ArticleProceedings of the National Academy of Sciences of the United States of America2016
First-order patterning transitions on a sphere as a route to cell morphology.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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Who cites it
17 citing papers in PubMed.
- The influence of anther locular fluid on exine self-assembly, investigated by in vivo transplantation experiments.Planta · 2025Article
- Mechanisms of pollen wall development in Lysimachia vulgaris.Protoplasma · 2024Article
- Notochord segmentation in zebrafish controlled by iterative mechanical signaling.Developmental cell · 2024Article
- Pollen wall development in Impatiens glandulifera: exine substructure and underlying mechanisms.Protoplasma · 2024Article
- Article
- Genome-Scale Analysis of the Grapevine KCS Genes Reveals Its Potential Role in Male Sterility.International journal of molecular sciences · 2023Article
- Axial segmentation by iterative mechanical signaling.bioRxiv : the preprint server for biology · 2023Article
- Pollen wall patterns as a model for biological self-assembly.Journal of experimental zoology. Part B, Molecular and developmental evolution · 2021Article
- Modeling mechanochemical pattern formation in elastic sheets of biological matter.The European physical journal. E, Soft matter · 2021Article
- Article
- Lateral heterogeneity and domain formation in cellular membranes.Chemistry and physics of lipids · 2020Article
- Review
- Mimicry of a biophysical pathway leads to diverse pollen-like surface patterns.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
- Mimicking pollen and spore walls: self-assembly in action.Annals of botany · 2019Article
- On the mechanism behind the inverse melting in systems with competing interactions.Scientific reports · 2019Article
- A Rationale for Mesoscopic Domain Formation in Biomembranes.Biomolecules · 2018Article
- Mechanics and Buckling of Biopolymeric Shells and Cell Nuclei.Biophysical journal · 2017Article
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Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an individual pattern is robustly reproducible by a single species and a similar set of developmental stages produces a variety of patterns. We argue that the pattern diversity and reproducibility may be explained by interpreting the pattern development as a first-order phase transition to a spatially modulated phase. Brazovskii showed that for such transitions on a flat, infinite sheet, the patterns are uniform striped or hexagonal. Biological objects, however, have finite extent and offer different topologies, such as the spherical surfaces of pollen grains. We consider Brazovskii transitions on spheres and show that the patterns have a richer phenomenology than simple stripes or hexagons. We calculate the free energy difference between the unpatterned state and the many possible patterned phases, taking into account fluctuations and the system's finite size. The proliferation of variety on a sphere may be understood as a consequence of topology, which forces defects into perfectly ordered phases. The defects are then accommodated in different ways. We also argue that the first-order character of the transition is responsible for the reproducibility and robustness of the pattern formation.
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