VARIATION IN ANATOMICAL AND MATERIAL PROPERTIES EXPLAINS DIFFERENCES IN HYDRODYNAMIC PERFORMANCES OF FOLIOSE RED MACROALGAE (RHODOPHYTA)(1)

Over the last two decades, many studies on functional morphology have suggested that material properties of seaweed tissues may influence their fitness. Because hydrodynamic forces are likely the largest source of mortality for seaweeds in high wave energy environments, tissues with material properties that behave favorably in these environments are likely to be selected for. However, it is very difficult to disentangle the effects of materials properties on seaweed performance because size, shape, and habitat also influence mechanical and hydrodynamic performance. In this study, anatomical and material properties of 16 species of foliose red macroalgae were determined, and their effects on hydrodynamic performance were measured in laboratory experiments holding size and shape constant. We determined that increased blade thickness (primarily caused by the addition of medullary tissue) results in higher flexural stiffness (EI), which inhibits the seaweed's ability to reconfigure in flowing water and thereby increases drag. However, this increase is concurrent with an increase in the force required to break tissue, possibly offsetting any risk of failure. Additionally, while increased nonpigmented medullary cells may pose a higher metabolic cost to the seaweed, decreased reconfiguration causes thicker tissues to expose more photosynthetic surface area incident to ambient light in flowing water, potentially ameliorating the metabolic cost of producing these cells. Material properties can result in differential performance of morphologically similar species. Future studies on ecomechanics of seaweeds in wave-swept coastal habitats should consider the interaction of multiple trade-offs.

FLOW-INDUCED MORPHOLOGICAL VARIATIONS AFFECT DIFFUSION BOUNDARY-LAYER THICKNESS OF MACROCYSTIS PYRIFERA (HETEROKONTOPHYTA, LAMINARIALES)(1)

In slow mainstream flows (<4-6 cm · s(-1) ), the transport of dissolved nutrients to seaweed blade surfaces is reduced due to the formation of thicker diffusion boundary layers (DBLs). The blade morphology of Macrocystis pyrifera (L.) C. Agardh varies with the hydrodynamic environment in which it grows; wave-exposed blades are narrow and thick with small surface corrugations (1 mm tall), whereas wave-sheltered blades are wider and thinner with large (2-5 cm) edge undulations. Within the surface corrugations of wave-exposed blades, the DBL thickness, measured using an O2 micro-optode, ranged from 0.67 to 0.80 mm and did not vary with mainstream velocities between 0.8 and 4.5 cm · s(-1) . At the corrugation apex, DBL thickness decreased with increasing seawater velocity, from 0.4 mm at 0.8 cm · s(-1) to being undetectable at 4.5 cm · s(-1) . Results show how the wave-exposed blades trap fluid within the corrugations at their surface. For wave-sheltered blades at 0.8 cm · s(-1) , a DBL thickness of 0.73 ± 0.31 mm within the edge undulation was 10-fold greater than at the undulation apex, while at 2.1 cm · s(-1) , DBL thicknesses were similar at <0.07 mm. Relative turbulence intensity was measured using an acoustic Doppler velocimeter (ADV), and overall, there was little evidence to support our hypothesis that the edge undulations of wave-sheltered blades increased turbulence intensity compared to wave-exposed blades. We discuss the positive and negative effects of thick DBLs at seaweed surfaces.

Hyperbolic non-Euclidean elastic strips and almost minimal surfaces

We study equilibrium configurations of thin and elongated non-Euclidean elastic strips with hyperbolic two-dimensional reference metrics ā which are invariant along the strip. In the vanishing thickness limit energy minima are obtained by minimizing the integral of the mean curvature squared among all isometric embeddings of ā. For narrow strips these minima are very close to minimal surfaces regardless of the specific form of the metric. We study the properties of these "almost minimal" surfaces and find a rich range of three-dimensional stable configurations. We provide some explicit solutions as well as a framework for the incorporation of additional forces and constraints.

