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ABSTRACT Developmental biology seeks to unravel the intricate regulatory mechanisms orchestrating the transformation of a single cell into a complex, multicellular organism. Dynamical systems theory provides a powerful quantitative, visual and intuitive framework for understanding this complexity. This Primer examines five core dynamical systems theory concepts and their applications to pattern formation during development: (1) analysis of phase portraits, (2) bistable switches, (3) stochasticity, (4) response to time-dependent signals, and (5) oscillations. We explore how these concepts shed light onto cell fate decision making and provide insights into the dynamic nature of developmental processes driven by signals and gradients, as well as the role of noise in shaping developmental outcomes. Selected examples highlight how integrating dynamical systems with experimental approaches has significantly advanced our understanding of the regulatory logic underlying development across scales, from molecular networks to tissue-level dynamics. 

Abstract Understanding crop plants responses to abiotic stress is increasingly important in this changing climate. We asked experts how discoveries in Arabidopsis thaliana have translated into advancements in abiotic crop stress resilience. The theme is that core regulatory networks identified in Arabidopsis are conserved in crops, but the molecular regulation varies among species. For cold tolerance, the regulatory framework is conserved, but MAP Kinase signaling promotes degradation of the INDUCER OF DREB1 EXPRESSION transcription factor in Arabidopsis but inhibits it in rice. For hypoxia, manipulation of the oxygen sensing Arg/N-degron pathway discovered in Arabidopsis has improved waterlogging and flood tolerance in barley, maize, wheat, and soybean. For light signaling, overexpression of PHYTOCHROME B reduces shade avoidance, improving yield under dense planting in potato, soybean, and maize. In rice, understanding of nitrogen responsiveness, uptake, and transport in Arabidopsis has inspired engineering of the NRT1 nitrate transceptor to increase yield. Arabidopsis research has provided leads for genetic manipulations that may improve drought resilience in crop species. Growing plants in space generates a complex array of stresses, and Arabidopsis experiments in the space station prepare for future development of robust crops as integral components of the life support systems. For environmental regulation of flowering time, the role of the GIGANTEA - CONTANS - FLOWERING LOCUS T module elucidated in Arabidopsis is largely conserved in crop plants, although additional regulators modify short-day responsiveness in rice, soybean, chrysanthemum, and potato. 

Abstract Research in Arabidopsis thaliana has a powerful influence on our understanding of gene functions and pathways. However, not everything translates from Arabidopsis to crops and other plants. Here, a group of experts consider instances where translation has been lost and why such translation is not possible or is challenging. First, despite great efforts, floral dip transformation has not succeeded in other species outside Brassicaceae. Second, due to gene duplications and losses throughout evolution, it can be complex to establish which genes are orthologs of Arabidopsis genes. Third, during evolution Arabidopsis has lost arbuscular mycorrhizal symbiosis. Fourth, other plants have evolved specialized cell types that are not present in Arabidopsis. Fifth, similarly, C4 photosynthesis cannot be studied in Arabidopsis, which is a C3 plant. Sixth, many other plant species have larger genomes, which has given rise to innovations in transcriptional regulation that are not present in Arabidopsis. Seventh, phenotypes such as acclimation to water stress can be challenging to translate due to different measurement strategies. And eighth, while the circadian oscillator is conserved, there are important nuances in the roles of circadian regulators in crop plants. A key theme emerging across these vignettes is that even when translation is lost, insights can still be gained through comparison with Arabidopsis. 

Living tissues display fluctuations—random spatial and temporal variations of tissue properties around their reference values—at multiple scales. It is believed that such fluctuations may enable tissues to sense their state or their size. Recent theoretical studies developed specific models of fluctuations in growing tissues and predicted that fluctuations of growth show long-range correlations. Here, we elaborated upon these predictions and we tested them using experimental data. We first introduced a minimal model for the fluctuations of any quantity that has some level of temporal persistence or memory, such as concentration of a molecule, local growth rate, or mechanical property. We found that long-range correlations are generic, applying to any such quantity, and that growth couples temporal and spatial fluctuations, through a mechanism that we call “fluctuation stretching”—growth enlarges the length scale of variation of this quantity. We then analyzed growth data from sepals of the model plant Arabidopsis and we quantified spatial and temporal fluctuations of cell growth using the previously developed cellular Fourier transform. Growth appears to have long-range correlations. We compared different genotypes and growth conditions: mutants with lower or higher response to mechanical stress have lower temporal correlations and longer-range spatial correlations than wild-type plants. Finally, we used theoretical predictions to merge experimental data from all conditions and developmental stages into a unifying curve, validating the notion that temporal and spatial fluctuations are coupled by growth. Altogether, our work reveals kinematic constraints on spatiotemporal fluctuations that have an impact on the robustness of morphogenesis. 

Abstract Arabidopsis leaf epidermal cells have a wide range of sizes and ploidies, but how large cells are spatially patterned alongside smaller cells remains unclear. Here, we demonstrate that the same genetic pathway that creates giant cells in sepals is also responsible for their formation in the leaf epidermis. In both sepals and leaves, giant cells are scattered among smaller cells; therefore, we asked whether the spatial arrangement of giant cells is random. By comparing sepal and leaf epidermises with computationally generated randomized tissues we show that giant cells are clustered more than is expected by chance. Our cell-autonomous and stochastic computational model recapitulates the observed giant cell clustering, indicating that clustering emerges as a result of the cell division pattern. Overall, cell size patterning is developmentally regulated by common mechanisms in leaves and sepals rather than a simple byproduct of cell growth. TeaserThe spatial pattern of giant cells becomes non-random as the surrounding cells divide. 

The cell plasma membrane is a two-dimensional, fluid mosaic material composed of lipids and proteins that create a semipermeable barrier defining the cell from its environment. Compared with soluble proteins, the methodologies for the structural and functional characterization of membrane proteins are challenging. An emerging tool for studies of membrane proteins in mammalian systems is a “plasma membrane on a chip,” also known as a supported lipid bilayer. Here, we create the “plant-membrane-on-a-chip,″ a supported bilayer made from the plant plasma membranes of Arabidopsis thaliana, Nicotiana benthamiana, or Zea mays. Membrane vesicles from protoplasts containing transgenic membrane proteins and their native lipids were incorporated into supported membranes in a defined orientation. Membrane vesicles fuse and orient systematically, where the cytoplasmic side of the membrane proteins faces the chip surface and constituents maintain mobility within the membrane plane. We use plant-membrane-on-a-chip to perform fluorescent imaging to examine protein–protein interactions and determine the protein subunit stoichiometry of FLOTILLINs. We report here that like the mammalian FLOTILLINs, FLOTILLINs expressed in Arabidopsis form a tetrameric complex in the plasma membrane. This plant-membrane-on-a-chip approach opens avenues to studies of membrane properties of plants, transport phenomena, biophysical processes, and protein–protein and protein–lipid interactions in a convenient, cell-free platform.