Theoretical approaches to understanding root vascular patterning: a consensus between recent models.

The root vascular tissues provide an excellent system for studying organ patterning, as the specification of these tissues signals a transition from radial symmetry to bisymmetric patterns. The patterning process is controlled by the combined action of hormonal signaling/transport pathways, transcription factors, and miRNA that operate through a series of non-linear pathways to drive pattern formation collectively. With the discovery of multiple components and feedback loops controlling patterning, it has become increasingly difficult to understand how these interactions act in unison to determine pattern formation in multicellular tissues. Three independent mathematical models of root vascular patterning have been formulated in the last few years, providing an excellent example of how theoretical approaches can complement experimental studies to provide new insights into complex systems. In many aspects these models support each other; however, each study also provides its own novel findings and unique viewpoints. Here we reconcile these models by identifying the commonalities and exploring the differences between them by testing how transferable findings are between models. New simulations herein support the hypothesis that an asymmetry in auxin input can direct the formation of vascular pattern. We show that the xylem axis can act as a sole source of cytokinin and specify the correct pattern, but also that broader patterns of cytokinin production are also able to pattern the root. By comparing the three modeling approaches, we gain further insight into vascular patterning and identify several key areas for experimental investigation.

Growth and tension in explosive fruit.

Exploding seed pods of the common weed Cardamine hirsuta have the remarkable ability to launch seeds far from the plant. The energy for this explosion comes from tension that builds up in the fruit valves. Above a critical threshold, the fruit fractures along its dehiscence zone and the two valves coil explosively, ejecting the seeds. A common mechanism to generate tension is drying, causing tissues to shrink. However, this does not happen in C. hirsuta fruit. Instead, tension is produced by active contraction of growing exocarp cells in the outer layer of the fruit valves. Exactly how growth causes the exocarp tissue to contract and generate pulling force is unknown. Here we show that the reorientation of microtubules in the exocarp cell cortex changes the orientation of cellulose microfibrils in the cell wall and the consequent cellular growth pattern. We used mechanical modeling to show how tension emerges through growth due to the highly anisotropic orientation of load-bearing cellulose microfibrils and their effect on cell shape. By explicitly defining the cell wall as multi-layered in our model, we discovered that a cross-lamellate pattern of cellulose microfibrils further enhances the developing tension in growing cells. Therefore, the interplay of cell wall properties with turgor-driven growth enables the fruit exocarp to generate sufficient tension to power explosive seed dispersal.

Cytokinin promotes growth cessation in the Arabidopsis root.

The Arabidopsis root offers good opportunities to investigate how regulated cellular growth shapes different tissues and organs, a key question in developmental biology. Along the root's longitudinal axis, cells sequentially occupy different developmental states. Proliferative meristematic cells give rise to differentiating cells, which rapidly elongate in the elongation zone, then mature and stop growing in the differentiation zone. The phytohormone cytokinin contributes to this zonation by positioning the boundary between the meristem and the elongation zone, called the transition zone. However, the cellular growth profile underlying root zonation is not well understood, and the cellular mechanisms that mediate growth cessation remain unclear. By using time-lapse imaging, genetics, and computational analysis, we analyze the effect of cytokinin on root zonation and cellular growth. We found that cytokinin promotes growth cessation in the distal (shootward) elongation zone in conjunction with accelerating the transition from elongation to differentiation. We estimated cell-wall stiffness by using osmotic treatment experiments and found that cytokinin-mediated growth cessation is associated with cell-wall stiffening and requires the action of an auxin influx carrier, AUX1. Our measurement of growth and cell-wall mechanical properties at a cellular resolution reveal mechanisms via which cytokinin influences cell behavior to shape tissue patterns.

Using positional information to provide context for biological image analysis with MorphoGraphX 2.0.

Positional information is a central concept in developmental biology. In developing organs, positional information can be idealized as a local coordinate system that arises from morphogen gradients controlled by organizers at key locations. This offers a plausible mechanism for the integration of the molecular networks operating in individual cells into the spatially coordinated multicellular responses necessary for the organization of emergent forms. Understanding how positional cues guide morphogenesis requires the quantification of gene expression and growth dynamics in the context of their underlying coordinate systems. Here, we present recent advances in the MorphoGraphX software (Barbier de Reuille et al., 2015⁠) that implement a generalized framework to annotate developing organs with local coordinate systems. These coordinate systems introduce an organ-centric spatial context to microscopy data, allowing gene expression and growth to be quantified and compared in the context of the positional information thought to control them.

A SOSEKI-based coordinate system interprets global polarity cues in Arabidopsis.

Multicellular development requires coordinated cell polarization relative to body axes, and translation to oriented cell division1-3. In plants, it is unknown how cell polarities are connected to organismal axes and translated to division. Here, we identify Arabidopsis SOSEKI proteins that integrate apical-basal and radial organismal axes to localize to polar cell edges. Localization does not depend on tissue context, requires cell wall integrity and is defined by a transferrable, protein-specific motif. A Domain of Unknown Function in SOSEKI proteins resembles the DIX oligomerization domain in the animal Dishevelled polarity regulator. The DIX-like domain self-interacts and is required for edge localization and for influencing division orientation, together with a second domain that defines the polar membrane domain. Our work shows that SOSEKI proteins locally interpret global polarity cues and can influence cell division orientation. Furthermore, this work reveals that, despite fundamental differences, cell polarity mechanisms in plants and animals converge on a similar protein domain.

Correction: Centering the Organizing Center in the Arabidopsis thaliana Shoot Apical Meristem by a Combination of Cytokinin Signaling and Self-Organization.

[This corrects the article DOI: 10.1371/journal.pone.0147830.].

Centering the Organizing Center in the Arabidopsis thaliana Shoot Apical Meristem by a Combination of Cytokinin Signaling and Self-Organization.

Plants have the ability to continously generate new organs by maintaining populations of stem cells throught their lives. The shoot apical meristem (SAM) provides a stable environment for the maintenance of stem cells. All cells inside the SAM divide, yet boundaries and patterns are maintained. Experimental evidence indicates that patterning is independent of cell lineage, thus a dynamic self-regulatory mechanism is required. A pivotal role in the organization of the SAM is played by the WUSCHEL gene (WUS). An important question in this regard is that how WUS expression is positioned in the SAM via a cell-lineage independent signaling mechanism. In this study we demonstrate via mathematical modeling that a combination of an inhibitor of the Cytokinin (CK) receptor, Arabidopsis histidine kinase 4 (AHK4) and two morphogens originating from the top cell layer, can plausibly account for the cell lineage-independent centering of WUS expression within SAM. Furthermore, our laser ablation and microsurgical experiments support the hypothesis that patterning in SAM occurs at the level of CK reception and signaling. The model suggests that the interplay between CK signaling, WUS/CLV feedback loop and boundary signals can account for positioning of the WUS expression, and provides directions for further experimental investigation.

Plant development. Integration of growth and patterning during vascular tissue formation in Arabidopsis.

Coordination of cell division and pattern formation is central to tissue and organ development, particularly in plants where walls prevent cell migration. Auxin and cytokinin are both critical for division and patterning, but it is unknown how these hormones converge upon tissue development. We identify a genetic network that reinforces an early embryonic bias in auxin distribution to create a local, nonresponding cytokinin source within the root vascular tissue. Experimental and theoretical evidence shows that these cells act as a tissue organizer by positioning the domain of oriented cell divisions. We further demonstrate that the auxin-cytokinin interaction acts as a spatial incoherent feed-forward loop, which is essential to generate distinct hormonal response zones, thus establishing a stable pattern within a growing vascular tissue.