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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 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.