ORIGINAL PAPER

Dynamic analysis of Arabidopsis seed shape reveals differencesin cellulose mutants

Jose Javier Martın • Angel Tocino •

Ramon Ardanuy • Juana G. de Diego •

Emilio Cervantes

Received: 16 September 2013 / Revised: 3 April 2014 / Accepted: 4 April 2014 / Published online: 24 April 2014

� Franciszek Gorski Institute of Plant Physiology, Polish Academy of Sciences, Krakow 2014

Abstract In a previous work, the shape of Arabidopsis

seed was described as a cardioid modified by a factor of

Phi. In addition, J index was defined as the similarity of the

seed (in an orthogonal, bi-dimensional image) to a cardi-

oid, thus allowing the quantitative comparison of seed

shape in seeds of varieties and mutants at different stages

of development. Here, J index is used for modeling chan-

ges in seed morphology during the dynamic process of seed

imbibition before germination. The analysis was carried

out by means of a general linear model with two fixed

factors (genotype and time) applied to two Arabidopsis

varieties: Columbia and Wassilewskija and two mutants in

cellulose synthesis: prc1-1 (CESA6 in Columbia) and

kor1-1 (in Wassilewskija). Equations representing the

changes in seed form during imbibition are given. The

analysis of changes in seed shape by this procedure

provides (1) a quantitative method to record changes in

seed shape and to compare between genotypes or treat-

ments showing the time points with maximum differences,

and (2) the observation of remarkable differences between

wild-type seeds and mutants in cellulose biosynthesis,

indicating new phenotypic characteristics previously

unknown in the latter. While wild-type seeds increase their

J index values during imbibition, in the cellulose mutants

J index values decrease. In addition, shape comparisons

were done with other mutants. Seeds of ga1-1 mutants

behave like cellulose mutants, whereas different ethylene

mutants present varied responses. Quantitative analysis of

seed morphology is a new basis for the record of differ-

ences between wild-type and mutants as well as for phe-

notypic characterization.

Keywords Arabidopsis � Cardioid � Cellulose mutants �Imbibition � Seed � Shape

Introduction

Shape is an important characteristic of living organisms.

Organ shape is determined genetically and changes

between individuals, as well as during development and in

response to environmental factors. In some instances,

organs are stable and their shape may be adjusted to geo-

metric models that, once identified, allow the quantitative

descriptions of differences and changes, making possible

the accurate description of organogenesis. The quantitative

description is based in geometric models and provides the

basis to compare between different sets of individuals that

belong to diverse mutant populations, varieties or species.

The shape of Arabidopsis seed was recently described as

a cardioid modified by a factor of Phi (Cervantes et al.

Communicated by M. Horbowicz.

Electronic supplementary material The online version of thisarticle (doi:10.1007/s11738-014-1534-8) contains supplementarymaterial, which is available to authorized users.

J. J. Martın � E. Cervantes (&)

IRNASA-CSIC, Cordel de Merinas, 40, 37008 Salamanca, Spain

e-mail: ecervant@usal.es

A. Tocino

Department of Mathematics, University of Salamanca,

Salamanca, Spain

R. Ardanuy

Department of Statistics, University of Salamanca, Salamanca,

Spain

J. G. de Diego

Department of Biochemistry and Molecular Biology, University

of Salamanca, Salamanca, Spain

123

Acta Physiol Plant (2014) 36:1585–1592

DOI 10.1007/s11738-014-1534-8

2010). This allows the quantification of shape by compar-

ison with a geometrical figure and thus provides a method

to analyze and quantify changes in shape in different

environmental conditions, during development or in mutant

seeds.

From a theoretical point of view it is remarkable how

this model associates the shape of seeds with two

important concepts in geometry and mathematics: the

cardioid and the number Phi (the golden ratio). The car-

dioid is the line described by a point of a circumference

that turns around another of equal radius. The model

associates the shape of Arabidopsis seed with the concept

of cycle (cardioid) as well as to the equiangular spiral

(golden ratio).

