RESEARCH ARTICLE

GTL1 and DF1 regulate root hair growth through transcriptionalrepression of ROOT HAIR DEFECTIVE 6-LIKE 4 in ArabidopsisMichitaro Shibata1,¶, Christian Breuer1,*,¶, Ayako Kawamura1, Natalie M. Clark2,3, Bart Rymen1,Luke Braidwood1,‡, Kengo Morohashi4, Wolfgang Busch5,§, Philip N. Benfey6, Rosangela Sozzani2,3 andKeiko Sugimoto1,**

ABSTRACTHow plants determine the final size of growing cells is an important,yet unresolved, issue. Root hairs provide an excellent model systemwith which to study this as their final cell size is remarkably constantunder constant environmental conditions. Previous studies havedemonstrated that a basic helix-loop helix transcription factor ROOTHAIR DEFECTIVE 6-LIKE 4 (RSL4) promotes root hair growth, buthow hair growth is terminated is not known. In this study, wedemonstrate that a trihelix transcription factor GT-2-LIKE1 (GTL1)and its homolog DF1 repress root hair growth in Arabidopsis. Ourtranscriptional data, combined with genome-wide chromatin-bindingdata, show that GTL1 and DF1 directly bind the RSL4 promoter andregulate its expression to repress root hair growth. Our data furthershow that GTL1 and RSL4 regulate each other, as well as a set ofcommon downstream genes, many of which have previously beenimplicated in root hair growth. This study therefore uncovers a coreregulatory module that fine-tunes the extent of root hair growth by theorchestrated actions of opposing transcription factors.

KEY WORDS: Root hair, Cell growth, Trihelix transcription factor,Gene regulatory network

INTRODUCTIONPlant cells often undergo extensive post-mitotic cell expansion andcan reach up to several hundred-fold their original size (Sugimoto-Shirasu and Roberts, 2003). Controlling the final size of post-mitotically growing cells is of fundamental importance, as failure inthis control can result in severe defects in plant organ growth anddevelopment (Braidwood et al., 2014; Breuer et al., 2010). Growing

to an optimal size is also physiologically relevant for somespecialized cell types such as root hairs, which must increase theirsurface area to permit better uptake of nutrients and water from thesurrounding environment (Grierson et al., 2014). Root hairs grow ina polarized fashion through a localized deposition of cell wallmaterials at the root hair apex. This is enabled by highly directionalmembrane trafficking towards the growing tip of cells andsubsequent exocytosis of vesicles that contain cell wallpolysaccharides and cell wall proteins that need to be incorporatedinto newly developing cell walls (Grierson et al., 2014). As formany other cell types in plants, root hair growth is oftenaccompanied by an increase in nuclear DNA content, or ploidy,through successive rounds of endoreduplication (Breuer et al., 2007;Sugimoto-Shirasu et al., 2005, 2002). It is also known, however,that root hair growth is ploidy independent to some degree as roothairs can elongate without changing their ploidy levels (Yi et al.,2010).

Root hairs in Arabidopsis thaliana (Arabidopsis) have served asan excellent model system for studying cell size control in plants,and molecular genetic studies over the past few decades haveuncovered key regulatory mechanisms that control root hair growth.Given that root hairs are formed in a specific pattern of cell files inArabidopsis roots, initiation of root hair outgrowth is regulated by agenetic program that determines cell fate (Grierson et al., 2014;Salazar-Henao et al., 2016). Key regulators that translate thesedevelopmental cues into hair initiation are the basic helix-loop-helix(bHLH) transcription factor ROOT HAIR DEFECTIVE 6 (RHD6)and its close homolog RHD6-LIKE 1 (RSL1) (Masucci andSchiefelbein, 1994; Menand et al., 2007). RHD6, together withRSL1, induces the expression of another RHD6 homolog ROOTHAIR DEFECTIVE 6-LIKE 4 (RSL4), leading to the accumulationof RSL4 proteins prior to the initiation of hair outgrowth (Dattaet al., 2015; Yi et al., 2010). Remarkably, constitutiveoverexpression of RSL4 by the Cauliflower Mosaic Virus 35Spromoter is able to maintain root hair elongation until the hair cellsdie (Yi et al., 2010), indicating that RSL4 is sufficient to promoteroot hair growth. Several recent studies have identified 132 genesthat are regulated by RSL4 and have shown that RSL4 promotes theexpression of these target genes by binding the root hair specific cis-element (RHE) in their promoter sequences (Hwang et al., 2017;Kim et al., 2006; Vijayakumar et al., 2016; Won et al., 2009; Yiet al., 2010). As expected, RSL4 target genes include those involvedin cell wall biosynthesis and remodeling, vesicle trafficking, cellularsignaling and metabolism, thus highlighting how the RSL4-mediated transcriptional program orchestrates various subcellularprocesses required for root hair growth.

Root hair growth is also fine-tuned by various hormonal andenvironmental cues, and several studies have shown that some ofthis regulation involves transcriptional upregulation of RSL4 andReceived 1 October 2017; Accepted 9 January 2018

1RIKEN Center for Sustainable Resource Science, Yokohama 230-0045, Japan.2Department of Plant and Microbial Biology, North Carolina State University,Raleigh, NC 27708, USA. 3Biomathematics Graduate Program, North Carolina StateUniversity, Raleigh, NC 27695, USA. 4Department of Applied Biological Science,Faculty of Science and Technology, Tokyo University of Science, Noda 278-8510,Japan. 5Gregor Mendel Institute (GMI), Austrian Academy of Sciences, ViennaBiocenter (VBC), Dr. Bohr-Gasse 3, 1030 Vienna, Austria. 6Department of Biology,Howard Hughes Medical Institute, Duke University, Durham, NC 27695, USA.*Present address: PtJ, Division Bioeconomy BIO7, Forschungszentrum Jülich,52425 Jülich, Germany. ‡Present address: Department of Plant Sciences,University of Cambridge, Cambridge CB2 3EA, UK. §Present address: PlantMolecular and Cellular Biology Laboratory, Salk Institute for Biological Studies, LaJolla, CA 92037, USA.¶These authors contributed equally to this work

**Author for correspondence (keiko.sugimoto@riken.jp)

M.S., 0000-0002-7008-8437; B.R., 0000-0003-3651-9579; L.B., 0000-0002-0233-3605; K.S., 0000-0002-9209-8230

This is an Open Access article distributed under the terms of the Creative Commons AttributionLicense (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,distribution and reproduction in any medium provided that the original work is properly attributed.

