Eleni Katifori

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.

Damage and fluctuations induce loops in optimal transport networks.

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e., loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.

Quantifying loopy network architectures.

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

Elastic building blocks for confined sheets

We study the behavior of thin elastic sheets that are bent and strained under a weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains. A focused-stress patch is subject to a geometric, piecewise-inextensibility constraint, whereas a diffuse-stress region is characterized by a mechanical constraint-the dominance of a single component of the stress tensor. We discuss the implications of our findings for the analysis of elastic sheets under various types of forcing.

Behavioral diversity in microbes and low-dimensional phenotypic spaces.

Systematic studies of phenotypic diversity—required for understanding evolution—lag behind investigations of genetic diversity. Here we develop a quantitative approach to studying behavioral diversity, which we apply to swimming of the ciliate Tetrahymena. We measure the full-lifetime behavior of hundreds of individual organisms at high temporal resolution, over several generations and in diverse nutrient conditions. To characterize population diversity and temporal variability we introduce a unique statistical framework grounded in the notion of a phenotypic space of behaviors. We show that this space is effectively low dimensional with dimensions that correlate with a two-state “roaming and dwelling” model of swimming behavior. Temporal variability over the lifetime of an individual is correlated with the fraction of time spent roaming whereas diversity between individuals is correlated with the speed of roaming. Quantifying the dynamics of behavioral variation shows that behavior over the lifetime of an individual is strongly nonstationary. Analysis of behavioral dynamics between generations reveals complex patterns of behavioral heritability that point to the importance of considering correlations beyond mothers and daughters. Our description of a low-dimensional behavioral space should enable the systematic study of the evolutionary and ecological bases of phenotypic constraints. Future experimental and theoretical studies of behavioral diversity will have to account for the possibility of nonstationary and environmentally dependent behavioral dynamics that we observe.

Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks.

Highly optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is nonconvex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that such an optimal state is slowly achieved through natural selection. However, general coarse grained models for flow networks with local positive feedback rules for the vessel conductivity typically get trapped in low efficiency, local minima. In this work we show how the growth of the underlying tissue, coupled to the dynamical equations for network development, can drive the system to a dramatically improved optimal state. This general model provides a surprisingly simple explanation for the appearance of highly optimized transport networks in biology such as leaf and animal vasculature.

Scaling of phloem structure and optimality of photoassimilate transport in conifer needles

The phloem vascular system facilitates transport of energy-rich sugar and signalling molecules in plants, thus permitting long-range communication within the organism and growth of non-photosynthesizing organs such as roots and fruits. The flow is driven by osmotic pressure, generated by differences in sugar concentration between distal parts of the plant. The phloem is an intricate distribution system, and many questions about its regulation and structural diversity remain unanswered. Here, we investigate the phloem structure in the simplest possible geometry: a linear leaf, found, for example, in the needles of conifer trees. We measure the phloem structure in four tree species representing a diverse set of habitats and needle sizes, from 1 (Picea omorika) to 35 cm (Pinus palustris). We show that the phloem shares common traits across these four species and find that the size of its conductive elements obeys a power law. We present a minimal model that accounts for these common traits and takes into account the transport strategy and natural constraints. This minimal model predicts a power law phloem distribution consistent with transport energy minimization, suggesting that energetics are more important than translocation speed at the leaf level.

Topological Phenotypes Constitute a New Dimension in the Phenotypic Space of Leaf Venation Networks.

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus constitutes a new dimension in the leaf venation phenotypic space. We apply our metric to a database of 186 leaves and leaflets representing 137 species, predominantly from the Burseraceae family, revealing diverse topological network traits even within this single family. We show that topological information significantly improves identification of leaves from fragments by calculating a “leaf venation fingerprint” from topology and geometry. Further, we present a phenomenological model suggesting that the topological traits can be explained by noise effects unique to specimen during development of each leaf which leave their imprint on the final network. This work opens the path to new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and is directly applicable to other planar or sub-planar networks such as blood vessels in the brain.

Thermal evolution of the non-supersymmetric metastable vacua in N = 2 SU(2) SYM softly broken to N = 1

A bstractIt has been shown that four dimensional

Collapse and folding of pressurized rings in two dimensions

\mathcal{N}=2