J. López-bucio, A. Cruz-ramírez, and L. Herrera-estrella, The role of nutrient availability in 1235 regulating root architecture, Curr. Opin. Plant Biol, vol.6, pp.280-287, 2003.

P. Marhava, Re-activation of Stem Cell Pathways for Pattern Restoration in Plant Wound 1237

, Healing. Cell, vol.177, pp.957-969, 2019.

M. Fendrych, J. Leung, and J. Friml, AFB-Aux/IAA auxin perception mediates rapid cell wall 1239 acidification and growth of Arabidopsis hypocotyls, 2016.

H. Marschner, Mineral nutrition of higher plants, 2008.

N. Von-wirén, S. Gazzarrini, and W. B. Frommer, Regulation of mineral nitrogen uptake in plants

, Plant Soil, vol.196, pp.191-199, 1997.

Z. Jia, N. Wirén, and . Von, Signaling pathways underlying nitrogen-dependent changes in root 1244 system architecture: from model to crop species, J. Exp. Bot, 2020.

S. Waidmann, E. Sarkel, and J. Kleine-vehn, Same same, but different: growth responses of 1246 primary and lateral roots, J. Exp. Bot, 2020.

B. D. Gruber, R. F. Giehl, S. Friedel, N. Wirén, and . Von, Plasticity of the Arabidopsis Root 1248 System under Nutrient Deficiencies, Plant Physiol, vol.163, pp.161-179, 2013.

B. G. Forde, Nitrogen signalling pathways shaping root system architecture: an update

, Opin. Plant Biol, vol.21, pp.30-36, 2014.

, Root Nutrient Foraging, Plant Physiol, vol.166, pp.509-517, 2014.

T. Remans, The Arabidopsis NRT1.1 transporter participates in the signaling pathway 1253 triggering root colonization of nitrate-rich patches, Proc. Natl. Acad. Sci, vol.103, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00124948

J. E. Lima, S. Kojima, H. Takahashi, and N. Von-wirén, Ammonium triggers lateral root branching 1256 in Arabidopsis in an AMMONIUM TRANSPORTER1;3-dependent manner, Plant Cell, vol.22, p.3633, 2010.

I. Fredes, S. Moreno, F. P. Díaz, and R. A. Gutiérrez, Nitrate signaling and the control of 1259

, Arabidopsis growth and development, Curr. Opin. Plant Biol, vol.47, pp.112-118, 2019.

P. Guan, Dancing with Hormones: A Current Perspective of Nitrate Signaling and Regulation in 1261

, Arabidopsis. Front. Plant Sci, vol.8, p.1697, 2017.

D. Ristova, Combinatorial interaction network of transcriptomic and phenotypic responses 1263 to nitrogen and hormones in the Arabidopsis thaliana root, Sci. Signal, vol.9, p.13, 2016.

, Hormones and nitrate: a two-way connection, Plant Mol. Biol, vol.91, pp.599-606, 2016.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

F. Chen, Evaluation of the yield and nitrogen use efficiency of the dominant maize hybrids 1266 grown in North and Northeast China, Sci. China Life Sci, vol.56, pp.552-560, 2013.

Q. Tian, F. Chen, J. Liu, F. Zhang, and G. Mi, Inhibition of maize root growth by high nitrate supply 1268 is correlated with reduced IAA levels in roots, J. Plant Physiol, vol.165, pp.942-951, 2008.

J. M. Caba, M. L. Centeno, B. Fernández, P. M. Gresshoff, and F. Ligero, Inoculation and nitrate 1270 alter phytohormone levels in soybean roots: differences between a supernodulating mutant and 1271 the wild type, Planta, vol.211, pp.98-104, 2000.

V. Tamaki and H. Mercier, Cytokinins and auxin communicate nitrogen availability as long-1273 distance signal molecules in pineapple (Ananas comosus), J. Plant Physiol, vol.164, p.1274, 2007.

