Traveling Perversion as Constant Torque Actuator.

Mechanical stress and conformation of helical elastic rods clamped at both ends were studied upon unwinding. By axial rotation of one end, the winding number was progressively changed from the natural one (n=n_{0}) to complete chirality inversion (n=-n_{0}) while keeping the total elongation fixed and monitoring the applied torque M and tension T. Along the unwinding process, the system crosses three distinct states: natural helix (+), mixed state (+/-), and inverted helix (-). The mixed state involves two helices with opposite chiralities spatially connected by a perversion (helicity inversion). Upon unwinding, the perversion is "injected" (nucleated) from one side and travels toward the opposite side where it is eventually "absorbed" (annihilated), leaving the system in the (-) state. In the mixed state, the profile of M(n) is almost flat: the system behaves as a constant torque actuator. The three states are quantitatively well described in the framework of a biphasic model which neglects the perversion energy and finite size effects. The latter are taken into account in a numerical simulation based on the Kirchhoff theory of elastic rods. The traveling perversion in helical elastic rods and related topological phenomena are universal, with applications from condensed matter to biological and bioinspired systems, including in particular mechanical engineering and soft robotics.

Emergence of tip singularities in dissolution patterns.

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

Streamwise Dissolution Patterns Created by a Flowing Water Film.

The dissolution of rocks by rainfall commonly generates streamwise parallel channels, yet the occurrence of these natural patterns remains to be understood. Here, we report the emergence in the laboratory of a streamwise dissolution pattern at the surface of an initially flat soluble material, inclined and subjected to a thin runoff water flow. Nearly parallel grooves about 1 mm wide and directed along the main slope spontaneously form. Their width and depth increase continuously with time until their crests emerge and channelize the flow. Our observations may constitute the early stage of the patterns observed in the field.

The hook shape of growing leaves results from an active regulatory process.

The rachis of most growing compound leaves observed in nature exhibits a stereotypical hook shape. In this study, we focus on the canonical case of Averrhoa carambola. Combining kinematics and mechanical investigation, we characterize this hook shape and shed light on its establishment and maintenance. We show quantitatively that the hook shape is a conserved bent zone propagating at constant velocity and constant distance from the apex throughout development. A simple mechanical test reveals non-zero intrinsic curvature profiles for the rachis during its growth, indicating that the hook shape is actively regulated. We show a robust spatial organization of growth, curvature, rigidity, and lignification, and their interplay. Regulatory processes appear to be specifically localized: in particular, differential growth occurs where the elongation rate drops. Finally, impairing the graviception of the leaf on a clinostat led to reduced hook curvature but not to its loss. Altogether, our results suggest a role for proprioception in the regulation of the leaf hook shape, likely mediated via mechanical strain.

Emergence of ribozyme and tRNA-like structures from mineral-rich muddy pools on prebiotic earth.

The RNA world hypothesis, although a viable one regarding the origin of life on earth, has so far failed to provide a compelling explanation for the synthesis of RNA enzymes from free nucleotides via abiotic processes. To tackle this long-standing problem, we develop a realistic model for the onset of the RNA world, using experimentally determined rates for polymerization reactions. We start with minimal assumptions about the initial state that only requires the presence of short oligomers or just free nucleotides and consider the effects of environmental cycling by dividing a day into a dry, semi-wet and wet phases that are distinguished by the nature of reactions they support. Long polymers, with maximum lengths sometimes exceeding 100 nucleotides, spontaneously emerge due to a combination of non-enzymatic, non-templated polymer extension and template-directed primer extension processes. The former helps in increasing the lengths of RNA strands, whereas the later helps in producing complementary copies of the strands. Strands also undergo hydrolysis in a structure-dependent manner that favour breaking of bonds connecting unpaired nucleotides. We identify the most favourable conditions needed for the emergence of ribozyme and tRNA-like structures and double stranded RNA molecules, classify all RNA strands on the basis of their secondary structures and determine their abundance in the population. Our results indicate that under suitable environmental conditions, non-enzymatic processes would have been sufficient to lead to the emergence of a variety of ribozyme-like molecules with complex secondary structures and potential catalytic functions.

Three-dimensional structural evolution of the cuttlefish Sepia officinalis shell from embryo to adult stages.