Seeds swell and its shape changes during water uptake

preceding germination. We reported previously that in this

process the length to width ratio (L/W) of Arabidopsis goes

through a value equal to the golden ratio (u = 1.6118), and

that fully imbibed seeds resemble more a u-modified car-

dioid than dry seeds (Cervantes et al. 2010). The adjust-

ment to this figure reaches a maximum early during the

imbibition process. In this work, the change in shape was

investigated quantitatively in seeds during the process of

water uptake that precedes seed germination. Varieties

used included Columbia and Wassilewskija and their

respective mutants in cellulose biosynthesis genes, prc1-1

(Fagard et al. 2000) and kor1-1 (Nicol et al. 1998), affected

respectively in cellulose synthase (catalytic subunit 6) and

endo-1,4-b-glucanase. Whereas in the wild-type varieties,

the adjustment to an elongated cardioid increases during

seed imbibition reaching a maximum at about 2 h of

imbibition and then decreasing; in the mutants, the

adjustment is maximum in the dry seeds decreasing in the

course of imbibition before radicle protrusion in

germination.

Quantification of seed shape has allowed the identifi-

cation of phenotypic differences between mutants and

wild-type seeds that may be useful to further investigate the

relation between cellulose synthesis and seed shape, or in

general in the investigation of the genetic basis of shape.

Materials and methods

Plant material

Seeds of Arabidopsis thaliana of the wild-type cv.

Columbia and Wassilewskija, and their respective mutants

(prc1-1 and kor1-1), were obtained from INRA Versailles.

Mutant prc1-1 of Columbia is defective in CESA6 gene.

Mutants for cellulose synthase isoforms CESA1, CESA3,

and CESA6 have cellulose defects in primary cell walls

(Desprez et al. 2007). CESA6 gene encodes the catalytic

subunit 6 (UDP-forming) of cellulose synthase A that

confers resistance to isoxaben (Fagard et al. 2000; Desprez

et al. 2002, 2007). Mutant kor1-1 of Wassilewskija is

altered in KORRIGAN, the gene encoding an endo-1,4-b-

glucanase with a transmembrane domain and two putative

polarized targeting signals in the cytosolic tail that plays a

critical role during cytokinesis (Zuo et al. 2000). Both

mutants have a severe deficiency in cellulose as well as in

cell elongation (Nicol et al. 1998). Other genotypes used

include the mutants ga1-1, deficient in Gibberellic acid

synthesis (Koornneef et al. 1983), as well as mutants in the

ethylene signaling pathway ctr1-1 (Kieber et al. 1993) and

etr1-1 (Chang et al. 1993).

Photography and image analysis

Seeds were sown in Petri dishes and observed with a Nikon

‘SMZ-2T’ stereo microscope. Photographs of orthogonal

views were taken with a digital camera Nikon ‘Coolpix

950’ and analyzed with the software image analysis (soft

imaging systems), specialized in image processing. Length

and width were directly obtained from the photographs. In

this process, graph paper allowed us to convert pixel into

lm. Seven seeds per genotype were photographed 17 times

(for Col and Ws) and 18 times (for the mutants) during the

time-course of imbibition.

Mathematical analysis

Circularity index (Schwartz 1980), given by

I ¼ 4parea

perimeter2;

is a measure of the similarity between a plane figure and a

circle. It ranges from 0 to 1 giving the value of 1 for circles

and is a useful magnitude as a first approximation to seed

shape.

The similarity between the seed shape and a cardioid was

estimated by the J index (Cervantes et al. 2010). It repre-

sents the proportion of common area of the figures, i.e.,

J ¼ area ðCÞarea ðCÞ þ areaðDÞ � 100

where C stands for the common region to the seed shape

and the cardioid, and D represents the union of the non-

shared regions (Fig. 1). Note that J is a measure of seed

shape, not of its area. It ranges between 0 and 100, is equal

to 100 when cardioid and seed image areas coincide, i.e.,

when area (D) is zero, and decreases when the size of the

non-shared region grows.

The change in seed shape during germination is a

dynamic process. Then, it is analyzed while comparing

at successive moments the seed shape with a cardioid.

