Simulation of Organ Patterning on the Floral Meristem Using a Polar Auxin Transport Model

An intriguing phenomenon in plant development is the timing and positioning of lateral organ initiation, which is a fundamental aspect of plant architecture. Although important progress has been made in elucidating the role of auxin transport in the vegetative shoot to explain the phyllotaxis of leaf formation in a spiral fashion, a model study of the role of auxin transport in whorled organ patterning in the expanding floral meristem is not available yet. We present an initial simulation approach to study the mechanisms that are expected to play an important role. Starting point is a confocal imaging study of Arabidopsis floral meristems at consecutive time points during flower development. These images reveal auxin accumulation patterns at the positions of the organs, which strongly suggests that the role of auxin in the floral meristem is similar to the role it plays in the shoot apical meristem. This is the basis for a simulation study of auxin transport through a growing floral meristem, which may answer the question whether auxin transport can in itself be responsible for the typical whorled floral pattern. We combined a cellular growth model for the meristem with a polar auxin transport model. The model predicts that sepals are initiated by auxin maxima arising early during meristem outgrowth. These form a pre-pattern relative to which a series of smaller auxin maxima are positioned, which partially overlap with the anlagen of petals, stamens, and carpels. We adjusted the model parameters corresponding to properties of floral mutants and found that the model predictions agree with the observed mutant patterns. The predicted timing of the primordia outgrowth and the timing and positioning of the sepal primordia show remarkable similarities with a developing flower in nature

A modular analysis of the Auxin signalling network

Auxin is essential for plant development from embryogenesis onwards. Auxin acts in large part through regulation of transcription. The proteins acting in the signalling pathway regulating transcription downstream of auxin have been identified as well as the interactions between these proteins, thus identifying the topology of this network implicating 54 Auxin Response Factor (ARF) and Aux/IAA (IAA) transcriptional regulators. Here, we study the auxin signalling pathway by means of mathematical modeling at the single cell level. We proceed analytically, by considering the role played by five functional modules into which the auxin pathway can be decomposed: the sequestration of ARF by IAA, the transcriptional repression by IAA, the dimer formation amongst ARFs and IAAs, the feedback loop on IAA and the auxin induced degradation of IAA proteins. Focusing on these modules allows assessing their function within the dynamics of auxin signalling. One key outcome of this analysis is that there are both specific and overlapping functions between all the major modules of the signaling pathway. This suggests a combinatorial function of the modules in optimizing the speed and amplitude of auxin-induced transcription. Our work allows identifying potential functions for homo- and hetero-dimerization of transcriptional regulators, with ARF:IAA, IAA:IAA and ARF:ARF dimerization respectively controlling the amplitude, speed and sensitivity of the response and a synergistic effect of the interaction of IAA with transcriptional repressors on these characteristics of the signaling pathway. Finally, we also suggest experiments which might allow disentangling the structure of the auxin signaling pathway and analysing further its function in plants

Multiscale modelling of auxin transport in the plant-root elongation zone

In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics

Adhesion Failures Determine the Pattern of Choroidal Neovascularization in the Eye: A Computer Simulation Study

Choroidal neovascularization (CNV) of the macular area of the retina is the major cause of severe vision loss in adults. In CNV, after choriocapillaries initially penetrate Bruch's membrane (BrM), invading vessels may regress or expand (CNV initiation). Next, during Early and Late CNV, the expanding vasculature usually spreads in one of three distinct patterns: in a layer between BrM and the retinal pigment epithelium (sub-RPE or Type 1 CNV), in a layer between the RPE and the photoreceptors (sub-retinal or Type 2 CNV) or in both loci simultaneously (combined pattern or Type 3 CNV). While most studies hypothesize that CNV primarily results from growth-factor effects or holes in BrM, our three-dimensional simulations of multi-cell model of the normal and pathological maculae recapitulate the three growth patterns, under the hypothesis that CNV results from combinations of impairment of: 1) RPE-RPE epithelial junctional adhesion, 2) Adhesion of the RPE basement membrane complex to BrM (RPE-BrM adhesion), and 3) Adhesion of the RPE to the photoreceptor outer segments (RPE-POS adhesion). Our key findings are that when an endothelial tip cell penetrates BrM: 1) RPE with normal epithelial junctions, basal attachment to BrM and apical attachment to POS resists CNV. 2) Small holes in BrM do not, by themselves, initiate CNV. 3) RPE with normal epithelial junctions and normal apical RPE-POS adhesion, but weak adhesion to BrM (e.g. due to lipid accumulation in BrM) results in Early sub-RPE CNV. 4) Normal adhesion of RBaM to BrM, but reduced apical RPE-POS or epithelial RPE-RPE adhesion (e.g. due to inflammation) results in Early sub-retinal CNV. 5) Simultaneous reduction in RPE-RPE epithelial binding and RPE-BrM adhesion results in either sub-RPE or sub-retinal CNV which often progresses to combined pattern CNV. These findings suggest that defects in adhesion dominate CNV initiation and progression

Comparing individual-based approaches to modelling the self-organization of multicellular tissues.

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage

A cell-based computational model of early embryogenesis coupling mechanical behaviour and gene regulation

The study of multicellular development is grounded in two complementary domains: cell biomechanics, which examines how physical forces shape the embryo, and genetic regulation and molecular signalling, which concern how cells determine their states and behaviours. Integrating both sides into a unified framework is crucial to fully understand the self-organized dynamics of morphogenesis. Here we introduce MecaGen, an integrative modelling platform enabling the hypothesis-driven simulation of these dual processes via the coupling between mechanical and chemical variables. Our approach relies upon a minimal ‘cell behaviour ontology’ comprising mesenchymal and epithelial cells and their associated behaviours. MecaGen enables the specification and control of complex collective movements in 3D space through a biologically relevant gene regulatory network and parameter space exploration. Three case studies investigating pattern formation, epithelial differentiation and tissue tectonics in zebrafish early embryogenesis, the latter with quantitative comparison to live imaging data, demonstrate the validity and usefulness of our framework

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

A phenomenological model for the evolution of shape transition of cells is considered. These transitions are determined by the emission of growth-factors, as well as mechanical interaction if cells are subjected to hard impingement. The originality of this model necessitates a formal treatment of the mathematical model, as well as the presentation of elementary cases in order to illustrate the consistence of the model. We will also show some small-scale relevant applications.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc