Geometric reconstruction of biological orthogonal plywoods

Band structure of a rotating helical phononic crystal

We consider an elastic helical medium whose tensor stiffness twirls uniformly along the helix axis. We are interested in analyzing the band structure when the whole material is externally forced to rotate around the helix axis to a fixed constant frequency. Departing from a general dynamic description of the elastic phenomena, we establish a set of equations for the displacement vector and the stress tensor. These equations allow us to calculate the band structure parametrized by the externally imposed rotating frequency. We find that the band structure strongly depends on the rotation frequency, and we show that backward and forward modes propagate differently, particularly for the longitudinal and right-polarized modes.

Dependence of the elastic band structure of a helical medium on thermal dilatation

We consider an elastic helical medium formed by uniformly rotating a triclinic crystal around a given axis to constitute a helical medium giving rise to a material whose tensor stiffness rotates uniformly and varies along the helix axis. A detailed analysis of its elastic properties has been done previously. Here, we are concerned in analyzing the role of thermal coupling with heat flow through the dilatation tensor. Starting from a general dynamic description of the thermoelastic phenomena which takes into account the finite speed of propagation of thermal waves, we establish a set of equations for the strains, stresses, temperature and heat flow. These equations allow to calculate the band structure and the logarithmic ratio between longitudinal and transverse strains. We express our results for different values of the thermoelastic coupling and period of the helix which show remarkable modifications when compared with the case in which no thermoelastic coupling is present.

Changes in the orientations of cellulose microfibrils during the development of collenchyma cell walls of celery (Apium graveolens L.)

During development, cellulose microfibrils in collenchyma walls become increasingly longitudinal, as determined by small-angle X-ray scattering, despite the walls maintaining a fine structure indicative of a crossed-polylamellate structure. Collenchyma cells have thickened primary cell walls and provide mechanical support during plant growth. During their development, these cells elongate and their walls thicken considerably. We used microscopy and synchrotron small-angle X-ray scattering to study changes in the orientations of cellulose microfibrils that occur during development in the walls of collenchyma cells present in peripheral strands in celery (Apium graveolens) petioles. Transmission electron microscopy showed that the walls consisted of many lamellae (polylamellate), with lamellae containing longitudinally oriented cellulose microfibrils alternating with microfibrils oriented at higher angles. The lamellae containing longitudinally oriented microfibrils predominated at later stages of development. Nevertheless, transmission electron microscopy of specially stained, oblique sections provided evidence that the cellulose microfibrils were ordered throughout development as crossed-polylamellate structures. These results are consistent with our synchrotron small-angle X-ray scattering results that showed the cellulose microfibrils become oriented increasingly longitudinally during development. Some passive reorientation of cellulose microfibrils may occur during development, but extensive reorientation throughout the wall would destroy ordered structures. Atomic force microscopy and field emission scanning electron microscopy were used to determine the orientations of newly deposited cellulose microfibrils. These were found to vary widely among different cells, which could be consistent with the formation of crossed-polylamellate structures. These newly deposited cellulose microfibrils are deposited in a layer of pectic polysaccharides that lies immediately outside the plasma membrane. Overall, our results show that during development of collenchyma walls, the cellulose microfibrils become increasingly longitudinal in orientation, yet organized, crossed-polylamellate structures are maintained.

Thermodynamic modelling of acidic collagenous solutions: from free energy contributions to phase diagrams

Tropocollagen is considered one of the main precursors in the fabrication of collagen-based biomaterials. Triple helix acidic solutions of collagen I have been shown experimentally to lead to chiral plywood architectures found in bone and "cornea" like tissues. As these plywoods are solid analogues of liquid crystal architectures, bio-inspired processing and fabrication platforms based on liquid crystal physics and thermodynamics will continue to play an essential role. For tissue engineering applications, it has been shown that dilute isotropic collagen solutions need to be flow processed first and then dehydrated. Thus, a complete fundamental understanding of the thermodynamics and free energy contributions in acidic collagen aqueous solutions is necessary to avoid expensive trial-and-error fabrication. To achieve this goal, we analyze the microscopic mechanisms of ordering and interactions in solutions of triple helix collagen, namely mixing, attraction, excluded-volume and chirality. To capture the mentioned physics, we then incorporate and integrate the Flory-Huggins, Maier-Saupe, Onsager and Frank theories. Nonetheless, they together are incapable of providing an acceptable mesophasic description in acidic collagenous solutions because tropocollagen biomacromolecules are positively charged. We then explore a simple and accurate electrostatic mean-field potential. Our results on collagen are in good agreement with experiments and include phase diagrams, phase transition thresholds, and critical isotropic/cholesteric order parameters. The present extended theory is shown to properly converge to classical liquid crystal models and is used to express the phenomenological Landau-de Gennes parameters with more fundamental quantities. This study provides a platform to derive accurate process models for the fabrication of collagen-based materials, considering and benefitting from the full range of underlying interactions.

Two-wavelength wrinkling patterns in helicoidal plywood surfaces: imprinting energy landscapes onto geometric landscapes

We present a model to investigate the formation of two-length scale surface patterns in biological and synthetic anisotropic soft matter materials through the high order interaction of anisotropic interfacial tension and capillarity at their free surfaces. The unique pattern-formation mechanism emerging from the presented model is based on the interaction between lower and higher order anchoring modes. Analytical and numerical solutions are used to shed light on why and how simple anisotropic anchoring generates two-lengthscale wrinkles whose amplitudes are given in terms of anchoring coefficients. The novel finding is that the surface energy landscape with its maxima and minima can be imprinted onto the surface geometric landscape. Symmetry relations and scaling laws are used to provide the explicit relations between the anchoring constants and surface profile of the two length scale wrinkles. These new findings establish a new paradigm for characterizing surface wrinkling in biological liquid crystals, and inspire the design of novel functional surface structures.

Cholesteric liquid crystals in living matter

Liquid crystals play an important role in biology because the combination of order and mobility is a basic requirement for self-organisation and structure formation in living systems. Cholesteric liquid crystals are omnipresent in living matter under both in vivo and in vitro conditions and address the major types of molecules essential to life. In the animal and plant kingdoms, the cholesteric structure is a recurring design, suggesting a convergent evolution to an optimised left-handed helix. Herein, we review the recent advances in the cholesteric organisation of DNA, chromatin, chitin, cellulose, collagen, viruses, silk and cholesterol ester deposition in atherosclerosis. Cholesteric structures can be found in bacteriophages, archaea, eukaryotes, bacterial nucleoids, chromosomes of unicellular algae, sperm nuclei of many vertebrates, cuticles of crustaceans and insects, bone, tendon, cornea, fish scales and scutes, cuttlebone and squid pens, plant cell walls, virus suspensions, silk produced by spiders and silkworms, and arterial wall lesions. This article specifically aims at describing the consequences of the cholesteric geometry in living matter, which are far from being fully defined and understood, and discusses various perspectives. The roles and functions of biological cholesteric liquid crystals include maximisation of packing efficiency, morphogenesis, mechanical stability, optical information, radiation protection and evolution pressure.