G. Krouk, Nitrate-regulated auxin transport by NRT1.1 defines a mechanism for nutrient 1276 sensing in plants, Dev. Cell, vol.18, pp.927-937, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00508268

W. Ma, Auxin biosynthetic gene TAR2 is involved in low nitrogen-mediated reprogramming 1278 of root architecture in Arabidopsis, Plant J. Cell Mol. Biol, vol.78, pp.70-79, 2014.

P. Walch-liu, L. Liu, T. Remans, M. Tester, and B. G. Forde, Evidence that L-glutamate can act 1280 as an exogenous signal to modulate root growth and branching in Arabidopsis thaliana

, Cell Physiol, vol.47, pp.1045-1057, 2006.

R. A. Gutiérrez, Qualitative network models and genome-wide expression data define 1283 carbon/nitrogen-responsive molecular machines in Arabidopsis, Genome Biol, vol.8, p.7, 2007.

M. L. Gifford, A. Dean, R. A. Gutierrez, G. M. Coruzzi, and K. D. Birnbaum, Cell-specific nitrogen 1285 responses mediate developmental plasticity, Proc. Natl. Acad. Sci. U. S. A, vol.105, pp.803-808, 2008.

E. A. Vidal, Nitrate-responsive miR393/AFB3 regulatory module controls root system 1287 architecture in Arabidopsis thaliana, Proc. Natl. Acad. Sci. U. S. A, vol.107, pp.4477-4482, 2010.

E. A. Vidal, T. C. Moyano, E. Riveras, O. Contreras-lópez, and R. A. Gutiérrez, Systems 1289 approaches map regulatory networks downstream of the auxin receptor AFB3 in the nitrate 1290 response of Arabidopsis thaliana roots, Proc. Natl. Acad. Sci. U. S. A, vol.110, pp.12840-12845, 2013.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

E. A. Vidal, Integrated RNA-seq and sRNA-seq analysis identifies novel nitrate-responsive 1292 genes in Arabidopsis thaliana roots, BMC Genomics, vol.14, p.701, 2013.

Y. F. Tsay, J. I. Schroeder, K. A. Feldmann, and N. M. Crawford, The herbicide sensitivity gene 1294 CHL1 of Arabidopsis encodes a nitrate-inducible nitrate transporter, Cell, vol.72, pp.705-713, 1993.

E. Mounier, M. Pervent, K. Ljung, A. Gojon, and P. Nacry, Auxin-mediated nitrate signalling by 1296

, the adaptive response of Arabidopsis root architecture to the spatial 1297 heterogeneity of nitrate availability, Plant Cell Environ, vol.37, pp.162-174, 2014.

M. L. Gifford, Plasticity Regulators Modulate Specific Root Traits in Discrete Nitrogen 1299

, Environments. PLoS Genet, vol.9, 2013.

D. Wangenheim, Live tracking of moving samples in confocal microscopy for vertically 1301 grown roots, 2017.

N. Yazdanbakhsh, R. Sulpice, A. Graf, M. Stitt, and J. Fisahn, Circadian control of root elongation 1303 and C partitioning in Arabidopsis thaliana, Plant Cell Environ, vol.34, pp.877-894, 2011.

F. Baluska, S. Mancuso, D. Volkmann, and P. W. Barlow, Root apex transition zone: a signalling-1305 response nexus in the root, Trends Plant Sci, vol.15, pp.402-408, 2010.

X. Kong, G. Liu, J. Liu, and Z. Ding, The Root Transition Zone: A Hot Spot for Signal Crosstalk

, Trends Plant Sci, vol.23, pp.403-409, 2018.

I. Pavelescu, A Sizer model for cell differentiation in Arabidopsis thaliana root growth

, Syst. Biol, vol.14, 2018.

A. N. Stepanova, TAA1-mediated auxin biosynthesis is essential for hormone crosstalk and 1311 plant development, Cell, vol.133, pp.177-191, 2008.

R. Ioio, A genetic framework for the control of cell division and differentiation in the 1313 root meristem, Science, vol.322, pp.1380-1384, 2008.