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© 2018. Published by The Company of Biologists Ltd | Development (2018) 145, dev159707. doi:10.1242/dev.159707

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subsequent activation of its downstream pathway (Franciosini et al.,2017; Marzol et al., 2017; Yi et al., 2010). Among various planthormones, auxin is well known to enhance root hair growth (Knoxet al., 2003; Lee and Cho, 2013; Pitts et al., 1998). A recent studydemonstrated that several AUXIN RESPONSE FACTORs (ARFs),which are central transcriptional regulators of auxin signaling, bindthe RSL4 promoter and directly activate its expression (Manganoet al., 2017), providing the first molecular link between auxinsignaling and transcriptional control of root hair development(Zhang et al., 2016). Exogenous application of ethylene alsopromotes root hair growth (Pitts et al., 1998) and this physiologicalresponse is accompanied by increased RSL4 expression. Limitedphosphate availability is another trigger for extended root hairgrowth, and this regulation also involves upregulation of RSL4expression (Datta et al., 2015; Yi et al., 2010).Accumulating genetic evidence suggests that plants are also

equipped with a regulatory system to actively repress root hairgrowth. For example, double mutants in the bHLH transcriptionfactors Lotus japonicas ROOTHAIRLESS LIKE 4 (LRL4) andLRL5 produce longer root hairs compared with wild-type plants(Breuninger et al., 2016), demonstrating that root hair growth isnegatively regulated by LRL4- and LRL5-dependent mechanisms.It has also been reported that ROOTHAIR SPECIFIC 1 (RHS1) andRHS10, which encode a calcium-binding protein and a receptor-likekinase, respectively, repress root hair growth, as mutating eithergene results in extended hair growth (Hwang et al., 2016;Won et al.,2009). These observations thus suggest that there are multiple levelsof regulation by which root hair growth can be blocked, although theexact molecular details of this control remain unknown.We have previously reported a transcriptional mechanism that

terminates cell growth in Arabidopsis leaf trichomes, another celltype that undergoes extensive post-mitotic cell expansion (Breueret al., 2009). Loss-of-function mutants in the trihelix transcriptionfactor GT-2-LIKE 1 (GTL1) develop larger trichomes than wildtype, and this phenotype is associated with an increase in nuclearDNA content (Breuer et al., 2009). We showed that GTL1terminates cell growth in a ploidy-dependent manner by

repressing the expression of CELL CYCLE SWITCH PROTEIN52 A1 (CCS52A1), a key driver of plant endoreduplication (Breueret al., 2012). Whether GTL1 acts as a general repressor of cellgrowth remains an unresolved issue as gtl1 single mutants do notdisplay obvious growth defects beyond trichomes (Breuer et al.,2009). We reasoned that there may be other transcription factorsacting redundantly with GTL1. In support of this notion, anothertrihelix protein, called DF1, has twin trihelix binding domains thatshow 70% amino acid sequence identity with GTL1 (Breuer et al.,2009). In this study, we have characterized gtl1 df1 double mutantsand tissue-specific overexpression lines of GTL1 and DF1 todemonstrate that both GTL1 and DF1 negatively regulate root hairgrowth. Our data from transcriptional and chromatinimmunoprecipitation (ChIP) studies suggest that GTL1 and DF1directly repress RSL4 as well as a set of genes previously implicatedin root hair growth. We further used gene regulatory network (GRN)inference and mathematical modeling to show that GTL1 and RSL4likely form a negative-feedback loop to cooperatively control roothair growth.

RESULTSGTL1 and DF1 repress root hair growth through a ploidy-independent mechanismTo explore the functional redundancy between GTL1 and DF1, weisolated an Arabidopsis T-DNA insertion mutant for DF1 thatresulted in a null allele (Fig. S1A). As shown in Fig. 1A, root hairgrowth of 7-day-old gtl1-1 and df1-1 single mutants isindistinguishable from wild type. In contrast, we found that roothairs in gtl1-1 df1-1 double mutants are significantly longercompared with wild type, and their final hair length is, on average,more than 200 μm longer than wild type (Fig. 1A,B). Long roothairs in gtl1-1 df1-1 could be caused by either faster growth and/oran extended period of their growth. Our time-lapse analysis showedthat the rate of root hair growth is comparable between wild type andgtl1-1 df1-1 but gtl1-1 df1-1 root hairs continue to grow after wild-type root hairs halt their growth (Fig. 1C). To confirm that thisgrowth phenotype is caused by the lack of GTL1 and DF1, we

Fig. 1. GTL1 and DF1 repress roothair growth in Arabidopsis. (A) Roothair phenotypes of wild-type, gtl1-1,df1-1, gtl1-1 df1-1, pEXP7:GTL1-GFPand pEXP7:DF1-GFP seedlings. Scalebar: 500 μm. (B) Quantitative analysisof root hair length. Data are mean±s.e.m. (n=120). Different letters indicatemeans that differ significantly (Tukey-Kramer test, P

transformed gtl1-1 df1-1 plants with pGTL1:GTL1-GFP or pDF1:DF1-GFP constructs. Introduction of either of these constructs fullyrescues the hair growth phenotype, indicating that both GTL1 andDF1 contribute to the termination of root hair growth (Fig. S1B,C).Confocal microscopy revealed that both GTL1-GFP and DF1-

GFP proteins are broadly expressed along the longitudinal axis ofroots, and we detected clear GFP expression in expanding root hairs(Fig. S2). To test whether overexpression of GTL1 and DF1 issufficient to inhibit root hair growth, we ectopically expressedGTL1-GFP andDF1-GFP under the root-hair specific EXPANSIN7(EXP7) promoter (Cho and Cosgrove, 2002). The resulting pEXP7:GTL1-GFP and pEXP7:DF1-GFP plants showed an increase in theexpression of GTL1-GFP and DF1-GFP by 15-fold and 30-fold,respectively (Fig. S1D). Importantly, these plants had significantlyshort, often undetectable, root hairs (Fig. 1A,B), demonstrating thatectopically expressed GTL1 and DF1 can repress root hair growth.Next, we tested whether the root hair phenotypes in gtl1-1 df1-1

mutants are accompanied by changes in ploidy levels by examining4′6-diamidino-2-phenylindole (DAPI)-stained nuclei in fully grownroot hairs. We observed that the size of DAPI-stained nuclei iscomparable between wild-type and gtl1-1 df1-1 root hairs, andquantitative analysis of DAPI-stained nuclei confirmed that thenuclear DNA content is not different between wild-type and gtl1-1df1-1 root hairs (Fig. S3). Consistently, unlike in trichomes, theccs52a1 mutation does not rescue the hair growth phenotype ofgtl1-1 df1-1 (Fig. S3C,D), indicating that CCS52A1 does not actdownstream of GTL1 and DF1 in root hair development. Theseobservations suggest that GTL1 and DF1 control root hair growthploidy independently.

