Vertex-element models for anisotropic growth of elongated plant organs

New tools are required to address the challenge of relating plant hormone levels, hormone responses, wall biochemistry and wall mechanical properties to organ-scale growth. Current vertex-based models (applied in other contexts) can be unsuitable for simulating the growth of elongated organs such as roots because of the large aspect ratio of the cells, and these models fail to capture the mechanical properties of cell walls in sufficient detail. We describe a vertex-element model which resolves individual cells and includes anisotropic non-linear viscoelastic mechanical properties of cell walls and cell division whilst still being computationally efficient. We show that detailed consideration of the cell walls in the plane of a 2D simulation is necessary when cells have large aspect ratio, such as those in the root elongation zone of Arabidopsis thaliana, in order to avoid anomalous transverse swelling. We explore how differences in the mechanical properties of cells across an organ can result in bending and how cellulose microfibril orientation affects macroscale growth. We also demonstrate that the model can be used to simulate growth on realistic geometries, for example that of the primary root apex, using moderate computational resources. The model shows how macroscopic root shape can be sensitive to fine-scale cellular geometries

Hybrid vertex-midline modelling of elongated plant organs

We describe a method for the simulation of the growth of elongated plant organs, such as seedling roots. By combining a midline representation of the organ on a tissue scale and a vertex-based representation on the cell scale, we obtain a multiscale method, which is able to both simulate organ growth and incorporate cell-scale processes. Equations for the evolution of the midline are obtained, which depend on the cell-wall properties of individual cells through appropriate averages over the vertex-based representation. The evolution of the organ midline is used to deform the cellular-scale representation. This permits the investigation of the regulation of organ growth through the cell-scale transport of the plant hormone auxin. The utility of this method is demonstrated in simulating the early stages of the response of a root to gravity, using a vertex-based template acquired from confocal imaging. Asymmetries in the concentrations of auxin between the upper and lower sides of the root lead to bending of the root midline, reflecting a gravitropic response

Diffusion-mediated HEI10 coarsening can explain meiotic crossover positioning in Arabidopsis.

In most organisms, the number and distribution of crossovers that occur during meiosis are tightly controlled. All chromosomes must receive at least one 'obligatory crossover' and crossovers are prevented from occurring near one another by 'crossover interference'. However, the mechanistic basis of this phenomenon of crossover interference has remained mostly mysterious. Using quantitative super-resolution cytogenetics and mathematical modelling, we investigate crossover positioning in the Arabidopsis thaliana wild-type, an over-expressor of the conserved E3 ligase HEI10, and a hei10 heterozygous line. We show that crossover positions can be explained by a predictive, diffusion-mediated coarsening model, in which large, approximately evenly-spaced HEI10 foci grow at the expense of smaller, closely-spaced clusters. We propose this coarsening process explains many aspects of Arabidopsis crossover positioning, including crossover interference. Consistent with this model, we also demonstrate that crossover positioning can be predictably modified in vivo simply by altering HEI10 dosage, with higher and lower dosage leading to weaker and stronger crossover interference, respectively. As HEI10 is a conserved member of the RING finger protein family that functions in the interference-sensitive pathway for crossover formation, we anticipate that similar mechanisms may regulate crossover positioning in diverse eukaryotes

Techniques for analysing pattern formation in populations of stem cells and their progeny

<p>Abstract</p> <p>Background</p> <p>To investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer. We assume that the fate of an individual cell is regulated by the signals it receives from neighbouring cells via either diffusive or juxtacrine signalling. We analyse simulated patterns using two different spatial statistical measures that are suited to planar multicellular systems: pair correlation functions (PCFs) and quadrat histograms (QHs).</p> <p>Results</p> <p>With a diffusive signalling mechanism, pattern size (revealed by PCFs) is determined by both morphogen decay rate and a sensitivity parameter that determines the degree to which morphogen biases differentiation; high sensitivity and slow decay give rise to large-scale patterns. In contrast, with juxtacrine signalling, high sensitivity produces well-defined patterns over shorter lengthscales. QHs are simpler to compute than PCFs and allow us to distinguish between random differentiation at low sensitivities and patterned states generated at higher sensitivities.</p> <p>Conclusions</p> <p>PCFs and QHs together provide an effective means of characterising emergent patterns of differentiation in planar multicellular aggregates.</p

A patch-based approach to 3D plant shoot phenotyping

The emerging discipline of plant phenomics aims to measure key plant characteristics, or traits, though as yet the set of plant traits that should be measured by automated systems is not well defined. Methods capable of recovering generic representations of the 3D structure of plant shoots from images would provide a key technology underpinning quantification of a wide range of current and future physiological and morphological traits. We present a fully automatic approach to image-based 3D plant reconstruction which represents plants as series of small planar sections that together model the complex architecture of leaf surfaces. The initial boundary of each leaf patch is refined using a level set method, optimising the model based on image information, curvature constraints and the position of neighbouring surfaces. The reconstruction process makes few assumptions about the nature of the plant material being reconstructed. As such it is applicable to a wide variety of plant species and topologies, and can be extended to canopy-scale imaging. We demonstrate the effectiveness of our approach on real images of wheat and rice plants, an artificial plant with challenging architecture, as well as a novel virtual dataset that allows us to compute distance measures of reconstruction accuracy. We also illustrate the method’s potential to support the identification of individual leaves, and so the phenotyping of plant shoots, using a spectral clustering approach

