification and quantitative analysis of symmetric membrane conformations. Using our SPIRE tool, we achieved a robust identification of the bicontinuous diamond surface as the dominant PLB geometry in angiosperm etioplasts in contrast to earlier long-standing assertions in the literature. Our data also provide insights into membrane storage capacities of PLBs with different volume proportions and hint at the limited role of a plastid ribosome localization directly inside the PLB grid for its proper functioning. This represents an important step in understanding their as yet elusive structure–function relationship.
Publisher: Royal Society of Chemistry (RSC)
Date: 2019
DOI: 10.1039/C9SM01460H
Abstract: Star copolymers on a sphere self-assemble into patchy particles with structure and coordination corresponding to those found in the famous Thomson problem.
Publisher: Cold Spring Harbor Laboratory
Date: 29-04-2021
DOI: 10.1101/2021.04.28.441812
Abstract: Bicontinuous membranes in cell organelles epitomise nature’s ability to create complex functional nanostructures. Like their synthetic counterparts, these membranes are characterised by continuous membrane sheets draped onto topologically complex saddle-shaped surfaces with a periodic network-like structure. In cell organelles, their structure sizes around 50–500 nm and fluid nature make Transmission Electron Microscopy (TEM) the analysis method of choice to decipher nanostructural features. Here we present a tool to identify bicontinuous structures from TEM sections by comparison to mathematical “nodal surface” models, including the hexagonal lonsdaleite geometry. Our approach, following pioneering work by Deng and Mieczkowski (1998), creates synthetic TEM images of known bicontinuous geometries for interactive structure identification. We apply the method to the inner membrane network in plant cell chloroplast precursors and achieve a robust identification of the bicontinuous diamond surface as the dominant geometry in several plant species. This represents an important step in understanding their as yet elusive structure-function relationship.
No related grants have been discovered for Tobias Hain.