GTL1 and DF1 directly repress RSL4 expression in rootsIt has been previously shown that RSL4 promotes root hair growthin a ploidy-independent manner and without affecting theelongation rate (Yi et al., 2010). As the extended root hair growthin the gtl1 df1 loss-of-function line resembles that of the 35S:RSL4line, we asked whether the level of RSL4 expression is increased ingtl1-1 df1-1 mutants. As shown in Fig. 2A, our RT-qPCR analysisrevealed that RSL4 expression is significantly upregulated in gtl1-1df1-1 double mutants, suggesting that GTL1 and DF1 are requiredto repress RSL4 expression. We also found that RSL4 expression isdownregulated in pEXP7:GTL1-GFP roots (Fig. 2A), indicatingthat ectopic overexpression of GTL1 is sufficient to block RSL4expression. Intriguingly, overexpression of DF1 does not causesignificant downregulation of RSL4 in pEXP7:DF1-GFP roots(Fig. 2A), implying that GTL1 has a stronger impact on RSL4expression. In addition, our RT-qPCR analysis revealed that, amongthe RHD6/RSL homologs, RHD6 expression is elevated in the gtl1-1df1-1 doublemutants but its expression is not significantly changed inpEXP7:GTL1-GFP and pEXP7:DF1-GFP roots (Fig. 2A).Conversely, we did not detect significant changes in RSL1, RSL2and RSL3 expression in the gtl1-1 df1-1 double mutant, but we didobserve that RSL2 and RSL3 are downregulated in pEXP7:GTL1-GFP and pEXP7:DF1-GFP roots (Fig. 2A). These results suggestthat the primary target of GTL1 and DF1 in root hair development isRSL4, because among the RHD6/RSL homologs, RSL4 shows asignificant transcriptional response in both GTL1/DF1 gain-of-function and loss-of-function lines.To investigate whether transcriptional activation of RSL4 leads to

the increased levels of RSL4 proteins in root hairs, we introducedthe pRSL4:GFP-RSL4 construct (Yi et al., 2010) into gtl1-1 df1-1double mutants and examined the GFP-RSL4 accumulation byconfocal microscopy. As previously reported, GFP-RSL4 proteins

accumulate in trichoblast cells prior to root hair initiation and theiraccumulation sharply declines when hair cells complete theiroutgrowth in thewild-type background (Yi et al., 2010 and Fig. 2B).In sharp contrast, we found that GFP-RSL4 detection persists muchlonger in maturing root hairs in the gtl1-1 df1-1 background.Accordingly, our quantitative analysis showed that the number ofRSL4-GFP-expressing cells in trichoblast cell files is significantlyincreased in gtl1-1 df1-1 roots (Fig. 2B,C). In order to test whetherRSL4 upregulation is responsible for the extended hair growth ingtl1-1 df1-1, we introduced the rsl4-1mutation into the gtl1-1 df1-1mutant background. As shown in Fig. 3A,B, introduction of rsl4-1into gtl1-1 df1-1 rescues the root hair phenotype in gtl1-1 df1-1,further substantiating that RSL4 is a key regulator of root hairgrowth acting downstream of GTL1 and DF1. We subsequentlyinvestigated whether GTL1 and DF1 directly bind the RSL4promoter by immunoprecipitating GTL1-GFP and DF1-GFPproteins from 7-day-old pGTL1:GTL1-GFP and pDF1:DF1-GFProots. Our chromatin immunoprecipitation (ChIP) followed byquantitative PCR (ChIP-qPCR) analysis showed an enrichment ofboth GTL1-GFP and DF1-GFP around 500-1000 bp upstream of theRSL4 start codon containing two binding motifs for GTL1 (Breueret al., 2012) (Fig. 3C). To further support these results, we co-bombarded the p35S:GTL1 construct and pRSL4:LUC promoterinto ArabidopsisMM2D culture cells and tested whether GTL1 canrepress the RSL4 promoter activity. As shown in Fig. S4, applicationof p35S:GTL1 significantly suppresses the expression of pRSL4:LUC compared with the vector control. These results thus suggestthat GTL1 and DF1 directly bind the promoter region of RSL4 torepress its expression.

GTL1 and DF1 act in a parallel pathway with auxin signalingto regulate root hair developmentAuxin is known to promote root hair growth by activating theexpression of RSL4 (Mangano et al., 2017; Yi et al., 2010). Toinvestigate whether GTL1 and DF1 are also involved in auxin-induced root hair growth, we first studied the auxin response in gtl1-1 df1-1 mutants, as well as in GTL1 and DF1 overexpression lines.As previously reported (Grierson et al., 2014), wild-type plantsgrown in the presence of 10 nM indole-3-acetic acid (IAA) displaysignificantly longer root hairs compared with control plants(Fig. 4A,B). In contrast, root hair growth is comparable betweencontrol and IAA-treated gtl1-1 df1-1 mutants (Fig. 4A,B). We nexttested whether IAA can rescue the compromised hair growth inpEXP7:GTL1-GFP and pEXP7:DF1-GFP plants but found thatIAA has little to no impact on root hair growth in theseoverexpression lines (Fig. 4A,B). Conversely, the application ofan auxin inhibitor, auxinole (Hayashi et al., 2012), completelysuppresses root hair growth in wild type, gtl1-1 df1-1 and GTL1 orDF1 overexpression lines (Fig. 4A,B). These results togethersuggest that GTL1 and DF1 likely function independently fromauxin signaling in controlling root hair growth.

It has been demonstrated previously that the application ofanother synthetic auxin, 1-naphthaleneacetic acid (NAA),upregulates RSL4 expression (Yi et al., 2010). Consistently, ourRT-qPCR analysis revealed that IAA promotes RSL4 expressionand that auxinole strongly suppresses its expression in both wild-type and gtl1-1 df1-1 roots (Fig. 4C). Our RT-qPCR data, inaddition, showed that overexpression of GTL1 and DF1 counteractsthis auxin-induced RSL4 upregulation as the level of RSL4expression is strongly reduced in pEXP7:GTL1-GFP and pEXP7:DF1-GFP plants, regardless of treatment with IAA or auxinole(Fig. 4C). Unlike RSL4, the expression of GTL1 and DF1 does not

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seem to be affected by IAA, although their expression tends to belower in plants treated with auxinole (Fig. 4D). These results,therefore, support the hypothesis that GTL1 and DF1 control roothair growth via regulation of RSL4 in a parallel pathway with auxin.In addition to auxin, phosphate (Pi) availability is well known toaffect root hair growth (Datta et al., 2015; Yi et al., 2010). Similar toauxin treatment, however, our RT-qPCR data showed thatphosphate conditions do not change the expression of GTL1 andDF1 (Fig. 4E), suggesting that GTL1 and DF1 do not act via thephosphate-mediated control of root hair growth.

