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ART I C L E S
Auxin regulates aquaporin function to facilitate lateralroot emergenceBenjamin Péret1,6,7, Guowei Li2,7, Jin Zhao3,7, Leah R. Band1,7, Ute Voß1, Olivier Postaire2, Doan-Trung Luu2,6,Olivier Da Ines3,6, Ilda Casimiro4, Mikaël Lucas1, Darren M. Wells1, Laure Lazzerini1, Philippe Nacry2,John R. King1, Oliver E. Jensen1,5, Anton R. Schäffner3,8, Christophe Maurel2,8 and Malcolm J. Bennett1,8
Aquaporins are membrane channels that facilitate water movement across cell membranes. In plants, aquaporins contribute towater relations. Here, we establish a new link between aquaporin-dependent tissue hydraulics and auxin-regulated rootdevelopment in Arabidopsis thaliana. We report that most aquaporin genes are repressed during lateral root formation and byexogenous auxin treatment. Auxin reduces root hydraulic conductivity both at the cell and whole-organ levels. The highlyexpressed aquaporin PIP2;1 is progressively excluded from the site of the auxin response maximum in lateral root primordia (LRP)whilst being maintained at their base and underlying vascular tissues. Modelling predicts that the positive and negativeperturbations of PIP2;1 expression alter water flow into LRP, thereby slowing lateral root emergence (LRE). Consistent with thismechanism, pip2;1 mutants and PIP2;1-overexpressing lines exhibit delayed LRE. We conclude that auxin promotes LRE byregulating the spatial and temporal distribution of aquaporin-dependent root tissue water transport.
The establishment of a mature root system is achieved throughrepetitive branching of the primary root. This process—called lateralroot formation—is initiated deep within the primary root from asmall subset of pericycle cells1. The growth of a new LRP coincideswith its emergence through the outer tissues2. The tight coordinationof lateral root formation and emergence is controlled by auxin3,4,which acts as a local inductive signal and favours cell separation inthe overlaying tissues5.The biomechanics of LRP growth and its potential link with auxin
are only partially understood5. In particular, the role of tissue watertransport during LRE has not been examined. In addition to theformation of new cells, plant tissues grow when cell walls relax andextend in response to the cell’s turgor pressure6. Sustained growthis primarily driven by solute uptake and maintenance of cell osmoticpotential, and requires sufficient water inflow to keep turgor above yieldthreshold7. The water needed for growth is typically supplied either
1Centre for Plant Integrative Biology, University of Nottingham, LE12 5RD, UK. 2Biochimie et Physiologie Moléculaire des Plantes, Institut de Biologie Intégrative desPlantes, Unité Mixte de Recherche 5004 Centre National de la Recherche Scientifique - Unité Mixte de Recherche 0386 Institut National de la RechercheAgronomique - MontpellierSupAgro - Université Montpellier 2, 2 Place Viala, F-34060 Montpellier Cedex 2, France. 3Institute of Biochemical Plant Pathology,Helmholtz Zentrum München, 85764 Neuherberg, Germany. 4Universidad de Extremadura, Facultad de Ciencias, Badajoz 06006, Spain. 5School of Mathematics,University of Manchester, M13 9PL, UK. 6Present addresses: Unité Mixte de Recherche 7265 Commissariat à l’Energie Atomique et aux Energies Alternatives, CentreNational de la Recherche Scientifique, Laboratoire de Biologie du Développement des Plantes, Université d’Aix-Marseille, 13108 Saint-Paul-lez-Durance, France (B.P.);Université des Sciences et Techniques de Hanoï, Institut de Recherche pour le Développement Laboratoire Mixte International Rice, Agronomical Genetics Institute,Ha Noi, Vietnam (D-T.L.); Génétique, Reproduction et Développement, Unité Mixte de Recherche 6293 Centre National de la Recherche Scientifique, Institut Nationalde la Santé et de la Recherche Médicale U1103, Université de Clermont-Ferrand, Aubière 63170, France (O.D.I.). 7These authors contributed equally to this work.8 Correspondence should be addressed to A.R.S., C.M. or M.J.B. (e-mail: [email protected] or [email protected][email protected])
Received 28 June 2011; accepted 8 August 2012; published online 16 September 2012; DOI: 10.1038/ncb2573
through the vasculature or the soil, before being transferred from cell tocell7. Therefore, the hydraulics of the whole plant or expanding tissuescan be critical8,9. Although water transport is known to affect growth ofleaves and primary roots8,10, its significance during LRE has not beenexplored. Yet, the LRP is symplastically isolated from the primary rootvasculature11, suggesting the need for efficient transcellular water fluxestowards the dividing and expanding cells.Aquaporins represent a large class of membrane channels present
in most living organisms12. In plants, aquaporins fall into sevensubfamilies13, which include plasma membrane intrinsic proteins(PIPs) and the tonoplast intrinsic proteins (TIPs). Their role inplant water relations has been studied and linked to a wide range offunctions14,15, including root water uptake and regulation of tissuehydraulic conductance under environmental stresses.To address the hydraulics of LRP growth and emergence, we studied
the role of aquaporins during early stages of lateral root development
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in Arabidopsis. We observed that most aquaporin genes are repressedduring lateral root formation in an auxin-dependent manner. As aresult, auxin represses root cell hydraulic conductivity. We describehow auxin-related changes in aquaporin distributionmay be importantfor organ emergence and provide converging mathematical and geneticevidence that aquaporins facilitate LRE. Our results demonstrate acomplex spatial and temporal interaction between auxin and aquaporinfunction, to support LRP growth.
RESULTSMost aquaporin genes are repressed by auxin during lateralroot formationWe initially considered whether aquaporin expression was alteredduring lateral root development. Lateral root initiation can be inducedby either mechanical16,17 or gravitropic18,19 stimuli. Following a 90◦
gravitropic stimulus, lateral roots develop in a highly synchronizedmanner at the outer edge of a bending root (Fig. 1a,b). Stage Iprimordia20 were first detected 18 h post-gravitropic induction (pgi);then primordia for each subsequent stage were detected approximatelyevery 3 h, until emergence at stage VIII,∼42 h pgi (Fig. 1b).We profiledaquaporin gene expression during lateral root development at hightemporal resolution (that is, at every stage of lateral root development)by micro-dissecting root bends every 6 h pgi.Profiling all 13 PIP and four highly expressed TIP isoforms by
real-time quantitative PCR with reverse transcription (RT–qPCR)revealed that 14 of the 17 genes were repressed during lateral rootdevelopment whereas PIP1;4 and PIP2;5 showed no or little induction(Fig. 1c,d). In contrast, PIP2;8 was induced up to tenfold 36 h pgi(Fig. 1d). Repression of most aquaporin genes occurred during earlylateral root formation (about 6 pgi), corresponding to when auxinaccumulates in pericycle founder cells21. However, four PIP genes,including the highly expressed isoforms PIP2;1 and PIP2;2 (refs 22,23),showed a delayed repression at>10 h pgi (Fig. 1c).Auxin is a key signal during early stages of lateral root development4.
Treatment of whole roots with the auxin indole-3-acetic acid (IAA)induced an overall inhibition of aquaporin gene expression (Fig. 1e).Whereas PIP1;3 and PIP2;4 showed up to twofold induction, the 15other PIP and TIP genes were repressed after IAA treatment (Fig. 1e,f).Only PIP2;5 and PIP2;8 recovered and even overshot their previouslevel. The similar expression profiles following gravity and auxintreatments suggest that auxin is responsible for the repression ofaquaporin gene expression during LRE. The temporal differencesobserved are likely to reflect the synchronous and asynchronous cellularresponses to endogenous and exogenous auxin sources, respectively.Nevertheless, our results reveal that auxin represses the expression ofmost aquaporin genes in the Arabidopsis root.