I. Blilou, The PIN auxin efflux facilitator network controls growth and patterning in 1315

, Arabidopsis roots, Nature, vol.433, pp.39-44, 2005.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

C. Liao, Reporters for sensitive and quantitative measurement of auxin response, p.1317
URL : https://hal.archives-ouvertes.fr/hal-02638240

, Methods, vol.12, p.210, 2015.

M. H. Goldsmith, The Polar Transport of Auxin, Annu. Rev. Plant Physiol, vol.28, pp.439-478, 1977.

M. Adamowski and J. Friml, PIN-dependent auxin transport: action, regulation, and evolution

, Plant Cell, vol.27, pp.20-32, 2015.

C. Luschnig, R. A. Gaxiola, P. Grisafi, and G. R. Fink, EIR1, a root-specific protein involved in auxin 1322 transport, is required for gravitropism in Arabidopsis thaliana, Genes Dev, vol.12, pp.2175-2187, 1998.

A. Müller, AtPIN2 defines a locus of Arabidopsis for root gravitropism control, EMBO J, vol.17, pp.6903-6911, 1998.

T. Hanzawa, Cellular Auxin Homeostasis under High Temperature Is Regulated through a 1326

, SORTING NEXIN1-Dependent Endosomal Trafficking Pathway, vol.25, pp.3424-3433, 2013.

G. Brunoud, A novel sensor to map auxin response and distribution at high spatio-temporal 1329 resolution, Nature, 2012.

J. Kleine-vehn, Recycling, clustering, and endocytosis jointly maintain PIN auxin carrier 1331 polarity at the plasma membrane, Mol. Syst. Biol, vol.7, p.540, 2011.

J. Kleine-vehn and J. Friml, Polar Targeting and Endocytic Recycling in Auxin-Dependent Plant 1333

, Development. Annu. Rev. Cell Dev. Biol, 2008.

?. ?angowski, Cellular mechanisms for cargo delivery and polarity maintenance at different 1335 polar domains in plant cells, Cell Discov, vol.2, p.16018, 2016.

I. C. Barbosa, U. Z. Hammes, and C. Schwechheimer, Activation and Polarity Control of PIN-1337 FORMED Auxin Transporters by Phosphorylation, Trends Plant Sci, vol.23, pp.523-538, 2018.

L. Abas, Intracellular trafficking and proteolysis of the Arabidopsis auxin-efflux facilitator 1339 PIN2 are involved in root gravitropism, Nat. Cell Biol, vol.8, pp.249-256, 2006.

P. Baster, SCFTIR1/AFB-auxin signalling regulates PIN vacuolar trafficking and auxin fluxes 1341 during root gravitropism, EMBO J, vol.32, pp.260-274, 2013.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

H. Tian, T. Niu, Q. Yu, T. Quan, and Z. Ding, Auxin gradient is crucial for the maintenance of root 1343 distal stem cell identity in Arabidopsis, Plant Signal. Behav, vol.8, 2013.

S. V. Petersson, An Auxin Gradient and Maximum in the Arabidopsis Root Apex Shown by 1345

, High-Resolution Cell-Specific Analysis of IAA Distribution and Synthesis, Plant Cell, vol.21, pp.1659-1668, 2009.

S. M. Velasquez, E. Barbez, J. Kleine-vehn, and J. M. Estevez, Auxin and cellular elongation, 1348.

. Physiol, , 2016.

E. J. Chapman and M. Estelle, Cytokinin and auxin intersection in root meristems, Genome Biol, vol.1350, 2009.

X. Kong, G. Liu, J. Liu, and Z. Ding, The Root Transition Zone: A Hot Spot for Signal Crosstalk

, Trends in Plant Science, 2018.

R. B. Jackson and M. M. Caldwell, The Scale of Nutrient Heterogeneity Around Individual Plants 1354 and Its Quantification with Geostatistics, Ecology, vol.74, pp.612-614, 1993.