1586 Acta Physiol Plant (2014) 36:1585–1592

123

A comparative analysis of the quantitative measurable

variables of seeds (area, circularity index, length–width

rate and J index) was carried out by means of a general

linear model (GLM; Christensen 2011; McCullagh and

Nelder 1989). This method allows to work with qualitative

variables (genotype) and combines regression analysis

throughout successive moments with ANOVA involving

values in all time points. GLM was done with two fixed

factors: genotype, with four levels (Col, Ws, prc1-1 and

kor1-1) and moment (each point in time), with 17 levels for

Col and Ws and 18 levels for the mutants; and one random

factor, seed; seven seeds were used for each moment and

each genotype; a total amount of 490 seeds were analyzed

[490 = (7 9 2 9 17) ? (7 9 2 9 18)]. When the ana-

lysis of variance revealed no differences between geno-

types, ANOVA was repeated discarding this factor (and

retaining the others). When differences between genotypes

were found, post hoc analysis was done by DHS-Tukey test

to obtain groups containing homogeneous sets of data. The

parameters of the model were estimated either for all

genotypes in the former case or for each of the homoge-

neous groups in the latter. A function of real time was

adjusted to the estimations by nonlinear regression. Loga-

rithmic, inverse, quadratic, cubic, composed, S, growth,

exponential and logistic models were used. The quality of

each adjustment was evaluated by means of the coefficient

of determination. Since, in general, the best results were

obtained with the logarithmic model, logarithm regression

equations:

y ¼ b0 þ b1 � log tð Þ;

where t stands for time, have been used to describe the

changes in seed shape during germination. Notice that b0

represents the value of the measured variable at the initial

instant and b1 the rate of growth. It is also noticeable that

logarithm equation shows a kind of growth that begins very

rapid and gets slower as time passes. Although the growth

is asymptotically unbounded, this does not represent a

drawback, since germination occurs in a finite interval of

time. Statistical treatment and graphics were done with

SPSS� v. 20. For the analysis, the significance level

p = 0.05 was established; in addition, six digits of preci-

sion were used through the calculations. Other graphics

were done with Microsoft Office Excel 2010�.

Results

Seed area

Changes in shape do not always occur simultaneously with

growth. Seed volume increases during imbibition, but it is

not known what happens with shape. To explore how

changes in shape are associated with growth, first we have

quantified seed growth during germination. Figure 2a rep-

resents the increase in area of seed images during imbibi-

tion. Seed growth, due to water uptake in the course of

imbibition, is rapid. The values of seed area increased in

the early hours reaching near 90 % of final value in

approximately 6 h. Growth slowed down during the fol-

lowing hours. ANOVA did not reveal any differences

between genotypes. Regression analysis gave for all

genotypes the logarithm regression equation (R2 = 0.98):

y ¼ 0:241þ 0:009 � log tð Þ:

Circularity index

Changes in shape were estimated by three magnitudes:

circularity index, length to width ratio and J index. Mean

values and standard deviation of the data used in the

experiment are presented in Table 1. Figure 2b represents

the increase in circularity index during seed imbibition in

all genotypes. ANOVA revealed differences between

genotypes, and post hoc analysis showed difference

Fig. 1 Morphological analysis is based in the similarity of seed shape

with a cardioid elongated in the horizontal axis by a factor of Phi

(golden ratio). The images present a seed with superimposed cardioid

(left), the common area between the seed and the cardioid (middle)

and the union of non-shared regions (right). Both the common and the

non-shared regions are used to calculate J index as indicated in

‘‘Materials and methods’’

Acta Physiol Plant (2014) 36:1585–1592 1587

123

between two groups: one formed by the wild-type varieties,

the other by the mutants. Regression analysis gave, for Col

and Ws, the logarithm regression equation (R2 = 0.91):

y ¼ 0:902þ 0:005 � log tð Þ

Regression analysis gave, for kor1-1 and prc1-1, the

logarithm regression equation (R2 = 0.82):

y ¼ 0:950þ 0:004� logðtÞ

Although circularity index increased in the course of

imbibition in all genotypes, values in the mutant seeds

where higher than in the wild-type seeds in all time points.

Length to width ratio

Similarly to circularity index, length to width ratio gives an

idea of the overall shape of the seeds. Both magnitudes are

inversely related, thus higher circularity index values observed

throughout the process are associated with lower values of

length to width ratio in the mutants. Length to width ratio

decreased during seed imbibition in all genotypes (Fig. 2c).

