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The plant growth regulator auxin controls cell identity, cell division and cell expansion. Auxin efflux facilitators (PINs) are associated with auxin maxima in distal regions of both shoots and roots. Here we model diffusion and PIN-facilitated auxin transport in and across cells within a structured root layout. In our model, the stable accumulation of auxin in a distal maximum emerges from the auxin flux pattern. We have experimentally tested model predictions of robustness and self-organization. Our model explains pattern formation and morphogenesis at timescales from seconds to weeks, and can be understood by conceptualizing the root as an 'auxin capacitor'. A robust auxin gradient associated with the maximum, in combination with separable roles of auxin in cell division and cell expansion, is able to explain the formation, maintenance and growth of sharply bounded meristematic and elongation zones. Directional permeability and diffusion can fully account for stable auxin maxima and gradients that can instruct morphogenesis.

To regulate shape changes, motility and chemotaxis in eukaryotic cells, signal transduction pathways channel extracellular stimuli to the reorganization of the actin cytoskeleton. The complexity of such networks makes it difficult to understand the roles of individual components, let alone their interactions and multiple feedbacks within a given layer and between layers of signalling. Even more challenging is the question of if and how the shape of the cell affects and is affected by this internal spatiotemporal reorganization. Here we build on our previous 2D cell motility model where signalling from the Rho family GTPases (Cdc42, Rac, and Rho) was shown to organize the cell polarization, actin reorganization, shape change, and motility in simple gradients. We extend this work in two ways: First, we investigate the effects of the feedback between the phosphoinositides (PIs) PIP₂, PIP₃ and Rho family GTPases. We show how that feedback increases heights and breadths of zones of Cdc42 activity, facilitating global communication between competing cell \"fronts\". This hastens the commitment to a single lamellipodium initiated in response to multiple, complex, or rapidly changing stimuli. Second, we show how cell shape feeds back on internal distribution of GTPases. Constraints on chemical isocline curvature imposed by boundary conditions results in the fact that dynamic cell shape leads to faster biochemical redistribution when the cell is repolarized. Cells with frozen cytoskeleton, and static shapes, consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes, the degree of the shape-induced effects being proportional to the extent of cell deformation. We explain these concepts in the context of several in silico experiments using our 2D computational cell model.

Lateral organ position along roots and shoots largely determines plant architecture, and depends on auxin distribution patterns. Determination of the underlying patterning mechanisms has hitherto been complicated because they operate during growth and division. Here, we show by experiments and computational modeling that curvature of the Arabidopsis root influences cell sizes, which, together with tissue properties that determine auxin transport, induces higher auxin levels in the pericycle cells on the outside of the curve. The abundance and position of the auxin transporters restricts this response to the zone competent for lateral root formation. The auxin import facilitator, AUX1, is up-regulated by auxin, resulting in additional local auxin import, thus creating a new auxin maximum that triggers organ formation. Longitudinal spacing of lateral roots is modulated by PIN proteins that promote auxin efflux, and pin2,3,7 triple mutants show impaired lateral inhibition. Thus, lateral root patterning combines a trigger, such as cell size difference due to bending, with a self-organizing system that mediates alterations in auxin transport.

A developing plant organ exhibits complex spatiotemporal patterns of growth, cell division, cell size, cell shape, and organ shape. Explaining these patterns presents a challenge because of their dynamics and cross-correlations, which can make it difficult to disentangle causes from effects. To address these problems, we used live imaging to determine the spatiotemporal patterns of leaf growth and division in different genetic and tissue contexts. In the simplifying background of the speechless (spch) mutant, which lacks stomatal lineages, the epidermal cell layer exhibits defined patterns of division, cell size, cell shape, and growth along the proximodistal and mediolateral axes. The patterns and correlations are distinctive from those observed in the connected subepidermal layer and also different from the epidermal layer of wild type. Through computational modelling we show that the results can be accounted for by a dual control model in which spatiotemporal control operates on both growth and cell division, with cross-connections between them. The interactions between resulting growth and division patterns lead to a dynamic distributions of cell sizes and shapes within a deforming leaf. By modulating parameters of the model, we illustrate how phenotypes with correlated changes in cell size, cell number, and organ size may be generated. The model thus provides an integrated view of growth and division that can act as a framework for further experimental study.

Key Points To analyse time-lapse video microscopy experiments of the immune system, quantification of cell migration is required. A toolbox of quantitative measures, such as cell speed, motility coefficient, confinement ratio and various angles of migration is available for that purpose. Time-lapse imaging of the immune system is associated with various artefacts than can affect the estimated cell positions over time. As a result, measures of cell migration are also affected by such artefacts, and this may obscure biologically relevant differences between experimental settings or generate spurious results. Imaging artefacts are related either to cell tracking (switching or splitting of tracks, double tracking of cells and errors of tracking near borders) or to imaging itself (imprecise calibration of the axial dimension and small tissue drift). Detection and correction for artefacts can be done using various migration angles. For example, plotting the average angle to the axial border plane versus the distance to that border can help to detect border tracking errors, calibration errors in the axial dimension and small tissue drift. Cell-based measurements are better at detecting distinct subpopulations among cells than step-based approaches. However, an important disadvantage of cell-based versus step-based parameters is that the shape of the imaged space affects the results, and this makes comparison between experiments problematic. Determining contact times between cells in imaging experiments is non-trivial because observed (underestimated) rather than exact contact time is known for most contacts. However, the true contact time distribution can be estimated using a mathematical approach. Time-lapse video microscopy is an important experimental tool for examining the dynamic behaviour of immune cells in situ and involves quantitative analysis of cell migration and cell–cell interactions. Here, several commonly measured parameters and imaging artefacts are described and potential solutions to detect and correct these artefacts are proposed. The visualization of the dynamic behaviour of and interactions between immune cells using time-lapse video microscopy has an important role in modern immunology. To draw robust conclusions, quantification of such cell migration is required. However, imaging experiments are associated with various artefacts that can affect the estimated positions of the immune cells under analysis, which form the basis of any subsequent analysis. Here, we describe potential artefacts that could affect the interpretation of data sets on immune cell migration. We propose how these errors can be recognized and corrected, and suggest ways to prevent the data analysis itself leading to biased results.

