Session V52: Focus Session: Extreme Mechanics - Biological Systems and Structures

Plant tendrils: Nature's hygroscopic springs

Plant tendrils are specialized climbing organs that have fascinated biologists and physicists alike for centuries. Initially straight tendrils attach at the tip to an elevated rigid support and then winch the plant upward by coiling into a helical morphology characterized by two helices of opposite handedness connected by a helical perversion. In his renowned treatise on twining and tendril-bearing plants, Charles Darwin surmised that coiled tendrils serve as soft, springy attachments for the climbing plant. Yet, the true effect of the perverted helical shape of a coiled plant tendril has not been fully revealed. Using a combination of experiments on Cucurbitaceae tendrils, physical models constructed from strained rubber sheets, and numerical models of helical perversions, we have uncovered that tendril coiling occurs via anisotropic shrinkage of a strip of specialized cells in the interior of the tendril. Furthermore, variations in the mechanical behavior of tendrils as they become drier and ``woodier'' adds a new twist to the story of tendril coiling.   

Radial force development during root growth measured by photoelasticity

The mechanical and topological properties of a soil like the global porosity and the distribution of void sizes greatly affect the development of a plant root, which in turn affects the shoot development. In particular, plant roots growing in heterogeneous medium like sandy soils or cracked substrates have to adapt their morphology and exert radial forces depending on the pore size in which they penetrate. We propose a model experiment in which a pivot root (chick-pea seeds) of millimetric diameter has to grow in a size-controlled gap $\delta $ ($\delta $ ranging 0.5-2.3 mm) between two photoelastic grains. By time-lapse imaging, we continuously monitored the root growth and the development of optical fringes in the photoelastic neighbouring grains when the root enters the gap. Thus we measured simultaneously and in situ the root morphological changes (length and diameter growth rates, circumnutation) as well as the radial forces the root exerts. Radial forces were increasing in relation with gap constriction and experiment duration but a levelling of the force was not observed, even after 5 days and for narrow gaps. The inferred mechanical stress was consistent with the turgor pressure of compressed cells. Therefore our set-up could be a basis for testing mechanical models of cellular growth.   

Digging Like Plants: Flexible Intruders in Granular Materials

Inspired by plant root growth in granular media, we report on the effects of flexibility on the mechanical work required to dig through granular systems. In the case where the digger is significantly thinner than the grain diameter, increased flexibility in one-dimension leads to savings of nearly 50\%. A simple numerical model based solely on the variability of forces in the granular substrate and the flexibility of the digger gives similar results to those observed in experiments.   

Helical Buckling of Plant Roots: Mechanics and Morphology

How do plant roots respond to heterogeneities in their environment as they grow? Using a simple model system consisting of a layered hydrogel, we present a controlled mechanical barrier to the roots allowing us to perturb their growth. Interestingly, we find a localized helical root morphology which forms prior to the root passing through the gel layer interface. We interpret this geometry as a combination of a purely mechanical buckling caused by continued root elongation modified by the growth medium and a simultaneous twisting near the root tip. We study the morphology of the helical deformation as the modulus of the gel is varied using 3D time-lapse imaging and demonstrate that its shape scales with gel stiffness as expected by a simple model based on the theory of buckled rods. Our results demonstrate that mechanics is sufficient to account for the shape and its variations. In addition, we hypothesize that the twisted growth near the root tip arises from a touch-activated growth response that we call thigmotorsion.   

Dislocations and Grain Boundaries in Optimally-Packed, Twisted Filament Bundles

From the collagen fiber to the parallel-actin bundle, twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross-section and out-of-plane interfilament twist in bundles based on the non-linear continuum elasticity theory of columnar materials. We find that interfilament twist generates in-plane stresses that couple favorably to the presence of topological defects, edge dislocations, in the cross-sectional packing, thereby restructuring the ground state filament packing of twisted bundles. The stability of dislocations increases with increases in both the degree of twist and lateral bundle size. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist. Remarkably, the ``polycrystalline'' texture of these optimal packings of twisted bundles show a striking similarity to models of the ``almost crystalline'' cross-section of collagen fibers.   

Mechanical Behavior of Bio-inspired Model Suture Joints

Suture joints of varying degrees of geometric complexity are prevalent throughout nature as a means of joining structural elements while providing locally tailored mechanical performance. Here, micromechanical models of general trapezoidal waveforms of varying hierarchy are formulated to reveal the role of geometric complexity in governing stiffness, strength, toughness and corresponding deformation and failure mechanisms. Physical constructs of model composite suture systems are fabricated via multi-material 3D printing (Object Connex500). Tensile tests are conducted on samples covering a range in geometry, thus providing quantitative measures of stiffness, strength, and failure. The experiments include direct visualization of the deformation and failure mechanisms and their progression, as well as their dependence on suture geometry, showing the interplay between shear and tension/compression of the interfacial layers and tension of the skeletal teeth and the transition in failure modes with geometry. The results provide quantitative guidelines for the design and tailoring of suture geometry to achieve the desired mechanical properties and also facilitate understanding of suture growth and fusion, and evolutionary phenotype.   

