Stéphane Douady

Formation and stability of transverse and longitudinal sand dunes

The shape of dunes depends on the history of wind regimes and sand availability. In deserts exposed to winds from two different directions but with comparable magnitude, dunes are found to be linear ridges, which are either perpendicular or parallel to the mean wind direction, depending on the angle between the two wind directions. These dunes, respectively observed for small and large angles between winds, are called transverse and longitudinal dunes. In both cases, their large width (hundreds of meters) and evolution time scale (years) strongly limit the investigation of their dynamics and thus our understanding of such structures. Here we show that, under water, similar structures can be obtained but at much smaller space and time scales. Performing controlled experiments together with numerical simulations, we highlight the physical mechanisms at play in the formation and long-term evolution of these structures. We show in particular that, while longitudinal dunes are stable and extend in time, transverse dunes are unstable. They evolve into wavy ridges and eventually break into barchans if the sand supply is too low. This fundamental difference is understood through the study of single sand piles and bars exposed to two winds. In the case of a large angle between winds, a sand pile grows a finger pointing in the average wind direction and transforms into a longitudinal dune. Such an elongation does not occur for a small angle where a sand pile evolves into a barchan. These results explain the morphological differences between straight and long longitudinal dunes and sinuous transverse dunes, while giving keys to infer the wind history or pattern state of development from the observation of dune shapes in the field.

Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants

Gravitropism, the slow reorientation of plant growth in response to gravity, is a key determinant of the form and posture of land plants. Shoot gravitropism is triggered when statocysts sense the local angle of the growing organ relative to the gravitational field. Lateral transport of the hormone auxin to the lower side is then enhanced, resulting in differential gene expression and cell elongation causing the organ to bend. However, little is known about the dynamics, regulation, and diversity of the entire bending and straightening process. Here, we modeled the bending and straightening of a rod-like organ and compared it with the gravitropism kinematics of different organs from 11 angiosperms. We show that gravitropic straightening shares common traits across species, organs, and orders of magnitude. The minimal dynamic model accounting for these traits is not the widely cited gravisensing law but one that also takes into account the sensing of local curvature, what we describe here as a graviproprioceptive law. In our model, the entire dynamics of the bending/straightening response is described by a single dimensionless “bending number” B that reflects the ratio between graviceptive and proprioceptive sensitivities. The parameter B defines both the final shape of the organ at equilibrium and the timing of curving and straightening. B can be estimated from simple experiments, and the model can then explain most of the diversity observed in experiments. Proprioceptive sensing is thus as important as gravisensing in gravitropic control, and the B ratio can be measured as phenotype in genetic studies.

The structure of gallery networks in the nests of termite Cubitermes spp. revealed by X-ray tomography

Recent studies have introduced computer tomography (CT) as a tool for the visualisation and characterisation of insect architectures. Here, we use CT to map the three-dimensional networks of galleries inside Cubitermes nests in order to analyse them with tools from graph theory. The structure of these networks indicates that connections inside the nest are rearranged during the whole nest life. The functional analysis reveals that the final network topology represents an excellent compromise between efficient connectivity inside the nest and defence against attacking predators. We further discuss and illustrate the usefulness of CT to disentangle environmental and specific influences on nest architecture.

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.

Branching geometry induced by lung self-regulated growth.

Branching morphogenesis is a widely spread phenomenon in nature. In organogenesis, it results from the inhomogeneous growth of the epithelial sheet, leading to its repeated branching into surrounding mesoderm. Lung morphogenesis is an emblematic example of tree-like organogenesis common to most mammals. The core signalling network is well identified, notably the Fgf10/Shh couple, required to initiate and maintain branching. In a previous study, we showed that the restriction by SHH of Fgf10 expression domain to distal mesenchyme spontaneously induces differential epithelial proliferation leading to branching. A simple Laplacian model qualitatively reproduced FGF10 dynamics in the mesenchyme and the spontaneous self-avoiding branching morphogenesis. However, early lung geometry has several striking features that remain to be addressed. In this paper, we investigate, through simulations and data analysis, if the FGF10-diffusion scenario accounts for the following aspects of lung morphology: size dispersion, asymmetry of branching events, and distal epithelium-mesothelium equilibrium. We report that they emerge spontaneously in the model, and that most of the underlying mechanisms can be understood as dynamical interactions between gradients and shape. This suggests that specific regulation may not be required for the emergence of these striking geometrical features.