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 analysis of auxin transport in the Arabidopsis root apex

Auxin is a key regulator of plant growth and development. Within the root tip, auxin distribution plays a crucial role specifying developmental zones and coordinating tropic responses. Determining how the organ-scale auxin pattern is regulated at the cellular scale is essential to understanding how these processes are controlled. In this study, we developed an auxin transport model based on actual root cell geometries and carrier subcellular localizations. We tested model predictions using the DII-VENUS auxin sensor in conjunction with state-of-the-art segmentation tools. Our study revealed that auxin efflux carriers alone cannot create the pattern of auxin distribution at the root tip and that AUX1/LAX influx carriers are also required. We observed that AUX1 in lateral root cap (LRC) and elongating epidermal cells greatly enhance auxin’s shootward flux, with this flux being predominantly through the LRC, entering the epidermal cells only as they enter the elongation zone. We conclude that the nonpolar AUX1/LAX influx carriers control which tissues have high auxin levels, whereas the polar PIN carriers control the direction of auxin transport within these tissues

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

ART DEMONSTRATES THAT FOOTBALL IS METASTASIZED, AND GIVES IT REFUGE

U ovom se radu problemski analiziraju obilježja nogometa u hit-romanu Alena Bovića Metastaze (2006) te u dvjema kasnijim obradama tog književnog djela – u kazališnoj predstavi Metastaze i istoimenom igranom filmu. Otuda ideja da se ondje zatečen, devijantnim pojavama obilježen nogomet, koji više baš i nema puno dodirnih točaka s igrom koja mu leži u korijenima, nazove metastaziralim. Umjetnička se stvarnost pritom promatra kao korespondentna društvenoj stvarnosti pa se za takvo etiketiranje nogometa prepoznaju razlozi na objema razinama. Na temelju takvog pristupa Metastazama, ali i na osnovi prethodno ponuđenog komparativnog uvida u nogometnu tematiku u nekim drugim književnim, kazališnim i filmskim ostvarenjima u Hrvatskoj i izvan nje, postavlja se teza o umjetnosti kao dokazu metastaziralog nogometa. No, još je izazovnije utvrditi može li umjetnost istodobno poslužiti i kao utočište metastaziralom nogometu tako da se njome revitalizira ponajprije estetska, ali istodobno i etička dimenzija tog sporta. Iz tih pobuda argumentacija u ovome radu uključuje tekstove i autore u širokom rasponu od književne kritike, antropologije igara i sociologije sporta do semiotike, kulturalnih studija i estetike. U ovom se radu problemski analiziraju obilježja nogometa u hit-romanu Alena Bovića Metastaze (2006) te u dvjema kasnijim obradama tog književnog djela – u kazališnoj predstavi Metastaze i istoimenom igranom filmu. Otuda ideja da se ondje zatečen, devijantnim pojavama obilježen nogomet, koji više baš i nema puno dodirnih točaka s igrom koja mu leži u korijenima, nazove metastaziralim. Umjetnička se stvarnost pritom promatra kao korespondentna društvenoj stvarnosti pa se za takvo etiketiranje nogometa prepoznaju razlozi na objema razinama. Na temelju takvog pristupa Metastazama, ali i na osnovi prethodno ponuđenog komparativnog uvida u nogometnu tematiku u nekim drugim književnim, kazališnim i filmskim ostvarenjima u Hrvatskoj i izvan nje, postavlja se teza o umjetnosti kao dokazu metastaziralog nogometa. No, još je izazovnije utvrditi može li umjetnost istodobno poslužiti i kao utočište metastaziralom nogometu tako da se njome revitalizira ponajprije estetska, ali istodobno i etička dimenzija tog sporta. Iz tih pobuda argumentacija u ovome radu uključuje tekstove i autore u širokom rasponu od književne kritike, antropologije igara i sociologije sporta do semiotike, kulturalnih studija i estetike.This article presents an analysis of the characteristics of football as depicted in the bestselling novel Metastaze (Metastases) (2006) by Alen Bović and in its two subsequent adaptations – the play Metastaze (Metastases) directed by Boris Svrtan and the film Metastaze (Metastases) directed by Branko Schmidt. Football as it appears in these three pieces is metastasized: it is deviant and in fact undergoes so many significant changes that it no longer has much in common with the original game. Artistic reality is seen as corresponding to social reality, and reasons for the metastasized nature of football are found on both levels. Based on the proposed analysis of Metastaze and a comparative analysis of descriptions of football in other books, plays and films in Croatia and abroad a hypothesis is put forward whereby art offers evidence as to the metastasized nature of football. A greater challenge still is to establish whether art might, at the same time, provide refuge to the metastasized football, revitalizing its aesthetic and ethical dimension. Given the scope of these claims, the arguments in the article are based on a wide array of texts and authors ranging from literary criticism, anthropology of games and sociology of sport to semiotics, cultural studies and aesthetics