GTL1 and DF1 directly regulate a subset of RSL4 targetgenesRecent studies have identified 132 genes that might be directlyactivated by RSL4 in Arabidopsis roots (Hwang et al., 2017;Vijayakumar et al., 2016; Won et al., 2009; Yi et al., 2010). Havinguncovered that GTL1 and DF1 repress RSL4 expression, we sought

to determine how much the GTL1/DF1-regulated gene regulatorynetwork overlaps with that of RSL4. To identify genes regulated byGTL1 and DF1 in root hairs, we collected root hair cellsoverexpressing GTL1-GFP and DF1-GFP, respectively, frompEXP7:GTL1-GFP and pEXP7:DF1-GFP plants by fluorescence-activated cell sorting. We also collected root hair cells from gtl1-1df1-1 plant expressing the root hair specific pEXP7:NLS-GFPmarker (Ikeuchi et al., 2015) and compared their transcriptionalprofile using the Affymetrix ATH1 microarray. We defined GTL1or DF1 response genes as those that show more than a twofoldchange of gene expression in gtl1-1 df1-1 plants compared withpEXP7:GTL1-GFP or pEXP7:DF1-GFP plants (P

genes are repressed by GTL1 (Fig. S5A and Table 1), stronglysuggesting that GTL1 and RSL4 share many common targets butthey act in opposing manners. For DF1, we identified 755 activatedand 918 repressed genes, but only 7 (5.3%) of the repressed genesare RSL4 response genes (Fig. S5A, Table S1). Given that all sevenof these RSL4 response genes are also repressed by GTL1(Fig. S5B), we focused our remaining analysis on the 36 genescommonly regulated by GTL1 and RSL4.The 36 GTL1-RSL4 common downstream genes include those

that encode proteins associated with cell wall biosynthesis andremodeling (e.g. EXT12, XTH26 and LRX2), those likely acting incellular signaling (e.g. RHS1, RLK genes and ACA12), and thosewith functions in membrane trafficking or membrane transport(e.g. ABCB3, ABCB5, IRT2 and COW1) (Table 1), suggesting thatGTL1 and RSL4 regulate a wide range of subcellular processesunderlying root hair growth. Having uncovered a substantialoverlap between RSL4-activated genes and GTL1/DF1-repressedgenes, we wanted to test whether GTL1 and DF1 also directly bindany of these genes. To achieve this, we performed awhole-genomeChIP-chip analysis using pGTL1:GTL1-GFP and pDF1:DF1-GFP roots. We identified 9200 putative direct targets for GTL1and 7803 putative targets for DF1, 5208 (66.7% of DF1 targets) ofwhich are common between GTL1 and DF1 (Z-score>1.5) (Fig.S6A and Table S2). Using these ChIP-chip data, we found that 12(33.3%) of the 36 targets shared between GTL1 and RSL4 aredirectly bound by GTL1 (Table 1). We also found that DF1directly binds 11 (30.6%) of the 36 genes but only four of these 11(36.4%) are transcriptionally repressed by DF1 (Table 1),implying that the physical binding of DF1 to the target promotersequence does not necessarily cause downstream transcriptionalrepression. These data demonstrate that GTL1, DF1 and RSL4control root hair growth by regulating partially overlappingtranscriptional pathways.

GTL1 and RSL4 control root hair growth through a negative-feedback loopOur transcriptome and ChIP-chip data suggest that GTL1 and DF1directly regulate RSL4 and a subset of its downstream targets. Tofurther investigate the regulatory roles of GTL1 and DF1, weemployed gene network inference with ensemble of tree 3(GENIE3) (Huynh-Thu et al., 2010) and inferred a generegulatory network (GRN) among GTL1, DF1, RSL4 and their36 common target genes using our expression data from GTL1 andDF1 mutants (gtl1-1, df1-1, gtl1-1 df1-1) and from GTL1 and DF1overexpression lines ( pEXP7:GTL1-GFP and pEXP7:DF1-GFP).We also obtained the sign (positive/negative) of regulation usingtime-course RNA-seq data from 3-, 4-, 5-, 6- and 7-day-old wild-type roots (de Luis Balaguer et al., 2017). Our GRN predicts thatGTL1 regulates 30 (83%) of the 36 downstream targets, 28 of which(93%) are also predicted to be regulated by RSL4 (Fig. 5A). Thesedata further substantiate that GTL1 and RSL4 co-regulate many ofthese root hair genes to control root hair growth. Of the 30 targetsGTL1 is predicted to regulate, our sign algorithm predicts that 29 ofthose (97%) are repressions (Fig. 6A). In contrast, our signalgorithm predicts that of the 28 genes regulated by RSL4, 21(75%) are activated by RSL4 (Fig. 5A). In agreement with DF1 notplaying a central role in transcriptional repression of root hair genes,we observed that DF1 has only one predicted downstream target,XTH26, which is not predicted to be regulated by RSL4 (Fig. 5A).

Our GRN, in addition, predicted that RSL4 and GTL1 form anegative-feedback loop (Fig. 5A). As positive regulation of GTL1by RSL4 has also been reported by a previous study using RSL4-inducible lines (Vijayakumar et al., 2016), we hypothesized that thismutual regulation is important for establishing proper root hairgrowth. To explore this reciprocal regulation further, we developeda mathematical model between RSL4 and GTL1, and tested whethertheir protein levels can reach a steady state. In addition to the

Fig. 3. GTL1 and DF1 directly bind the RSL4 promoterand regulate its expression. (A) Root hair phenotypes ofwild-type, gtl1-1 df1-1, rsl4-1 and gtl1-1 df1-1 rsl4-1seedlings. Scale bar: 500 μm. (B) Quantitative analysis ofroot hair length. Data are mean±s.e.m. (n=120). Differentletters indicate means that differ significantly (Tukey-Kramertest, P

negative-feedback loop between GTL1 and RSL4, our ChIP-chipdata and transient promoter-LUC data suggested that GTL1 is ableto repress itself (Table S2 and Fig. S4). Thus, we incorporated theauto-repression of GTL1 into the model. We incorporated severalparameters, such as production and degradation rates of GTL1 andRSL4, to estimate the levels of GTL1 and RSL4 over time. Ourmodel predicted that for certain parameter values, there exists asteady state for GTL1 and RSL4, likely representing the wild-typesituation where root hairs grow to a constant size (Fig. 5B andFig. S7A). We subsequently used a sensitivity analysis to identifythe most important parameters in the model that influence the steady

states of GTL1 and RSL4. Using Sobol decomposition, we foundthat the production rate of RSL4, k1, and the production rate ofGTL1, k2, are the two most important parameters in the model(Fig. S7B and Table S4).

