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Journal of Plant Physiology 162 (2005) 1038—1045

KEYWORDArabidopsiBezier curCurvatureDevelopmeEthylene;Root apex

0176-1617/$ - sdoi:10.1016/j.

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www.elsevier.de/jplph

Geometric analysis of Arabidopsis root apex revealsa new aspect of the ethylene signal transductionpathway in development

Emilio Cervantesa,�, Angel Tocinob

aDepartamento de Produccion Vegetal, IRNASA-CSIC, Salamanca, Apartado 257, Salamanca, SpainbDepartamento de Matematicas, Universidad de Salamanca, Plaza de la Merced, 1. 37008 Salamanca, Spain

Received 16 September 2004; accepted 25 October 2004

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ee front matter & 200jplph.2004.10.013

ing author. Tel.: 34 92esses: ecervant@usal.

SummaryStructurally, ethylene is the simplest phytohormone and regulates multiple aspects ofplant growth and development. Its effects are mediated by a signal transductioncascade involving receptors, MAP kinases and transcription factors. Many morpholo-gical effects of ethylene in plant development, including root size, have beenpreviously described. In this article a combined geometric and algebraic approach hasbeen used to analyse the shape and the curvature in the root apex of Arabidopsisseedlings. The process requires the fitting of Bezier curves that reproduce the rootapex shape, and the calculation of the corresponding curvatures. The application ofthe method has allowed us to identify significant differences in the root curvatures ofethylene insensitive mutants (ein2-1 and etr1-1) with respect to the wild-typeColumbia.& 2005 Elsevier GmbH. All rights reserved.

Introduction

The Arabidopsis root has been used in recentyears as a unique model system to study celldifferentiation during development. In the embryo-nic root, a group of four central cells in thequiescent center is surrounded by distinct initialcells. This group is the origin of the different celltypes, including the columella root-cap, cortical

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3 219606; fax: 34 923 219609.es (E. Cervantes), bacon@usal.e

and endodermal cell files, epidermis, and thesteele (pericycle and vascular tissue) (Schiefelbeinand Benfey, 1994; Schiefelbein et al., 1997). Thus,in a reduced number of cell layers, differentiationgoes from the non-dividing and non-differentiatedstatus in the quiescent center, to cells differen-tiated in distinct cell types, passing throughdividing non-differentiated meristematic cells.The molecular basis of cell differentiation involves

rved.

s (A. Tocino).

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Geometric analysis of Arabidopsis root apex 1039

the coordinated expression of genes encoding keyregulatory proteins such as scarecrow, a member ofthe GRAS family of DNA binding proteins (Sabatiniet al., 2003). Hormonal regulatory networks controlthe expression of these genes (Fu and Harberd,2003).

During seed imbibition, embryonic root cells takewater and increase their size, leading to germina-tion. After radicle protrusion, some cells begin todivide. Once the developmental program is in-itiated, root shape will be established by thecoordinated action of their cells in response tohormones and environmental conditions (Beemsteret al., 2003). As is well known, variables measuringcharacteristics (e.g., root length, width or root hairnumber) which depend on the additive effect ofmany low intensity factors follow normal distribu-tions.

Ethylene, structurally the simplest known planthormone, is produced in plants in two steps fromthe amino acid methionine via SAM (S-adenosylmethionine) and ACC (1-aminocyclopropane-1-car-boxylic acid) by the consecutive action of twoenzymes: ACC synthase and ACC oxidase. Ethyleneaffects diverse aspects of plant development,ranging from germination and seedling morphologyto fruit ripening and senescence (Abeles et al.,1992). The effects of ethylene on plant develop-ment were first described in etiolated pea seedlings(Neljubov, 1901), and included swelling of thehypocotyl, growth inhibition in the root and in thehypocotyl and an exaggerated hook curvature.These characteristics of seedlings grown in thedark in the presence of ethylene were called thetriple response, and have been useful in theidentification of mutants in the ethylene biosynth-esis and signal transduction pathways (Guzman andEcker, 1990). Other effects of ethylene in develop-ment and in the modulation of several aspects ofplant form include the response to physical stress,leaf abscission, flower development and sex deter-mination (for a review see Dolan, 1997).