Auxin controls root aquaporin expression through ARF7Auxin response factor (ARF) proteins function as transcription factorscontrolling auxin-responsive genes24. ARF7 plays a key role duringlateral root formation and emergence5,25–28. Thus, we determinedthe effects of the arf7 loss-of-function on PIP and TIP expression.For PIP1;1, PIP1;4, PIP2;1, PIP2;2 and PIP2;7 showing sustainedauxin-dependent repression, a diminution of hormone effects wasobserved in the arf7 mutant (Fig. 2a and Supplementary Fig. S1).Expression of the remaining auxin-repressed PIP genes was similar
between the two backgrounds. Interestingly, auxin induction of PIP1;3and PIP2;5 was also ARF7 dependent.Next, we investigated whether transcriptional repression of
aquaporin genes by auxin resulted in reduced aquaporin proteincontent. Enzyme-linked immunosorbent assays (ELISAs) using anantibody specific for PIP2;1, PIP2;2 and PIP2;3 (ref. 29) revealeda strong diminution of these aquaporins in the root, to 79% and45%, at 18 and 42 h after auxin treatment, respectively (Fig. 2b). Incontrast, the arf7 mutation counteracted the auxin-induced reductionof these aquaporins (Fig. 2b). We conclude that auxin diminishes theaccumulation of these aquaporins by inhibiting their expression in anARF7-dependent manner.
Auxin controls root hydraulics and cell turgor through ARF7To examine the effects of auxin on aquaporin function, rootsof hydroponically grown plants were treated with IAA and theirwater-transport properties were characterized30. The root waterpermeability measured with a pressure chamber (hydrostatic hydraulicconductivity, Lpr-h; ref. 30) was not affected on short auxin treatments(Supplementary Fig. S2a). However, longer treatments triggereda large drop in Lpr-h (by up to 69%; Fig. 2c). When measuredunder conditions of free sap exudation30, root water permeability(osmotic hydraulic conductivity, Lpr-o) also showed a marked (−51%)inhibition after 42 h of auxin treatment (Supplementary Fig. S2b).Interestingly, Lpr-h of arf7 was insensitive to auxin inhibition (Fig. 2c).Yet, the arf7 Lpr-h was inhibited by 5mM H2O2 (SupplementaryFig. S2c). This aquaporin-blocking treatment31 demonstrates thatarf7 specifically altered aquaporin inhibition by auxin. Hence, ARF7plays a central role in auxin-dependent regulation of aquaporinsin the Arabidopsis root.To determine whether auxin-dependent regulation of aquaporin
function also applies to root cortical cells, the water relation parametersof these cells were deduced using a cell pressure probe30 (SupplementaryFig. S2d–f). A drop in cortical cell hydraulic conductivity (Lpcell) by48% was observed 18 h after IAA application (Fig. 2d). A longer (42 h)auxin treatment triggered a strong reduction of cortical cell turgor, inaccordance with older reports in cucumber hypocotyls32. In contrast,the cortical cell turgor remained constant in the arf7 mutant (Fig. 2e).Our data indicate a dual effect of auxin on cortical cell water relations,both of which are under the control of ARF7.
Auxin alters aquaporin spatial expression during lateralroot developmentOur expression and functional studies suggest that auxin-regulatedaquaporin gene expression may play an important role during lateralroot development. To investigate this further, we focused on PIP2;1,one of the most highly expressed aquaporins in roots22,23 that wasregulated by auxin in an ARF7-dependent manner. A loss-of-functionmutant (pip2;1-2; ref. 33) showed a decrease by 14% (p< 0.01) inLpr-o, indicating that PIP2;1 contributes significantly to root hydraulics(Fig. 2f and Supplementary Fig. S2g–j).Expression studies using transcriptional (proPIP2;1:GUS) and
translational (proPIP2;1:PIP2;1–mCHERRY ) fusions revealed thatPIP2;1 is highly expressed in the stele and less in outer root layers(Fig. 3a,d,e). PIP2;1 is expressed in stage I LRP (Fig. 3a,d), but fromstage III onwards PIP2;1 expression is excluded from LRP tips
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Figure 1 Transcriptional downregulation of aquaporins during lateral rootformation is mediated by auxin. (a,b) Lateral root synchronization wasobtained after a 90◦ gravitropic stimulus. (a) An LRP was induced at theroot bend created after the stimulus according to previous reports18. (b) LRPstages (from I to VIII according to previous descriptions20) were determinedevery 6 h post-stimulus and are represented as a percentage of the totalnumber of induced LRP. (c,d) The aquaporin gene expression level wasfollowed after gravistimulation of lateral root formation and dissection ofthe root bend. The relative level of expression is shown as a function oftime after gravistimulus. (c) Out of the 17 major aquaporin genes, 14genes are repressed during lateral root formation (PIP1;1, PIP1;2, PIP1;3,
PIP1;5, PIP2;1, PIP2;2, PIP2;3, PIP2;4, PIP2;6, PIP2;7, TIP1;1, TIP1;2,TIP2;2 and TIP2;3). (d) PIP1;4 and PIP2;5 show little induction duringlateral root formation whereas PIP2;8 is induced. (e,f) Auxin generallydownregulates aquaporin gene expression. The aquaporin gene expressionlevel was determined in the whole root after treatment with auxin (1 µMIAA) for the indicated time. (e) 14 aquaporin genes are repressed by auxin(PIP1;1, PIP1;2, PIP1;4, PIP1;5, PIP2;1, PIP2;2, PIP2;3, PIP2;4, PIP2;6,PIP2;7, TIP1;1, TIP1;2, TIP2;2 andTIP2;3). (f) PIP1;3 and PIP2;8 showlittle induction during lateral root formation whereas PIP2;5 is induced.For clarity, error bars are not included in the graph. Numerical values areprovided in Supplementary Table S1.
(Fig. 3b,d). This expression pattern was the exact opposite of theauxin response reporter DR5 (refs 5,21; Fig. 3c), consistent withour results that auxin represses PIP2;1 expression (Fig. 1e,f). Wealso observed that auxin treatment resulted in a strong reductionof the proPIP2;1:GUS signal (Fig. 3e,f), whereas treatment with theauxin response inhibitor p-chlorophenoxy-isobutyric acid (PCIB)resulted in a strong increase of the proPIP2;1:GUS signal andextended the spatial pattern into the outer layers (Fig. 3e,g). Ourobservations suggest that auxin accumulation causes a reduction inPIP2;1 expression in the LRP.
Expression of PIP2;8, which was upregulated at a later phase oflateral root development or after long exogenous auxin treatments(Fig. 1d,f) is largely restricted to the stele (Supplementary Fig. S3a–f).From stage IV onwards, PIP2;8 expression is induced at the LRPbase and underlying stele (Supplementary Fig. S3c–f) but is notaltered by exogenous IAA or PCIB treatment (Supplementary Fig.S3g–m). Thus, the auxin-induced enhancement of lateral root numberaccounts for the apparent auxin-dependent PIP2;8 upregulation(Supplementary Fig. S3g–i). Taken together, the PIP2;1 and PIP2;8expression data suggest that lateral root development involves a fine
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Figure 2 Auxin reduces aquaporin accumulation and hydraulicconductivity. (a) Auxin-dependent repression of one of the most highlyexpressed root isoforms, PIP2;1, is ARF7 dependent. (b) The proteincontent was determined by ELISA with a anti-PIP2 antibody thatrecognizes PIP2;1, PIP2;2 and PIP2;3. Roots were collected aftertreatment with 1 µM IAA for the indicated time on wild-type (Col-0)and arf7 mutant plants. Values are indicated as a percentage of theuntreated control from three independent plant cultures. (c) Lpr−h wasmeasured after 1 µM IAA treatment for 18 and 42h on Col-0 and thearf7 mutant. Values are indicated as a percentage of the untreated Col-0
(9<n<29). (d) Lpcell of Col-0 roots was measured after treatment for 18 hwith 1 µM IAA (n =22) and compared with the Lpcell of non-treated (NT)roots. (e) Cortical cell turgor was reduced on auxin treatment in Col-0 butnot in the arf7 mutant. (f) Lpr−o was determined in the wild type (Col-0),pip2;1-2 mutant and complemented pip2;1-2 mutant (pip2;1-2 PIP2;1).Data shown are mean value± s.e.m. with n = 21, 18 and 22 assessedfrom two independent plant cultures. The asterisks indicate a significantdifference from the corresponding control experiment by Student’s t -test(∗P <0.05; ∗∗P <0.01; ∗∗∗P <0.001). The letters indicate independentgroups according to one-way analysis of variance test (c).
spatial and temporal control of water exchanges between the stele,LRP and overlaying cells.
