A landmark of developmental biology is the production of reproducible shapes, through stereotyped morphogenetic events. At the cell level, growth is often highly heterogeneous, allowing shape diversity to arise. Yet, how can reproducible shapes emerge from such growth heterogeneity? Is growth heterogeneity filtered out? Here, we focus on rapidly growing trichome cells in the Arabidopsis sepal, a reproducible floral organ. We show via computational modeling that rapidly growing cells may distort organ shape. However, the cortical microtubule alignment along growth-derived maximal tensile stress in adjacent cells would mechanically isolate rapidly growing cells and limit their impact on organ shape. In vivo, we observed such microtubule response to stress and consistently found no significant effect of trichome number on sepal shape in wild-type and lines with trichome number defects. Conversely, modulating the microtubule response to stress in katanin and spiral2 mutant made sepal shape dependent on trichome number, suggesting that, while mechanical signals are propagated around rapidly growing cells, the resistance to stress in adjacent cells mechanically isolates rapidly growing cells, thus contributing to organ shape reproducibility.

When a Brownian object interacts with non-interacting gas particles under non-equilibrium conditions, the energy dissipation associated to the Brownian motion causes an additional force on the object as a 'momentum transfer deficit'. This principle is demonstrated first by a new NESS model and then applied to several known models such as adiabatic piston for which simple explanation has been lacking. 05.70.Ln, 05.20.Dd In nonequilibrium statistical mechanics the mechanical coupling between a system and environments still remains poorly understood. In the Langevin description, the framework of energetics was developed during the last decade [1,2] but there are certainly many aspects which cannot be grasped by such a level of description. For example, when a Brownian object is not symmetric, such as a cone or wedge shape, its asymmetric properties are not fully reflected in the linear friction constant or tensor, γ, of the Langevin equation because γ is non-polar.Related to this limitation, or due to our lack of comprehension about nonequilibrium Brownian motion, there are a class of nonequilibrium phenomena which have refused to be understood at a fundamental level. An interesting example is the adiabatic piston separating two gases of different temperatures under pressure equilibrium [3][4][5]. The laws of thermodynamics cannot tell whether the piston moves or not [3]. Feynman [4] pointed out that the fluctuations of piston's velocity should be taken into account. However, the Langevin description with linear friction falsely predicts zero mean velocity. The adiabatic piston is, therefore, still listed among major unsolved thermodynamics problems [6]. This difficulty is also shared by some models of Brownian ratchet motors working between ideal gas reservoirs [7].A common solution to these problems is to resort to full and general microscopic descriptions, such as the molecular dynamic (MD) simulation or master-Boltzmann equation under pertinent perturbative approximations [8]. These methods are effective in predicting the outcome. For the adiabatic piston, the MD simulations [9] and perturbative master-Boltzmann equation [5,[9][10][11] give quite consistent results showing that the piston moves towards the hotter reservoir. For the ratchet models the agreement between MD simulation and perturbative theory is excellent [7]. When higher order terms are taken into account, the perturbative theories can tell the effect of the shape of Brownian object [7] or of the inelasticity of collisions, called inelastic piston [12,13] and their combinations [14,15].Yet, we still have no physical explanation why the nonequilibrium processes give rise to a force and what determines its direction.In this paper, we will develop a general theoretical framework to answer to this fundamental problem. The key is to explicitly take into account the momentum and mass balances under nonequilibrium condition, in addition to the energy balance considered by the stochastic energetics [2]. Briefly, the nonequilibrium energy transfer, or ...

Cell migration is important for the function of many eukaryotic cells. Recently the nucleus has been shown to play an important role in cell motility. After giving an overview of cell motility mechanisms we review what is currently known about the mechanical properties of the nucleus and the connections between it and the cytoskeleton. We also discuss connections to the extracellular matrix and mechanotransduction. We identify key physical roles of the nucleus in cell migration.