In Arabidopsis, ethylene has a remarkable effecton root development: it inhibits elongation andpromotes radial expansion. Similar effects areobtained with ACC, the ethylene precursor. Treat-ments with ethylene and ACC are effective ininducing root hairs (Masucci and Schiefelbein,1996; Pitts et al., 1999; Tanimoto et al., 1995).The response is rapid; changes in cell elongationand the induction of root hairs can be observedafter minutes of incubation (Le et al., 2001). Withlonger incubation times, ethylene affects theoverall root shape, resulting in decreased rootlength and increased width. Thus, ethylene maystrongly influence root shape at early developmen-

tal stages. Treatment of wild-type seedlings withethylene results in morphological changes that aresimilar to the phenotypes of ethylene overproduc-tion (eto1-1) (Chae et al., 2003; Woeste et al.,1999), or constitutive triple response mutants(ctr1-1) (Kieber et al., 1993). Treatment of wild-type seedlings with ethylene action inhibitorsresults in a morphology that resembles ethylene-insensitive mutants (etr1-1, ein2-1) (Bleecker etal., 1988; Roman et al., 1995). Thus both groupsrepresent two extreme patterns of developmentwith opposite phenotypes: short and thick rootswith long root hairs in the case of eto1-1 and ctr1-1, and long, thin roots with small root hairsdispersed through the root in the case of etr1-1and ein2-1.

Ethylene receptors form a protein family (ETR1,ERS1, ETR2, EIN4 and ERS2) that interacts withother regulatory proteins. For example, ETR1regulates CTR1, a MAP kinase similar to RAF (Clarket al., 1998; Huang et al., 2003; Kieber et al., 1993;Ouaked et al., 2003). Constitutive dominant etr1-1mutants have a phenotype of ethylene insensitivity,with longer hypocotyls, longer roots and shorterroot hairs than the wild-type in the presence ofethylene (Bleecker et al., 1988; Hall et al., 1999;Masucci and Schiefelbein, 1996).

In a further attempt to investigate the effects ofthe ethylene in root development, we describe inthis work a method for the analysis of shape andcurvature in roots of Arabidopsis seedlings. Theresults show differences between the ethyleneinsensitive mutant lines (etr1-1 and ein2-1) andthe wild-type Columbia, suggesting that the ethy-lene signal transduction pathway is involved in thedetermination of curvature in the root apex. Themethod can be applied a short time after radicleprotrusion in germination, before other develop-mental differences are detected.

Materials and methods

Plant material

Seeds of Arabidopsis thaliana cv Columbia (col)and the mutant genotypes eto1-1 (eto) (Chae etal., 2003; Woeste et al., 1999), ein2-1 (ein)(Guzman and Ecker, 1990) and etr1-1 (etr) (Changet al., 1993) were imbibed in 1% water-agar platesand stored for 3 days at 4 1C to allow coldstratification. Afterwards, the plates were incu-bated in a growth chamber under a light/dark cycle(18 h light, 25 1C; 6 h dark, 20 1C). After 24 and 48 hof incubation, seedlings were carefully collected

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with forceps and deposited individually in micro-scope slides with a drop of water and covered withcover-slides for their observation.

Microscopic examination and image analysis

The slides were observed with transmitted lightunder an inverted microscope (Leica DMIRB) withan objective of 20� . Images of the roots weretaken and stored for their analysis.

The program AnalySISs was used to obtain datafrom the images; the process is shown schemati-cally in Fig. 1. A grid of 10 microns width was drawnover the root image, and with the aid of the grid, aseries of approximately 20 points was regularlymarked throughout the root outline. The coordi-nates of every point marked were provided byAnalySISs. In this way, for each image, a data seriesof the form (xi; yi) was obtained. These data pointswere used to create a function representing thecurve that approximated the shape of the rootoutline.

Curve approximation

Because we focus on the shape of the root,traditional methods forcing the curve to passthroughout the points are inappropriate. Withthese fitting methods, the approximated curve isclose to the ‘‘real’’ shape (in L2 or L1 sense, forexample), but oscillates around it (Yang, 2001). Wechose Bezier curves to approximate the shape ofthe roots, and curvature as a measure of shapefidelity.

Bezier curves (Bezier, 1968; Gordon and Riesen-feld, 1974) do not pass throughout data points(except the first and the last ones), but data points

Figure 1. Process of data acquisition. The images of theroot apex were visualized with AnalySISs and points weremarked along their outline with the help of a grid. Theprogram gives the coordinates of the points.

are used as control points. The multiplicity of datapoints can be used to improve the fitting. Beziercurves have been widely used in computer drawing(Rogers and Adams, 1989). They have suitablefeatures for our purposes: (1) Bezier curves haveno great oscillations around the points; (2) theyfollow the polygonal lines joining the points andconserve the convexity, i.e. spurious inflectionpoints do not appear; (3) their equations are givenby polynomials, and then, are easy to handle (witha computer code).

