During plant growth, dividing cells in meristems must coordinate transitions from division to expansion and differentiation, thus generating three distinct developmental zones: the meristem, elongation zone and differentiation zone 1 . Simultaneously, plants display tropisms, rapid adjustments of their direction of growth to adapt to environmental conditions. It is unclear how stable zonation is maintained during transient adjustments in growth direction. In Arabidopsis roots, many aspects of zonation are controlled by the phytohormone auxin and auxin-induced PLETHORA (PLT) transcription factors, both of which display a graded distribution with a maximum near the root tip 2-12 . In addition, auxin is also pivotal for tropic responses 13,14 . Here, using an iterative experimental and computational approach, we show how an interplay between auxin and PLTs controls zonation and gravitropism. We find that the PLT gradient is not a direct, proportionate readout of the auxin gradient. Rather, prolonged high auxin levels generate a narrow PLT transcription domain from which a gradient of PLT protein is subsequently generated through slow growth dilution and cell-to-cell movement. The resulting PLT levels define the location of developmental zones. In addition to slowly promoting PLT transcription, auxin also rapidly influences division, expansion and differentiation rates. We demonstrate how this specific regulatory design in which auxin cooperates with PLTs through different mechanisms and on Reprints and permissions information is available at www.nature.com/reprints.

Spatial patterns of the hormone auxin are important drivers of plant development. The observed feedback between the active, directed transport that generates auxin patterns and the auxin distribution that influences transport orientation has rendered this a popular subject for modelling studies. Here we propose a new mathematical framework for the analysis of polar auxin transport and present a detailed mathematical analysis of published models. We show that most models allow for selforganised patterning for similar biological assumptions, and find that the pattern generated is typically unidirectional, unless additional assumptions or mechanisms are incorporated. Our analysis thus suggests that current models cannot explain the bidirectional fountain-type patterns found in plant meristems in a fully self-organised manner, and we discuss future research directions to address the gaps in our understanding of auxin transport mechanisms.

Highlights d Upon germination, cell divisions generate a PLT drop that forms the transition zone d A PLTs-ARR12 mutual antagonism restricts early root meristem expansion d ARR1 repression of cell division via KRP2 is key for meristem size stabilization

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Yield of harvestable plant organs depends on photosynthetic assimilate production in source leaves, long‐distance sucrose transport and sink‐strength. While photosynthesis optimization has received considerable interest for optimizing plant yield, the potential for improving long‐distance sucrose transport has received far less attention. Interestingly, a recent potato study demonstrates that the tuberigen StSP6A binds to and reduces activity of the StSWEET11 sucrose exporter. While the study suggested that reducing phloem sucrose efflux may enhance tuber yield, the precise mechanism and physiological relevance of this effect remained an open question. Here, we develop the first mechanistic model for sucrose transport, parameterized for potato plants. The model incorporates SWEET‐mediated sucrose export, SUT‐mediated sucrose retrieval from the apoplast and StSP6A‐StSWEET11 interactions. Using this model, we were able to substantiate the physiological relevance of the StSP6A‐StSWEET11 interaction in the long‐distance phloem for potato tuber yield, as well as to show the non‐linear nature of this effect.

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Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

Priming is the process through which periodic elevations in auxin signalling prepattern future sites for lateral root formation, called prebranch sites. Thusfar is has remained a matter of debate to what extent elevations in auxin concentration and/or auxin signalling are critical for priming and prebranch site formation. Recently, we discovered a reflux-and-growth mechanism for priming generating periodic elevations in auxin concentration that subsequently dissipate. Here we reverse engineer a mechanism for prebranch site formation that translates these transient elevations into a persistent increase in auxin signalling, resolving the prior debate into a two-step process of auxin concentration mediated initial signal and auxin signalling capacity mediated memorization. A critical aspect of the prebranch site formation mechanism is its activation in response to time integrated rather than instantaneous auxin signalling. The proposed mechanism is demonstrated to be consistent with prebranch site auxin signalling dynamics, lateral inhibition and symmetry breaking mechanisms and perturbations in auxin homeostasis.