Modelling suggests that distinct spatial domains of aquaporinexpression are required during LRETo gain further understanding of the biomechanics of LRE and howthis process is affected by the presence of auxin and aquaporins, wedeveloped a mathematical model, which simulates water movementbetween stele, LRP and overlaying tissues. We considered thetissue scale and modelled the primordium and overlaying tissue asdistinct fluid-like compartments, lumping the effects of cell-wallextension and cell-to-cell reorganization into the properties of theboundaries (Fig. 4a).In the model (see Supplementary Information), we assumed that
emergence is driven by increasing osmotic pressure within dividingprimordium cells, drawing water into the LRP and resulting in abuild-up in turgor pressure. This pressure increases the stress in theLRP boundary, which eventually yields and extends, enabling the LRPto force through the overlaying tissues. The predicted emergence timedepends on the material properties of the LRP boundary (characterizedby extensibility and yield), initial tissue configuration (consideredto be a stage I primordium) and magnitude of water fluxes. Thepresence of aquaporins increases the boundary permeability whereasauxin accumulation leads to its decrease. Thus, the model enabledus to deduce how LRE is affected by the aquaporin distribution andits regulation by auxin.
The model can be described using differential equations withappropriate initial conditions and kinetic parameters estimated fromexperiments (see Supplementary Information). We adjusted the rateof increase of the primordium’s osmotic pressure so that LRE took28 h in wild-type plants (Fig. 4b). The model predicted the hydrostaticpressures in the primordium and overlaying tissue, and the directionof the water fluxes through each boundary (shown by arrows inFig. 4a). The model also revealed how the boundary permeabilities(k1 to k4) affect the emergence time (Fig. 4c,d); we obtained asignificant influence provided the yield stress of the primordium’sboundary is small, suggesting significant cell-wall remodelling asreported previously5,34. The model predicted that increasing k2 or k4inhibits emergence by facilitating water movement into overlayingtissues (Fig. 4c,d). In contrast, increasing k1 promotes emergenceby facilitating water inflow into the primordium whereas increasingk3 has an opposite effect on emergence by favouring water outflowtowards the stele (Fig. 4c,d).Owing to the direction of the water fluxes, the model predicted
that, by reducing aquaporin activity in the overlaying tissue (reducingpermeability k2), auxin promotes emergence. However, auxin alsoinhibits emergence by reducing aquaporin activity in the primordium(reducing permeability k1). To understand these opposing effects,we removed the influence of auxin from the model (making k1and k2 constant); with appropriate parameter values, we foundemergence to be delayed by 8.7 h, indicating that, indeed, auxin hasan accelerating effect on LRE. Thus, the model exemplifies how spatial
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Figure 3 PIP2;1 expression oppositely mirrors auxin accumulationduring lateral root formation. (a,b) PIP2;1 expression determined with atranscriptional proPIP2;1:GUS fusion. (c) Schematic drawing showing auxinaccumulation in the LRP and the overlaying tissue as reported by the auxinresponsive promoter DR5 (refs 5,21). (d) PIP2;1 expression determined witha translational proPIP2;1:PIP2;1–mCHERRY fusion (magenta). Cell shapesare indicated by the plasma-membrane-localized marker (green) encodedby proUBQ:YFP–NPSN12. (e–g) Auxin controls the PIP2;1 expressionpattern: untreated seven-day-old plants (e), plants treated with 1 µM IAAfor 48h (f) and plants treated with 10 µM PCIB for 24h (g). The lateralroot developmental stages are indicated by roman numbers as describedpreviously20. Scale bars, 50 µm.
and temporal control of auxin-dependent cell hydraulic conductivitycould be critical during LRE.We next used the model to investigate the importance of the cell-
specific and dynamic PIP2;1 distribution. We first simulated LRE withPIP2;1 expression being ectopic and independent of auxin. This PIP2;1distribution facilitated water fluxes into the overlaying tissue, resultingin this tissue providing a greater resistance to primordium expansionand therefore delaying LRE by >20 h (Fig. 4e). We then considered aloss-of-function mutant, pip2;1, by reducing permeabilities k1 and k3and removing auxin’s influence on k1. Reducing k1 (inhibiting LRE byreducing fluxes into the primordium) dominates over the influence ofreducing k3 (promoting LRE by reducing fluxes out of the primordium),so that LRE should again occur later than in the wild type (emergencetime: 42.5 h), owing to reduced water fluxes from the overlaying tissueto the primordium (Fig. 4e). Thus, the model shows how the spatialdistribution of PIP2;1 promotes LRE.
Phenotypes of PIP2;1-knockout and -overexpressing linesvalidate model predictionsTo test model predictions, we studied transgenic lines expressing PIP2;1under the control of the strong, constitutive double 35S promoter
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Figure 4 Mathematical model of LRE. (a) Two-dimensional tissue-scalemodel of LRE representing the cross-section of an LRP (dark grey) protrudinginto the outer tissue (light grey). The arrows show the predicted directionof the water fluxes between compartments; the magnitude of each waterflux depends on the boundary’s permeability (k1 to k4) and the difference inhydrostatic pressure and osmotic potential. (b) Simulation of the wild-typeLRP emerging through the overlaying tissue. (c) Diagram summarizing howauxin and aquaporins affect the permeabilities, and how these in turn affectthe predicted emergence time. (d) The influence of the permeability valueson the predicted emergence time. (e) The predicted and observed emergencetimes in the wild type, the pip2;1 mutant and the PIP2;1 overexpressor (seeSupplementary Information for choice of parameter values). Data shown aremean value±s.e.m., and n=20.
(d35S:PIP2;1). PIP2;1 overexpression led to a concomitant increase inPIP2 abundance and Lpr-h (+47−63%—Supplementary Fig. S4a,b).In addition, the transgenic lines showed a complete insensitivity ofLpr-h to auxin inhibition (Supplementary Fig. S4c). Next, wild-typeand transgenic roots were given a gravitropic stimulus and LRPwere counted and staged at 18 and 42 h pgi (Fig. 5a,b). Wild-type(Col-0) plants accumulated stage I and II LRP 18 h pgi and stageVII and VIII 42 h pgi, respectively (Fig. 5a). Lateral root initiationand first divisions were not affected in d35S:PIP2;1, but showedan accumulation of stage II–VIII LRP 42 h pgi (Fig. 5b). This resultindicates impaired LRE after aquaporin overexpression, as predictedin the mathematical model (Fig. 4e).In parallel, we analysed the effects of two independent loss-of-
function alleles in PIP2;1. Lateral root initiation and first divisionswere not affected in the pip2;1-1 and pip2;1-2mutants, but LRE wasdelayed at 42 h pgi (Fig. 5a,c,d). Mutant pip2;1-1 and pip2;1-2 plantstransformed with a 4.6-kilobase (kb) genomic fragment containing thefull PIP2;1 gene or a proPIP2;1:PIP2;1–mCHERRY construct exhibiteda wild-type LRE phenotype on lateral root induction (Fig. 5e,f and
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Figure 5 LRE is delayed in the pip2;1 mutant and the PIP2;1 overexpressor.(a–f) LRE phenotyping was achieved by synchronizing lateral root formationwith a gravistimulus. Primordia were grouped according to developmentalstages as defined previously20 18hpgi (black bars) and 42hpgi (greybars). (a) Wild-type (Col-0) plants showed accumulation of stage I andII primordium 18hpgi and accumulation of stage VII and VIII 42 h pgi.(b) The PIP2;1-overexpression line (d35S:PIP2;1) showed similar stages oflateral root formation at 18hpgi when compared with the wild type, therebysuggesting that early stages of lateral root development were not affected.However, most LRP accumulated at stage IV–VI at 42h pgi, indicating anemergence defect. (c,d) LRE is delayed in loss-of-function pip2;1 mutants.