From a series of arranged data pi ¼ ðxi; yiÞ; i ¼0; . . . ; n; the parametric Bezier curve is obtained(see e.g. Risler, 1992) as X(t) ¼ (x(t),y(t)) with

xðtÞ ¼Xni¼0

xiBi;nðtÞ; yðtÞ ¼Xni¼0

yiBi;nðtÞ,

where t A [0,1] and

Bi;nðtÞ ¼n

i

� �ð1� tÞn�iti i ¼ 0; . . . ; n

represent the nþ 1 Bernstein polynomials (Lorentz,1986). So, xðtÞ and yðtÞ are polynomials of degree nand the parameter t; which varies in the interval[0,1], expresses the percentage of the total curvelength traversed. Notice that X (0) is the initialpoint (x0; y0) and X (1) is the final point (xn; yn).

Geometric analysis

The curvatures of the adjusted Bezier curveswere calculated from their parametric equations(xðtÞ; yðtÞ) by means of formula (DoCarmo, 1976):

kðtÞ ¼x0ðtÞy00ðtÞ � x00ðtÞy0ðtÞ�� ��

ðx0ðtÞ2 þ y0ðtÞ2Þ3=2; t 2 0; 1½ �.

Curvature measures the rate at which the unittangent vector is changing with respect to arclength. Therefore, all graphical representations ofthe curvatures of Bezier curves approximatingroot outlines have similar bell-shaped form (seeFig. 2b). The values of the curvature near to theextremes of the interval are low, since the curve issimilar to a line in their proximities. When theparameter goes up to the root tip, curvatureincreases. The maximum value of the curvature isattained on the apex vertex. Bezier curves fittingpointed roots lead to ‘‘tall and narrow’’ bells,whereas those corresponding to blunt roots give‘‘flattened’’ bells.

Once the maximum value of the curvaturefunction for each root was calculated, a variablecalled APEXCUR, containing these values, wascreated. For each root, this variable measurescurvature value in the root tip.

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0.2 0.4 0.6 0.8 1

0.5

1

1.5

2

(a) (b)

Figure 2. (a) Adjusted Bezier curve taking 19 points throughout the profile of the root surface. (b) Graphicalrepresentation of corresponding curvature values through the length of the curve represented in (a).

Geometric analysis of Arabidopsis root apex 1041

A Mathematicas code, which, from a set of inputdata points, gives the Bezier curve, its graphicalrepresentation (Fig. 1a), the graphic of a curverepresenting the curvatures (Fig. 1b), and themaximum value of the curvature has been writtenout and is available upon request at the authors’ e-mail addresses.

Statistical analysis

We were interested in the homogeneity ofpopulations col, ein and etr with respect tovariable APEXCUR. Thus, a sample of six rootimages for each population (24 h after imbibition)was analysed and, following the process describedabove, their APEXCUR values were obtained. Mainstatistics of variable APEXCUR were calculated.

ANOVA (Fisher, 1935; Bliss, 1967) was used to testthe significance of the difference between thethree populations. The null hypothesis, H0, wasthat they represent samples from the same normaldistributed population, i.e. populations col, ein andetr are normally distributed and their parameters(mean and variance) coincide. We tested H0 at alevel of significance a ¼ 0:01:

To determine whether the data showed signifi-cant differences in dispersion, i.e. to test thevariance homogeneity, a Levene test was applied(Levene, 1960). In this case, the null hypothesis,H1, was that the samples come from normallydistributed populations with the same variance(level of significance a ¼ 0:01).

If H0 is rejected by the ANOVA, and H1 is acceptedin Levene test, then we must conclude thatpopulations col, ein and etr differ in their meansbut not in their variances with respect to variableAPEXCUR. In this case, to find which pair or pairs ofpopulations (col-ein, col-etr, ein-etr) produce this

heterogeneity, many multiple comparison tests areavailable. In our case, a Scheffe multiple compar-ison test (Scheffe, 1953) was performed.

The analysis was repeated with an equal sizesample of seedlings taken at 48 h after imbibition.

Results

For each image, a Bezier curve fitting the rootoutline and the corresponding curvature functionwere obtained. Fig. 3, which contains one exampleof each genotype, illustrates this process. Subse-quently, APEXCUR values for this sample werecalculated. Main statistics of variable APEXCURare summarized in Table 1.

The significance of the difference between roottip curvatures of groups col, ein and etr was testedby analysis of variance. From the F value obtainedin Levene test (Table 2), there is insufficientevidence to reject the hypothesis that the var-iances are equal. So we accept that our threesamples represent normal populations with thesame variance.

