Verônica A. Grieneisen

Auxin transport is sufficient to generate a maximum and gradient guiding root growth

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.

How Cells Integrate Complex Stimuli: The Effect of Feedback from Phosphoinositides and Cell Shape on Cell Polarization and Motility

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.

An intracellular partitioning-based framework for tissue cell polarity in plants and animals

Tissue 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.

Morphogengineering roots: comparing mechanisms of morphogen gradient formation.

BackgroundIn developmental biology, there has been a recent focus on the robustness of morphogen gradients as possible providers of positional information. It was shown that functional morphogen gradients present strong biophysical constraints and lack of robustness to noise. Here we explore how the details of the mechanism which underlies the generation of a morphogen gradient can influence those properties.ResultsWe contrast three gradient-generating mechanisms, (i) a source-decay mechanism; and (ii) a unidirectional transport mechanism; and (iii) a so-called reflux-loop mechanism. Focusing on the dynamics of the phytohormone auxin in the root, we show that only the reflux-loop mechanism can generate a gradient that would be adequate to supply functional positional information for the Arabidopsis root, for biophysically reasonable kinetic parameters.ConclusionsWe argue that traits that differ in spatial and temporal time-scales can impose complex selective pressures on the mechanism of morphogen gradient formation used for the development of the particular organism.

The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics

BackgroundThe biophysical characteristics of cells determine their shape in isolation and when packed within tissues. Cells can form regular or irregular epithelial structures, round up and form clusters, or deform and attach to substrates. The acquired shape of cells and tissues is a consequence of (i) internal cytoskeletal processes, such as actin polymerisation and cortical myosin contraction, (ii) adhesion molecules within the cell membrane that interact with substrates and neighbouring cells, and (iii) processes that regulate cell volume. Although these processes seem relatively simple, when combined they unleash a rich variety of cellular behaviour that is not readily understandable outside a theoretical framework.MethodsWe perform a mathematical analysis of a commonly used class of model formalisms that describe cell surface mechanics using an energy-based approach. Predictions are then confirmed through comparison with the computational outcomes of a Vertex model and 2D and 3D simulations of the Cellular Potts model.ResultsThe analytical study reveals the complete possible spectrum of single cell behaviour and tissue packing in both 2D and 3D, by taking the typical core elements of cell surface mechanics into account: adhesion, cortical tension and volume conservation. We show that from an energy-based description, forces and tensions can be derived, as well as the prediction of cell behaviour and tissue packing, providing an intuitive and biologically relevant mapping between modelling parameters and experiments.ConclusionsThe quantitative cellular behaviours and biological insights agree between the analytical study and the diverse computational model formalisms, including the Cellular Potts model. This illustrates the generality of energy-based approaches for cell surface mechanics and highlights how meaningful and quantitative comparisons between models can be established. Moreover, the mathematical analysis reveals direct links between known biophysical properties and specific parameter settings within the Cellular Potts model.

Auxin minimum triggers the developmental switch from cell division to cell differentiation in the Arabidopsis root

Significance The maintenance of boundaries between neighboring groups of distinct cell types is vital during development of multicellular organisms, as groups of cells with distinct functions must be kept physically separated to guarantee correct control of organ and body growth and function. In the Arabidopsis root, the transition zone is a developmental boundary in the meristem that separates dividing from differentiating cells. Here, we infer that a well-defined and tightly controlled minimum of the hormone auxin acts as a signal to establish the position of the transition zone by controlling the developmental switch from cell division to cell differentiation. We provide the mechanistic and genetic basis of how another hormone, cytokinin, controls and positions this auxin minimum, thus regulating root size. 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.

Mathematical Modeling and Experimental Validation of the Spatial Distribution of Boron in the Root of Arabidopsis thaliana Identify High Boron Accumulation in the Tip and Predict a Distinct Root Tip Uptake Function

Boron, an essential micronutrient, is transported in roots of Arabidopsis thaliana mainly by two different types of transporters, BORs and NIPs (nodulin26-like intrinsic proteins). Both are plasma membrane localized, but have distinct transport properties and patterns of cell type-specific accumulation with different polar localizations, which are likely to affect boron distribution. Here, we used mathematical modeling and an experimental determination to address boron distributions in the root. A computational model of the root is created at the cellular level, describing the boron transporters as observed experimentally. Boron is allowed to diffuse into roots, in cells and cell walls, and to be transported over plasma membranes, reflecting the properties of the different transporters. The model predicts that a region around the quiescent center has a higher concentration of soluble boron than other portions. To evaluate this prediction experimentally, we determined the boron distribution in roots using laser ablation-inductivity coupled plasma-mass spectrometry. The analysis indicated that the boron concentration is highest near the tip and is lower in the more proximal region of the meristem zone, similar to the pattern of soluble boron distribution predicted by the model. Our model also predicts that upward boron flux does not continuously increase from the root tip toward the mature region, indicating that boron taken up in the root tip is not efficiently transported to shoots. This suggests that root tip-absorbed boron is probably used for local root growth, and that instead it is the more mature root regions which have a greater role in transporting boron toward the shoots.

Parsimonious Model of Vascular Patterning Links Transverse Hormone Fluxes to Lateral Root Initiation: Auxin Leads the Way, while Cytokinin Levels Out.

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.

Juicy Stories on Female Reproductive Tissue Development： Coordinating the Hormone Flows

In the past 20-30 years, developmental biologists have made tremendous progress in identifying genes required for the specification of individual cell types of an organ and in describing how they interact in genetic networks. In comparison, very little is known about the mechanisms that regulate tissue polarity and overall organ patterning. Gynoecia and fruits from members of the Brassicaceae family of flowering plants provide excellent model systems to study organ patterning and tissue specification because they become partitioned into distinct domains whose formation is determined by polarity establishment both at a cellular and whole tissue level. Interactions among key regulators of Arabidopsis gynoecium and fruit development have revealed a network of upstream transcription factor activities required for such tissue differentiation. Regulation of the plant hormone auxin is emerging as both an immediate downstream output and input of these activities, and here we aim to provide an overview of the current knowledge regarding the link between auxin and female reproductive development in plants. In this review, we will also demonstrate how available data can be exploited in a mathematical modeling approach to reveal and understand the feedback regulatory circuits that underpin the polarity establishment, necessary to guide auxin flows.

Morphometrics of complex cell shapes: lobe contribution elliptic Fourier analysis (LOCO-EFA)

ABSTRACT Quantifying cell morphology is fundamental to the statistical study of cell populations, and can help unravel mechanisms underlying cell and tissue morphogenesis. Current methods, however, require extensive human intervention, are highly parameter sensitive, or produce metrics that are difficult to interpret biologically. We therefore developed a method, lobe contribution elliptical Fourier analysis (LOCO-EFA), which generates from digitalised two-dimensional cell outlines meaningful descriptors that can be directly matched to morphological features. This is shown by studying well-defined geometric shapes as well as actual biological cells from plant and animal tissues. LOCO-EFA provides a tool to phenotype efficiently and objectively populations of cells, here demonstrated by applying it to the complex shaped pavement cells of Arabidopsis thaliana wild-type and speechless leaves, and Drosophila amnioserosa cells. To validate our methods applicability to large populations, we analysed computer-generated tissues. By controlling in silico cell shape, we explored the potential impact of cell packing on individual cell shape, quantifying through LOCO-EFA deviations between the specified shape of single cells in isolation and the resultant shape when they interact within a confluent tissue. Summary: A novel method for automated and quantitative assessment of complex cell shapes, including features such as protrusion number and amplitude, is demonstrated for Arabidopsis, Drosophila and in silico cells.