Morphogenesis of protrusions from confined lipid bilayers mediated by mechanics

Biological membranes adopt a wide range of shapes that structure and give functionality to cells, compartmentalizing the cytosol, forming organelles, or regulating their area. The formation, stabilization, and remodeling of these structures is generally attributed to localized forces or to biochemical processes (insertion of proteins, active compositional regulation). Noting that in the crowded intra and extra-cellular environments membranes are highly constrained, we explore to what extent can mechanics explain the shape of protrusions out of confined membranes. For this purpose, we developed an in-vitro system coupling a lipid bilayer to the strain-controlled deformation of an elastic sheet (Staykova et al, PNAS 108, 2011). We show that upon contracting the elastic support, tubular or spherical protrusions grow out of the adhered membrane, which can be reversibly controlled with strain and osmolarity without resorting to localized forces or chemical alterations of the bilayer. The morphologies produced by our minimal system are ubiquitous in cells, suggesting mechanics may be a simple and generic organizing principle. We can understand most of our observations in terms of a phase diagram accounting for elasticity, adhesion, and the limited amount of area and volume available.   

Thin-shell model for faceting of multicomponent elastic vesicles

We use a discretized version of a thin elastic shell model to show that a two-component elastic vesicle can lower its energy by faceting into a wide variety of polyhedral shapes. The elastic shell model allows us to completely remove effects of the topological defects necessarily present in spherical topology. Therefore, we show that the faceting mechanism of multicomponent elastic vesicles is fundamentally different than the familiar defect-driven buckling into icosahedra. We present a detailed gallery of faceted shapes and discuss how the interplay between bending and stretching energies leads to faceting. Present work extends our recent study of the faceting of a two-component shell in the presence of topological defects [1]. [1] G. Vernizzi, R. Sknepnek, M. Olvera de la Cruz, Proc. Natl. Acad. Sci. USA 108, 4292 (2011).   

Charge Effects on Mechanical Properties of Elastomeric Proteins

Several biological molecules of nanoscale dimensions, such as elastin and resilin, are capable of performing diverse tasks with minimal energy loss. These molecules are efficient in that the ratio of energy output to energy consumed is very close to unity. This is in stark contrast to some of the best synthetic materials that have been created. For example, it is known that resilin found in dragonflies has a hysteresis loss of only 0.8{\%} of the energy input while the best synthetic rubber made to date, polybutadiene, has a loss of roughly 20{\%}.We simulate tensile tests of naturally occurring motifs found in resilin (a highly hydrophilic protein), as well as similar simulations found in reduced-polarity counterparts (i.e. the same motif with the charge on each individual atom set to half the natural value, the same motif with the charge on each individual atom set to zero, and a motif in which all the polar amino acids have been replaced with nonpolar amino acids). The results show a strong correlation between charge and extensibility. In order to further understand the effect of properties such as charge on the system, we will run simulations of elastomeric proteins such as resilin in different solvents.   

Denaturation of Circular DNA: Supercoils, overtwist and condensation

The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of the unconstrained DNA. Past work suggests that the nature of this constrained melting transition is sensitive to the mechanism that relaxes the torsional stress induced on the bound portions by the loops. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed in expense of 1) overtwist, 2) supercoils. Recent work has shown that the supercoiling mechanism results in a BEC-like picture where a macroscopic loop appears at $T_c$ and grows steadily with temperature while no such phenomenon has been reported for the overtwisting case. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above $T_c$, with a cusp at the critical point.   

Mechanics of short rod-like molecules in tension

Rod like macromolecules such as actin, DNA etc., are most commonly stretched using optical tweezers or fluid flow. In this presentation we will describe the mechanics of short rod like molecules in tension. The mechanics is dominated by the competition between tensile forces (exerted by fluid flow, or by a device, such as, optical tweezers) and the thermal fluctuations of the molecule. For molecules whose contour length is comparable to the persistence length we show that the boundary conditions play major role in determining the mechanical behavior. We use the equipartition theorem of statistical mechanics to obtain expressions for the amplitude of the transverse fluctuations of the molecule and its force-extension relation for various boundary conditions. We then apply our theory to an experiment on short fluctuating actin filaments trapped by various means. We estimate the tension in these filaments by fitting our theory to the measured values of transverse fluctuations as a function of the position along the filament.   

Turning by buckling: a cheap evolutionary strategy for turning among marine bacteria

Marine bacteria have long been known to swim forward and backward (`run and reverse') by controlling the rotational direction of a 20 nm helical flagellum. Recent detailed observations have shown that these bacteria can also make sharp, $\sim90^{\circ}$ turns, an astounding feature for a micron-scale organism with just one degree of freedom under its control. We demonstrate that a buckling instability originating from the flexible linkage (`hook') between the body and the flagellum is responsible for the reorientation. Using high-magnification (40$\sim$100X) observations based on high-speed video microscopy (420$\sim$1000 fps), we captured the extreme deformation of the flagellum and the hook involved in this process. The mechanical properties of the hook are finely tuned to the hydrodynamic loads experienced by the cell: the hook becomes unstable only when the compressive load during the onset of forward swimming exceeds the threshold for Euler buckling. Combining the data with a model of buckling of thin structures, we show that bacteria take advantage of the flexibility of the flagellum and the hook to generate a turn, which may represent the evolutionarily cheapest bacterial strategy to actively change direction.