The pip2;1-1 and pip2;1-2 mutants showed similar stages of lateral rootformation at 18hpgi when compared to the wild type, thereby suggestingthat early stages of lateral root development were not affected. However, onlya small amount of LRP reached stages VII and VIII at 42 h pgi in the mutant,indicating an emergence defect. (e–f) Complementation of both the pip2;1-1and pip2;1-2 mutant alleles with the PIP2;1 genomic sequence resulted inrestoration of the wild-type LRE phenotype. (g–i) Differential interferencecontrast imaging at 42hpgi showed abnormal LRP in the d35S:PIP2;1line and the pip2;1-1 mutant when compared with the dome-shapedwild-type primordium. Data shown are mean value±s.e.m. and n=20 (a–f).Scale bars, 25 µm.
Supplementary Fig. S5), demonstrating that the LRE defect was dueto disruption of the PIP2;1 gene. In addition, the LRP shape of bothPIP2;1-knockout and overexpressing lines was altered when comparedwith the wild type (Fig. 5g–i). Whereas wild-type LRP form a dome-shape,mutant LRPwere flattened and failed to protrude into overlayingtissues (Fig. 5h,i). Hence, loss of PIP2;1 function resulted in defectiveLRE, consistent with the predictionsmade by themodel (Fig. 4e).
DISCUSSIONThe hormone auxin represents a key regulator of lateral rootdevelopment3. Previous work has demonstrated that specialized effluxand influx transport proteins cause auxin to accumulate at the apexof new LRP and in overlaying cells, respectively5,21. Auxin triggerscell-wall remodelling gene expression in the overlaying cells34, therebyfacilitating primordium emergence through the outer tissues5. It was
proposed that LRE and concomitant physical modification of the outertissues must be tightly co-regulated. Here, we demonstrate that auxinalso regulates tissue hydraulics to promote LRE.Auxin regulates root tissue hydraulics by coordinating the repression
of aquaporin gene expression in the LRP and overlaying tissues. Appli-cation of exogenous auxin andmutant analysis revealed crucial featuresof hormone action, namely its marked effects on root hydraulics atboth the whole-root (Lpr-o and Lpr-h) and single-cell (Lpcell) levels;dependency on auxin response factor ARF7; and the similar phenotypicdefects in LRP shape and LRE kinetics in arf7 and pip2;1 mutants(Fig. 5 and Supplementary Fig. S6a–d). These features indicate thatregulation of the tissue distribution of aquaporins by auxin fine-tunesthe spatial and temporal control of root tissue hydraulics. Althoughthese hydraulic effects can lead to a dynamic decrease in overlayingcells’ turgor, as exemplified in the model, turgor measurements in
996 NATURE CELL BIOLOGY VOLUME 14 | NUMBER 10 | OCTOBER 2012
Figure 6 Diagram illustrating the regulation of LRE by PIP2;1. (a) OptimalLRE requires water transport into the overlaying tissue to be repressed asa result of auxin accumulation. (b) In the pip2;1 loss-of-function mutant,water transport within the primordium and towards the vasculature is altered,resulting in a reduced LRE rate. (c) In the PIP2;1 gain-of-function mutant,water transport is globally increased, notably in the outer tissue where watertransport is normally repressed by auxin. As a result, LRE is delayed.
auxin-treated roots (Fig. 2e) suggested that auxin may also exert moredirect effects on steady-state cell turgor. The overall result points to thepivotal role of auxin in controlling the biomechanics of LRE, wherebythis hormone affects tissue plasticity (through cell-wall enzymes), watersupply (through aquaporins) and turgor maintenance to promote theemergence of developing LRP through overlaying tissues.Plant roots express numerous aquaporin isoforms22,23. The present
work focused on the regulation and function of PIP2;1, one ofmost highly expressed PIPs. Using a high-resolution lateral rootsynchronization procedure, we showed that disrupting PIP2;1 genefunction impacts lateral root morphogenesis, causing the normaldome-like shape to become flattened, and significantly delays the timetaken for the new organ to emerge. PIP2;1 belongs to a subset of PIP2genes (PIP2;1, PIP2;4 and PIP2;6) whose messenger RNA abundanceexhibits a transient induction before they are repressed along withmost other aquaporin genes expressed during lateral root development(Fig. 1c). In only two cases (PIP2;5 and PIP2;8) are PIP2 transcript levelsenhanced throughout lateral root development (Fig. 1d). The spatialpattern of PIP2;8 expression revealed that it was specifically upregulatedat the base of LRP and in the underlying stele (Supplementary Fig. S3).Monitoring the expression patterns and functional importance of everyother aquaporin gene family member during lateral root developmentwould provide more insight into their potentially contrasting rolesduring organ emergence. Preliminary characterization of knockoutmutations in other PIP2 genes has revealed that, similarly to pip2;1, theycause a delay in LRE (Supplementary Fig. S6c,e–g). As PIP2;2 is anothermajor root aquaporin with an expression profile similar to PIP2;1during LRE (Fig. 1c), we also examined the combined loss-of-functionmutations in PIP2;1 and PIP2;2. The double mutant showed a delay inLRE similar to the pip2;1mutant (Supplementary Fig. S6c,h) consistentwith PIP2;1 being the main aquaporin in root tissues. Thus, the presentstudy opens the way to a detailed genetic dissection of the hydrauliccontrol of tissue growth involving other PIP isoforms, at a level ofresolution not previously achieved in a plant system.To probe the tissue-scale regulatory mechanism(s) for how auxin
control of aquaporin activity affects LRE, we developed a mathematical
model of the root cross-section that describes water fluxes andprimordium expansion. Our results suggested that optimal LRErequires water transport into the overlaying tissue to be repressedas a result of auxin accumulation, whereas aquaporins wouldpromote water transfer from the overlaying cells into the primordium(Figs 4a,c and 6a) . These opposing effects on LRE have thereforeto be precisely tuned in time and space to explain an overallbeneficial effect of auxin and aquaporin activation and repression onLRE. Simulations help provide insight into this integrated processand predict that adding ectopic constitutive PIP2;1 expression,or removing either tissue-specific PIP2;1 distribution or auxininhibition of aquaporins resulted in a reduced emergence rate (Fig. 4),in agreement with experimental observations (Fig. 5). Thus, themodel revealed that, in the pip2;1 loss-of-function mutant, LREwas delayed owing to reduced water transport from the overlayingtissue into the primordium (the k1 pathway; Fig. 4a and Fig. 6b),whereas in roots of PIP2;1-overexpressing plants, it was caused byan increased water supply to the overlaying cells (the k2 and k4pathways; Figs 4a and 6c).Although the modelling approach allowed us to explain counter-
intuitive behaviour, in particular when considering similar LREphenotypes caused by gain- or loss-of-function of PIP2, the phenotypiccharacterization of additional aquaporin genotypes will help refinethis approach and estimates of crucial parameter values. By focusingon the tissue scale, the model also provides a building block indeveloping future models, which should incorporate the cell scaleand three-dimensionality, which we believe will assist in understandingthe interplay between the regulation of the water fluxes investigatedhere, and the remodelling of cell walls, to provide an optimal separationof the overlaying cells. �
METHODSMethods and any associated references are available in the onlineversion of the paper.
Note: Supplementary Information is available in the online version of the paper
ACKNOWLEDGEMENTSThis workwas supported by aMarie Curie Intra-European Fellowshipwithin the 7thEuropean Community Framework Programme PIEF-GA-2008-220506 (B.P.) andby a Grand Federative Project (Rhizopolis) of the Agropolis Fondation (Montpellier,France) to C.M. We are indebted to H. Scherb (Helmholtz Zentrum München) forhis help with statistical analyses. L.R.B., U.V.,M.L., D.M.W., J.R.K., O.E.J. andM.J.B.acknowledge the support of the Biotechnology and Biological Sciences ResearchCouncil (BBSRC) and Engineering and Physical Sciences Research Council (EPSRC)funding to the Centre for Plant Integrative Biology (CPIB), BBSRC responsivemodegrant support to U.V., L.R.B. and M.J.B. and the BBSRC Professorial ResearchFellowship funding to D.M.W. and M.J.B. A.R.S. and O.D.I. acknowledge thesupport of the Deutsche Forschungsgemeinschaft priority programme SPP1108(SCHA 454/8).
