Hierarchical helical order in the twisted growth of plant organs

Study on the Mechanism of Elastic Instability Caused by Natural Growth in Orthotropic Material

Compared to synthetic materials, naturally grown biological materials have more specific behavioral patterns and life connotations in their morphological evolution over millions of years of environmental evolution on Earth. In this paper, we investigate the physical mechanisms and manifestations of out-of-plane deformation instability. Firstly, the origin of the instability phenomenon caused by the growth of the leaf is introduced. Leaf instability problems are modeled using rectangular thin plates. Secondly, the variation in the critical intrinsic strain with the principal shear modulus is obtained by numerical solution. The post-buckling behavior of the growth instability is further analyzed by general static analysis, and we obtain the phase diagram of morphogenesis of thin plant organs as functions of the principal shear modulus and off-axis angle. The research results enhance the understanding of the mechanism of elastic instability caused by natural growth in orthotropic materials.

Formation of chiral morphologies of biological materials induced by chirality

Chiral growth exists prevalently in natural materials. The mechanism underlying the formation of chiral morphologies in biological and man-made materials has been an important issue of both theoretical and technological interest. In this paper, an elastic rod model taking into account chiral microstructures is developed to investigate the formation of chiral morphologies of biological materials. The curvature and twist of chiral shapes are investigated with this model using the variational method of energy. The result shows the misfit of chirality of two-layer structured biological materials may induce various chiral morphologies, such as helices and twisting belts. Furthermore, it was found that cooperative or competitive interactions between anisotropic elasticity and chirality can also lead to the formation of chiral morphologies, and the fibre orientation angles and chiral parameters are the determining factors to the shape, size and handedness of chiral morphologies. This work is expected to shed new light on the physical mechanisms of the formation of various chiral morphologies in the biological world and provide useful guidance for the design of deformation driving and shape control of soft robots and machines.

Handedness in plant cell expansion: a mutant perspective on helical growth

Many plant mutants are known that exhibit some degree of helical growth. This 'twisted' phenotype has arisen frequently in mutant screens of model organisms, but it is also found in cultivars of ornamental plants, including trees. The phenomenon, in many cases, is based on defects in cell expansion symmetry. Any complete model which explains the anisotropy of plant cell growth must ultimately explain how helical cell expansion comes into existence - and how it is normally avoided. While the mutations observed in model plants mainly point to the microtubule system, additional affected components involve cell wall functions, auxin transport and more. Evaluation of published data suggests a two-way mechanism underlying the helical growth phenomenon: there is, apparently, a microtubular component that determines handedness, but there is also an influence arising in the cell wall that feeds back into the cytoplasm and affects cellular handedness. This idea is supported by recent reports demonstrating the involvement of the cell wall integrity pathway. In addition, there is mounting evidence that calcium is an important relayer of signals relating to the symmetry of cell expansion. These concepts suggest experimental approaches to untangle the phenomenon of helical cell expansion in plant mutants.

Morphological analysis of chiral rod clusters from a coarse-grained single-site chiral potential

We present a coarse-grained single-site potential for simulating chiral interactions, with adjustable strength, handedness, and preferred twist angle. As an application, we perform basin-hopping global optimisation to predict the favoured geometries for clusters of chiral rods. The morphology phase diagram based upon these predictions has four distinct families, including previously reported structures for potentials that introduce chirality based on shape, such as membranes and helices. The transition between these two configurations reproduces some key features of experimental results for fd bacteriophage. The potential is computationally inexpensive, intuitive, and versatile; we expect it will be useful for large scale simulations of chiral molecules. For chiral particles confined in a cylindrical container we reproduce the behaviour observed for fusilli pasta in a jar. Hence this chiropole potential has the capability to provide insight into structures on both macroscopic and molecular length scales.

Differential growth and shape formation in plant organs

Morphogenesis is a phenomenon by which a wide variety of functional organs are formed in biological systems. In plants, morphogenesis is primarily driven by differential growth of tissues. Much effort has been devoted to identifying the role of genetic and biomolecular pathways in regulating cell division and cell expansion and in influencing shape formation in plant organs. However, general principles dictating how differential growth controls the formation of complex 3D shapes in plant leaves and flower petals remain largely unknown. Through quantitative measurements on live plant organs and detailed finite-element simulations, we show how the morphology of a growing leaf is determined by both the maximum value and the spatial distribution of growth strain. With this understanding, we develop a broad scientific framework for a morphological phase diagram that is capable of rationalizing four configurations commonly found in plant organs: twisting, helical twisting, saddle bending, and edge waving. We demonstrate the robustness of these findings and analyses by recourse to synthetic reproduction of all four configurations using controlled polymerization of a hydrogel. Our study points to potential approaches to innovative geometrical design and actuation in such applications as building architecture, soft robotics and flexible electronics.