ANOVA revealed differences between genotypes and post

hoc analysis indicated difference between two groups: one

formed by the wild-type varieties, the other by the mutants.

Regression analysis gave the logarithm regression equation

Fig. 2 Results of the application of a general lineal model (GLM;

Christensen 2011; McCullagh and Nelder 1989). GLM was done with

two fixed factors: genotype, with four levels (Col, Ws, prc1-1 and

kor1-1) and moment (each point in time), with 17 levels for Col and

Ws and 18 levels for the mutants; and one random factor, seed; seven

seeds were used for each moment and each genotype, to a total

amount of 490 seeds analyzed [490 = (7 9 2 9 17) ? (7 9 2 9

18)]. a Changes in seed image area in the course of imbibition.

b Changes in circularity index of seed images in the course of

imbibition. c Changes in length to width ratio of seed images in the

course of imbibition. d Changes in J index of seed images in the

course of imbibition

1588 Acta Physiol Plant (2014) 36:1585–1592

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y ¼ 1:403� 0:026 � logðtÞ

for Col and Ws (R2 = 0.95), and

y ¼ 1:37� 0:021 � log tð Þ

for kor1-1 and prc1-1 (R2 = 0.96).

J index

The changes in values of seed area during imbibition rep-

resent changes in size. Circularity index and length to

width ratio are magnitudes that give a general approxi-

mation to seed shape. To estimate change in shape with

more precision we need a magnitude that gives an idea of

the amount of similarity or difference with a cardioid curve

(J index; Fig. 1). J index increased rapidly to a maximum

value in the early minutes after imbibition in wild type Col

and Ws seeds (see video 1; Fig. 3), whereas it decreased

constantly in the mutants (video 2; Fig. 3). ANOVA

revealed differences between genotypes and post hoc

analysis indicated two groups: one formed by the wild-type

varieties, the other by the mutants. Regression analysis

gave for Col and Ws (R2 = 0.34) the equation

y ¼ 94:57þ 0:319 � logðtÞ

and for kor1-1 and prc1-1 (R2 = 0.87):

y ¼ 87:57� 0:586 � log tð Þ

Shape analysis in other mutants

The identification of 2 h of imbibition as the time point of

maximum differences in shape between wild-type seeds

and cellulose mutants allows optimized comparison of

shape between wild-type seeds and other mutants. Values

of seed area, circularity index, length to width ratio and

J index were obtained for the mutants ga1-1, deficient in

Gibberellic acid synthesis (Koornneef et al. 1983) as well

as mutants in the ethylene signaling pathway ctr1-1 (Kie-

ber et al. 1993) and etr1-1 (Chang et al. 1993). While

changes in J index in the mutants ga1-1 resemble those

observed in cellulose mutants, decreasing from the dry

seed, seed shape in the mutants etr1-1 and ctr1-1 follows a

similar pattern as in wild type, increasing to maximum

values after 2 h of imbibition (Fig. 4).

Discussion

A mathematical-geometrical model to quantify the shape of

Arabidopsis seeds was described recently (Cervantes et al.

2010). The model is based in the comparison of the outline

of the orthogonal view of the seed with a transformed

cardioid. The cardioid is the trajectory described by a point

of a circle that rolls around another fixed circle with the

same radius. Transforming it by multiplying the x axis by

the scaling factor / (&1.61803399), the so-called ‘golden

ratio’, the figure obtained resembled the image of an

Arabidopsis dry seed.

This model fits the shape of Arabidopsis seeds better

than a former model based on a prolate spheroid (Robert

Table 1 Mean values and standard deviation of the raw data used in

the experiment described in Fig. 1

Time

(h:min)

J index Length/width Circularity index

Mean (standard

deviation)

Mean (standard

deviation)

Mean (standard

deviation)

Wild type

0:0 86.13 (3.839) 1.660 (0.098) 0.862 (0.028)

0:5 91.83 (2.097) 1.423 (80.068) 0.918 (0.018)

0:15 92.28 (2.479) 1.423 (0.050) 0.911 (0.025)

0:30 93.20 (1.686) 1.422 (0.056) 0.912 (0.015)

0:50 94.33 (3.450) 1.400 (0.049) 0.912 (0.025)

1:25 93.18 (1.958) 1.384 (0.050) 0.916 (0.018)