AUTHOR CONTRIBUTIONSB.P., G.L., J.Z., U.V., O.P., D-T.L., O.D.I., I.C., M.L., D.M.W., L.L. and P.N.performed experimental work; B.P., G.L., J.Z., L.R.B., J.R.K., O.E.J., A.R.S., C.M. andM.J.B. performed data analysis; B.P., L.R.B., J.R.K., O.E.J., A.R.S., C.M. and M.J.B.oversaw project planning; B.P., L.R.B., A.R.S., C.M. and M.J.B. wrote the paper.
COMPETING FINANCIAL INTERESTSThe authors declare no competing financial interests.
Published online at www.nature.com/doifinder/10.1038/ncb2573Reprints and permissions information is available online at www.nature.com/reprints
NATURE CELL BIOLOGY VOLUME 14 | NUMBER 10 | OCTOBER 2012 997
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998 NATURE CELL BIOLOGY VOLUME 14 | NUMBER 10 | OCTOBER 2012
METHODSGrowth conditions and plant material. Wild-type Columbia (Col-0), mutants(arf7-125, pip2;1 and pip2;1 pip2;2) and reporter lines were grown on vertical 1/2Murashige–Skoog (MS) plates at 23 ◦C under continuous light (150 µmolm−2 s−1).pip2;1-1 is derived from the AMAZE collection35 and the En-transposon is insertedafter the 69th nucleotide of the second exon; pip2;1-2, pip2;2-3 and pip2;2-4have been described previously33. pip2;4-1 (SM_3_20853; ref. 36) and pip2;6-3(SALK_ 092140; ref. 37) were obtained from the Nottingham Arabidopsis StockCentre38 and verified by genotyping and RT–PCR. The pip2;1 pip2;2 doublemutant was generated by crossing pip2;1-2 and pip2;2-3. proPIP2;1:GUS lines havebeen described previously33. A fragment comprising 2,526 base pairs upstreamof the start codon of PIP2;8 (At2g16850) was cloned into pBGWFS7 to generatetranscriptional proPIP2;8:GUS fusions. For lateral root phenotypical analysis, lateralroot induction was performed on three-day-old seedlings by rotating the plates at90◦. For expression analysis, six-day-old plants were transferred on vertical 1/2 MSplates supplemented with 1 µM IAA or 10 µMPCIB for the indicated time. For rootwater transport measurements and ELISA assays, plants were germinated and grownon plates for 10 days before transfer to hydroponic culture, as previously described30.Plants were further grown for 10–20 days, in a growth chamber at 70% relativehumidity with cycles of 16 h of light (250 µmolm−2 s−1) at 22 ◦C and 8 h of darkat 21 ◦C.
Nucleic-acid manipulations and constructs. For overexpression of A. thalianaPIP2;1, the complementary DNA of PIP2;1 was placed under the control of a doubleenhanced CaMV 35S promoter and transferred into plants through Agrobacteriumby floral dipping39 using a pGreen179 binary transformation vector. Three plantlines that showed the highest expression of the transgene were selected among200 transformed lines by western blot analyses on leaf extract using an anti-PIP2antibody29 (see below). Plants co-expressing thePIP2;1–mCHERRY construct underthe control of 1.5 kb of genomic sequences upstream of the PIP2;1 start codon,and the YFP–AtNPSN12 construct under the control of a promoter of ubiquitin 10gene40 were obtained by crossing the plants that individually express the constructs.At NPSN12 is a SNARE protein, which has been localized in the plasmamembrane40.
Mutant complementation. A 4.6 kb genomic PIP2;1 fragment was amplifiedby PCR using primers 5′-ATTTGTCCTTTCCGGTACAAT-3′ (forward) and 5′-ACTCTCAATCCTCAGCCAAGT-3′ (reverse) and cloned into pDONR221 vector,verified by sequencing and subsequently cloned into pBGW and transformed by flo-ral dipping39 into the two pip2;1mutant alleles. Homozygous, complemented plantswith single insertion were confirmed on the basis of antibiotic (phosphinotricine)resistance and further confirmed by RT–PCR.
qRT–PCR. Total RNA was extracted from roots using a Qiagen RNeasy plantmini kit with on-column DNAse treatment (RNAse free DNAse set, Qiagen).Poly(dT) cDNA was prepared from 2 µg total RNA using the Transcriptor first-strand cDNA synthesis kit (Roche). qPCR was performed using SYBR GreenSensimix (Quantace) on Roche LightCycler 480 apparatus. PCR was carried outin 384-well optical reaction plates heated for 1min to 95 ◦C, followed by 40cycles of denaturation for 5 s at 95 ◦C, annealing for 8 s at 62 ◦C and extensionfor 30 s at 72 ◦C. Target quantifications were performed with the specific primerpairs described in Supplementary Fig. S7. Expression levels were normalized tothe ubiquitin-associated gene UBA (At1g04850) using the following primers UBAforward 5′-agtggagaggctgcagaaga-3′ and UBA reverse 5′-ctcgggtagcacgagcttta-3′.
All qRT–PCR experiments were performed in triplicate and the values representmeans± s.e.m.
Hydraulic conductivity measurement. Measurements of root hydrostatic hy-draulic conductivity (Lpr-h) and root osmotic hydraulic conductivity (Lpr-o) wereperformed as described previously30,41. Pressure probe measurements in root cor-tical cells and calculation of cell hydraulic conductivity were made as previouslydescribed30.
Immunodetections. Serial twofold dilutions in a carbonate buffer (30mMNa2CO3, 60mM NaHCO3, at pH 9.5) of 0.5 µg of membrane extracts were loadedin triplicate on immunoplates (Maxisorp). The ELISA assay was performed as previ-ously described42 using a 1:2,000 dilution of an anti-PIP2 antibody raised against a17-amino-acid carboxy-terminal peptide of At PIP2;1 (ref. 29). Western blot analy-sis was performed using classical procedures29 and the same anti-PIP2 antibody.
Histochemical analysis and microscopy. GUS staining was done as previouslydescribed43. Plants were cleared for 24 h in 1M chloral hydrate and 33% glycerol.Seedlings were mounted in 50% glycerol and observed with a Leica DMRBmicroscope. For confocal microscopy, images were captured with an invertedconfocal laser-scanningmicroscope (Inverse 1 Axiovert 200MZeiss/LSM510METAConfocal) with a 63× oil-immersion objective. The emitted fluorescence signal wascaptured by alternately switching the 488 nm and 543 nm excitation lines. Lateralroots were imaged as 1 µm step z series.
Mathematical modelling. Full details of the model formulation and predictionsare provided in the Supplementary Information. Details of the modelling areavailable in Supplementary Note S1 and Matlab code is available in SupplementaryData S1. Simulations were performed in Matlab and the numerical code can bedownloaded from www.cpib.ac.uk/tools-resources/models.
35. Wisman, E., Cardon, G. H., Fransz, P. & Saedler, H. The behaviour of theautonomous maize transposable element En/Spm in Arabidopsis thaliana allowsefficient mutagenesis. Plant Mol. Biol. 37, 989–99 (1998).
36. Tissier, A. F. et al. Multiple independent defective suppressor-mutator transposoninsertions in Arabidopsis : a tool for functional genomics. Plant Cell 11,1841–52 (1999).
37. Alonso, J. M. et al. Genome-wide insertional mutagenesis of Arabidopsis thaliana.Science 301, 653–657 (2003).
38. Scholl, R. L., May, S. T. & Ware, D. H. Seed and molecular resources for Arabidopsis.Plant Physiol. 124, 1477–1480 (2000).
39. Clough, S. J. & Bent, A. F. Floral dip: a simplified method for Agrobacterium-mediated transformation of Arabidopsis thaliana. Plant J. 16, 735–43 (1998).
40. Geldner, N. et al. Rapid, combinatorial analysis of membrane compartments in intactplants with a multicolor marker set. Plant J. 59, 169–78 (2009).
