Shaping of a three-dimensional carnivorous trap through modulation of a planar growth mechanism.

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.

Systems Biology Approach Pinpoints Minimum Requirements for Auxin Distribution during Fruit Opening.

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.

Spatiotemporal coordination of cell division and growth during organ morphogenesis.

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.

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

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 method's 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.

Pavement cells and the topology puzzle.

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.

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

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.

A Sigmoid Functional Response Emerges When Cytotoxic T Lymphocytes Start Killing Fresh Target Cells.

Cytotoxic T lymphocyte (CTL)-mediated killing involves the formation of a synapse with a target cell, followed by delivery of perforin and granzymes. Previously, we derived a general functional response for CTL killing while considering that CTLs form stable synapses (i.e., single-stage) and that the number of conjugates remains at steady state. However, the killing of target cells sometimes requires multiple engagements (i.e., multistage). To study how multistage killing and a lack of steady state influence the functional response, we here analyze a set of differential equations as well as simulations employing the cellular Potts model, in both cases describing CTLs that kill target cells. We find that at steady state the total killing rate (i.e., the number of target cells killed by all CTLs) is well described by the previously derived double saturation function. Compared to single-stage killing, the total killing rate during multistage killing saturates at higher CTL and target cell densities. Importantly, when the killing is measured before the steady state is approached, a qualitatively different functional response emerges for two reasons: First, the killing signal of each CTL gets diluted over several targets and because this dilution effect is strongest at high target cell densities; this can result in a peak in the dependence of the total killing rate on the target cell density. Second, the total killing rate exhibits a sigmoid dependence on the CTL density when killing is a multistage process, because it takes typically more than one CTL to kill a target. In conclusion, a sigmoid dependence of the killing rate on the CTLs during initial phases of killing may be indicative of a multistage killing process. Observation of a sigmoid functional response may thus arise from a dilution effect and is not necessarily due to cooperative behavior of the CTLs.

Tissue Dimensionality Influences the Functional Response of Cytotoxic T Lymphocyte-Mediated Killing of Targets.

Cytotoxic T lymphocyte (CTL)-mediated killing of virus infections and tumors occurs over a wide range of conditions. The spatial environments in which CTLs encounter target cells vary from narrow vessels, to two-dimensional epithelial tissues, to densely populated 3-dimensional (3D) T cell areas within lymphoid tissues. How such spatial environments alter the functional response of CTL-mediated killing, i.e., how the killing efficiency depends on cell densities, is unclear. In this study, we perform cellular Potts model simulations in different spatial configurations to investigate how the dimensionality of the space affects the functional response of CTL-mediated killing. Irrespective of the spatial configuration, the function with separate saturation constants for CTL and for target cell densities that we previously proposed can in all cases describe the response, demonstrating its generality. However, the tissue dimensionality determines at which cell densities the killing rate starts to saturate. We show that saturation in a fully 3D environment is stronger than in a "flat" 3D environment, which is largely due to accompanying differences in the CTL-target encounter rates.

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.

Ethylene-Mediated Regulation of A2-Type CYCLINs Modulates Hyponastic Growth in Arabidopsis.

Upward leaf movement (hyponastic growth) is frequently observed in response to changing environmental conditions and can be induced by the phytohormone ethylene. Hyponasty results from differential growth (i.e. enhanced cell elongation at the proximal abaxial side of the petiole relative to the adaxial side). Here, we characterize Enhanced Hyponasty-d, an activation-tagged Arabidopsis (Arabidopsis thaliana) line with exaggerated hyponasty. This phenotype is associated with overexpression of the mitotic cyclin CYCLINA2;1 (CYCA2;1), which hints at a role for cell divisions in regulating hyponasty. Indeed, mathematical analysis suggested that the observed changes in abaxial cell elongation rates during ethylene treatment should result in a larger hyponastic amplitude than observed, unless a decrease in cell proliferation rate at the proximal abaxial side of the petiole relative to the adaxial side was implemented. Our model predicts that when this differential proliferation mechanism is disrupted by either ectopic overexpression or mutation of CYCA2;1, the hyponastic growth response becomes exaggerated. This is in accordance with experimental observations on CYCA2;1 overexpression lines and cyca2;1 knockouts. We therefore propose a bipartite mechanism controlling leaf movement: ethylene induces longitudinal cell expansion in the abaxial petiole epidermis to induce hyponasty and simultaneously affects its amplitude by controlling cell proliferation through CYCA2;1. Further corroborating the model, we found that ethylene treatment results in transcriptional down-regulation of A2-type CYCLINs and propose that this, and possibly other regulatory mechanisms affecting CYCA2;1, may contribute to this attenuation of hyponastic growth.