An auxin maximum is positioned along the xylem axis of the Arabidopsis root tip. The pattern depends on mutual feedback between auxin and cytokinins mediated by the PIN class of auxin efflux transporters and AHP6, an inhibitor of cytokinin signalling. This interaction has been proposed to regulate the size and the position of the hormones' respective signalling domains and specify distinct boundaries between them. To understand the dynamics of this regulatory network, we implemented a parsimonious computational model of auxin transport that considers hormonal regulation of the auxin transporters within a spatial context, explicitly taking into account cell shape and polarity and the presence of cell walls. Our analysis reveals that an informative spatial pattern in cytokinin levels generated by diffusion is a theoretically unlikely scenario. Furthermore, our model shows that such a pattern is not required for correct and robust auxin patterning. Instead, auxin-dependent modifications of cytokinin response, rather than variations in cytokinin levels, allow for the necessary feedbacks, which can amplify and stabilise the auxin maximum. Our simulations demonstrate the importance of hormonal regulation of auxin efflux for pattern robustness. While involvement of the PIN proteins in vascular patterning is well established, we predict and experimentally verify a role of AUX1 and LAX1/2 auxin influx transporters in this process. Furthermore, we show that polar localisation of PIN1 generates an auxin flux circuit that not only stabilises the accumulation of auxin within the xylem axis, but also provides a mechanism for auxin to accumulate specifically in the xylem-pole pericycle cells, an important early step in lateral root initiation. The model also revealed that pericycle cells on opposite xylem poles compete for auxin accumulation, consistent with the observation that lateral roots are not initiated opposite to each other.

Leaves display a remarkable range of forms, from flat sheets with simple outlines to cup-shaped traps. Although much progress has been made in understanding the mechanisms of planar leaf development, it is unclear whether similar or distinctive mechanisms underlie shape transformations during development of more complex curved forms. Here, we use 3D imaging and cellular and clonal analysis, combined with computational modelling, to analyse the development of cup-shaped traps of the carnivorous plant Utricularia gibba. We show that the transformation from a near-spherical form at early developmental stages to an oblate spheroid with a straightened ventral midline in the mature form can be accounted for by spatial variations in rates and orientations of growth. Different hypotheses regarding spatiotemporal control predict distinct patterns of cell shape and size, which were tested experimentally by quantifying cellular and clonal anisotropy. We propose that orientations of growth are specified by a proximodistal polarity field, similar to that hypothesised to account for Arabidopsis leaf development, except that in Utricularia, the field propagates through a highly curved tissue sheet. Independent evidence for the polarity field is provided by the orientation of glandular hairs on the inner surface of the trap. Taken together, our results show that morphogenesis of complex 3D leaf shapes can be accounted for by similar mechanisms to those for planar leaves, suggesting that simple modulations of a common growth framework underlie the shaping of a diverse range of morphologies.

Recent work has demonstrated that following the clearance of infection a stable population of memory T cells remains present in peripheral organs and contributes to the control of secondary infections. However, little is known about how tissue-resident memory T cells behave in situ and how they encounter newly infected target cells. Here we demonstrate that antigen-specific CD8 ⁺ T cells that remain in skin following herpes simplex virus infection show a steady-state crawling behavior in between keratinocytes. Spatially explicit simulations of the migration of these tissue-resident memory T cells indicate that the migratory dendritic behavior of these cells allows the detection of antigen-expressing target cells in physiologically relevant time frames of minutes to hours. Furthermore, we provide direct evidence for the identification of rare antigen-expressing epithelial cells by skin-patrolling memory T cells in vivo. These data demonstrate the existence of skin patrol by memory T cells and reveal the value of this patrol in the rapid detection of renewed infections at a previously infected site.

In multicellular organisms, a stringent control of the transition between cell division and differentiation is crucial for correct tissue and organ development. In the Arabidopsis root, the boundary between dividing and differentiating cells is positioned by the antagonistic interaction of the hormones auxin and cytokinin. Cytokinin affects polar auxin transport, but how this impacts the positional information required to establish this tissue boundary, is still unknown. By combining computational modeling with molecular genetics, we show that boundary formation is dependent on cytokinin’s control on auxin polar transport and degradation. The regulation of both processes shapes the auxin profile in a well defined auxin minimum. This auxin minimum positions the boundary between dividing and differentiating cells, acting as a trigger for this developmental transition, thus controlling meristem size.