Convergent Evolution and the Diverse Ontogenetic Origins of Tendrils in Angiosperms

Climbers are abundant in tropical forests, where they constitute a major functional plant type. The acquisition of the climbing habit in angiosperms constitutes a key innovation. Successful speciation in climbers is correlated with the development of specialized climbing strategies such as tendrils, i.e., filiform organs with the ability to twine around other structures through helical growth. Tendrils are derived from a variety of morphological structures, e.g., stems, leaves, and inflorescences, and are found in various plant families. In fact, tendrils are distributed throughout the angiosperm phylogeny, from magnoliids to asterids II, making these structures a great model to study convergent evolution. In this study, we performed a thorough survey of tendrils within angiosperms, focusing on their origin and development. We identified 17 tendril types and analyzed their distribution through the angiosperm phylogeny. Some interesting patterns emerged. For instance, tendrils derived from reproductive structures are exclusively found in the Core Eudicots, except from one monocot species. Fabales and Asterales are the orders with the highest numbers of tendrilling strategies. Tendrils derived from modified leaflets are particularly common among asterids, occurring in Polemoniaceae, Bignoniaceae, and Asteraceae. Although angiosperms have a large number of tendrilled representatives, little is known about their origin and development. This work points out research gaps that should help guide future research on the biology of tendrilled species. Additional research on climbers is particularly important given their increasing abundance resulting from environmental disturbance in the tropics.

Structural mechanics and helical geometry of thin elastic composites

Helices are ubiquitous in nature, and helical shape transition is often observed in residually stressed bodies, such as composites, wherein materials with different mechanical properties are glued firmly together to form a whole body. Inspired by a variety of biological examples, the basic physical mechanism responsible for the emergence of twisting and bending in such thin composite structures has been extensively studied. Here, we propose a simplified analytical model wherein a slender membrane tube undergoes a helical transition driven by the contraction of an elastic ribbon bound to the membrane surface. We analytically predict the curvature and twist of an emergent helix as functions of differential strains and elastic moduli, which are confirmed by our numerical simulations. Our results may help understand shapes observed in different biological systems, such as spiral bacteria, and could be applied to novel designs of soft machines and robots.

Actin-Dependent and -Independent Functions of Cortical Microtubules in the Differentiation of Arabidopsis Leaf Trichomes

Arabidopsis thaliana tortifolía2 carries a point mutation in α-tubulin 4 and shows aberrant cortical microtubule dynamics. The microtubule defect of tortifolia2 leads to overbranching and right-handed helical growth in the single-celled leaf trichomes. Here, we use tortifolia2 to further our understanding of microtubules in plant cell differentiation. Trichomes at the branching stage show an apical ring of cortical microtubules, and our analyses support that this ring is involved in marking the prospective branch site. tortifolia2 showed ectopic microtubule bundles at this stage, consistent with a function for microtubules in selecting new branch sites. Overbranching of tortifolia2 required the C-terminal binding protein/brefeldin A-ADP ribosylated substrate protein ANGUSTIFOLIA1, and our results indicate that the angustifolia1 mutant is hypersensitive to alterations in microtubule dynamics. To analyze whether actin and microtubules cooperate in the trichome cell expansion process, we generated double mutants of tortifolia2 with distorted1, a mutant that is defective in the actin-related ARP2/3 complex. The double mutant trichomes showed a complete loss of growth anisotropy, suggesting a genetic interaction of actin and microtubules. Green fluorescent protein labeling of F-actin or microtubules in tortifolia2 distorted1 double mutants indicated that F-actin enhances microtubule dynamics and enables reorientation. Together, our results suggest actin-dependent and -independent functions of cortical microtubules in trichome differentiation.

Plant cell shape: modulators and measurements

Plant cell shape, seen as an integrative output, is of considerable interest in various fields, such as cell wall research, cytoskeleton dynamics and biomechanics. In this review we summarize the current state of knowledge on cell shape formation in plants focusing on shape of simple cylindrical cells, as well as in complex multipolar cells such as leaf pavement cells and trichomes. We summarize established concepts as well as recent additions to the understanding of how cells construct cell walls of a given shape and the underlying processes. These processes include cell wall synthesis, activity of the actin and microtubule cytoskeletons, in particular their regulation by microtubule associated proteins, actin-related proteins, GTP'ases and their effectors, as well as the recently-elucidated roles of plant hormone signaling and vesicular membrane trafficking. We discuss some of the challenges in cell shape research with a particular emphasis on quantitative imaging and statistical analysis of shape in 2D and 3D, as well as novel developments in this area. Finally, we review recent examples of the use of novel imaging techniques and how they have contributed to our understanding of cell shape formation.