To test whether RSL4 and GTL1 alone are able to account forthe observed root hair phenotypes, we subsequently modified thevalues of their production rates (k1 and k2, respectively) andexamined the changes in the steady state. First, to simulate GTL1overexpression, we increased the production rate of GTL1 (k2)until the steady state value of GTL1 was 15-fold higher than inwild type, as estimated by our RT-qPCR data on pEXP7:GTL1-GFP plants (Fig. S1D). Our model predicts that the steady stateof RSL4 is 16% of the value in wild type (Fig. 5B, Fig. S7A),suggesting that, as GTL1 increases, RSL4 decreases and causesshorter root hairs, which is the phenotype we observed inpEXP7:GTL1-GFP plants (Fig. 1A). Next, to simulate the gtl1-1df1-1 mutant, we set the production rate of GTL1 (k2) to 0, as ourRT-qPCR data show that GTL1 expression is effectively zero ingtl1-1 df1-1 (Fig. S1D). Our model shows that in this scenariothe steady state of RSL4 is 1.5-fold higher than in wild type,which is supported by our RT-qPCR data (Figs 2A and 5B,Fig. S6A). These results thus suggest how the expression levelsof GTL1 and RSL4 can be altered to determine the final lengthof root hairs.

DISCUSSIONThe GTL1-RSL4 module in the GRN of root hair growthIn this study we demonstrate that the final size of root hair cells isregulated by coordinated action of GTL1 and RSL4, which serve asa repressor and activator, respectively, of root hair growth. Previousstudies have identified several negative regulators of root hairgrowth (Breuninger et al., 2016; Hwang et al., 2016), but how theysuppress root hair growth is not known. Our data uncover aneffective strategy to fine-tune root hair growth that relies on thenegative regulation of RSL4, which is one of the central hubs in thetranscriptional network of root hair growth (Datta et al., 2015;Marzol et al., 2017; Yi et al., 2010). It is interesting that GTL1 andDF1 control only the duration of root hair growth and not the rate ofhair growth. These observations are consistent with previous datashowing that the ectopic RSL4 expression does not change the rateof hair growth and only prolongs hair growth (Yi et al., 2010). Theseresults thus suggest that these two parameters of root hair growth canbe mechanistically uncoupled and, although the GTL1-RSL4module controls the extent of root hair growth, other as yetunknown pathways control the rate of root hair growth. As gtl1-1df1-1 double mutants, but not their single mutants, display root hairphenotypes (Fig. 1A,B), we hypothesized that GTL1 and DF1 workredundantly on root hair development. In agreement with this, thereis a large overlap between GTL1- and DF1-response genes(Fig. S5B and Table S1). DF1, however, has less of an impact onRSL4 expression than GTL1 (Fig. 2A), and our GRN predicts thatthe contribution of DF1 to regulating known root hair genes is muchless than GTL1 (Fig. 5A). These results thus suggest that DF1 mayfunction as a backup system for GTL1.

Our data show that GTL1 and RSL4 regulate a set of commondownstream genes (Figs 5 and 6), which allows robust control oftarget gene expression. Another important aspect of our root hairGRN is that GTL1 and RSL4 form a negative-feedback loop thatresults in steady-state levels of their expression, thus permittingconsistent hair growth in wild-type plants (Fig. 5). In addition toRSL4, our RT-qPCR analysis shows that RHD6 is also upregulatedin gtl1-1 df1-1 mutants (Fig. 2A), suggesting that RHD6 is another

Fig. 4. GTL1 and DF1 regulate root hair growth in a parallel pathway toauxin signaling. (A) Root hair phenotypes of wild-type, gtl1-1 df1-1, pEXP7:GTL1-GFP and pEXP7:DF1-GFP seedlings treated with 10 nM IAA or 10 μMauxinole. Scale bars: 300 μm. (B) Quantitative analysis of root hair length. Dataare mean±s.e.m. (n=60). Different letters indicate means that differsignificantly (Tukey-Kramer test, P

potential target of GTL1 and/or DF1. Indeed, our ChIP-chip datasupport this notion as both GTL1 and DF1 bind the promotersequence of RHD6 (Table S2). Given that RHD6 directly bindsRSL4 (Yi et al., 2010), this suggests a feed-forward loop betweenGTL1, RHD6 and RSL4. Interestingly, expression levels ofLotus japonicus ROOTHAIRLESS1-LIKE1 (LRL1), whichencodes a bHLH transcription factor that acts as an activator ofroot hair growth (Karas et al., 2009; Lin et al., 2015), is alsocorrelated with GTL1 and DF1 expression based on ourtranscriptome data (Table S1). Thus, the GTL1-RSL4 GRN weunveiled in this study may be expanded in future studies toinclude RHD6, LRL1 and perhaps other root hair regulators tofurther understand the core transcriptional modules that controlroot hair growth.

Physiological roles of GTL1 in root hair growthWe found that the majority of the 36 GTL1-RSL4 common targetsare genes related to cell wall biosynthesis and remodeling (Table 1and Fig. 6). We believe this is reasonable as cell-wall construction isdirectly involved in cell expansion. In addition, RHS1, one of theGTL1-RSL4 common downstream genes (Table 1 and Fig. 6), is acalmodulin-like protein that is thought to regulate root hair growththrough Ca2+ signaling (Won et al., 2009). Another GTL1-RSL4target, CAN OF WORMS 1 (COW1), is implicated in membranetrafficking and required for root hair tip growth, as its loss-of-function mutation causes shorter root hairs (Böhme et al., 2004;Grierson et al., 1997). GTL1-RSL4 common targets also includegenes associated with several other physiological functions. IRONREGULATED TRANSPORTER 2 (IRT2), for example, regulates

Table 1. Genes commonly regulated by GTL1, DF1 and RSL4

AGIdesignation

Genesymbol Molecular and biological function

Transcriptionalregulation

Promoterbinding

ReferenceGTL1 DF1 GTL1 DF1

At1g05990 RHS1 EF hand calcium-binding protein family −2.04 − + + 3At1g12950 RHS2 MATE efflux family protein −1.00 −1.15 + ++ 3At1g27740 RSL4 bHLH transcription factor −1.08 − + + 1At1g30850 RHS4 A hypothetical protein of unknown function −1.59 − − − 1At1g31750 Proline-rich family protein −1.60 − − − 1At1g34330 Pseudogene, putative peroxidase −2.83 − NA NA 1At1g34510 Peroxidase superfamily protein −5.99 − − − 1At1g34540 CYP94D1 Cytochrome P450, involved in oxidation-reduction process −5.14 − − − 1At1g59850 ARM repeat superfamily protein −4.57 − + − 1At1g61080 Hydroxyproline-rich glycoprotein family protein −5.02 −3.97 − − 1At1g62440 LRX2 Leucine-rich repeat/extensin, involved in cell wall organization −1.41 − − − 3At1g63600 Receptor-like protein kinase-related family protein −3.60 −1.17 − + 1At2g02990 RNS1 Ribonuclease T2 family −1.96 − − − 1At2g03980 GDSL-like lipase/acylhydrolase superfamily protein, involved in lipid