Growth, geometry, and mechanics of a blooming lily

Despite the common use of the blooming metaphor, its floral inspiration remains poorly understood. Here we study the physical process of blooming in the asiatic lily Lilium casablanca. Our observations show that the edges of the petals wrinkle as the flower opens, suggesting that differential growth drives the deployment of these laminar shell-like structures. We use a combination of surgical manipulations and quantitative measurements to confirm this hypothesis and provide a simple theory for this change in the shape of a doubly curved thin elastic shell subject to differential growth across its planform. Our experiments and theory overturn previous hypotheses that suggest that blooming is driven by differential growth of the inner layer of the petals and in the midrib by providing a qualitatively different paradigm that highlights the role of edge growth. This functional morphology suggests new biomimetic designs for deployable structures using boundary or edge actuation rather than the usual bulk or surface actuation.

The Föppl-von Kármán equations for plates with incompatible strains

We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses in an elastic plate with incompatible or residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three-dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials with complex non-Euclidean geometries.

Classification and quantification of leaf curvature

Various mutants of Arabidopsis thaliana deficient in polarity, cell division, and auxin response are characterized by certain types of leaf curvature. However, comparison of curvature for clarification of gene function can be difficult without a quantitative measurement of curvature. Here, a novel method for classification and quantification of leaf curvature is reported. Twenty-two mutant alleles from Arabidopsis mutants and transgenic lines deficient in leaf flatness were selected. The mutants were classified according to the direction, axis, position, and extent of leaf curvature. Based on a global measure of whole leaves and a local measure of four regions in the leaves, the curvature index (CI) was proposed to quantify the leaf curvature. The CI values accounted for the direction, axis, position, and extent of leaf curvature in all of the Arabidopsis mutants grown in growth chambers. Comparison of CI values between mutants reveals the spatial and temporal variations of leaf curvature, indicating the strength of the mutant alleles and the activities of the corresponding genes. Using the curvature indices, the extent of curvature in a complicated genetic background becomes quantitative and comparable, thus providing a useful tool for defining the genetic components of leaf development and to breed new varieties with leaf curvature desirable for the efficient capture of sunlight for photosynthesis and high yields.

The shape of a long leaf

Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.

PHENOTYPIC PLASTICITY RECONCILES INCONGRUOUS MOLECULAR AND MORPHOLOGICAL TAXONOMIES: THE GIANT KELP, MACROCYSTIS (LAMINARIALES, PHAEOPHYCEAE), IS A MONOSPECIFIC GENUS(1)

The giant kelp genus Macrocystis C. Agardh (Laminariales, Phaeophyceae) is one of the world's most ecologically and economically important seaweed taxa, yet its taxonomy remains uncertain. Although the genus currently contains four accepted species based on variable holdfast and blade morphology [M. pyrifera (L.) C. Agardh, M. integrifolia Bory, M. angustifolia Bory, and M. laevis C. H. Hay], numerous recent studies on Macrocystis interfertility, genetic relatedness, and morphological plasticity all suggest that the genus is monospecific. We reviewed this evidence and present an explanation for the extreme phenotypic plasticity that results in morphological variability within Macrocystis, driven by the effects of environmental factors on early development of macroscopic sporophytes. We propose that the genus be collapsed back to a single species, with nomenclatural priority given to M. pyrifera.

Environmental effects on spatial and temporal patterns of leaf and root growth

Leaves and roots live in dramatically different habitats, but are parts of the same organism. Automated image processing of time-lapse records of these organs has led to understanding of spatial and temporal patterns of growth on time scales from minutes to weeks. Growth zones in roots and leaves show distinct patterns during a diel cycle (24 h period). In dicot leaves under nonstressful conditions these patterns are characterized by endogenous rhythms, sometimes superimposed upon morphogenesis driven by environmental variation. In roots and monocot leaves the growth patterns depend more strongly on environmental fluctuations. Because the impact of spatial variations and temporal fluctuations of above- and belowground environmental parameters must be processed by the plant body as an entire system whose individual modules interact on different levels, growth reactions of individual modules are often highly nonlinear. A mechanistic understanding of plant resource use efficiency and performance in a dynamically fluctuating environment therefore requires an accurate analysis of leaf and root growth patterns in conjunction with knowledge of major intraplant communication systems and metabolic pathways.