P. Nacry, E. Bouguyon, and A. Gojon, Nitrogen acquisition by roots: physiological and 1356 developmental mechanisms ensuring plant adaptation to a fluctuating resource, Plant Soil, vol.370, pp.1357-1358, 2013.

D. Mambro and R. , Auxin minimum triggers the developmental switch from cell division to cell 1359 differentiation in the Arabidopsis root, Proc. Natl. Acad. Sci. U. S. A, vol.114, pp.7641-7649, 2017.

E. Barbez, K. Dünser, A. Gaidora, T. Lendl, and W. Busch, Auxin steers root cell expansion via, p.1361

, apoplastic pH regulation in Arabidopsis thaliana, Proc. Natl. Acad. Sci, vol.114, pp.4884-4893, 2017.

, PNAS Plus: Auxin steers root cell expansion via apoplastic pH regulation in Arabidopsis thaliana, vol.62

S. Su, N. M. Gibbs, A. L. Jancewicz, and P. Masson, , p.1365

. Gravitropism, Curr. Biol. CB, vol.27, pp.964-972, 2017.

M. Zwiewka, V. Bilanovi?ová, Y. W. Seifu, and T. Nodzy?ski, The Nuts and Bolts of PIN Auxin Efflux 1367

, Carriers. Front. Plant Sci, vol.10, 2019.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

H. Zhang, Quantitative phosphoproteomics after auxin-stimulated lateral root induction 1369 identifies an SNX1 protein phosphorylation site required for growth, Mol. Cell. Proteomics MCP, vol.1370, pp.1158-1169, 2013.

S. Kumar, G. Stecher, M. Li, C. Knyaz, K. Tamura et al., Molecular Evolutionary Genetics 1372 Analysis across Computing Platforms, Mol. Biol. Evol, vol.35, pp.1547-1549, 2018.

N. Geldner, Rapid, combinatorial analysis of membrane compartments in intact plants with 1374 a multicolor marker set, Plant J. Cell Mol. Biol, vol.59, pp.169-178, 2009.

A. Vieten, Functional redundancy of PIN proteins is accompanied by auxin-dependent 1376 cross-regulation of PIN expression, Dev. Camb. Engl, vol.132, pp.4521-4531, 2005.

J. Jásik, PIN2 Turnover in Arabidopsis Root Epidermal Cells Explored by the 1378

, Photoconvertible Protein Dendra2, PLOS ONE, vol.8, p.61403, 2013.

G. Brunoud, A novel sensor to map auxin response and distribution at high spatio-temporal 1380 resolution, Nature, vol.482, pp.103-106, 2012.

Y. Salanenka, Gibberellin DELLA signaling targets the retromer complex to redirect protein 1382 trafficking to the plasma membrane, Proc. Natl. Acad. Sci. U. S. A, vol.115, pp.3716-3721, 2018.

T. Ulmasov, J. Murfett, G. Hagen, and T. J. Guilfoyle, Aux/IAA proteins repress expression of 1384 reporter genes containing natural and highly active synthetic auxin response elements, Cell, vol.9, pp.1963-1971, 1385.

E. Marin, Arabidopsis TAS3 tasiRNAs, and Their AUXIN RESPONSE FACTOR Targets 1387

, Define an Autoregulatory Network Quantitatively Regulating Lateral Root Growth, Plant Cell, vol.22, pp.1104-1117, 2010.

A. Colón-carmona, R. You, T. Haimovitch-gal, and P. Doerner, Technical advance: spatio-1390 temporal analysis of mitotic activity with a labile cyclin-GUS fusion protein, Plant J. Cell Mol. Biol, vol.1391, issue.20, pp.503-508, 1999.

M. Glanc, M. Fendrych, and J. Friml, Mechanistic framework for cell-intrinsic re-establishment of 1393 PIN2 polarity after cell division, Nat. Plants, vol.4, pp.1082-1088, 2018.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

T. Pasternak, Protocol: an improved and universal procedure for whole-mount 1395 immunolocalization in plants, Plant Methods, vol.11, p.50, 2015.

