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"Dumais, Jacques"
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Do plants know math? : unwinding the story of plant spirals, from Leonardo da Vinci to now
\"Charles Darwin was driven to distraction by plant spirals, growing so exasperated that he once begged a friend to explain the mystery \"if you wish to save me from a miserable death.\" The legendary naturalist was hardly alone in feeling tormented by these patterns. Plant spirals captured the gaze of Leonardo da Vinci and became Alan Turing's final obsession. This book tells the stories of the physicists, mathematicians, and biologists who found themselves magnetically drawn to Fibonacci spirals in plants, seeking an answer to why these beautiful and seductive patterns occur in botanical forms as diverse as pine cones, cabbages, and sunflowers. Do Plants Know Math? takes you down through the centuries to explore how great minds have been captivated and mystified by Fibonacci patterns in nature. It presents a powerful new geometrical solution, little known outside of scientific circles, that sheds light on why regular and irregular spiral patterns occur. Along the way, the book discusses related plant geometries such as fractals and the fascinating way that leaves are folded inside of buds. Your neurons will crackle as you begin to see the connections. The book will inspire you to look at botanical patterns-and the natural world itself-with new eyes. Featuring hundreds of gorgeous color images, Do Plants Know Math? includes a dozen creative hands-on activities and even spiral-plant recipes, encouraging readers to explore and celebrate these beguiling patterns for themselves\"--Publisher's description.
BOOK
Mechanics and hydraulics of pollen tube growth
All kingdomsof lifehave evolved tip-growing cells able tomine their environment or deliver cargo to remote targets. The basic cellular processes supporting these functions are understood in increasing detail, but the multiple interactions between them lead to complex responses that require quantitative models to be disentangled. Here, I review the equations that capture the fundamental interactions between wall mechanics and cell hydraulics starting with a detailed presentation of James Lockhart’s seminal model. The homeostatic feedbacks needed to maintain a steady tip velocity are then shown to offer a credible explanation for the pulsatile growth observed in some tip-growing cells. Turgor pressure emerges as a central variable whose role in the morphogenetic process has been a source of controversy for more than 50 yr. I argue that recasting Lockhart’s work as a process of chemical stress relaxation can clarify how cells control tip growth and help us internalise the important but passive role played by turgor pressure in the morphogenetic process.
Journal Article
Design of a unidirectional water valve in Tillandsia
The bromeliad
Tillandsia landbeckii
thrives in the Atacama desert of Chile using the fog captured by specialized leaf trichomes to satisfy its water needs. However, it is still unclear how the trichome of
T. landbeckii
and other
Tillandsia
species is able to absorb fine water droplets during intermittent fog events while also preventing evaporation when the plant is exposed to the desert’s hyperarid conditions. Here, we explain how a 5800-fold asymmetry in water conductance arises from a clever juxtaposition of a thick hygroscopic wall and a semipermeable membrane. While absorption is achieved by osmosis of liquid water, evaporation under dry external conditions shifts the liquid-gas interface forcing water to diffuse through the thick trichome wall in the vapor phase. We confirm this mechanism by fabricating artificial composite membranes mimicking the trichome structure. The reliance on intrinsic material properties instead of moving parts makes the trichome a promising basis for the development of microfluidics valves.
The valve-like trichomes of the desert plant
Tillandsia landbeckii
allow water acquisition from fog while minimising transpiration. Here, Raux et al. show that a hygroscopic cell-wall adjacent to a semi-permeable plasma membrane at the base of the trichome confers this asymmetry in water conductance.
Journal Article
Universal rule for the symmetric division of plant cells
The division of eukaryotic cells involves the assembly of complex cytoskeletal structures to exert the forces required for chromosome segregation and cytokinesis. In plants, empirical evidence suggests that tensional forces within the cytoskeleton cause cells to divide along the plane that minimizes the surface area of the cell plate (Errera's rule) while creating daughter cells of equal size. However, exceptions to Errera's rule cast doubt on whether a broadly applicable rule can be formulated for plant cell division. Here, we show that the selection of the plane of division involves a competition between alternative configurations whose geometries represent local area minima. We find that the probability of observing a particular division configuration increases inversely with its relative area according to an exponential probability distribution known as the Gibbs measure. Moreover, a comparison across land plants and their most recent algal ancestors confirms that the probability distribution is widely conserved and independent of cell shape and size. Using a maximum entropy formulation, we show that this empirical division rule is predicted by the dynamics of the tense cytoskeletal elements that lead to the positioning of the preprophase band. Based on the fact that the division plane is selected from the sole interaction of the cytoskeleton with cell shape, we posit that the new rule represents the default mechanism for plant cell division when internal or external cues are absent.
