A multi-layered mechanistic modelling approach to understand how effector genes extend beyond phytoplasma to modulate plant hosts, insect vectors and the environment.

Members of the Candidatus genus Phytoplasma are small bacterial pathogens that hijack their plant hosts via the secretion of virulence proteins (effectors) leading to a fascinating array of plant phenotypes, such as witch's brooms (stem proliferations) and phyllody (retrograde development of flowers into vegetative tissues). Phytoplasma depend on insect vectors for transmission, and interestingly, these insect vectors were found to be (in)directly attracted to plants with these phenotypes. Therefore, phytoplasma effectors appear to reprogram plant development and defence to lure insect vectors, similarly to social engineering malware, which employs tricks to lure people to infected computers and webpages. A multi-layered mechanistic modelling approach will enable a better understanding of how phytoplasma effector-mediated modulations of plant host development and insect vector behaviour contribute to phytoplasma spread, and ultimately to predict the long reach of phytoplasma effector genes.

Rapid transporter regulation prevents substrate flow traffic jams in boron transport.

Nutrient uptake by roots often involves substrate-dependent regulated nutrient transporters. For robust uptake, the system requires a regulatory circuit within cells and a collective, coordinated behaviour across the tissue. A paradigm for such systems is boron uptake, known for its directional transport and homeostasis, as boron is essential for plant growth but toxic at high concentrations. In Arabidopsis thaliana, boron uptake occurs via diffusion facilitators (NIPs) and exporters (BORs), each presenting distinct polarity. Intriguingly, although boron soil concentrations are homogenous and stable, both transporters manifest strikingly swift boron-dependent regulation. Through mathematical modelling, we demonstrate that slower regulation of these transporters leads to physiologically detrimental oscillatory behaviour. Cells become periodically exposed to potentially cytotoxic boron levels, and nutrient throughput to the xylem becomes hampered. We conclude that, while maintaining homeostasis, swift transporter regulation within a polarised tissue context is critical to prevent intrinsic traffic-jam like behaviour of nutrient flow.

Formation of polarity convergences underlying shoot outgrowths.

The development of outgrowths from plant shoots depends on formation of epidermal sites of cell polarity convergence with high intracellular auxin at their centre. A parsimonious model for generation of convergence sites is that cell polarity for the auxin transporter PIN1 orients up auxin gradients, as this spontaneously generates convergent alignments. Here we test predictions of this and other models for the patterns of auxin biosynthesis and import. Live imaging of outgrowths from kanadi1 kanadi2 Arabidopsis mutant leaves shows that they arise by formation of PIN1 convergence sites within a proximodistal polarity field. PIN1 polarities are oriented away from regions of high auxin biosynthesis enzyme expression, and towards regions of high auxin importer expression. Both expression patterns are required for normal outgrowth emergence, and may form part of a common module underlying shoot outgrowths. These findings are more consistent with models that spontaneously generate tandem rather than convergent alignments.

The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics.

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.