2:03 92.60 (1.962) 1.368 (0.049) 0.925 (0.016)

2:57 92.24 (1.572) 1.348 (0.050) 0.929 (0.016)

4:04 92.34 (2.157) 1.341 (0.048) 0.924 (0.016)

5:23 92.11 (2.262) 1.329 (0.048) 0.930 (0.018)

6:09 91.45 (2.065) 1.331 (0.044) 0.930 (0.016)

7:56 91.48 (2.554) 1.329 (0.046) 0.928 (0.018)

10:35 91.19 (2.900) 1.326 (0.048) 0.927 (0.018)

23:45 91.63 (2.561) 1.327 (0.046) 0.929 (0.017)

26:05 91.90 (2.807) 1.331 (0.041) 0.932 (0.017)

28:00 91.56 (3.056) 1.324 (0.039) 0.931 (0.018)

30:00 91.16 (2.389) 1.323 (0.040) 0.933 (0.014)

Mutants

0:0 91.14 (2.877) 1.471 (0.109) 0.889 (0.025)

0:5 88.95 (3.756) 1.319 (0.082) 0.931 (0.017)

0:15 89.08 (3.585) 1.300 (0.070) 0.935 (0.026)

0:41 87.66 (3.554) 1.281 (0.064) 0.939 (0.021)

1:03 87.28 (3.558) 1.270 (0.059) 0.941 (0.015)

1:35 87.20 (3.564) 1.252 (0.066) 0.944 (0.015)

2:03 85.24 (3.965) 1.239 (0.056) 0.944 (0.015)

3:00 85.86 (4.427) 1.232 (0.060) 0.946 (0.013)

4:04 85.61 (3.585) 1.224 (0.060) 0.941 (0.012)

5:03 85.43 (3.383) 1.223 (0.061) 0.946 (0.013)

6:30 84.82 (3.934) 1.220 (0.063) 0.945 (0.012)

24:00 84.72 (4.093) 1.216 (0.062) 0.944 (0.015)

25:00 84.81 (3.635) 1.215 (0.063) 0.946 (0.014)

26:00 84.65 (3.482) 1.214 (0.062) 0.946 (0.015)

27:00 84.75 (3.672) 1.212 (0.059) 0.944 (0.019)

28:00 84.71 (3.666) 1.219 (0.065) 0.942 (0.018)

29:00 84.63 (4.060) 1.217 (0.067) 0.943 (0.017)

30:00 84.69 (3.982) 1.218 (0.066) 0.943 (0.017)

Means are from 14 values. The first table contains data pooled for the

two wild-type varieties (Col and Ws). In the second table, data cor-

respond to the two mutants (prc1-1 and kor)

Acta Physiol Plant (2014) 36:1585–1592 1589

123

et al. 2008) and was the basis to the morphological analysis

for the seeds of the model legumes Lotus japonicus and

Medicago truncatula (Cervantes et al. 2012).

The u-modified cardioid method was applied in this

work to compare the changes in shape of seeds during

imbibition between ecotypes Columbia and Wassilewskija,

and their respective mutants in cellulose synthesis, prc1-1

and kor1-1. Changes in seed area follow similar patterns in

the four genotypes and a logarithmic equation was adjusted

that fitted all the data. Changes in seed shape were ana-

lyzed by three magnitudes: circularity index, length to

width ratio and J index.

In contrast with the results obtained for seed area, the

analysis of circularity index, length to width ratio and J index

resulted in different equations for wild-type and mutant

seeds. Mutants in cellulose synthase genes had higher cir-

cularity index values throughout the process of seed imbi-

bition than their wild-type counterparts (b0 values were

higher in equations corresponding to the mutants). Circularity

index measurements give an idea of the similarity of the seed

images to circumferences and thus, higher circularity index is

associated with lower values of length to with ratio. In con-

sequence, mutants in cellulose synthase genes had lower

values of length to width ratio throughout the process of seed

imbibition than their wild-type counterparts (b0 values were

higher in equations corresponding to the wild-type seeds).