The cuttlefish shell is an internal structure with a composition and general organization unique among molluscs. Its formation and the structure-function relation are explored during Sepia officinalis development, using computerized axial tomography scanning (CAT-scan) three-dimensional analyses coupled to physical measurements and modelling. In addition to the evolution of the overall form, modifications of the internal structure were identified from the last third embryonic stages to adult. Most of these changes can be correlated to life cycle stages and environmental constraints. Protected by the capsule during embryonic life, the first internal chambers are sustained by isolated pillars formed from the dorsal to the ventral septum. After hatching, the formation of pillars appears to be a progressive process from isolated points to interconnected pillars forming a wall-delineated labyrinthine structure. We analysed the interpillar space, the connectivity and the tortuosity of the labyrinth. The labyrinthine pillar network is complete just prior to the wintering migration, probably to sustain the need to adapt to high pressure and to allow buoyancy regulation. At that time, the connectivity in the pillar network is compensated by an increase in tortuosity, most probably to reduce liquid diffusion in the shell. Altogether these results suggest adjustment of internal calcified structure development to both external forces and physiological needs.

Fluttering of growing leaves as a way to reach flatness: experimental evidence on Persea americana.

Simple leaves show unexpected growth motions: the midrib of the leaves swings periodically in association with buckling events of the leaf blade, giving the impression that the leaves are fluttering. The quantitative kinematic analysis of this motion provides information about the respective growth between the main vein and the lamina. Our three-dimensional reconstruction of an avocado tree leaf shows that the conductor of the motion is the midrib, presenting continuous oscillations and inducing buckling events on the blade. The variations in the folding angle of the leaf show that the lamina is not passive: it responds to the deformation induced by the connection to the midrib to reach a globally flat state. We model this movement as an asymmetric growth of the midrib, which directs an inhomogeneous growth of the lamina, and we suggest how the transition from the folded state to the flat state is mechanically organized.

Motions of leaves and stems, from growth to potential use.

The study on aerial plant organs (leaves and stems) motions is reviewed. The history of observations and studies is put in the perspective of the ideas surrounding them, leading to a presentation of the current classification of these motions. After showing the shortcomings of such a classification, we present, following an idea of Darwin's, the various movements in a renewed and observation-based perspective of the plant development. With this perspective, the different movements fit together logically, and in particular we point out that the mature reversible movements, such as the sensitive or circadian movements, are just partial regressions of the developmental ones.

Quantifying hydrostatic pressure in plant cells by using indentation with an atomic force microscope.

Plant cell growth depends on a delicate balance between an inner drive-the hydrostatic pressure known as turgor-and an outer restraint-the polymeric wall that surrounds a cell. The classical technique to measure turgor in a single cell, the pressure probe, is intrusive and cannot be applied to small cells. In order to overcome these limitations, we developed a method that combines quantification of topography, nanoindentation force measurements, and an interpretation using a published mechanical model for the pointlike loading of thin elastic shells. We used atomic force microscopy to estimate the elastic properties of the cell wall and turgor pressure from a single force-depth curve. We applied this method to onion epidermal peels and quantified the response to changes in osmolality of the bathing solution. Overall our approach is accessible and enables a straightforward estimation of the hydrostatic pressure inside a walled cell.

Multiparametric analyses reveal the pH-dependence of silicon biomineralization in diatoms.

Diatoms, the major contributors of the global biogenic silica cycle in modern oceans, account for about 40% of global marine primary productivity. They are an important component of the biological pump in the ocean, and their assemblage can be used as useful climate proxies; it is therefore critical to better understand the changes induced by environmental pH on their physiology, silicification capability and morphology. Here, we show that external pH influences cell growth of the ubiquitous diatom Thalassiosira weissflogii, and modifies intracellular silicic acid and biogenic silica contents per cell. Measurements at the single-cell level reveal that extracellular pH modifications lead to intracellular acidosis. To further understand how variations of the acid-base balance affect silicon metabolism and theca formation, we developed novel imaging techniques to measure the dynamics of valve formation. We demonstrate that the kinetics of valve morphogenesis, at least in the early stages, depends on pH. Analytical modeling results suggest that acidic conditions alter the dynamics of the expansion of the vesicles within which silica polymerization occurs, and probably its internal pH. Morphological analysis of valve patterns reveals that acidification also reduces the dimension of the nanometric pores present on the valves, and concurrently overall valve porosity. Variations in the valve silica network seem to be more correlated to the dynamics and the regulation of the morphogenesis process than the silicon incorporation rate. These multiparametric analyses from single-cell to cell-population levels demonstrate that several higher-level processes are sensitive to the acid-base balance in diatoms, and its regulation is a key factor for the control of pattern formation and silicon metabolism.