catabolic process−6.19 −1.46 − − 1

At2g20520 FLA6 FASCICLIN-like arabinogalactan 6, plasma membrane protein −1.01 − ++ − 1At2g25240 CCP3 Serine protease inhibitor (SERPIN) family protein −3.01 − + − 1At3g60280 UCC3 Blue copper-binding protein III, involved in the oxidation-reduction process −2.27 − NA NA 1At3g63380 ACA12 ATPase E1-E2 type family protein/haloacid dehalogenase-like hydrolase

family protein−1.25 − − − 1

At4g01820 ABCB3 ATP-BINDING CASSETTE B3, involved in basipetal auxin transport −1.02 − − − 1At4g01830 ABCB5 ATP-BINDING CASSETTE B5, involved in basipetal auxin transport −1.02 − − − 1At4g02270 RHS13 Required for optimal hair growth −2.06 − − − 1At4g13390 EXT12 Proline-rich extensin-like family protein, involved in cell wall organization −1.55 − − ++ 1At4g19680 IRT2 Iron and zinc transporter −1.96 − ++ + 1At4g22080 RHS14 Involved in pectin catabolic process −2.75 − − − 1At4g22090 Involved in pectin catabolic process −2.75 − ++ − 1At4g25220 RHS15 Involved in carbohydrate transport −5.68 −1.82 − − 1At4g25790 CAP (cysteine-rich secretory proteins, antigen 5 and pathogenesis-related

1 protein) superfamily protein−5.10 −1.92 − + 1

At4g28850 XTH26 Xyloglucan endotransglucosylase/hydrolase, involved in cell wallbiogenesis and organization

−1.42 − ++ ++ 1

At4g34580 COW1 A phosphatidylinositol transfer protein, involved in cell tip growth −1.85 − − + 1At5g19800 HRGP2 A hydroxyproline-rich glycoprotein family protein −1.01 − − − 1At5g22410 RHS18 Involved in hydrogen peroxide catabolic process −1.11 − − − 1At5g24880 Chromodomain cec-like protein −1.01 − + − 1At5g26080 Proline-rich family protein −2.84 1.11 − − 1At5g43580 UPI Serine-type endopeptidase inhibitor, functions in resistance to

necrotrophic fungi and insect herbivory−5.05 −2.37 + + 1

At5g58375 Methyltransferase-related protein −1.21 − NA NA 2At5g61650 CYCP4 P-type cyclins, involved in the cell cycle −1.15 − ++ ++ 1

Root hair-specific microarray analysis identifies 36 genes regulated by both GTL1 and RSL4. Among them, seven genes are co-regulated by DF1. Transcriptionalregulation by GTL1 and DF1 are shown as log2(pEXP7:GTL1-GFP/gtl1-1 df1-1) and log2(pEXP7:DF1-GFP/gtl1-1 df1-1), respectively. Promoter binding ofGTL1 and DF1 is based on ChIP-chip analysis using pGTL1:GTL1-GFP and pDF1:DF1-GFP plants.++, direct targets with a cut-off Z-score of 2.0; +, direct targets with a cut-off Z-score of 1.5; −, no signal enrichment; NA, not applicable.RSL4-dependent transcriptional regulation of these genes has been reported by Yi et al. (2010)1, Vijayakumar et al. (2016)2 and Won et al. (2009)3.These transcriptome data of RSL4 are taken using whole roots, thus they are not necessarily specific to root hairs.

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iron uptake from soil (Vert et al., 2009), and UNUSUAL SERINEPROTEASE INHIBITOR (UPI) is involved in pathogen resistance(Laluk andMengiste, 2011). Since root hairs result from outgrowth ofthe root epidermis, they directly interact with the microenvironmentof the soil. It is thus likely that these microenvironments influence theextent of root hair growth, and this interaction also needs to beregulated by GTL1. Consistently, our GO analysis of GTL1 targetssuggests that GTL1 affects ‘response to stimulus’, ‘response to stress’and ‘response to chemical stimulus’ (Fig. S5B), suggesting thatGTL1 regulates diverse arrays of physiological processes associatedwith root hair growth.

ConclusionsIn this study we demonstrate that the final size of root hair cells isregulated by coordinated action of GTL1 and RSL4, which serve asa repressor and activator, respectively, of root hair growth. Ourmathematical analysis suggests that GTL1-RSL4 functions as a coremodule in root hair growth and regulates cell expansion, as well asseveral other physiological responses such as nutrient uptake andpathogen response. Our data, in addition, suggest that otherpreviously described root hair regulators, such as RHD6 andLRL1, may function within a larger GRN that controls root hairgrowth downstream of the GTL1-RSL4 module.

MATERIALS AND METHODSPlant materials and growth conditionsThe gtl1-1, ccs52a1-2, rsl4-1, pGTL1:GTL1-GFP, pRSL4:RSL4-GFP,pEXP7:GTL1-GFP and pEXP7:NLS-GFP lines have been previously

described (Breuer et al., 2009, 2012; Ikeuchi et al., 2015; Yi et al., 2010).The df1-1 (SALK_106258) mutant was obtained from the ArabidopsisBiological Resource Center. All mutants and transgenic lines used in thisstudy were in the Columbia-0 background. Plants were grown on half-strength Johnson media with 6 g/l gelzan (Sigma) and final concentration ofphosphate adjusted to 1 mM (Johnson et al., 1957; Ma et al., 2001). Forauxin and auxin inhibitor treatment, a solution of 1 mM IAA and 30 mMauxinole (Hayashi et al., 2012) in mixed DMSO and ethanol were added tothe Johnson media to final concentrations of 10 nM and 10 μM,respectively. Phosphate media were prepared based on recipes of Ma et al.(2001).

Plasmid construction and plant transformationFor the construction of the pDF1:DF1-GFP vector, a 4900 bp genomicfragment of the DF1 locus was amplified from the BAC clone F7O12 andcloned into the pENTR/D-TOPO vector (Invitrogen). A SmaI restriction sitewas introduced upstream of the translational stop codon by site-directedmutagenesis. A SmaI-digested GFP fragment was then inserted to create aC-terminal translational fusion construct and the resulting construct wascloned into the pGWB1 binary vector (Nakagawa et al., 2007). The pEXP7:DF1-GFP vector was generated by combining pDONR-pEXP7 and pENTR-DF1-GFP together with the R4pGW501 destination vector (Nakagawaet al., 2008) as described by Ikeuchi et al. (2015). A set of primers used forPCR amplification is provided in Table S5. All plant transformation wascarried out using the floral dip method (Clough and Bent, 1998).