In the case of J index, different equations were adjusted

for wild-type varieties and for the mutants reflecting a

Fig. 3 Seeds in the course of imbibition. Above Columbia and prc1-

1. Below Wassilewskija and kor1-1. For each genotype, three images

are shown corresponding to dry seeds (left), seeds imbibed during 1 h

(middle), and seeds imbibed during 7 h. Each figure contains four

data: above (left): J index; below (left): area; below (right): circularity

index and length/width ratio. Data are means of three repetitions

1590 Acta Physiol Plant (2014) 36:1585–1592

123

different evolution of this magnitude during seed imbibi-

tion. Seeds of the wild types Columbia and Wassilewskija

reached a maximum similarity to the cardioid figure in the

course of imbibition. In the mutants, dry seeds had a

maximum similarity to the cardioid and the J index values

decreased in the course of imbibition. The adjustment to a

logarithm regression equations was good in the mutants

(R2 = 0.87), but bad in the wild-type seeds (R2 = 0.34).

The increase observed in the J index of the wild-type seeds

in the first 2 h of imbibition introduced an additional

inflexion point in their curves. Excluding this initial

ascending phase, and considering only time points from the

maximum values, the curves are more similar. Whereas

wild-type seeds increase their J index values in the first 2 h

of imbibition, cellulose synthesis mutants have lost this

capacity.

The method described allowed the identification of the

time points in which differences between genotypes are at a

maximum, thus indicating the optimal moments to do

shape comparison with other mutants.

Changes in seed shape were then analyzed in three

additional mutants, two in the pathway of ethylene sensing

(ctr1-1 and etr1-1) and in the gibberellic acid-deficient

mutant ga1-1.

In the two ethylene mutants, ctr1-1 and etr1-1, seed

shape changed in the course of germination in a similar

way as in the wild-type seeds. J index values increased in

the course of imbibition. In contrast, analysis of seed shape

in the gibberellic acid-deficient mutat ga1-1 showed

similarity with cellulose mutants. Thus, maximum values

of J index were obtained for the cellulose mutants and ga1-

1 in dry seeds. In these genotypes, dry seeds are more

rounded and adjust better to a cardioid than wild-type

seeds. In the course of imbibition, seeds depart from

maximum similarity with the cardioid and become more

rounded. This alteration in shape observed in the dry seeds

of mutants may be due to defects in cell elongation during

embryogenesis. In the cellulose mutants, it remains unclear

if this is a direct consequence of cellulose deficiency

because the same effect is observed under other hormonal

alterations such as in the absence of gibberellic acid syn-

thesis (ga1-1). Mutants altered in cellulose biosynthesis

present phenotypes related with altered sensitivity in

response to hormones, such as for example ethylene in ctl1

(Hermans et al. 2011). The cobra mutant presents a mas-

sive induction of defense- and stress-related genes, many of

which are regulated by the plant stress signal jasmonic acid

(JA) (Ko et al. 2006).

In this work, we have applied the general linear model to

the comparison of seed shape during the sustained period

of seed imbibition in wild-type and mutant Arabidopsis

seeds. The method reveals differences during the process of

change in shape during imbibition between wild-type and

mutant seeds. Time points in the course of imbibition in

which values of J index reach a maximum in the wild type

have been identified. Differences in shape between wild-

type varieties and cellulose synthesis mutants are at a

maximum in these time points. Our results show that (1)

Fig. 4 Dry seeds (top) and seeds imbibed during 1 h (middle) of Columbia, ctr1-1, etr1-1 and ga1-1 mutants. Graphics show the values of

J index in dry seeds (above) and imbibed seeds (below)

Acta Physiol Plant (2014) 36:1585–1592 1591

123

cellulose mutants are unable to experiment increases in

J index during imbibition, (2) this effect is observed in

other hormone mutants such as ga1-1. To better understand

the bases of shape change during seed imbibition, it may be

interesting to apply this method to other mutant genotypes.

Author contribution This work is part of JJ Martin’s

Ph.D. Thesis. Ramon Ardanuy and Angel Tocino did the

Mathematical and Statistics Analysis. JJ Martin performed

all image analysis, measurement and quantification. JG de

Diego and E Cervantes coordinated the work.

Acknowledgments We thank Samantha Vernhettes for kindly

providing us with seeds of wild type Arabidopsis varieties and

mutants.

Conflict of interest The authors declare that they have no conflict

of interest.

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