41. Postaire, O. et al. A PIP1 aquaporin contributes to hydrostatic pressure-inducedwater transport in both the root and rosette of Arabidopsis. Plant Physiol. 152,1418–30 (2010).
42. Boursiac, Y. et al. Early effects of salinity on water transport in Arabidopsisroots. Molecular and cellular features of aquaporin expression. Plant Physiol. 139,790–805 (2005).
43. Péret, B. et al. Auxin influx activity is associated with Frankia infectionduring actinorhizal nodule formation in Casuarina glauca. Plant Physiol. 144,1852–62 (2007).
Figure S1 Expression analysis of the major aquaporin genes. Average relative level of expression and sem values of aquaporin genes (PIP1;1, PIP1;2, PIP1;3, PIP1;4, PIP1;5, PIP2;2, PIP2;3, PIP2;4, PIP2;6,
PIP2;7, TIP1;1, TIP1;2, TIP2;2, and TIP2;3) upon 1 µM IAA treatment in the wild type (WT) and arf7 mutant backgrounds. Time is indicated in hours.
Figure S2 Supplementary root hydraulic conductivity measurements. (a) Short time 1 µM IAA treatment did not affect hydrostatic root hydraulic conductivity (Lpr-h) of the wild-type (Col-0) plants (n = 5). (b) Lpr-o of Col-0 roots treated with 1 µM IAA for 18 h and 42 h was determined. Data shown are mean value ± sem with n =14, 14, 15 from 2 independent plant cultures..(c) The arf7 mutant Lpr-h is strongly affected by a H2O2 treatment (5 mM for 20 min) The mean of 2 experiments is shown.( NT, non-treated roots (d-f) Water relation parameters were determined in single root cortical cells of non-treated plants (NT) or plants treated with 1 µM IAA for 18 hours (IAA). Cell hydraulic conductivity was calculated from the half-time of water exchange (T1/2) (d), the stationary turgor pressure (e) and the volumetric elastic modulus (Epsilon)
(f) (n = 22) (g-h) Characterization of free sap exudation in roots from wild type (Col-0) and pip1;2-2 mutant plants complemented (pip2;1-2 PIP2;1) or not (pip2;1-2) with a PIP2;1 genomic fragment. Sap flow rate (g) and osmolarity (h) was used to deduce the Lpr-h Lpr-o values shown in Fig. 2f. Data shown are mean value ± sem from 2 independent plant cultures (n=21, 18, 22). (i, j) Lpr-h (i), data shown are mean value ± sem with n =35, 13, 18 from 2 independent plant cultures and Lpr-o (j), data shown are mean value ± sem with n =27, 21, 14 from 3 independent plant cultures, of Col-0 and single or double knock-outs for PIP2;1 (pip2;1) and PIP2;2 (pip2;2). Asterisks indicate a significant difference with corresponding control experiment by Student’s t-test (*: p < 0.05; **: p < 0.01; ***: p < 0.001).
Figure S3 Characterization of the PIP2;8::GUS reporter lines. (a-f) PIP2;8 expression determined with a transcriptional proPIP2;8:GUS fusion during lateral root development. LR developmental stages are indicated by Roman numbers as described previsouly20. Expression pattern was verified with three independent transgenic lines. (g-m) Auxin and anti-auxin treatments
did not affect proPIP2;8:GUS expression pattern. Untreated 7 day-old plants (g, j, k), plants treated with 1 µM IAA for 48 hours (h,i) and plants treated with 10 µM PCIB for 24 hours (l,m). The results were verified using an independent transgenic line. Scale bars represent 50 µm (a-f), 75 µm (j-m) and 100 µm (g-i).
Figure S4 Characterization of the PIP2;1 over-expression lines. (a) Western blot of three independent d35S:PIP2;1 lines (lanes 1 to 3) showing strong accumulation of the PIP2 proteins compared to wild type (Col-0). The two bands correspond to monomeric and dimeric forms. Representative experiment with 5 μg proteins per lane. ELISA assays on the same samples showed that, with respect to Col-0, proteins immunoreactive to the anti-PIP2 antibody were increased by 2.6-2.9-fold in the d35S:PIP2;1 lines (b) Hydrostatic root hydraulic conductivity (Lpr-h) is increased in three
independent d35S:PIP2;1 lines (1 to 3). Data shown are mean value ± sem with n =21, 20, 17, 16 from 3 independent plant cultures (c) The reduction of root hydraulic conductivity by auxin is suppressed in the PIP2;1 over-expression lines. Lpr-h was determined upon 18 and 42 hours treatments with 1 µM IAA and indicated as a percentage of untreated control. Data shown are mean value ± sem with n =21, 13, 19, 9, 8, 12, 7, 6, 10 from 2 independent plant cultures. Asterisks indicate a significant difference with corresponding control experiment by Student’s t-test (*: p < 0.05; ***: p < 0.001).
Figure S5 The PIP2;1-mCHERRY fusion rescues the pip2;1 LR emergence phenotype. (a-b) Expressing the proPIP2;1:PIP2;1-mCHERRY construct in the pip2;1-2 mutant background (b) restores kinetics of LR emergence similar to those in wild-type (Col-0, a). (c)
Expression pattern driven by the proPIP2;1:PIP2;1-mCHERRY construct in the pip2;1-2 background is similar to the expression driven when expressing the same construct in the wild-type (Col-0) background (as shown in Figure 3d).
Figure S6 Lateral root emergence is defective in arf7 mutants and in single or multiple pip2 mutants. LRE phenotyping was achieved by synchronizing LR formation with a gravistimulus (a,b) Differential interference contrast imaging at 42 hours post-induction (hpi) showed abnormal LR primordia of arf7 mutants (b) compared to dome-shaped wild-type primordium (a). Scale bars represent 25 µm (c-h) Primordia were grouped according to developmental stages as previously defined20 18 hpi (black bars) and 42 hpi (grey bars). (c) Wild-type (Col-0) plants showed accumulation of stage I and II primordium 18 hpi and accumulation of stage VII and VIII 42 hpi. (d) arf7 mutants showed similar stages of LR formation at 18 hpi compared
to wild type thereby suggesting that early stages of LR development were not affected. However, most LRP accumulated at stage IV and V 42 hpi indicating a strong emergence defect. (c-e) The pip2;2, pip2;4 and pip2;6 single mutants and the double pip2;1 pip2;2 mutant showed similar stages of LR formation at 18 hpi compared to wild type thereby suggesting that early stages of LR development were not affected. However, they present an accumulation of stages IV to VI LR primordia at 42 hpi indicating an emergence defect. The double pip2;1 pip2;2 mutant (h) also showed a reduced amount of LRP reaching stage VIII at 42 hpi Data shown are mean value ± sem and n = 20 (c-h).
the permeabilities of the four boundaries bounding the two tissue compartments by ki (for i = 1, 2, 3, 4),
as shown in figure M2, the volumes (per unit length) of the two regions satisfy
dV1
dt= l1Q1 − 2X1Q3, (1.6a)
dV2
dt= l2Q2 − l1Q1 + 2(X2 −X1)Q4, (1.6b)
1Although the presence of auxin may cause gradual weakening (Swarup et al., 2008), we focus here on constructing a
minimal model that describes how emergence is affected by changes in aquaporin activity.2Note that the factor of 4 arises in (1.2) from the standard Trouton viscosity model, see for example Van der Fliert et al.
(1995).