RNA extraction and RT-qPCR analysisTotal RNAwas extracted from 7-day-old roots using an RNeasy Plant MiniKit (Qiagen). Extracted RNA was reverse transcribed using a PrimeScriptRT-PCR kit with DNase I (Perfect Real Time) (Takara) in accordance with

Fig. 5. Modeling predicts that GTL1 and RSL4 form a negative-feedback loop and regulate a set of common target genes. (A) Gene regulatory network(GRN) of GTL1, RSL4 and their shared downstream targets. Transcriptional activation and repression are indicated by arrows and bars, respectively. A time-course transcriptome of elongation and differentiation zones was used to predict the transcriptional activation and repression of target genes. Red edgesrepresent direct promoter binding validated using ChIP-chip data. (B) Model simulation of GTL1 and RSL4 dynamics in wild-type (left), pEXP7:GTL1-GFP(middle) and gtl1-1 df-1 mutant (right) roots. Red and blue lines represent model solutions for the RSL4 and GTL1 equations, respectively. The value of k2, theproduction rate of GTL1, was varied from the wild-type case so that the steady-state values of GTL1 in pEXP7:GTL1-GFP and gtl1-1 df-1 roots meet the valueestimated from our RT-qPCR data.

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the accompanying protocol. Transcript levels were determined by RT-qPCRusing a THUNDERBIRD SYBR qPCR Mix kit (Toyobo) and an Mx399PQPCR system (Agilent). The expression of the UBQ10 gene was used as areference (Shibata et al., 2013). A set of primers used for RT-qPCR isprovided in Table S5.

Fluorescence-activated cell sorting and microarray analysisTo identify genes regulated by GTL1 and DF1 in root hairs, GFP-positivecells were sorted from 5-day-old wild-type and gtl1-1 df1-1 roots carryingpEXP7:NLS-GFP, as well as from pEXP7:GTL1-GFP and pEXP7:DF1-GFP roots. The root tips were dissected at ∼0.5 cm from root tips and GFP-positive protoplasts were isolated by fluorescence-activated cell sorting,following the protocol described by Sozzani et al. (2010). Total RNA wasextracted from three biological replicates and labeled probes were used forhybridization on ATH1 chips (Affymetrix). Microarray data were analyzedusing R software and the gcRMA implementation with AffylmGUI(Wettenhall et al., 2006) of the Bioconductor package as previouslydescribed (Morohashi and Grotewold, 2009; Sozzani et al., 2010).Microarray data have been deposited in Gene Expression Omnibus(https://www.ncbi.nlm.nih.gov/geo/) under accession number GSE103917.

ChIP-chip and ChIP-qPCR analysisChIP-chip experiment was performed using 5-day-old pGTL1:GTL1-GFPand pDF1:DF1-GFP roots as previously described (Sozzani et al., 2010).GTL1-GFP and DF1-GFP proteins were immunoprecipitated from threebiological replicates using antibodies against GFP (ab290, Abcam). Bovineserum albumin was used as a negative control. Labeled DNAwas hybridizedto a custom-made Arabidopsis promoter microarray (Sozzani et al., 2010).ChIP-chip datawere analyzed as previously described (Sozzani et al., 2010).

Relatively low Z-scores were chosen to decrease the number of falsenegatives and identify meaningful overlaps with the expression data. ChIP-chip data have been deposited in Gene Expression Omnibus (https://www.ncbi.nlm.nih.gov/geo/) under accession number GSE104010. ChIP-qPCRanalysis was performed using 7-day-old pGTL1:GTL1-GFP and pDF1:DF1-GFP roots as previously described (Rymen et al., 2017). Data werenormalized against input DNA and shown as relative enrichment of DNAimmunoprecipitated at the TA3 retrotransposon locus (Yamaguchi et al.,2014). A set of primers used for ChIP-qPCR is provided in Table S5.

Promoter-luciferase assayTo construct the firefly luciferase (LUC) reporter vector, a 1.8 kb promoterofGTL1was amplified by PCR and introduced into the LUC reporter vector(Ohta et al., 2001), as reported by Rymen et al. (2017). For the constructionof the effector vector, the coding sequence of GTL1 was amplified by PCRand cloned into the p35SSG vector (Mitsuda et al., 2005) using the SmaI sitelocated between the CaMV p35S promoter-Omega and the NOS terminatorsequence of the p35SSG vector. The set of primers used for PCRamplification is provided in Table S5.

The p35S:GTL1 and the empty p35SSG vectors were used as an effectorand control vector, respectively. The pRSL4:LUC and pGTL1:LUC vectorswere used as reporters. As an internal control, the pPTRL vector, whichdrives the expression of a Renilla LUC gene under the control of the CaMVp35S promoter, was used. The constructions were introduced intoArabidopsis MM2D culture cells (Menges and Murray, 2002) using agold particle bombardment system. Luciferase activities were quantifiedusing a Mithras LB940 microplate luminometer (Berthold Technologies)according to the protocol described previously (Hiratsu et al., 2002).

MicroscopyRoot hair phenotypes were recorded using a Leica M165 FC dissectionmicroscope equipped with a digital Leica DFC 7000T camera. The length of120 root hairs from at least six seedlings were quantified for each genotypewith ImageJ version 1.50a. For auxin and auxin inhibitor treatment, thelengths of 60 root hairs from at least six seedlings were quantified. Toquantify the rate of root hair growth, hair growth of 7-day-old wild-type andgtl1-1 df1-1 seedlings was recorded every 1 h and root hair length wasquantified by ImageJ. To estimate the ploidy level of nuclei, nuclei werestained with DAPI (Partec) and visualized using an Olympus BX51fluorescence microscope equipped with a digital Olympus DP70 cameraand Olympus DP Manager software version 1.2.1.107 (Zhang andOppenheimer, 2004). Fluorescence signals of over 40 root cap nuclei and120 root hair nuclei from at least five seedlings were quantified per genotypewith ImageJ as previously described (Ikeuchi et al., 2015). Expressionpatterns of GTL1-GFP, DF1-GFP and RSL4-GFP proteins were examinedusing a SP5 confocal laser scanning microscope (Leica). Recorded imageswere exported as a 16-bit TIFF image. Fluorescence intensity was quantifiedusing ImageJ. To produce a merged image from multiple images,‘photomerge’ was applied on Photoshop CS3 Extended (Adobe). Contrastand brightness were adjusted using Photoshop.

