Coupling water fluxes with cell wall mechanics in a multicellular model of plant development

Abstract

The growth of plant organs is a complex process powered by osmosis that attracts water inside the cells; this influx induces simultaneously an elastic extension of the walls and pressure in the cells, called turgor pressure; above a threshold, the walls yield and the cells grow. Based on Lockhart's seminal work, various models of plant morphogenesis have been proposed, either for single cells, or focusing on the wall mechanical properties. However, the synergistic coupling of fluxes and wall mechanics has not yet been fully addressed in a multicellular model. This work lays the foundations of such a model, by simplifying as much as possible each process and putting emphasis on the coupling itself. Its emergent properties are rich and can help to understand plant morphogenesis. In particular, we show that the model can display a new type of lateral inhibitory mechanism that could contribute to the amplification of growth heterogeneities, essential for shape differentiation.Plant growth and morphogenesis | Biophysics | Mathematical modelling | Emergence | Lateral inhibition P lants grow throughout their lifetime at the level of small regions containing undifferentiated cells, the meristems, located at the extremities of their axes. Growth is powered by osmosis that tends to attract water inside the cells. The corresponding increase in volume leads to simultaneous tension in the walls and hydrostatic pressure (so-called turgor pressure) in the cells. Continuous growth occurs thanks to the yielding of the walls to these stretching forces [1][2][3].This interplay between growth, water fluxes, wall stress and turgor was first modelled by Lockhart in 1965 [4], in the context of a single elongating cell. Recent models focused on how genes regulate growth at more integrated levels [5][6][7][8][9]. To accompany genetic, molecular, and biophysical analyses of growing tissues, various extensions of Lockhart's model to multicellular tissues have been developed. The resulting models are intrinsically complex as they represent collections from tens to thousands of cells in 2-or 3-dimensions interacting with each other. To cut down the complexity, several approaches abstract organ multicellular structures as polygonal networks of 1D visco-elastic springs either in 2D [7,[10][11][12] or in 3D [6,13] submitted to a steady turgor pressure. Other approaches try to represent more realistically the structure of the plant walls by 2D deformable wall elements able to respond locally to turgor pressure by anisotropic growth [8,14,15].Most of these approaches consider turgor as a constant driving force for growth, explicitely or implicitly assuming that fluxes occur much faster than wall synthesis. Cells then regulate the tissue deformations by locally modulating the material structure of their walls (stiffness and anisotropy) [6,[16][17][18][19][20]. However, the situation in real plants is more complex: turgor heterogeneity has been observed at cellular level [21,22], which challenges the assumption of very fast fluxes. As a matter of f...

A hydro-osmotic coarsening theory of biological cavity formation

“…Here, we have shown that active ion pumping may be an additional source of spatial bias for coarsening. Active osmotic volume control emerges hence as a novel mode of symmetry breaking for tissue patterning, that could be relevant also to oogenesis Alsous et al ( 2021 ); Lamiré et al ( 2020 ); Chartier et al ( 2020 ), liquid phase transition of biological condensates Jalihal et al ( 2021 ) and plant tissue growth Cheddadi et al ( 2019 ); Long et al ( 2020 ). Active ion pumping can also largely affect the collective lumen dynamics, with the emergence of a novel coarsening regime dominated by coalescence.…”

“…In spite of these simplifications, we have shown importantly that active ion pumping can bias coarsening spatially. Active osmotic volume control emerges hence as a novel mode of symmetry breaking for tissue morphogenesis, that could be relevant also to oogenesis [36,39,40], to liquid phase transition of biological condensates [68] and to plant tissue growth [42,44]. This symmetry breaking may complement or compete with mechanical gradients, that were shown to play a major role in mouse embryo blastocoel formation [18] or in the coarsening of membrane-less organelles [69,70].…”

“…Hydraulic and osmotic flows are indeed more and more recognized as essential determinants of embryo and tissue shaping Dasgupta et al ( 2018 ); Lamiré et al ( 2020 ); Chan et al ( 2019 ); Dumortier et al ( 2019 ); Narayanan et al ( 2020 ); Alsous et al ( 2021 ); Chartier et al ( 2020 ). However only a few physical models describe the interplay between cell mechanics, osmotic effects and fluid flow in morphogenesis Alim ( 2018 ); Cheddadi et al ( 2019 ); Dolega et al ( 2021 ); Long et al ( 2020 ) and in previous models, osmolarity is mostly considered spatially homogeneous. Here, we propose a generic hydro-osmotic physical model that explicitly accounts for ion pumping and osmotic gradients.…”

“…Hydraulic and osmotic flows are indeed more and more recognized as essential determinants of embryo and tissue shaping [18,[35][36][37][38][39][40]. However only a few physical models describe the interplay between cell mechanics, osmotic effects and fluid flow in morphogenesis [41][42][43][44], and in all those previous models, osmolarity is considered July 15, 2021 2/21 spatially homogeneous. Here, we propose a generic physical model to describe the hydro-osmotic coupling between pressurized compartments, explicitly accounting for osmotic gradients and ion pumping.…”

A hydro-osmotic coarsening theory of biological cavity formation

“…Hydraulic and osmotic flows are indeed more and more recognized as essential determinants of embryo and tissue shaping [19,[36][37][38][39][40][41]. However only a few physical models describe the interplay between cell mechanics, osmotic effects and fluid flow in morphogenesis [42][43][44][45], and in all those previous models, osmolarity is considered spatially homogeneous. Here, we propose a generic physical model to describe the hydro-osmotic coupling between pressurized compartments, explicitly accounting for osmotic gradients and ion pumping.…”