4
Primordium
tissueOverlying
Line of symmetry
β1(t)
β2(t)R1(t)R2(t)
X1 X2
Y1(t)
Y2(t)
Figure M3: The sheets each form an arc of a cylinder which has radius Rj(t) and which meets the x-axis
k1init Initial permeability of boundary 1 2.4× 10−6 ms−1 MPa−1
k1min Minimum Permeability of boundary 1 2.4× 10−7 ms−1 MPa−1
k2init Initial permeability of boundary 2 0.8× 10−6 ms−1 MPa−1
k2min Minimum permeability of boundary 2 0.8× 10−7 ms−1 MPa−1
k3 Permeability of boundary 3 2.4× 10−6 ms−1 MPa−1
k4 Permeability of boundary 4 0.8× 10−6 s−1 MPa−1
k1g Rate of decrease of boundary 1 permeability due to auxin 3.6× 10−6 s−1
k2g Rate of decrease of boundary 2 permeability due to auxin 1.8× 10−5 s−1
Table 1: Summary of the estimates of the dimensional parameters in the model. As described in §3,
plausible estimates are available for all parameters other than π1g, φ1, φ2, Γ1 and Γ2.
boundaries 1 and 2 (i.e. considering the influence of parameters k∗1g and k∗2g). We also consider the
importance of the PIP2;1 distribution by simulating the emergence dynamics in i) the d35S;PIP2;1 over-
expression mutant (i.e. with ectopic PIP2;1 expression), by letting k∗1g = k∗2g = 0 and increasing k∗2init and
k∗4 , and ii) the pip2;1 knockout mutant, by letting k∗1g = 0 and reducing k∗1init and k∗3 . The magnitudes of
the permeability changes in these mutants are unknown, although we find that the specific choices do not
affect our key conclusions. For these mutants, our predictions were confirmed experimentally (as described
in the main text), providing accurate measurements of the emergence time in each case; we find that the
model can mimic the observed emergence times if we use the parameter values stated in Table 3.
11
Parameter Description Value
π∗r1 Relative osmotic potential of vasculature 1.375
P ∗r1 Relative turgor pressure of vasculature 1
π∗r2 Relative osmotic potential of adjacent overlaying cells 1
P ∗r2 Turgor pressure of adjacent overlaying cells 1
π∗2 Relative osmotic potential of overlaying cells 1
π∗1g Rate of increase of osmotic potential of primordium 0.0001332†
X∗2 Ratio between length scales 1.5
φ∗2 Ratio between boundaries’ effective extensibilities 1†
Γ∗1 Relative yield stress of boundary 1 0.01†
Γ∗2 Relative yield stress of boundary 2 3†
k∗1init Initial permeability of boundary 1 3
k∗1min Minimum permeability of boundary 1 0.3
k∗2init Initial permeability of boundary 2 1
k∗2min Minimum permeability of boundary 2 0.1
k∗3 Permeability of boundary 3 3
k∗4 Permeability of boundary 4 1
k∗1g Rate of decrease of boundary 1 permeability due to auxin 5.6× 10−4
k∗2g Rate of decrease of boundary 2 permeability due to auxin 0.0028
T ∗ Ratio between key time scales 1†
Table 2: Summary of the parameter groupings in the nondimensionalised model. Where available, estimates
of these parameter groupings are obtained using the dimensional parameter values given in Table 1. The
parameter groupings for which such estimates are not available are marked with daggers; we note that
π∗1g is chosen to ensure emergence occurs over 28 hours. In §4, we discuss how varying the value of each
parameter grouping affects the emergence time (see figure M8).
12
4 Model results
The governing equations, (2.5), are simulated numerically using Matlab, and we provide the numerical code
both as a supplementary file and at www.cpib.ac.uk/tools-resources/models. We solve equations (2.5a,b)
using the in-built ODE solver ode15s, with (2.5c,d) solved at each time step using the fsolve function.
We view the primordium as having emerged when the distance between the two boundaries is less than a
prescribed constant, Y ∗m i.e. when Y ∗
2 (t)− Y ∗1 (t) < Y ∗
m (which we determine numerically using the Events
option in the ODE solver). In the simulations presented, we use Y ∗m = 0.08, unless otherwise stated.
4.1 The emergence dynamics in wild-type plants
In figure M5, we show a typical simulation, using the parameter values stated in Table 2. The model predicts
that throughout emergence the prescribed increasing osmotic potential within the primordium (figure M5a)
draws in water from the overlaying tissue, Q∗1 > 0, (figure M5b). In contrast, the relatively high osmotic
potential of the vasculature (together with the evolving hydrostatic pressure in the primordium) cause
the flux between the primordium and vasculature to be toward the vasculature, Q∗3 > 0 (figure M5c).
Meanwhile, water is supplied to the overlaying tissue from both the adjacent tissue and the external
environment, Q∗2 > 0 and Q∗
4 > 0 (figure M5b,c).
The model also predicts the evolution of the pressures within the primordium and overlaying tissue. Prior
to yielding, the pressures evolve according to (2.8) due to the prescribed time dependence of π1, k1 and k2.
We note that the pressures vary nonlinearly with time and that the sudden change in the pressure gradient
(at 13.7 hours) occurs when the prescribed decrease of k2 ceases and k2 reaches its minimal plateau value.
At the beginning of the simulation, the hydrostatic pressure in the overlaying tissue is larger than that in
the primordium, due to the flow of water towards the vasculature (driven by its high osmotic potential);
however, as the osmotic potential of the primordium increases, the hydrostatic pressure there becomes
greater than that in the overlaying tissue (figure M5d), creating tension within boundary 1. Once this
becomes larger than the yield stress, boundary 1 begins to lengthen and the volume of the primordium
increases. Since we choose the yield stress of boundary 2, Γ∗2, to be sufficiently large that the initial state
is steady, we find that boundary 2 never yields, remaining stationary (figure M5e,f). We note that should
we have assumed boundary 2 to be stationary from the outset, our model would be governed by a simpler
system of equations: a single ODE (2.5a) and two algebraic expressions (2.5c,d), with H2=0 and β2 being
a prescribed constant. Eventually (at t = 28.0 hours) boundary 1 becomes sufficiently close to boundary 2
that emergence can be taken to have occurred (figure M5e,f).
The magnitude of each water flux depends on the respective boundary permeabilities, which in turn depend
on the levels of aquaporin present; the model shows how changing the permeability of each boundary affects
the emergence times (figure M6). It should be emphasised, however, that the system is fully coupled:
changing one permeability alters the hydrostatic pressures, which affects how the other permeabilities
influence the emergence time. We predict that increasing k∗1 (via an increase in k∗1init) promotes emergence
by increasing the flux into the primordium, whereas increasing k∗3 inhibits emergence by increasing the
13
flux away from the primordium (figure M6a). Increasing k∗2 (via an increase in k∗2init) or k∗4 increases
the flux into the overlaying tissue, leading to a higher pressure within the overlaying tissue that prevents
the primordium from expanding and results in inhibited emergence (figure M6a). The permeabilities of
boundaries 1 and 2 are also affected by auxin inhibiting the aquaporins (via parameters k∗jg). Reducing k∗1gand k∗2g results in higher values of k∗1 and k∗2 , respectively; as shown in figure M6b, we see that reducing
k∗1g and k∗2g has the opposite effect on emergence to reducing k∗1init and k∗
2init (as one would expect from
equation (1.8) and figure M4). Figure 4c in the main text summarises how auxin and the boundaries
permeabilities affect the emergence time.
The simulations in figure M6 also reveal that the system exhibits switch-type behaviour, whereby a small
change in one of the permeabilities causes a dramatic change in emergence time. Simulations show that
the switch-type behaviour is due to sensitivity in the time at which boundary 1 yields. As shown in
figure M7, a small change in one of the permeabilities causes a small change in the pressures of the two
compartments. For example, with k∗1init = 2.5, the primordium pressure becomes sufficiently greater than
the overlaying-tissue pressure that boundary 1 yields at t = 32.8 hours; however, the small change in
the pressures that occurs if we instead set k∗1init = 2.3, results in the pressure difference not becoming
large enough for yielding until t = 77.0 hours. This predicted switch-type behaviour may have significant
biological implications: away from the critical permeability, small changes in the permeability would have
little effect on the emergence time, whereas close to the critical level, a small change (in the right direction)
would result in a dramatic delay to the emergence time. Since the permeabilities depend on the amount of
aquaporin present, the switch-type behaviour corresponds to the emergence time depending on whether the
aquaporin level is above or below a threshold value. Switches are commonly found in regulatory systems;
this phenomenon would provide a biologically robust mechanism to enable the plant to control the timing
of emergence (for example, via auxin regulating the aquaporins).
