Control of meiotic crossover interference by a proteolytic chaperone network.

Meiosis is a specialized eukaryotic division that produces genetically diverse gametes for sexual reproduction. During meiosis, homologous chromosomes pair and undergo reciprocal exchanges, called crossovers, which recombine genetic variation. Meiotic crossovers are stringently controlled with at least one obligate exchange forming per chromosome pair, while closely spaced crossovers are inhibited by interference. In Arabidopsis, crossover positions can be explained by a diffusion-mediated coarsening model, in which large, approximately evenly spaced foci of the pro-crossover E3 ligase HEI10 grow at the expense of smaller, closely spaced clusters. However, the mechanisms that control HEI10 dynamics during meiosis remain unclear. Here, through a forward genetic screen in Arabidopsis, we identified high crossover rate3 (hcr3), a dominant-negative mutant that reduces crossover interference and increases crossovers genome-wide. HCR3 encodes J3, a co-chaperone related to HSP40, which acts to target protein aggregates and biomolecular condensates to the disassembly chaperone HSP70, thereby promoting proteasomal degradation. Consistently, we show that a network of HCR3 and HSP70 chaperones facilitates proteolysis of HEI10, thereby regulating interference and the recombination landscape. These results reveal a new role for the HSP40/J3-HSP70 chaperones in regulating chromosome-wide dynamics of recombination via control of HEI10 proteolysis.

Coarsening dynamics can explain meiotic crossover patterning in both the presence and absence of the synaptonemal complex.

The shuffling of genetic material facilitated by meiotic crossovers is a critical driver of genetic variation. Therefore, the number and positions of crossover events must be carefully controlled. In Arabidopsis, an obligate crossover and repression of nearby crossovers on each chromosome pair are abolished in mutants that lack the synaptonemal complex (SC), a conserved protein scaffold. We use mathematical modelling and quantitative super-resolution microscopy to explore and mechanistically explain meiotic crossover pattering in Arabidopsis lines with full, incomplete, or abolished synapsis. For zyp1 mutants, which lack an SC, we develop a coarsening model in which crossover precursors globally compete for a limited pool of the pro-crossover factor HEI10, with dynamic HEI10 exchange mediated through the nucleoplasm. We demonstrate that this model is capable of quantitatively reproducing and predicting zyp1 experimental crossover patterning and HEI10 foci intensity data. Additionally, we find that a model combining both SC- and nucleoplasm-mediated coarsening can explain crossover patterning in wild-type Arabidopsis and in pch2 mutants, which display partial synapsis. Together, our results reveal that regulation of crossover patterning in wild-type Arabidopsis and SC-defective mutants likely acts through the same underlying coarsening mechanism, differing only in the spatial compartments through which the pro-crossover factor diffuses.

Localization of stomatal lineage proteins reveals contrasting planar polarity patterns in Arabidopsis cotyledons.

Many plant cells exhibit polarity, revealed by asymmetric localization of specific proteins within each cell.1,2,3,4,5,6 Polarity is typically coordinated between cells across a tissue, raising the question of how coordination is achieved. One hypothesis is that mechanical stresses provide cues.7 This idea gains support from experiments in which cotyledons were mechanically stretched transversely to their midline.8 These previously published results showed that without applied tension, the stomatal lineage cell polarity marker, BREVIS RADIX-LIKE 2 (BRXL2), exhibited no significant excess in the transverse orientation. By contrast, 7 h after stretching, BRXL2 polarity distribution exhibited transverse excess, aligned with the stretch direction. These stretching experiments involved statistical comparisons between snapshots of stretched and unstretched cotyledons, with different specimens being imaged in each case.8 Here, we image the same cotyledon before and after stretching and find no evidence for reorientation of polarity. Instead, statistical analysis shows that cotyledons contain a pre-existing transverse excess in BRXL2 polarity orientation that is not significantly modified by applied tension. The transverse excess reflects BRLX2 being preferentially localized toward the medial side of the cell, nearer to the cotyledon midline, creating a weak medial bias. A second polarity marker, BREAKING OF ASYMMETRY IN THE STOMATAL LINEAGE (BASL), also exhibits weak medial bias in stomatal lineages, whereas ectopic expression of BASL in non-stomatal cells exhibits strong proximal bias, as previously observed in rosette leaves. This proximal bias is also unperturbed by applied tension. Our findings therefore show that cotyledons contain two near-orthogonal coordinated biases in planar polarity: mediolateral and proximodistal.

The Virtual Root : Mathematical Modeling of Auxin Transport in the Arabidopsis Root Tip Using the Open-Source Software SimuPlant.