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.

A general functional response of cytotoxic T lymphocyte-mediated killing of target cells.

Cytotoxic T lymphocytes (CTLs) kill virus-infected cells and tumor cells, and play a critical role in immune protection. Our knowledge of how the CTL killing efficiency varies with CTL and target cell numbers is limited. Here, we simulate a region of lymphoid tissue using a cellular Potts model to characterize the functional response of CTL killing of target cells, and find that the total killing rate saturates both with the CTL and the target cell densities. The relative saturation in CTL and target cell densities is determined by whether a CTL can kill multiple target cells at the same time, and whether a target cell can be killed by many CTLs together. We find that all the studied regimes can be well described by a double-saturation (DS) function with two different saturation constants. We show that this DS model can be mechanistically derived for the cases where target cells are killed by a single CTL. For the other cases, a biological interpretation of the parameters is still possible. Our results imply that this DS function can be used as a tool to predict the cellular interactions in cytotoxicity data.

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.

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.

Chemotactic migration of T cells towards dendritic cells promotes the detection of rare antigens.

In many immunological processes chemoattraction is thought to play a role in guiding cells to their sites of action. However, based on in vivo two-photon microscopy experiments in the absence of cognate antigen, T cell migration in lymph nodes (LNs) has been roughly described as a random walk. Although it has been shown that dendritic cells (DCs) carrying cognate antigen in some circumstances attract T cells chemotactically, it is currently still unclear whether chemoattraction of T cells towards DCs helps or hampers scanning. Chemoattraction towards DCs could on the one hand help T cells to rapidly find DCs. On the other hand, it could be deleterious if DCs become shielded by a multitude of attracted yet non-specific T cells. Results from a recent simulation study suggested that the deleterious effect dominates. We re-addressed the question whether T cell chemoattraction towards DCs is expected to promote or hamper the detection of rare antigens using the Cellular Potts Model, a formalism that allows for dynamic, flexible cellular shapes and cell migration. Our simulations show that chemoattraction of T cells enhances the DC scanning efficiency, leading to an increased probability that rare antigen-specific T cells find DCs carrying cognate antigen. Desensitization of T cells after contact with a DC further improves the scanning efficiency, yielding an almost threefold enhancement compared to random migration. Moreover, the chemotaxis-driven migration still roughly appears as a random walk, hence fine-tuned analysis of cell tracks will be required to detect chemotaxis within microscopy data.

Tissue-resident memory CD8+ T cells continuously patrol skin epithelia to quickly recognize local antigen.

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.

Deterministic versus stochastic cell polarisation through wave-pinning.

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.

A bistable circuit involving SCARECROW-RETINOBLASTOMA integrates cues to inform asymmetric stem cell division.

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.

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) 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.

Ethylene-induced differential petiole growth in Arabidopsis thaliana involves local microtubule reorientation and cell expansion.

• Hyponastic growth is an upward petiole movement induced by plants in response to various external stimuli. It is caused by unequal growth rates between adaxial and abaxial sides of the petiole, which bring rosette leaves to a more vertical position. The volatile hormone ethylene is a key regulator inducing hyponasty in Arabidopsis thaliana. Here, we studied whether ethylene-mediated hyponasty occurs through local stimulation of cell expansion and whether this involves the reorientation of cortical microtubules (CMTs). • To study cell size differences between the two sides of a petiole in ethylene and control conditions, we analyzed epidermal imprints. We studied the involvement of CMT orientation in epidermal cells using the tubulin marker line as well as genetic and pharmacological means of CMT manipulation. • Our results demonstrate that ethylene induces cell expansion at the abaxial side of the- petiole and that this can account for the observed differential growth. At the abaxial side, ethylene induces CMT reorientation from longitudinal to transverse, whereas, at the adaxial side, it has an opposite effect. The inhibition of CMTs disturbed ethylene-induced hyponastic growth. • This work provides evidence that ethylene stimulates cell expansion in a tissue-specific manner and that it is associated with tissue-specific changes in the arrangement of CMTs along the petiole.