Figure M8 shows the sensitivity of the emergence times to the values of the remaining parameters. For
these parameters, we find that switch-like behaviour does not occur close to their wild-type values suggested
in Table 2. We find that increasing the rate, π∗1g, at which the primordium’s osmotic potential increases
promotes emergence by increasing water fluxes to the primordium (figure M8a), whereas increasing the
osmotic potential of the vasculature, π∗r1, inhibits emergence by increasing water flow away from the pri-
mordium (figure M8b). Softening boundary 1 (leading to an increase in T ∗, (2.2), via a rise in extensibility,
φ1), enables the primordium to grow more easily and the emergence time is reduced (figure M8c). With
a larger boundary 1 yield stress, Γ∗1, the pressure within the primordium must be larger before boundary
1 can lengthen, resulting in delayed emergence (figure M8d). Since boundary 2 remains stationary, its
mechanical properties (characterised by φ∗2 and Γ∗
2) do not affect the emergence time. The emergence time
also depends on the prescribed geometry of the tissue: if we reduce X∗2 , increase β1(0) or reduce β2(0),
boundaries 1 and 2 are initially closer together, which leads to a reduction in the emergence time (figure
M8e,f,g). Finally, we consider the influence of the distance between the two boundaries at which we suggest
that emergence has occured, Y ∗m: reducing this distance delays emergence (figure M8h).
14
0 10 20
1
1.05
1.1
Time (hours)
Osm
otic
pre
ssur
e
0 10 200.7
0.75
0.8
0.85
0.9
Time (hours)
Hyd
rost
atic
pre
ssur
e
0 10 200
0.1
0.2
0.3
0.4
Time (hours)F
lux
0 10 200
0.1
0.2
0.3
0.4
Time (hours)
Flu
x
0 10 200.4
0.6
0.8
1
Time (hours)
Dis
tanc
e
Q4∗
Q1∗
π1∗ Q
3∗
Q2∗
P1∗
P2∗
Y1∗
Y2∗
π2∗
a) b) c)
d) e)
−1.5 −1 −0.5 0 0.5 1 1.50
0.5
1
x∗
y∗
Boundary 2
Boundary 1
f)
Figure M5: The emergence dynamics with the wild-type parameter values listed in Table 2 and β1(0) =
β2(0) = 1. The subfigures show the evolution of a) the osmotic potentials of the primordium, π∗1(t), and the
overlaying tissue, π∗2(t), b) the fluxes Q∗
1(t∗) and Q∗
2(t), c) the fluxes Q∗3(t) and Q∗
4(t), d) the hydrostatic
pressures, P ∗j (t), e) the heights, Y ∗
j (t), and f) the boundary positions. In panel f), we show the position of
boundary 1 at 0.5 hour intervals (blue lines) and the stationary position of boundary 2 (red dashed line).
The primodium emerges at t = 28 hours.
15
0 1 2 3 4 50
50
100
150
Permeability
Em
erge
nce
time
(hou
rs)
k1init∗
k2init∗
k4∗
k3∗
a)
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10−3
20
40
60
80
100
120
Rate of permeability decrease, kjg∗
Em
erge
nce
time
(hou
rs)
k2g∗
k1g∗
b)
Figure M6: The influence of the permeability parameters on the predicted emergence time. In each case,
the other parameter values are given in Table 2 and β1(0) = β2(0) = 1. a) The influence of the boundary
permeabilities, k∗jinit, k
∗3 and k∗4 . Recall that during emergence the permeabilities of boundaries 1 and 2
gradually reduce from these initial values (see (1.8) and figure M4), whereas the permeabilities of boundaries
3 and 4 remain constant. When considering different k∗jinit, we set k∗
jmin = 0.1k∗jinit in each case. b) The
influence of the rate of decrease of the permeabilities of boundaries 1 and 2, k∗jg. These permeabilities
gradually decrease during emergence because auxin causes a reduction the activity of the aquaporins.
16
0 10 20 30 40 50 60 70 800.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
Time (hours)
Pre
ssur
e
P1∗
P2∗
Yielding with k1init∗ =2.5
Yielding with k1init∗ =2.3
Figure M7: The evolution of the pressures in the primordium and overlaying tissue for k∗1init = 2.3 (solid
lines) and k∗1init = 2.5 (dashed lines). In each case, boundary 1 yields once the pressure difference P ∗
1 −P ∗2
is greater than Γ∗1 sin(β1(0)); as shown with the arrows, with k∗
1init = 2.5 boundary 1 yields at 32.8 hours,
whereas with k∗1init = 2.3 boundary 1 yields at 77.0 hours. Thus, the small difference in the pressures
between the two cases results in a significant difference in emergence time.
4.2 The influence of auxin on the emergence dynamics
As discussed above, auxin represses aquaporin expression and we capture this repression by prescribing
a gradual reduction in the permeabilities of boundaries 1 and 2, at rates k∗1g and k∗2g respectively. Thus,
from figure M6b, we see that auxin has opposing effects in the primordium and in the overlaying tissue.
Considering boundary 1, auxin increases k∗1g, which reduces the fluxes into the primordium from the over-
laying tissue, inhibiting emergence. In contrast, considering boundary 2, auxin increases k∗2g, which reduces
the fluxes into the overlaying tissue, enabling the primordium to emerge more easily. With the parameter
values stated in Table 2, we predict that neglecting the effects of auxin on either boundary has dramatic
consequences for the emergence time; however, if we neglect auxin’s influence entirely (i.e. removing its
effect on both boundaries) the two opposing effects partly cancel each other, and we predict emergence
to be only 8.7 hours later than wild-type (figure M9). However, since auxin has two opposing effects,
the simulations reveal how the values of k∗1g and k∗2g affect whether setting k∗1g = 0 dominates (resulting
in earlier emergence when auxin’s influence is removed) or whether setting k∗2g = 0 dominates (causing
delayed emergence when auxin’s influence is removed). In particular, we predict a delay in emergence when
we neglect auxin’s influence entirely because auxin’s inhibition of PIP2;1 (present on boundary 1) is slower
than that of the other aquaporins (present on boundary 2) (so that the regions of rapid variation shown in
figure M6b cause the change in k∗2g to dominate). For example, if we consider auxin to have the same effect
on the permeabilities of boundaries 1 and 2 by decreasing k∗2g, i.e. k∗1g = k∗2g = 5.6×10−4 (and then adjust
17
0 0.5 1 1.5 2
x 10−3
0
20
40
60
80
100
120
πg1∗
Em
erge
nce
time
(hou
rs)
a) influence of π∗1g
1 1.1 1.2 1.3 1.40
5
10
15
20
25
30
35
40
πr1∗
Em
erge
nce
time
(hou
rs)
b) influence of π∗r1
0 0.5 1 1.5 227
28
29
30
31
32
33
T∗
Em
erge
nce
time
(hou
rs)
c) Influence of T ∗.
0 0.01 0.02 0.03 0.0420
25
30
35
40
45
50
Γ1∗
Em
erge
nce
time
(hou
rs)
d) influence of Γ∗1
1.2 1.3 1.4 1.5 1.6 1.7 1.815
20
25
30
35
40
45
X2∗
Em
erge
nce
time
(hou
rs)
e) influence of X∗2
0.2 0.4 0.6 0.8 1 1.224
25
26
27
28
29
30
31
32
β1(0)
Em
erge
nce
time
(hou
rs)
f) influence of β1(0)
0.8 1 1.2 1.4 1.6 1.8 226
28
30
32
34
36
β2(0)
Em
erge
nce
time
(hou
rs)
g) Influence of β2(0).
0 0.05 0.1 0.15 0.2 0.2526.5
27
27.5
28
28.5
Ym∗
Em
erge
nce
time
(hou
rs)
h) Influence of Y ∗m.
Figure M8: Influence of model parameters on the predicted emergence time. In each case, the remaining
parameters are equal those given in Table 2 and β1(0) = β2(0) = 1.
18
0
20
40
60
80
100
120
Em
erge
nce
time
(hou
rs)
k∗
1g = 0 k∗
2g = 0 k∗
1g = k∗
2g = 0Wild type
Figure M9: The influence of auxin on the predicted emergence time (via changes in the rates k∗1g and k∗2g).
The remaining parameter values are given in Table 2 and β1(0) = β2(0) = 1.