Hormone signals like auxin play a critical role controlling plant growth and development. Determining the mechanisms that regulate auxin distribution in cells and tissues is a vital step in understanding this hormone's role during plant development. Recent mathematical models have enabled us to understand the essential role that auxin influx and efflux carriers play in auxin transport in the Arabidopsis root tip (Band et al., Plant Cell 26(3):862-875, 2014; Grieneisen et al., Nature 449(7165):1008-1013, 2007; van den Berg et al., Development 143(18):3350-3362, 2016). In this chapter, we describe SimuPlant: The Virtual Root (SimuPlant, University of Nottingham. https://www.simuplant.org/ . Accessed 20 Sept 2019); an open source software suite, built using the OpenAlea (Pradal et al., Funct Plant Biol 35(10):751-760, 2008) framework, that is designed to simulate vertex-based models in real plant tissue geometries. We provide guidance on how to install SimuPlant, run 2D auxin transport models in the Arabidopsis root tip, manipulate parameters, and visualize model outputs.SimuPlant features a graphical user interface (GUI) designed to allow users with no programming experience to simulate auxin dynamics within the Arabidopsis root tip. Within the user interface, users of SimuPlant can select from a range of model assumptions and can choose to manipulate model and simulation parameter values. Users can then investigate how their choices affect the predicted distribution of auxin in the Arabidopsis root tip. The results of the model simulations are shown visually within the root geometry and can be exported and saved as PNG image files.

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.

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.

Root hydrotropism is controlled via a cortex-specific growth mechanism.

Plants can acclimate by using tropisms to link the direction of growth to environmental conditions. Hydrotropism allows roots to forage for water, a process known to depend on abscisic acid (ABA) but whose molecular and cellular basis remains unclear. Here we show that hydrotropism still occurs in roots after laser ablation removed the meristem and root cap. Additionally, targeted expression studies reveal that hydrotropism depends on the ABA signalling kinase SnRK2.2 and the hydrotropism-specific MIZ1, both acting specifically in elongation zone cortical cells. Conversely, hydrotropism, but not gravitropism, is inhibited by preventing differential cell-length increases in the cortex, but not in other cell types. We conclude that root tropic responses to gravity and water are driven by distinct tissue-based mechanisms. In addition, unlike its role in root gravitropism, the elongation zone performs a dual function during a hydrotropic response, both sensing a water potential gradient and subsequently undergoing differential growth.

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.

Multiscale models in the biomechanics of plant growth.

Plant growth occurs through the coordinated expansion of tightly adherent cells, driven by regulated softening of cell walls. It is an intrinsically multiscale process, with the integrated properties of multiple cell walls shaping the whole tissue. Multiscale models encode physical relationships to bring new understanding to plant physiology and development.

Mechanical modelling quantifies the functional importance of outer tissue layers during root elongation and bending.

Root elongation and bending require the coordinated expansion of multiple cells of different types. These processes are regulated by the action of hormones that can target distinct cell layers. We use a mathematical model to characterise the influence of the biomechanical properties of individual cell walls on the properties of the whole tissue. Taking a simple constitutive model at the cell scale which characterises cell walls via yield and extensibility parameters, we derive the analogous tissue-level model to describe elongation and bending. To accurately parameterise the model, we take detailed measurements of cell turgor, cell geometries and wall thicknesses. The model demonstrates how cell properties and shapes contribute to tissue-level extensibility and yield. Exploiting the highly organised structure of the elongation zone (EZ) of the Arabidopsis root, we quantify the contributions of different cell layers, using the measured parameters. We show how distributions of material and geometric properties across the root cross-section contribute to the generation of curvature, and relate the angle of a gravitropic bend to the magnitude and duration of asymmetric wall softening. We quantify the geometric factors which lead to the predominant contribution of the outer cell files in driving root elongation and bending.

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.

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.

Buckling as an origin of ordered cuticular patterns in flower petals.

The optical properties of plant surfaces are strongly determined by the shape of epidermal cells and by the patterning of the cuticle on top of the cells. Combinations of particular cell shapes with particular nanoscale structures can generate a wide range of optical effects. Perhaps most notably, the development of ordered ridges of cuticle on top of flat petal cells can produce diffraction-grating-like structures. A diffraction grating is one of a number of mechanisms known to produce 'structural colours', which are more intense and pure than chemical colours and can appear iridescent. We explore the concept that mechanical buckling of the cuticle on the petal epidermis might explain the formation of cuticular ridges, using a theoretical model that accounts for the development of compressive stresses in the cuticle arising from competition between anisotropic expansion of epidermal cells and isotropic cuticle production. Model predictions rationalize cuticle patterns, including those with long-range order having the potential to generate iridescence, for a range of different flower species.

Multiscale systems analysis of root growth and development: modeling beyond the network and cellular scales.

Over recent decades, we have gained detailed knowledge of many processes involved in root growth and development. However, with this knowledge come increasing complexity and an increasing need for mechanistic modeling to understand how those individual processes interact. One major challenge is in relating genotypes to phenotypes, requiring us to move beyond the network and cellular scales, to use multiscale modeling to predict emergent dynamics at the tissue and organ levels. In this review, we highlight recent developments in multiscale modeling, illustrating how these are generating new mechanistic insights into the regulation of root growth and development. We consider how these models are motivating new biological data analysis and explore directions for future research. This modeling progress will be crucial as we move from a qualitative to an increasingly quantitative understanding of root biology, generating predictive tools that accelerate the development of improved crop varieties.

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

BACKGROUND: 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). RESULTS: 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. CONCLUSIONS: PCFs and QHs together provide an effective means of characterising emergent patterns of differentiation in planar multicellular aggregates.