Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling and experimental observations. In contrast to most prior work, models are not designed or tuned with the aim to produce a specific auxin pattern. Instead, we use well-established techniques from dynamical systems theory to uncover and classify ranges of auxin patterns as exhaustively as possible as parameters are varied. Previous work using these techniques has shown how a multitude of stable auxin patterns may coexist, each attainable from a specific ensemble of initial conditions. When a key parameter spans a range of values, these steady patterns form a geometric curve with successive folds, often nicknamed a snaking diagram. As we introduce growth and cell division into a one-dimensional model of auxin distribution, we observe new behaviour which can be explained in terms of this diagram. Cell growth changes the shape of the snaking diagram, and this corresponds in turn to deformations in the patterns of auxin distribution. As divisions occur this can lead to abrupt creation or annihilation of auxin peaks. We term this phenomenon 'snake-jumping'. Under rhythmic cell divisions, we show how this can lead to stable oscillations of auxin. We also show that this requires a high level of synchronisation between cell divisions. Using 18 hour time-lapse imaging of the auxin reporter DII:Venus in roots of Arabidopsis thaliana, we show auxin fluctuates greatly, both in terms of amplitude and periodicity, consistent with the snake-jumping events observed with non-synchronised cell divisions. Periodic signals downstream of the auxin signalling pathway have previously been recorded in plant roots. The present work shows that auxin alone is unlikely to play the role of a pacemaker in this context.

Systems approaches reveal that ABCB and PIN proteins mediate co-dependent auxin efflux.

Members of the B family of membrane-bound ATP-binding cassette (ABC) transporters represent key components of the auxin efflux machinery in plants. Over the last two decades, experimental studies have shown that modifying ATP-binding cassette sub-family B (ABCB) expression affects auxin distribution and plant phenotypes. However, precisely how ABCB proteins transport auxin in conjunction with the more widely studied family of PIN-formed (PIN) auxin efflux transporters is unclear, and studies using heterologous systems have produced conflicting results. Here, we integrate ABCB localization data into a multicellular model of auxin transport in the Arabidopsis thaliana root tip to predict how ABCB-mediated auxin transport impacts organ-scale auxin distribution. We use our model to test five potential ABCB-PIN regulatory interactions, simulating the auxin dynamics for each interaction and quantitatively comparing the predictions with experimental images of the DII-VENUS auxin reporter in wild-type and abcb single and double loss-of-function mutants. Only specific ABCB-PIN regulatory interactions result in predictions that recreate the experimentally observed DII-VENUS distributions and long-distance auxin transport. Our results suggest that ABCBs enable auxin efflux independently of PINs; however, PIN-mediated auxin efflux is predominantly through a co-dependent efflux where co-localized with ABCBs.

Dual expression and anatomy lines allow simultaneous visualization of gene expression and anatomy.

Studying the developmental genetics of plant organs requires following gene expression in specific tissues. To facilitate this, we have developed dual expression anatomy lines, which incorporate a red plasma membrane marker alongside a fluorescent reporter for a gene of interest in the same vector. Here, we adapted the GreenGate cloning vectors to create two destination vectors showing strong marking of cell membranes in either the whole root or specifically in the lateral roots. This system can also be used in both embryos and whole seedlings. As proof of concept, we follow both gene expression and anatomy in Arabidopsis (Arabidopsis thaliana) during lateral root organogenesis for a period of over 24 h. Coupled with the development of a flow cell and perfusion system, we follow changes in activity of the DII auxin sensor following application of auxin.

Auxin fluxes through plasmodesmata modify root-tip auxin distribution.

Auxin is a key signal regulating plant growth and development. It is well established that auxin dynamics depend on the spatial distribution of efflux and influx carriers on the cell membranes. In this study, we employ a systems approach to characterise an alternative symplastic pathway for auxin mobilisation via plasmodesmata, which function as intercellular pores linking the cytoplasm of adjacent cells. To investigate the role of plasmodesmata in auxin patterning, we developed a multicellular model of the Arabidopsis root tip. We tested the model predictions using the DII-VENUS auxin response reporter, comparing the predicted and observed DII-VENUS distributions using genetic and chemical perturbations designed to affect both carrier-mediated and plasmodesmatal auxin fluxes. The model revealed that carrier-mediated transport alone cannot explain the experimentally determined auxin distribution in the root tip. In contrast, a composite model that incorporates both carrier-mediated and plasmodesmatal auxin fluxes re-capitulates the root-tip auxin distribution. We found that auxin fluxes through plasmodesmata enable auxin reflux and increase total root-tip auxin. We conclude that auxin fluxes through plasmodesmata modify the auxin distribution created by efflux and influx carriers.

Cellular Patterning of Arabidopsis Roots Under Low Phosphate Conditions.

Phosphorus is a crucial macronutrient for plants playing a critical role in many cellular signaling and energy cycling processes. In light of this, phosphorus acquisition efficiency is an important target trait for crop improvement, but it also provides an ecological adaptation for growth of plants in low nutrient environments. Increased root hair density has been shown to improve phosphorus uptake and plant health in a number of species. In several plant families, including Brassicaceae, root hair bearing cells are positioned on the epidermis according to their position in relation to cortex cells, with hair cells positioned in the cleft between two underlying cortex cells. Thus the number of cortex cells determines the number of epidermal cells in the root hair position. Previous research has associated phosphorus-limiting conditions with an increase in the number of cortex cell files in Arabidopsis thaliana roots, but they have not investigated the spatial or temporal domains in which these extra divisions occur or explored the consequences this has had on root hair formation. In this study, we use 3D reconstructions of root meristems to demonstrate that the radial anticlinal cell divisions seen under low phosphate are exclusive to the cortex. When grown on media containing replete levels of phosphorous, A. thaliana plants almost invariably show eight cortex cells; however when grown in phosphate limited conditions, seedlings develop up to 16 cortex cells (with 10-14 being the most typical). This results in a significant increase in the number of epidermal cells at hair forming positions. These radial anticlinal divisions occur within the initial cells and can be seen within 24 h of transfer of plants to low phosphorous conditions. We show that these changes in the underlying cortical cells feed into epidermal patterning by altering the regular spacing of root hairs.