p3 2. Dynamics of signalling in self-organized stem cell assemblies: Idse Heemskerk, Aryeh Warmflash -p4 3. Interplay between tissue growth, morphogen signalling, and pattern formation in development: Laura Bocanegra-Moreno, Kasumi Kishi, Anna Kicheva -p7 4. The biophysical basis of robust plant morphogenesis: Yuchen Long, Antoine Fruleux, Arezki Boudaoud -p11 5. Dynamics of morphogen gradient formation and signalling during development: Timothy E. Saunders -p14 6. Coupling morphogenesis and patterning during amniote gastrulation: Paolo Caldarelli, Arthur Michaut, Jerome Gros -p18 7. Supra-cellular actin fiber arrays and their role in animal morphogenesis: Yonit Maroudas-Sacks, Kinneret Keren -p22 8. Mechano-chemical models for morphogenesis and collective cell migration: Edouard Hannezo -p26 9. Guiding the formation of tissue structure through self-organization: Zev J Gartner -p30 10. Phase transitions, spatial control of mRNA localization and gene expression in syncytial fungi: Benjamin Stormo and Amy Gladfelter -p33 11. The role of mechanics in a "post-molecular" conception of morphogenesis: Alan Rodrigues, Amy Shyer -p37 12. Dynamic interplay between cell shape and division positioning in the morphogenesis of early embryos: Nicolas Minc -p41 13. Building a mechanical atlas of the preimplantation embryo: Jean-Léon Maître -p44 14. Physical principles of organization of the cell cycle and morphogenesis in early Drosophila embryos: Stefano Di Talia -p48 15. Dynamic interplay of cell contact geometry and signalling: Bassma Khamaisi, David Sprinzak -p51 16. From locally generated forces to global shape and back: Sham Tlili, Pierre-François Lenne -p55

Mechanical signals have recently emerged as a major cue in plant morphogenesis, notably influencing cytoskeleton organization, gene expression, protein polarity, or cell division. Although many putative mechanosensing proteins have been identified, it is unclear what mechanical cue they might sense and how this would occur. Here we briefly explain the notions of mechanical stress and strain. We present the challenges to understand their sensing by plants, focusing on the cell wall and the plasma membrane, and we review putative mechanosensing structures. We propose minimal biophysical models of mechanosensing, revealing the modes of mechanosensing according to mechanosensor lifetime, threshold force for mechanosensor dissociation, and type of association between the mechanosensor and the cell wall, as the sensor may be associated to a major load-bearing structure such as cellulose or to a minor load-bearing structure such as pectins or the plasma membrane. Permanent strain, permanent expansion, and relatively slow variations thereof are sensed in all cases; variations of stress are sensed in all cases; permanent stress is sensed only in the following specific cases: sensors associated to minor load-bearing structures slowly relaxing in a growing wall, long-lived sensors with high dissociation force and associated to major-load-bearing structures, and sensors with low dissociation force associated to major-load-baring structures behaving elastically. We also find that all sensors respond to variations in the composition or the mechanical properties of the cell wall. The level of sensing is modulated by the properties of all of mechanosensor, cell wall components, and plasma membrane. Although our models are minimal and not fully realistic, our results yield a framework to start investigating the possible functions of putative mechanosensors.

A drop of moderate size deposited inside a circular hydraulic jump remains trapped at the shock front and does not coalesce with the liquid flowing across the jump. For a small inclination of the plate on which the liquid is impacting, the drop does not always stay at the lowest position and oscillates around it with a sometimes large amplitude, and a frequency that slightly decreases with flow rate. We suggest that this striking behavior is linked to a gyroscopic instability in which the drop tries to keep constant its angular momentum while sliding along the jump.

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The growth and division of cells in plant leaves is highly dynamic in time and space, all while the cells cannot move relative to their neighbors. Given these constraints, models predict that long range regulatory systems must exist to maintain flat forms. Juxtaposed microRNA (miRNA) networks could serve as one of these regulatory systems. One of these miRNAs, miR319 is thought to be expressed from the base of leaves and to promote growth by degrading class II TCP transcription factor mRNAs. A miR319 overexpression mutant,jagged and wavy (jaw-D)exhibits rippling and undulating leaves, consistent with biomechanical predictions that without genetic spatial coordination, tissues will deform. It has been theorized thatjaw-Drippling results from overgrowth at the margins, however this does not fully address how miR319 expression from the base of wild-type (WT) leaves allows them to flatten. Here, we track the growth, cell division and cell maturation in live WT andjaw-Dleaves to ask how miR319 expression in WT promotes flattening. This data revealed the importance of spatially distinct growth, division and differentiation patterns in WT leaves, which are missing injaw-D. We propose that WT leaf cells respond to differentiation cues to dynamically re-orient growth in specific tissue locations and regulate flattening.