A. Johnson and G. Vert, Single Event Resolution of Plant Plasma Membrane Protein Endocytosis 1397 by TIRF Microscopy, Front. Plant Sci, vol.8, p.612, 2017.

S. Hille, M. Akhmanova, M. Glanc, A. Johnson, and . Friml, J. Relative Contribution, p.1399

, Containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: 1400 Theoretical Estimation, Int. J. Mol. Sci, vol.19, 2018.

J. Schindelin, Fiji: an open-source platform for biological-image analysis, Nat. Methods, vol.9, pp.1402-676, 2012.
URL : https://hal.archives-ouvertes.fr/pasteur-02616466

J. Tinevez, TrackMate: An open and extensible platform for single-particle tracking
URL : https://hal.archives-ouvertes.fr/pasteur-01799353

, Methods, vol.115, pp.80-90, 2017.

D. R. Lewis and G. K. Muday, Measurement of auxin transport in Arabidopsis thaliana, Nat. Protoc, vol.4, pp.437-451, 1406.

S. Arvidsson, M. Kwasniewski, D. M. Riaño-pachón, and B. Mueller-roeber, QuantPrime -a 1408 flexible tool for reliable high-throughput primer design for quantitative PCR, BMC Bioinformatics, vol.9, p.465, 1409.

M. Kuhn, caret: Classification and Regression Training, 2020.

M. L. Delignette-muller and C. Dutang, fitdistrplus: An R Package for Fitting Distributions, J. Stat, vol.84
URL : https://hal.archives-ouvertes.fr/hal-02044954

. Softw, , vol.64, pp.1-34, 2015.

H. D. Rosario-martinez, J. Fox, . &-r-core, and . Team, , 2015.

R. Lenth, H. Singmann, J. Love, P. Buerkner, and M. Herve,

, Means, aka Least-Squares Means, 2020.

T. Hothorn and A. Zeileis, partykit: A Modular Toolkit for Recursive Partytioning in

, Learn. Res, vol.16, pp.3905-3909, 2015.

, International license (which was not certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint this version posted, 2020.

, doi: bioRxiv preprint 88. Karwowski, R. & Prusinkiewicz, P. The L?system?based plant?modeling environment L?studio, p.1419

, The L-system-based plant-modeling environment L-studio 4.0, Proceedings of the 4th 1420 International Workshop on Functional?Structural Plant Models, 2004.

A. N. Stepanova, TAA1-Mediated Auxin Biosynthesis Is Essential for Hormone Crosstalk and 1422

, Plant Development. Cell, 2008.

W. Xuan, Cyclic programmed cell death stimulates hormone signaling and root 1424 development in Arabidopsis, Science, 2016.

J. Kleine-vehn, Differential degradation of PIN2 auxin efflux carrier by retromer-dependent 1426 vacuolar targeting, Proc. Natl. Acad. Sci. U. S. A, 2008.

, BMC Syst. Biol, 2010.

, Development Core Team, R. R: A Language and Environment for Statistical Computing. R 1430 Foundation for Statistical Computing, 2011.

, ggplot2: Elegant Graphics for Data Analysis, J. R. Stat. Soc. Ser. A Stat. Soc, p.1432, 2011.

B. , Stan: A probabilistic programming language, J. Stat. Softw, p.1434, 2017.

P. C. Bürkner, brms: An R package for Bayesian multilevel models using Stan, J. Stat. Softw, vol.1436, 2017.

A. Vehtari, A. Gelman, and J. Gabry, Practical Bayesian model evaluation using leave-one-out 1438 cross-validation and WAIC, Stat. Comput, 2017.

M. Sauer, Canalization of auxin flow by Aux/IAA-ARF-dependent feedback regulation of PIN 1440 polarity, Genes Dev, 2006.

K. Wabnik, Emergence of tissue polarization from synergy of intracellular and extracellular 1442 auxin signaling, Mol. Syst. Biol, 2010.