Phyllotaxis, disk packing and Fibonacci numbers

Speaker : Dr Adil Mughal – Aberystwyth University, Wales

Venue    : Thu 15 Sept 2016, 3pm (Murdoch University, Senate Room)

Phyllotaxis (the arrangement of buds or branches on a stem, or  flowerets on a flower) has long been debated [1, 2], particularly in regard to the widespread occurrence of spiral structures that are related to the Fibonacci sequence [3-7]. Over the years hundreds of papers, and several books, have attempted to provide explanations of this phenomenon using models of varying complexity, sophistication and ad hoc inventiveness.

Here we offer a theoretical model which relates the problem to disk packings, extending previous work [8, 9] that seeks explanations in that way. Our method
is to adapt the closely related problem of the dense packing of hard disks on a cylinder [10{12], where helical symmetry arises naturally, to the present case of
buds on a gradually enlarging stem.

Buds are introduced at the top of a “bullet-shaped” surface – roughly representative of a plant stem, see Fig (1) – and migrate downwards, while conforming to three principles: dense packing, homogeneity and continuity. Typical results are presented in a video. We show that spiral structures characterised by the Fibonacci sequence (1,1,2,3,5,8,13…), as well as related structures, occur naturally under such rules.

A. M. acknowledges financial support through Aberystwyth University Research Fund.

[1] H. Airy, Proceedings of the Royal Society of London 21, 176 (1872).
[2] D. Hofstadter and C. Teuscher, Alan Turing: Life and legacy of a great thinker (Springer Science & Business Media, 2013).
[3] L. Levitov, JETP letters 54, 542 (1991).
[4] L. Levitov, EPL (Europhysics Letters) 14, 533 (1991).
[5] S. Douady and Y. Couder, Physical Review Letters 68, 2098 (1992).
[6] P. Atela, C. Gole, and S. Hotton, Journal of Nonlinear Science 12, 641 (2002).
[7] M. Pennybacker and A.C. Newell, Physical Review Letters 110, 248104 (2013).
[8] G.J. Mitchison, Science (1977).
[9] G. Van Iterson, Mathematische und mikroskopisch-anatomische Studien uber Blattstellungen: nebst Betrachtungen über den Schalenbau der Miliolinen, Ph.D. thesis, TU Delft, Delft University of Technology (1907).
[10] A. Mughal, H. Chan, and D. Weaire, Physical Review Letters 106, 115704 (2011).
[11] A. Mughal, H. Chan, D. Weaire, and S. Hutzler, Physical Review E 85, 051305 (2012).
[12] A. Mughal and D. Weaire, Physical Review E (2014).

Soil Water Repellence: A Molecular Dynamics Study of Amphiphilic Compounds on Mineral Surfaces

Speaker : Dr David Henry – Murdoch University

Venue    : Fri 2 Sept 2016 @ 3pm (Murdoch University, Senate Room)

This talk describes joint work with Nicholas Daniel, S. M. Mijan Uddin, Richard. J. Harper from the School of Veterinary and Life Sciences, Murdoch University, 90 South Street, Murdoch WA. 6150 Australia.

Hydrophobic soils have been observed around the world, under different climates and land uses¹. It is estimated that southern Australia alone has between two and five million hectares affected by hydrophobic soils². Non-wettable soils cause both environmental and economic problems including increased surface runoff, enhanced erosion rates and chemical leaching, decreased nutrient storage and plant-available water and reduced crop yields.³ This hydrophobicity is caused by amphiphilic organic compounds deposited in the soil that originate from plant materials.⁴ Our experimental investigation of this phenomenon is complemented by computer modelling of the structuring and interaction of organic species, on different soil types, to identify key driving forces. This study examines intermolecular interactions of monolayers of hexadecanol (CH₃(CH₂)₁₅OH) and hexadecanoic acid (CH₃(CH₂)₁₄COOH) on quartz, silica and kaolinite as a function of surface density, using classical molecular dynamics simulations. The computer simulations clearly indicate quite different packing and interfacial interactions between wax molecules on sand/quartz (Fig. 1a) and clay/kaolinite surfaces (Fig. 1b), respectively.⁵ Consequently, higher levels of wax material are required to render clay particles hydrophobic compared with sand particles.

Analysis of the trajectories also reveals that acid mobility is greatest on the quartz surface, and lowest on the silica surface. While the interactions between the surface and acid chains are of primary interest, the interactions between acid chains are also important in determining the structure of the layers formed. Hydrogen-bonding is dominant between the acidic hydrogen and carbonyl oxygen atoms of the neighbouring acid chains. The structuring of water around the functional groups of the surfaces and the waxes also provides insight into the susceptibility of different surfaces to develop water repellence.

 

¹ S. H. Doerr, C. J. Ritsema, L. W. Dekker, D. F. Scott, D. Cater, D. Hydrological Procs. 2007, 21, 2223-2228.

² R. J. Harper, I. McKissock, R. J. Gilkes, D. J. Carter, P. S. Blackwell, J. Hydrology 2000, 231-232, 371-383.

³ S. H. Doerr, R. A. Shakesby, R. P. D. Walsh, Earth-Sci. Revs. 2000, 51, 33-65.

⁴ F. A. Hansel, C. T. Aoki, C. M. B. F. Maia, A. Cunha Jr, R. A. Dedecek, R.A. Geoderma 2008, 148, 167-172.

⁵ L. Walden, R. Harper, D. Mendham, D. Henry, J. Fontaine, Soil Res. 2015, 53, 168-177.

