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.

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.

SummaryTo overcome nitrogen deficiencies in the soil, legumes enter symbioses with rhizobial bacteria that convert atmospheric nitrogen into ammonium. Rhizobia are accommodated as endosymbionts within lateral root organs called nodules that initiate from the inner layers of Medicago truncatula roots in response to rhizobial perception. In contrast, lateral roots emerge from predefined founder cells as an adaptive response to environmental stimuli, including water and nutrient availability. CYTOKININ RESPONSE 1 (CRE1)-mediated signaling in the pericycle and in the cortex is necessary and sufficient for nodulation, whereas cytokinin is antagonistic to lateral root development, with cre1 showing increased lateral root emergence and decreased nodulation. To better understand the relatedness between nodule and lateral root development, we undertook a comparative analysis of these two root developmental programs. Here, we demonstrate that despite differential induction, lateral roots and nodules share overlapping developmental programs, with mutants in LOB-DOMAIN PROTEIN 16 (LBD16) showing equivalent defects in nodule and lateral root initiation. The cytokinin-inducible transcription factor NODULE INCEPTION (NIN) allows induction of this program during nodulation through activation of LBD16 that promotes auxin biosynthesis via transcriptional induction of STYLISH (STY) and YUCCAs (YUC). We conclude that cytokinin facilitates local auxin accumulation through NIN promotion of LBD16, which activates a nodule developmental program overlapping with that induced during lateral root initiation.

SUMMARY In plants, where cells cannot migrate, asymmetric cell divisions (ACDs) must be confined to the appropriate spatial context. We investigate tissue-generating asymmetric divisions in a stem cell daughter within the Arabidopsis root. Spatial restriction of these divisions requires physical binding of the stem cell regulator SCARECROW (SCR) by the RETINOBLASTOMA-RELATED (RBR) protein. In the stem cell niche, SCR activity is counteracted by phosphorylation of RBR through a cyclinD6;1-CDK complex. This cyclin is itself under transcriptional control of SCR and its partner SHORT ROOT (SHR), creating a robust bistable circuit with either high or low SHR-SCR complex activity. Auxin biases this circuit by promoting CYCD6;1 transcription. Mathematical modeling shows that ACDs are only switched on after integration of radial and longitudinal information, determined by SHR and auxin distribution, respectively. Coupling of cell-cycle progression to protein degradation resets the circuit, resulting in a “flip flop” that constrains asymmetric cell division to the stem cell region.

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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 welldefined 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.plant hormones | cell differentiation | root meristem | computational modeling

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) , 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.

SummaryTissue cell polarity plays a major role in plant and animal development. We propose that a fundamental building block for tissue cell polarity is the process of intracellular partitioning, which can establish individual cell polarity in the absence of asymmetric cues. Coordination of polarities may then arise through cell-cell coupling, which can operate directly, through membrane-spanning complexes, or indirectly, through diffusible molecules. Polarity is anchored to tissues through organisers located at boundaries. We show how this intracellular partitioning-based framework can be applied to both plant and animal systems, allowing different processes to be placed in a common evolutionary and mechanistic context.