Turning a plant tissue into a living cell froth through isotropic growth.

The forms resulting from growth processes are highly sensitive to the nature of the driving impetus, and to the local properties of the medium, in particular, its isotropy or anisotropy. In turn, these local properties can be organized by growth. Here, we consider a growing plant tissue, the shoot apical meristem of Arabidopsis thaliana. In plants, the resistance of the cell wall to the growing internal turgor pressure is the main factor shaping the cells and the tissues. It is well established that the physical properties of the walls depend on the oriented deposition of the cellulose microfibrils in the extracellular matrix or cell wall; this order is correlated to the highly oriented cortical array of microtubules attached to the inner side of the plasma membrane. We used oryzalin to depolymerize microtubules and analyzed its influence on the growing meristem. This had no short-term effect, but it had a profound impact on the cell anisotropy and the resulting tissue growth. The geometry of the cells became similar to that of bubbles in a soap froth. At a multicellular scale, this switch to a local isotropy induced growth into spherical structures. A theoretical model is presented in which a cellular structure grows through the plastic yielding of its walls under turgor pressure. The simulations reproduce the geometrical properties of a normal tissue if cell division is included. If not, a "cell froth" very similar to that observed experimentally is obtained. Our results suggest strong physical constraints on the mechanisms of growth regulation.

The role of elastic stresses on leaf venation morphogenesis.

We explore the possible role of elastic mismatch between epidermis and mesophyll as a driving force for the development of leaf venation. The current prevalent 'canalization' hypothesis for the formation of veins claims that the transport of the hormone auxin out of the leaves triggers cell differentiation to form veins. Although there is evidence that auxin plays a fundamental role in vein formation, the simple canalization mechanism may not be enough to explain some features observed in the vascular system of leaves, in particular, the abundance of vein loops. We present a model based on the existence of mechanical instabilities that leads very naturally to hierarchical patterns with a large number of closed loops. When applied to the structure of high-order veins, the numerical results show the same qualitative features as actual venation patterns and, furthermore, have the same statistical properties. We argue that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.

Structure, scaling, and phase transition in the optimal transport network.

The structure and properties of optimal networks depend on the cost functional being minimized and on constraints to which the minimization is subject. We show here two different formulations that lead to identical results: minimizing the dissipation rate of an electrical network under a global constraint is equivalent to the minimization of a power-law cost function introduced by Banavar et al. [Phys. Rev. Lett. 84, 4745 (2000)10.1103/PhysRevLett.84.4745]. An explicit scaling relation between the currents and the corresponding conductances is derived, proving the potential flow nature of the latter. Varying a unique parameter, the topology of the optimized networks shows a transition from a tree topology to a very redundant structure with loops; the transition corresponds to a discontinuity in the slope of the power dissipation.

Rod-climbing effect in Newtonian fluids.

When a rotating rod is brought into a polymer melt or concentrated polymer solution, the meniscus climbs the rod. This spectacular rod climbing is due to the normal stresses present in the polymer fluid and is thus a purely non-Newtonian effect. A similar rod climbing of an interface between two fluids has therefore been taken as a signature that one of the fluids exhibits normal stress effects. We show here, however, that the effect can occur with simple Newtonian fluids: it occurs when a Taylor-Couette instability happens in the less viscous of the two liquids but not in the more viscous one.