The obtained ANOVA value F ¼ 17:586 (Table 3)corresponds to a probability lower than P ¼ 0:001:On this basis, it was concluded that the groups col,ein and etr have different means, with a degree ofreliability higher than 99.9%.

Finally, Scheffe’s multiple comparison test pos-tulates that a pair of populations have unequalmeans if their sample means mi;mj fulfil theinequality

mi � mj�� ��X ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0:0193F1�a;2;12

p.

With a ¼ 0:01; the value of the term on the right is0.366; we conclude that, with this level ofsignificance, the col population differs from ein

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(b)

(c)

(b’)

(c’)

6.5 7 7.5 8 8.5 9 9.5 10

6

6.5

7

7.5

8

8.5

9

9.5

(b’’)

(c’’) 0.2 0.4 0.6 0.8 1

0.25

0.5

0.75

1

1.25

1.5

8 9 10 11 12 13

10

11

12

13

14

2 3 4 5 6

13

13.5

14

14.5

15

15.5

16

0.2 0.4 0.6 0.8 1

0.5

1

1.5

2

0.2 0.4 0.6 0.8 1

0.5

1

1.5

2

(a) (a’) (a’’)

Figure 3. Root images (top, a), adjusted Bezier curves (middle, b) and their corresponding graphics showing curvaturevalues (bottom, c) for representative samples of: col (left), etr (middle) and ein (right) genotypes. Bar represents100 mm.

Table 1. Summary statistics for variable APEXCUR

TYPE Mean Cases Std. Dev. Var. Min. Max.

col 2.17450 6 .225846 .051006 1.921 2.509ein 1.66496 6 .129154 .016680 1.509 1.848etr 1.67350 6 .139406 .019434 1.432 1.847Total 1.83766 18 .329275 .108422 1.432 2.509

Table 2. Levene test for homogeneity of variances

Levene DF1 DF2 Sig.

1.969 2 15 .174

E. Cervantes, A. Tocino1042

and etr in curvature. Obviously, there is noevidence to reject the hypothesis that the popula-tions ein and etr have the same mean.

Fig. 4 contains the twelve curvature functionscorresponding to col and etr samples (green, colfunctions; red, etr). It shows the differences

between the curvature functions for both popula-tions and, in particular, the lack of overlap betweentheir APEXCUR values.

The analysis was repeated taking different sets ofpoints, with similar results. Also, similar conclu-sions were obtained when the analysis was re-peated for a sample consisting of six seedlings foreach genotype at 48 h after imbibition.

On the other hand, seedlings of the mutantgenotype eto1-1 were included in a similar analysis.The mean curvature value for eto1-1 was 1.965.The values were included between 1.65 and 2.47

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0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.5

1

1.5

2

2.5

3

Figure 4. Curvature functions corresponding to Beziercurves for six root samples of col (green) and etr (red)genotypes.

Table 3. Results of ANOVA test comparing the means ofgroups col, ein and etr for variable APEXCUR

APEXCUR�TYPE ANOVA table

SS DF MS F Sig.

Between groups 1.021 2 .511 17.586 .000Within groups .436 15 .029

Total 1.457 17

Geometric analysis of Arabidopsis root apex 1043

and the standard deviation for this genotype was0.29. Scheffe’s test revealed that curvature valuesfor eto1-1 are not statistically different from thevalues corresponding to the other genotypes understudy.

Discussion

Plant shape results from the coordinated growthof many thousands of cells. From fertilization andearly embryonic development, very efficient com-munication mechanisms are established involvingthe different organs of a plant. During plantdevelopment, a multiplicity of mechanisms exerttheir effects both in short (i.e. between neighbourcells) and long distance (e.g. hormonal signalstransmitted throughout the plant). Recently, rootlength has been shown to be partly controlled byshoot produced phytohormones and regulated bythe coordinated action of gibberellins, auxins andethylene (Achard et al., 2003; Cervantes, 2003; Fuand Harberd, 2003).

In a recent article, Rolland-Lagan et al. (2003)proposed that growth is governed by three factors:growth rate, anisotropy and direction. In root

growth the main axis determines the directionand, after germination, growth is predominantlydriven by the gravitropic stimulus. Major variationsmay concern rate of growth and anisotropy.Changes in anisotropy are related to variability inradial expansion. Ethylene is known to inhibitgrowth and to promote radial expansion in roots(Dolan and Davies, 2004). Thus, this phytohormoneregulates crucial aspects in root morphogenesisallowing the adaptation of root growth to rapidresponses in environmental changes (Le et al.,2001).