Stuttering Min oscillations within E. coli bacteria: a stochastic polymerization model.

We have developed a 3D off-lattice stochastic polymerization model to study the subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding and fragmentation of MinD filaments due to MinE. Processivity, protection and fragmentation each reduce stuttering, speed oscillations and MinD filament lengths. Neither processivity nor tip protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations is consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization under experimental conditions.

Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences.

During the origin of life, the biological information of nucleic acid polymers must have increased to encode functional molecules (the RNA world). Ribozymes tend to be compositionally unbiased, as is the vast majority of possible sequence space. However, ribonucleotides vary greatly in synthetic yield, reactivity and degradation rate, and their non-enzymatic polymerization results in compositionally biased sequences. While natural selection could lead to complex sequences, molecules with some activity are required to begin this process. Was the emergence of compositionally diverse sequences a matter of chance, or could prebiotically plausible reactions counter chemical biases to increase the probability of finding a ribozyme? Our in silico simulations using a two-letter alphabet show that template-directed ligation and high concatenation rates counter compositional bias and shift the pool toward longer sequences, permitting greater exploration of sequence space and stable folding. We verified experimentally that unbiased DNA sequences are more efficient templates for ligation, thus increasing the compositional diversity of the pool. Our work suggests that prebiotically plausible chemical mechanisms of nucleic acid polymerization and ligation could predispose toward a diverse pool of longer, potentially structured molecules. Such mechanisms could have set the stage for the appearance of functional activity very early in the emergence of life.

Monodisperse domains by proteolytic control of the coarsening instability.

The coarsening instability typically disrupts steady-state cluster-size distributions. We show that degradation coupled to the cluster size, such as arising from biological proteolysis, leads to a fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the fixed-point size distribution. At the fixed point, we show how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism is consistent with the phenomenology of pseudopilus length control in the general secretion pathway of bacteria.

Inhibition of bacterial conjugation by phage M13 and its protein g3p: quantitative analysis and model.

Conjugation is the main mode of horizontal gene transfer that spreads antibiotic resistance among bacteria. Strategies for inhibiting conjugation may be useful for preserving the effectiveness of antibiotics and preventing the emergence of bacterial strains with multiple resistances. Filamentous bacteriophages were first observed to inhibit conjugation several decades ago. Here we investigate the mechanism of inhibition and find that the primary effect on conjugation is occlusion of the conjugative pilus by phage particles. This interaction is mediated primarily by phage coat protein g3p, and exogenous addition of the soluble fragment of g3p inhibited conjugation at low nanomolar concentrations. Our data are quantitatively consistent with a simple model in which association between the pili and phage particles or g3p prevents transmission of an F plasmid encoding tetracycline resistance. We also observe a decrease in the donor ability of infected cells, which is quantitatively consistent with a reduction in pili elaboration. Since many antibiotic-resistance factors confer susceptibility to phage infection through expression of conjugative pili (the receptor for filamentous phage), these results suggest that phage may be a source of soluble proteins that slow the spread of antibiotic resistance genes.

Self-organization of the MinE protein ring in subcellular Min oscillations.

We model the self-organization of the MinE ring that is observed during subcellular oscillations of the proteins MinD and MinE within the rod-shaped bacterium Escherichia coli. With a steady-state approximation, we can study the MinE ring generically--apart from the other details of the Min oscillation. Rebinding of MinE to depolymerizing MinD-filament tips controls MinE-ring formation through a scaled cell shape parameter r. We find two types of E-ring profiles near the filament tip: either a strong plateaulike E ring controlled by one-dimensional diffusion of MinE along the bacterial length or a weak cusplike E ring controlled by three-dimensional diffusion near the filament tip. While the width of a strong E ring depends on r, the occupation fraction of MinE at the MinD-filament tip is saturated and hence the depolymerization speed does not depend strongly on r. Conversely, for weak E rings both r and the MinE to MinD stoichiometry strongly control the tip occupation and hence the depolymerization speed. MinE rings in vivo are close to the threshold between weak and strong, and so MinD-filament depolymerization speed should be sensitive to cell shape, stoichiometry, and MinE-rebinding rate. We also find that the transient to MinE-ring formation is quite long in the appropriate open geometry for assays of ATPase activity in vitro, explaining the long delays of ATPase activity observed for smaller MinE concentrations in those assays without the need to invoke cooperative MinE activity.