Cellular-level mechanisms of polarity and their role in plant growth

Coordinated cell polarity fields are essential for plant and animal development. Several models have been proposed for how these cell polarity fields are established. However, it remains unclear how different models are related to each other and how coordinated cell polarity fields are generated. Here, I present a hypothesis that both plant and animal cell polarity fields are based on a common intracellular partitioning (IP) mechanism that spontaneously generates cell polarity independently from pre-established asymmetries. I show how plant polarity fields may be accounted for through an auxin-mediated indirect cell-cell coupling mechanism that coordinates polarities established by IP, and provides an explicit molecular hypothesis that is consistent with current experimental data. I show that this model behaves similarly to a flux-based model of plant polarity in several scenarios, and that these models make testable predictions that differ from those of published up-the-gradient models. To test the different plant models, I use kanadi1kanadi2 (kan1kan2) mutant Arabidopsis leaves, which develop ectopic outgrowths, as a simple system to study the dynamics of polarity reorientations. I compare contrasting model predictions with observed polarity changes and patterns of auxin-related gene expression preceding the development of ectopic outgrowths. Together with an analysis of wild-type leaves, this reveals that indirect cell-cell coupling and flux-based models are more compatible than the up-the-gradient model with patterns of auxin biosynthesis and import in leaves. I next show that the CUC2 transcription factor is essential for kan1kan2 outgrowth development. Through modelling and experiments, I show that CUC2-regulation of auxin biosynthesis most-likely plays an important role in polarity reorientations. Finally, I present models for how epidermal and subepidermal PIN polarity patterns may be coordinated and lead to changes in growth. This work reveals the value of comparing different computational models with experimental data when investigating mechanisms of polarity generation

Modelling polarity-driven laminar patterns in bilayer tissues with mixed signalling mechanisms

Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localised signalling activity in the development and disease of numerous biological systems. The investigation of multiple signal pathways often introduces different methods of cell-cell communication, i.e. contact-based or diffusive signalling, which generates both a spatial and temporal dependence on cell behaviours. Motivated by cellular mechanisms that control cell-fate decisions in developing bilayer tissues, we use dynamical systems coupled with multilayer graphs to analyse the role of signalling polarity and pathway crosstalk in fine-grain pattern formation of protein activity. Specifically, we study how multilayer graph edge structures and weights influence the layer-wise (laminar) patterning of cells in bilayer structures, which are commonly found in glandular tissues. We present sufficient conditions for existence, uniqueness and instability of homogeneous cell states in the large-scale spatially discrete dynamical system. Using methods of pattern templating by graph partitioning to generate quotient systems in combination with concepts from monotone dynamical systems, we exploit the extensive dimensionality reduction to provide existence conditions for the polarity required to induce fine-grain laminar patterns with multiple spatially dependent intracellular components. We then explore the spectral links between the quotient and large-scale dynamical systems to extend the laminar patterning criteria from existence to convergence for sufficiently large amounts of cellular polarity in the large-scale dynamical system, independent of spatial dimension and number of cells in the tissue