Journal Article
Foldable structures and the natural design of pollen grains
Upon release from the anther, pollen grains of angiosperm flowers are exposed to a dry environment and dehydrate. To survive this process, pollen grains possess a variety of physiological and structural adaptations. Perhaps the most striking of these adaptations is the ability of the pollen wall to fold onto itself to prevent further desiccation. Roger P. Wodehouse coined the term harmomegathy for this folding process in recognition of the critical role it plays in the survival of the pollen grain. There is still, however, no quantitative theory that explains how the structure of the pollen wall contributes to harmomegathy. Here we demonstrate that simple geometrical and mechanical principles explain how wall structure guides pollen grains toward distinct folding pathways. We found that the presence of axially elongated apertures of high compliance is critical for achieving a predictable and reversible folding pattern. Moreover, the intricate sculpturing of the wall assists pollen closure by preventing mirror buckling of the surface. These results constitute quantitative structure-function relationships for pollen harmomegathy and provide a framework to elucidate the functional significance of the very diverse pollen morphologies observed in angiosperms.
Journal Article
Are microtubules tension sensors?
Mechanical signals play many roles in cell and developmental biology. Several mechan-otransduction pathways have been uncovered, but the mechanisms identified so far only address the perception of stress intensity. Mechanical stresses are tensorial in nature, and thus provide dual mechanical information: stress magnitude and direction. Here we propose a parsimonious mechanism for the perception of the principal stress direction. In vitro experiments show that microtubules are stabilized under tension. Based on these results, we explore the possibility that such microtubule stabilization operates in vivo, most notably in plant cells where turgor-driven tensile stresses exceed greatly those observed in animal cells.
Journal Article
Wall mechanics and exocytosis define the shape of growth domains in fission yeast
The amazing structural variety of cells is matched only by their functional diversity, and reflects the complex interplay between biochemical and mechanical regulation. How both regulatory layers generate specifically shaped cellular domains is not fully understood. Here, we report how cell growth domains are shaped in fission yeast. Based on quantitative analysis of cell wall expansion and elasticity, we develop a model for how mechanics and cell wall assembly interact and use it to look for factors underpinning growth domain morphogenesis. Surprisingly, we find that neither the global cell shape regulators Cdc42-Scd1-Scd2 nor the major cell wall synthesis regulators Bgs1-Bgs4-Rgf1 are reliable predictors of growth domain geometry. Instead, their geometry can be defined by cell wall mechanics and the cortical localization pattern of the exocytic factors Sec6-Syb1-Exo70. Forceful re-directioning of exocytic vesicle fusion to broader cortical areas induces proportional shape changes to growth domains, demonstrating that both features are causally linked.
Cell shape is determined by a combination of biochemical regulation and mechanical forces. By imaging the dynamic behaviour of growth regulatory proteins in fission yeast and integrating these data within a mechanical model, Abenza
et al
. find that exocytosis plays a dominant role in shaping growth domains.
Journal Article
Modes of deformation of walled cells
The bewildering morphological diversity found in cells is one of the starkest illustrations of life’s ability to self-organize. Yet the morphogenetic mechanisms that produce the multifarious shapes of cells are still poorly understood. The shared similarities between the walled cells of prokaryotes, many protists, fungi, and plants make these groups particularly appealing to begin investigating how morphological diversity is generated at the cell level. In this review, I attempt a first classification of the different modes of surface deformation used by walled cells. Five modes of deformation were identified: inextensional bending, equi-area shear, elastic stretching, processive intussusception, and chemorheological growth. The two most restrictive modes—inextensional and equi-area deformations—are embodied in the exine of pollen grains and the wall-like pellicle of euglenoids, respectively. For these modes, it is possible to express the deformed geometry of the cell explicitly in terms of the undeformed geometry and other easily observable geometrical parameters. The greatest morphogenetic power is reached with the processive intussusception and chemorheological growth mechanisms that underlie the expansive growth of walled cells. A comparison of these two growth mechanisms suggests a possible way to tackle the complexity behind wall growth.
Journal Article
Strategies for cell shape control in tip-growing cells
• Premise of the study: Despite the large diversity in biological cell morphology, the processes that specify and control cell shape are not yet fully understood. Here we study the shape of tip-growing, walled cells, which have evolved a polar mode of cell morphogenesis leading to characteristic filamentous cell morphologies that extend only apically.• Methods: We identified the relevant parameters for the control of cell shape and derived scaling laws based on mass conservation and force balance that connect these parameters to the resulting geometrical phenotypes. These laws provide quantitative testable relations linking morphological phenotypes to the biophysical processes involved in establishing and modulating cell shape in tip-growing, walled cells.• Key results and conclusions: By comparing our theoretical results to the observed morphological variation within and across species, we found that tip-growing cells from plant and fungal species share a common strategy to shape the cell, whereas oomycete species have evolved a different mechanism.
Journal Article