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Plant tissue architecture and organ morphogenesis rely on the proper orientation of cell divisions. Previous attempts to predict division planes from cell geometry in plants mostly focused on 2D symmetric divisions. Using the stereotyped division patterns of Arabidopsis thaliana early embryogenesis, we investigated geometrical principles underlying plane selection in symmetric and in asymmetric divisions within complex 3D cell shapes. Introducing a 3D computational model of cell division, we show that area minimization constrained on passing through the cell centroid predicts observed divisions. Our results suggest that the positioning of division planes ensues from cell geometry and gives rise to spatially organized cell types with stereotyped shapes, thus underlining the role of self-organization in the developing architecture of the embryo. Our data further suggested the rule could be interpreted as surface minimization constrained by the nucleus position, which was validated using live imaging of cell divisions in the stomatal cell lineage., Competing Interests: The authors have declared that no competing interests exist.

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.

Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

Sequence dependency of DNA intrinsic bending properties has been emphasized as a possible key ingredient to in vivo chromatin organization. We use atomic force microscopy (AFM) in air and liquid to image intrinsically straight (synthetic), uncorrelated (hepatitis C RNA virus) and persistent long-range correlated (human) DNA fragments in various ionic conditions such that the molecules freely equilibrate on the mica surface before being captured in a particular conformation. 2D thermodynamic equilibrium is experimentally verified by a detailed statistical analysis of the Gaussian nature of the DNA bend angle fluctuations. We show that the worm-like chain (WLC) model, commonly used to describe the average conformation of long semiflexible polymers, reproduces remarkably well the persistence length estimates for the first two molecules as consistently obtained from (i) mean square end-to-end distance measurement and (ii) mean projection of the end-to-end vector on the initial orientation. Whatever the operating conditions (air or liquid, concentration of metal cations Mg(2+) and/or Ni(2+)), the persistence length found for the uncorrelated viral DNA underestimates the value obtained for the straight DNA. We show that this systematic difference is the signature of the presence of an uncorrelated structural intrinsic disorder in the hepatitis C virus (HCV) DNA fragment that superimposes on local curvatures induced by thermal fluctuations and that only the entropic disorder depends upon experimental conditions. In contrast, the WLC model fails to describe the human DNA conformations. We use a mean-field extension of the WLC model to account for the presence of long-range correlations (LRC) in the intrinsic curvature disorder of human genomic DNA: the stronger the LRC, the smaller the persistence length. The comparison of AFM imaging of human DNA with LRC DNA simulations confirms that the rather small mean square end-to-end distance observed, particularly for G+C-rich human DNA molecules, more likely results from a large-scale intrinsic curvature due to a persistent distribution of DNA curvature sites than from some increased flexibility.

The ability of the telomeric DNA-binding protein, TRF2, to stimulate t-loop formation while preventing t-loop deletion is believed to be crucial to maintain telomere integrity in mammals. However, little is known on the molecular mechanisms behind these properties of TRF2. In this report, we show that TRF2 greatly increases the rate of Holliday junction (HJ) formation and blocks the cleavage by various types of HJ resolving activities, including the newly identified human GEN1 protein. By using potassium permanganate probing and differential scanning calorimetry, we reveal that the basic domain of TRF2 induces structural changes to the junction. We propose that TRF2 contributes to t-loop stabilisation by stimulating HJ formation and by preventing resolvase cleavage. These findings provide novel insights into the interplay between telomere protection and homologous recombination and suggest a general model in which TRF2 maintains telomere integrity by controlling the turnover of HJ at t-loops and at regressed replication forks.