Cancer cell migration in 3D biological matrices

Speaker : Prof Ben Fabry – Friedrich-Alexander-Universität Erlangen-Nürnberg

Venue    : Thu 18 Aug 2016, 4pm (Murdoch University, Senate Conference Room)

In cancer metastasis and other physiological processes, cells that migrate through the 3-dimensional (3D) extracellular matrix of the connective tissue must overcome the steric hindrance posed by small pores. It is currently assumed that low cell stiffness promotes cell migration through confined spaces. In my talk I will present data showing that a host of other factors such as adhesion and traction forces may be at least equally important. I will also present new assays that we recently developed to quantify cell migration and traction forces in 3D matrices.

Micro-moth discoveries in southern Australia: a new understanding of evolution, biology and distribution of primitive Lepidoptera

Speaker : Dr Andy Young – Kangaroo Island

Venue    : Thu 4 Aug 2016, 4pm (Murdoch University, ECL2.031)

During the period 2010-2015, we have made three notable discoveries while researching the micro-moth fauna of southern Australia.

The first was the discovery of the new Monotrysian moth Family, the Aenigmatidae. The second the discovery of a large obligate-mutualism association between a group of moths within the Heliozelidae of the south-west of Western Australia and plants within the genus Boronia (Rutaceae). Finally, several species of Microptergidae (Lepidoptera, Zeugloptera) were discovered, for the first time, in the the south-west of Western Australia.

Possibly the most significant finding, was the discovery of the previously unknown Monotrysian Family, the Aenigmatinidae, in the form of the new species Aenigmatinea glatzii. It was discovered on Kangaroo Island, off the southern coast of South Australia.

Initially the placement of this Family was uncertain, due to a combination of ‘primitive’ and ‘advanced’ morphology. Molecular tools were used to elucidate the position of the Family, in combination with detailed morphological analysis.

Our work with Aenigmatinea has demonstrated that transcriptome sequencing is a efficient method for generating many gene sequences, enabling us to resolve older splits, including up to Superfamily level. In the Aenigmatinea study, we used a combination of PCR to amplify two conserved genes and transcriptome sequencing to obtain a further 14 nuclear genes. The combined data set (19512 bp in total) allowed us to place the new family Anigmatineae amongst the Glossata (or ‘tongue moths’), as a sister group to the Neopseustidae, and forming a clade which is sister to all Heteroneura, the vast majority of known Lepidoptera.

The second discovery was that of the complex association within the Australian Heliozelidae (Lepidoptera; Adeloidea), of a new genera closely allied to the described genus Pseliastis, involved in an obligate pollination/early-biology mutualism with the pinnate-leaved members of the section Boronia species (Rutaceae).

A sister family of the Heliozelidae, the Prodoxidae, are the only other members of the order Lepidoptera currently described as having such an association with a similar grouping of plants.

We have discovered that pollination is enacted by the use of a specialised organ on the abdomen of the female moth during oviposition.

As with the prodoxids, it appears that a second genus of related opportunist moths has arisen from the pollinators and lays their eggs into the already fertilised flowers. Our discovery of these associations is ongoing, with around 50 new species to science, known and in the process of being described as a result of our ongoing work.

We have been constructing both higher level and genus group specific phylogenies of the Australian Heliozelidae.

Initially we produced a preliminary phylogeny of Heliozelidae using two mitochondrial (COI and COII) and two nuclear genes (28S and H3). We sequenced a number of specimens from most Heliozelidae genera, including several genera recently discovered in Australia but not yet described. This phylogeny resulted in a number of strongly supported clades, with clear separation between most Australian and Northern Hemisphere groups. However, this phylogeny did not resolve the older, higher level relationships between the clades. To address these issues, we have collected fresh specimens from almost every Heliozelidae genera from which we will generate full transcriptomes. Our aim is to use transcriptome data to produce a well-resolved phylogeny of the Heliozelidae.

Finally, the discovery of a species of Sabatinca (New Zealand group) by Professor Doug Hilton has led to the discovery of a further three species of Western Australian Micropterigidae bu our group. These later three species appear to be in a separate genus apparently unique to WA and possibly related to the eastern Australian genus Tasmantrix. They are the subject of further research by Dr. George Gibbs of the Victoria University, Wellington, New Zealand, and will be published in the near future.

Simulation of diffusive front in ordered porous material and its link with butterflies’ color

Speaker : Ms Manon Marchand – University Paris Sud 11

Venue    : Wed 6 July 2016, 4pm (Murdoch Univ, Senate Conference Room **)

“Les papillons ne sont que des fleurs envolées un jour de fête où la Nature était en veine d’invention” (George Sand, *)

Looking like a flower is a good way of avoiding predators. Red-like colors (long wavelength ones) are often produced by pigments on butterflies wings. But a good way of avoiding predators is also to mimic leaves or sky. Green and blue pigments are extremely rare in nature. Most of green and blue butterflies produces color by interference, diffraction, absorption and reflection of light on structures present on their wings [1].

Butterflies wings present 0.1 mm-long scales [2]. This is where their latin and scientific name, Lepidoptera, comes from. Lepidos- means scales (as in leprosy) and -ptera stands for wings (as in pterodactyl). The structure that interact with light is present on those scales.

We will not discuss here the production of colors on butterflies’ wings but the mechanism forming interesting structures inside the scales by modelling it as a diffusion process in a two-dimensional grid.

[1] How nature produces blue color, Berthier S. and Simonis P.

[2] Light and color on the wing : structural colors in butterflies and moths, H. Giradella

 

* Butterflies are flying flowers invented a day Nature had no idea what to do

** Apologies for the date change. Originally this was advertised for Thursday 7 July