Abaxial growth and steric constraints guide leaf folding and shape in Acer pseudoplatanus

PREMISE OF THE STUDY How leaf shape is regulated is a long-standing question in botany. For diverse groups of dicotyledon species, lamina folding along the veins and geometry of the space available for the primordia can explain the palmate leaf morphology. Dubbed the kirigami theory, this hypothesis of fold-dependent leaf shape regulation has remained largely theoretical. Using Acer pseudoplatanus, we investigated the mechanisms behind the two key processes of kirigami leaf development. METHODS Cytological examination and quantitative analyses were used to examine the course of the vein-dependent lamina folding. Surgical ablation and tissue culturing were employed to test the effects of physical constraints on primordia growth. The final morphology of leaves growing without steric constraints were predicted mathematically. KEY RESULTS The cytological examination showed that the laminas abaxial side along the veins grows substantially more than the adaxial side. The abaxial hypergrowth along the veins and the lamina extension correlated with the lamina folding. When a primordium was released from the physical constraints imposed by the other primordia, it rapidly grew into the newly available space, while maintaining the curvature inward. The morphology of such a leaf was predicted to lack symmetry in the lobe shapes. CONCLUSIONS The enhanced growth on the abaxial side of the lamina along the veins is likely to drive lamina folding. The surgical ablation provided clear support for the space-filling nature of leaf growth; thus, steric constraints play a role in determination of the shapes of folded leaves and probably also of the final leaf morphology.

A Unified Model of Shoot Tropism in Plants: Photo-, Gravi- and Propio-ception

Land plants rely mainly on gravitropism and phototropism to control their posture and spatial orientation. In natural conditions, these two major tropisms act concurrently to create a photogravitropic equilibrium in the responsive organ. Recently, a parsimonious model was developed that accurately predicted the complete gravitropic and proprioceptive control over the movement of different organs in different species in response to gravitational stimuli. Here we show that the framework of this unifying graviproprioceptive model can be readily extended to include phototropism. The interaction between gravitropism and phototropism results in an alignment of the apical part of the organ toward a photogravitropic set-point angle. This angle is determined by a combination of the two directional stimuli, gravity and light, weighted by the ratio between the gravi- and photo-sensitivities of the plant organ. In the model, two dimensionless numbers, the graviproprioceptive number B and the photograviceptive number M, control the dynamics and the shapes of the movement. The extended model agrees well with two sets of detailed quantitative data on photogravitropic equilibrium in oat coleoptiles. It is demonstrated that the influence of light intensity I can be included in the model in a power-law-dependent relationship M(I). The numbers B and M and the related photograviceptive number D are all quantitative genetic traits that can be measured in a straightforward manner, opening the way to the phenotyping of molecular and mechanical aspects of shoot tropism.

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand. More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d--with g the gravity and d the diameter of the grains--explaining why all the singing dunes in the same vicinity sing at the same frequency. We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound. Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.

KymoRod: A method for automated kinematic analysis of rod‐shaped plant organs

A major challenge in plant systems biology is the development of robust, predictive multiscale models for organ growth. In this context it is important to bridge the gap between the, rather well-documented molecular scale and the organ scale by providing quantitative methods to study within-organ growth patterns. Here, we describe a simple method for the analysis of the evolution of growth patterns within rod-shaped organs that does not require adding markers at the organ surface. The method allows for the simultaneous analysis of root and hypocotyl growth, provides spatio-temporal information on curvature, growth anisotropy and relative elemental growth rate and can cope with complex organ movements. We demonstrate the performance of the method by documenting previously unsuspected complex growth patterns within the growing hypocotyl of the model species Arabidopsis thaliana during normal growth, after treatment with a growth-inhibiting drug or in a mechano-sensing mutant. The method is freely available as an intuitive and user-friendly Matlab application called KymoRod.

On Necessary and Sufficient Conditions for Proto-cell Stationary Growth

We consider a generic proto-cell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of one of the chemical species (membrane precursor) and is semi-permeable to some other chemical species (nutrients) diffusing from an outside growth medium into the proto-cell. Inside the proto-cell, nutrients are metabolized into all other chemical species including the membrane precursor, and the membrane grows in area and the proto-cell in volume. Investigating the conditions under which such a proto-cell may reach stationary growth, we prove that a simple necessary condition is that each moiety be fed with some nutrient flux; and that a sufficient condition for the existence of a stationary growth regime is that every siphon containing any species participating in the membrane precursor incorporation kinetics also contains the support of a moiety that is fed with some nutrient flux. These necessary and sufficient conditions hold regardless of chemical reaction kinetics, membrane parameters or nutrient flux diffusion characteristics.