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The phytohormone auxin is implied in steering various developmental decisions during plant morphogenesis in a concentration-dependent manner. Auxin maxima have been shown to maintain meristematic activity, for example, of the root apical meristem, and position new sites of outgrowth, such as during lateral root initiation and phyllotaxis. More recently, it has been demonstrated that sites of auxin minima also provide positional information. In the developing Arabidopsis fruit, auxin minima are required for correct differentiation of the valve margin. It remains unclear, however, how this auxin minimum is generated and maintained. Here, we employ a systems biology approach to model auxin transport based on experimental observations. This allows us to determine the minimal requirements for its establishment. Our simulations reveal that two alternative processes—which we coin "flux-barrier" and "flux-passage"—are both able to generate an auxin minimum, but under different parameter settings. Both models are in principle able to yield similar auxin profiles but present qualitatively distinct patterns of auxin flux. The models were tested by tissue-specific inducible ablation, revealing that the auxin minimum in the fruit is most likely generated by a flux-passage process. Model predictions were further supported through 3D PIN localization imaging and implementing experimentally observed transporter localization. Through such an experimental–modeling cycle, we predict how the auxin minimum gradually matures during fruit development to ensure timely fruit opening and seed dispersal. We investigate the mechanism leading to a spatially confined auxin minimum required for Arabidopsis fruit opening and seed dispersal. Our experiment–modeling cycle reveals a counterintuitive mechanism of its formation: efflux activity creates an auxin minimum strip that is accompanied by high auxin fluxes crossing it perpendicularly. This dynamical process can be associated with the maturation of the fruit. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 difficult to interpret biologically. We therefore developed a method, Lobe Contribution Elliptical Fourier Analysis (LOCO-EFA), which generates from digitalised 2D 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 method's applicability on 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. [ABSTRACT FROM AUTHOR]

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 difficult to interpret biologically. We therefore developed a method, Lobe Contribution Elliptical Fourier Analysis (LOCO-EFA), which generates from digitalised 2D 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 method's applicability on 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. [ABSTRACT FROM AUTHOR]

D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: The 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. Methods: We 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. Results: The 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. Conclusions: The 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. [ABSTRACT FROM AUTHOR]

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 plasmamass 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cell polarization is an important part of the response of eukaryotic cells to stimuli, and forms a primary step in cell motility, differentiation, and many cellular functions. Among the important biochemical players implicated in the onset of intracellular asymmetries that constitute the early phases of polarization are the Rho GTPases, such as Cdc42, Rac, and Rho, which present high active concentration levels in a spatially localized manner. Rho GTPases exhibit positive feedback-driven interconversion between distinct active and inactive forms, the former residing on the cell membrane, and the latter predominantly in the cytosol. A deterministic model of the dynamics of a single Rho GTPase described earlier by Mori et al. exhibits sustained polarization by a wave-pinning mechanism. It remained, however, unclear how such polarization behaves at typically low cellular concentrations, as stochasticity could significantly affect the dynamics. We therefore study the low copy number dynamics of this model, using a stochastic kinetics framework based on the Gillespie algorithm, and propose statistical and analytic techniques which help us analyse the equilibrium behaviour of our stochastic system. We use local perturbation analysis to predict parameter regimes for initiation of polarity and wave-pinning in our deterministic system, and compare these predictions with deterministic and stochastic spatial simulations. Comparing the behaviour of the stochastic with the deterministic system, we determine the threshold number of molecules required for robust polarization in a given effective reaction volume. We show that when the molecule number is lowered wave-pinning behaviour is lost due to an increasingly large transition zone as well as increasing fluctuations in the pinning position, due to which a broadness can be reached that is unsustainable, causing the collapse of the wave, while the variations in the high and low equilibrium levels are much less affected. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: In 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. Results: We 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. Conclusions: We 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. [ABSTRACT FROM AUTHOR]

Experimental data and computer modeling show that lateral root positioning can be controlled by the physical stimulus of root curvature, which triggers self-organizing alterations in auxin transport. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3. In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte. [ABSTRACT FROM AUTHOR]

Abstract: A novel biological principle of cell-to-cell interaction based on membrane continuity of nanotubular channels has recently been described. These contacts are extremely dynamic and sensitive to mechanical stress, which causes their rapid breakage and retraction. Here we demonstrate that functional mechanical stress generated during cell division can disrupt membrane nanotubes, which are formed de novo when filopodia-like projections on one cell make contact with a neighbouring cell, using the SW620 colon carcinoma cell line. Considering the general principal of decreasing cell–cell interactions during tumour progression, our observation is appealing because this new phenomenon may be valid for neoplastic cells. [Copyright &y& Elsevier]