Gene regulatory network inferenceGene network inference with ensemble of trees 3 (GENIE3) (Huynh-Thuet al., 2010) was used to predict the downstream targets of GTL1 and RSL4.GENIE3 uses regression tree inference to build the GRN that best fits theexperimental data. Microarray data from gtl1-1, df1-1, gtl1-1 df1-1, pEXP7:GTL1-GFP and pEXP7:DF1-GFP were used to infer 10,000 directedregression trees using the Random Forest method (Breiman, 2001), and thetrees were then averaged to form the final GRN. Once the final GRN wasobtained, a threshold was set on the number of edges to increase theprecision. The threshold was chosen using ChIP-chip data to validate thedownstream targets of GTL1 in the network. The number of edges waschosen as floor (1.65×36)=59 edges (1.65×number of genes), as this numberresulted in the highest precision for the network (Table S3).

A time-course RNAseq dataset of the root meristem (de Luis Balagueret al., 2017) was used to determine the sign of the regulation from gene A togene B. According to the first-order Markov assumption, if gene B increases(or decreases) at one time point after gene A increases (decreases), the

Fig. 6. A schematic diagram of the proposed transcriptional networkregulating root hair growth inArabidopsis.RHD6 inducesRSL4 expressionto promote root hair outgrowth. GTL1 binds the RSL4 promoter and directlyrepresses its expression to terminate root hair growth. RSL4, in addition,activates GTL1, thus forming a negative-feedback loop. RSL4 and GTL1regulate, both directly and indirectly, a set of common downstream genesinvolved in cell wall biosynthesis and remodeling, cellular signaling, membranetransport, membrane trafficking, metabolism, pathogenesis and unknownfunctions. Auxin promotes root hair growth by activating RSL4 but not GTL1.

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regulation at that time point is assumed to be positive. Similarly, if gene Bincreases (or decreases) after gene A decreases (increases), the regulation atthat time point is assumed to be negative (de Luis Balaguer et al., 2017). TheMarkov assumption was used to calculate the sign for all the time points, andthen the majority sign was used for the edge.

Mathematical modeling and sensitivity analysisThe mathematical model consisted of two ordinary differential equations:one measuring RSL4 concentration (R) and the other measuring GTL1concentration (G). It was assumed that transcription and translation happenquickly, such that transcription and protein degradation could be modeled inthe same equation. Additionally, it was assumed that GTL1 and RSL4proteins degrade linearly.

The gene regulatory network and experimental data predicted that GTL1represses RSL4. Thus, a Hill equation was used to model RSL4transcription, where increased levels of GTL1 result in decreased levels ofRSL4. As the oligomeric state of GTL1 is unknown, there was a possibilityof GTL1 forming higher oligomers, where n1 is the number of GTL1proteins bound to each other.

dR

dt¼ k1 K

n11D

Kn11D þ Gn1� �

� d1R

The gene regulatory network predicted that RSL4 activates GTL1. Inaddition, the experimental data suggested that GTL1 represses itself. Thus,the Hill equation for GTL1 takes into account what happens when bothRSL4 and GTL1 bind the TL1 promoter at the same time. One possibility isthat GTL1 inhibition overcomes the RSL4 activation. This means that, inorder for GTL1 to be transcribed, GTL1 must be unbound (Eqn 1). In theother case, RSL4 activation could overcome GTL1 inhibition. This meansthat, as long as RSL4 is bound, GTL1 will be transcribed, even if GTL1 isbound to its own promoter (Eqn 2). As in the RSL4 equation, there is apossibility of higher oligomeric states.

dG

dt¼ k2 K

n22DK

n33D þ Kn33DRn2

Kn22DKn33D þ Kn33DRn2 þ Kn22DGn3 þ Rn2Gn3

� �� d2G ð1Þ

dG

dt¼ k2 K

n22DK

n33D þ Kn33DRn2 þ Rn2Gn3

Kn22DKn33D þ Kn33DRn2 þ Kn22DGn3 þ Rn2Gn3

� �� d2G ð2Þ

After constructing the two models, nullcline analysis was performed tocheck for steady-state solutions. Mathematica was used to analytically solvefor the nullclines as well as for steady states. As concentrations must bepositive values, only the region where R≥0 andG≥0 was considered. In thisregion, the model with Eqn 1 has no steady states, whereas the model withEqn 2 has one steady state. In a wild-type case, there should be a steady statevalue of R and G that produces root hairs with normal length. Thus, themodel with Eqn 2 was used for the simulations.

A sensitivity analysis was used to identify the parameters that most greatlyaffect the model outcome, as these parameters could give insight into theeffects of RSL4 and GTL1 mutants and overexpression lines. Soboldecomposition, which quantifies sensitivity by calculating the variance inthe model outcome as the parameters are changed (Sobol, 2001), was used tocalculate the sensitivity indices. The index was calculated for eachparameter using 1000 Monte Carlo evaluations and repeated 10 times fortechnical replicates (Clark et al., 2016).

AcknowledgementsWe are grateful to the members of K.S.’s lab for discussions and to Momoko Ikeuchiand David Favero for comments on the manuscript. We thank Mariko Mouri, ChikaIkeda and Noriko Doi for their technical assistance.

Competing interestsThe authors declare no competing or financial interests.

Author contributionsConceptualization: M.S., C.B., K.S.; Validation: M.S., C.B., N.M.C., B.R., L.B., K.M.;Formal analysis: M.S., C.B., N.M.C., K.M., W.B., R.S.; Investigation: M.S., C.B.,A.K., N.M.C., B.R., L.B., K.M.; Resources: A.K., B.R.; Data curation: M.S., C.B.,N.M.C., B.R., W.B., P.N.B., R.S.; Writing - original draft: M.S., N.M.C., R.S., K.S.;

Writing - review & editing: M.S., C.B., N.M.C., B.R., L.B., K.M., W.B., P.N.B., R.S.,K.S.; Visualization: M.S., C.B., K.S.; Supervision: R.S., K.S.; Project administration:P.N.B., K.S.; Funding acquisition: M.S., N.M.C., K.S.

FundingThis work was supported by a National Science Foundation CAREER grant (MCB-1453130) to R.S., by a National Science Foundation EAPSI grant (1514779) toN.M.C. and by grants from Ministry of Education, Culture, Sports and Technology ofJapan to M.S. (16J07464) and to K.S. (26291064 and 15H05961). N.M.C. issupported by a National Science Foundation GRF (DGE-1252376) and M.S. issupported by a Japan Society for the Promotion of Science postdoctoral fellowship.Deposited in PMC for immediate release.

Data availabilityMicroarray and ChIP-chip data have been deposited in Gene Expression Omnibus(https://www.ncbi.nlm.nih.gov/geo/) under accession numbers GSE103917 andGSE104010, respectively.

Supplementary informationSupplementary information available online athttp://dev.biologists.org/lookup/doi/10.1242/dev.159707.supplemental

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RESEARCH ARTICLE Development (2018) 145, dev159707. doi:10.1242/dev.159707

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