From a practical point of view it may beconvenient to analyse developmental aspects that:(1) may be observed at early developmental stages,(2) can respond to known signals or environmentalfactors, and (3) can be expressed in mathematicalterms. Growth characteristics observed at earlystages of development are the consequence ofinteractions among a lower number of cells andorgans involving, in general, simpler signal-re-sponse networks. The development of mathematicformulae is essential in the accurate description ofdevelopmental phenotypes.

Recently, the application of image analysisresulted in the precise description of growth inthe root apical zone including the meristem andelongation zone (van der Weele et al., 2003).

To analyse the shape of the root in the apex wehave used root images from transmitted lightmicroscopy and obtained adjusting curves forthem. Their curvature is a descriptive measure ofroot shape.

The method has been applied to compare etr1-1,ein2-1, eto1-1 and wild-type Columbia genotypes.Differences in root morphology among these geno-types were described previously, and are related toroot length and root hair size and shape (Bleeckeret al., 1988; Guzman and Ecker, 1990; Roman etal., 1995; Hall et al., 1999; Masucci and Schiefel-bein, 1996).

The application of the method has allowed toidentify differences in the root curvatures ofethylene insensitive mutants (ein2-1 and etr1-1)with respect to wild-type Columbia that arestatistically significant at a p ¼ 0; 01 confidencelevel. The study of curvatures here presented wasdone on seedlings at 24 and 48 h after germinationand can be applied at earlier times after germina-tion, or in embryos before other major differencesin growth parameters, e.g. root length, are visible.

The activity of ETR1 protein as ethylene receptorhas been demonstrated (Shiu and Bleecker, 2001).The current model of ethylene action admits thatthe wild-type ETR1 protein activity is negativelymodulated by the binding of ethylene, whereas the

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E. Cervantes, A. Tocino1044

mutant allele etr1-1 encodes a protein unable tobind ethylene, and thus constitutively activated(Kende, 2001). EIN2 is related to metal transportersof the NRAMP family (Hirayama and Alonso, 2000).EIN2 is downstream of ETR1, and the phenotype ofein2-1 mutant is of ethylene insensitivity (Roman etal., 1995), thus resembling etr1-1 phenotype(Bleecker et al., 1988). ETR1 protein is active inthe absence of ethylene and its activity is modu-lated by the phytohormone. Thus, in theory,aspects not controlled by ethylene can be differentbetween wild-type Columbia and etr1-1 genotypes.This situation may occur when ETR1 is active in adevelopmental stage in which the hormone isabsent or the receptor is unable to bind thehormone (e.g. due to physical isolation).

In this article, we have defined and expressedmathematically the curvature of the root apex, adevelopmental characteristic detectable earlyupon seed imbibition or even in embryonic roots.Statistical analysis has shown that root tip curva-ture values are smaller in ethylene-insensitivemutants (etr1-1 and ein2-1) when compared withwild-type seedlings. Curvature is, thus, a newphenotypic feature that may be useful to studythe cellular basis of root growth. Different curva-ture values may result from the effect of mutationsin hormone sensing pathways (as it is shown here)or in response to environmental factors.

We have demonstrated that curvature is depen-dent on the activities of ETR1 and EIN2 proteins inthe ethylene signal transduction pathway. This doesnot necessarily imply that curvature is ethylenedependent. Our results with eto1-1 suggest that, atleast at early root development stages, curvaturedoes not respond to increased ethylene levels.

Although ethylene-insensitive mutants have beenobtained in screening experiments designed todisrupt the ethylene signalling pathway, the path-way may be active in absence of the phytohormoneand may regulate important processes related withcell growth and structure. The analysis of curvaturevalues of Columbia seedlings treated with ethyleneinhibitors can give more data to illustrate whetherthis characteristic is controlled by ethylene or isregulated by ETR1 protein activity, independentlyof this phytohormone.

It would be interesting to observe whetherethylene insensitive mutants have lower curvaturevalues at earlier times after germination, or in theirembryos. Another question is if low curvature is aspecific feature for ethylene insensitive lines or if itis a shared feature with other hormone responsemutants. Curvature analysis in roots of mutants indifferent signal transduction pathways and in wild-type seedlings grown under different treatments

may give new lights on the molecular basis ofdevelopment and hormone signal transductionmechanisms. These possibilities are currently underinvestigation. Finally, the tools developed in thiswork may be applied to analyse whether curvaturevalues in the root tip are associated with size anddistribution of cells in the root apex. The methodswill be extended and completed by confocalimaging into the third dimension and the analysisof available Arabidopsis lines tagged with GFP inthe cell wall.

Acknowledgements

We thank Jose Javier Martın Gomez for his help inthe elaboration of figures.

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