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641
Research
Blackwell Publishing, Ltd.
Methods
Morphometric analysis of root shape
A. Grabov
1
, M.K. Ashley
1
, S. Rigas
2
, P. Hatzopoulos
2
, L. Dolan
3
and F. Vicente-Agullo
1
1
Department of Agricultural Sciences, Imperial College London, Wye Campus, Wye, Ashford, Kent TN25 5AH, UK;
2
Laboratory of Molecular Biology,
Agricultural University of Athens, Iera Odos 75, 118 55 Athens, Greece;
3
Department of Cell and Developmental Biology, John Innes Centre, Norwich Research
Park, Colney, Norwich NR4 7UH, UK
Summary
• Alterations in the root shape in plant mutants indicate defects in hormonal signalling,transport and cytoskeleton function.• To quantify the root shape, we introduced novel parameters designated verticalgrowth index (
VGI
) and horizontal growth index (
HGI
).
VGI
was defined as a ratiobetween the root tip ordinate and the root length.
HGI
was the ratio between theroot tip abscissa and the root length.• To assess the applicability of
VGI
and
HGI
for quantification of root shape, weanalysed root development in agravitropic
Arabidopsis
mutants. Statistical analysisindicated that
VGI
is a sensitive morphometric parameter enabling detection of weakgravitropic defects.
VGI
dynamics were qualitatively similar in auxin-transport mutants
aux1
,
pin2
and
trh1
, but different in the auxin-signalling mutant
axr2
. Analysisof
VGI
and
HGI
of roots grown on tilted plates showed that the
trh1
mutation affecteddownstream cellular responses rather than perception of the gravitropic stimulus.• All these tests indicate that the
VGI
and
HGI
analysis is a versatile and sensitivemethod for the study of root morphology.
Key words:
auxin, gravitropism, image analysis, root development, root morphology.
New Phytologist
(2005)
165
: 641–652
©
New Phytologist
(2004)
doi
: 10.1111/j.1469-8137.2004.01258.x
Author for correspondence:
A. Grabov
Tel: +44 207 594 2748
Fax: +44 207 594 2640
E-mail: [email protected]
Received:
14 June 2004
Accepted:
8 September 2004
Introduction
Root development is affected by a variety of environmentalfactors including gravity (Chen
et al
., 2002); light (Mullen
et al
.,2002); mechanical impedance of the substrate (Croser
et al
.,1999); availability of water (Eapen
et al
., 2003); and mineralnutrients (Linkohr
et al
., 2002). These environmental signalsare translated to the differential growth of root cells through theactivity of a variety of genes controlling plant morphologicalphenotype. Deficiencies in some of these genes result in impair-ments in root development, which can be seen as agravitropic(Marchant
et al
., 1999), wavy (Buer
et al
., 2003), slanting(Ferrari
et al
., 2000), coiling (Mullen
et al
., 1998) or relatedphenotypes. The pattern of primary root growth is a usefulindicator of gene morphogenic activity and is widely used fordetection of mutants deficient in hormonal signalling, transportor cytoskeleton formation (Friml, 2003; Yuen
et al
., 2003).
Because of the complex nature of the trait, until recentlyconclusions on root geometry were mainly qualitative orsemiquantitative in character. Quantitative characterizationof root geometry would be beneficial for molecular-geneticand physiological studies of root development, as it will revealfine differences between different phenotypes, signals andexogenous regulatory substances. Importantly, this approachwill enable the use of root shape as a quantitative trait for thegenetic analysis of root growth and development.
The few quantitative methods reported recently for assaysof root gravitropism are based on microscopic imaging ofindividual roots that have been subjected to gravitropicstimulation (Perbal
et al
., 2002; Wolverton
et al
., 2002). Animage-processing algorithm was described to study the patternof individual root-tip growth (van der Weele
et al
., 2003). Noneof these methods, however, is practical for high-throughputanalysis, and they quantify short-term effects of physiological
New Phytologist
(2005)
165
: 641–652
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©
New Phytologist
(2005)
Research642
Methods
stimuli rather than the root developmental pattern. Someassessments of root-growth patterns are based on measurementsof angular deviation of the root tip from the vertical axis (Fujita& Syono, 1996; Rutherford & Masson, 1996; Fujita & Syono,1997; Marchant
et al
., 1999). However, this parameter is notapplicable to the description of roots with complex geometry.
In this work we demonstrate that the complex descriptionof root shape can be reduced to a set of a few independentparameters, which can easily be derived using computer-aidedimage analysis. This approach enables quantification of thegrowth pattern of individual roots, and the application ofstandard statistical methods for evaluating differences betweenplant populations, various developmental signals and actionsof plant growth regulators.
Materials and Methods
Plant material
Arabidopsis
lines
aux1-7
(N3074),
axr2
(N3077) and Col-0(N6673) were obtained from Nottingham Arabidopsis StockCentre.
pin2/eir1-1
was kindly donated by Professor KlausPalme. Plants were grown on vertical or tilted plates onMurashige–Skoog media (Duchefa, Haarlem, the Netherlands)supplemented with 0.05% MES–KOH buffer pH 5.7, 1%sucrose and solidified with 0.4% phytagel (Sigma, Gillingham,UK). After 48 h stratification in the dark at 4
°
C, the seedlingswere cultivated on plates for 2–8 d after germination (dag) at16 : 8 h, 23 : 20
°
C, day : night cycle.
Image analyses
Plates with intact plants were either photographed usinga DP-10 digital camera (Olympus, Tokyo, Japan) attached toan SZX9 stereomicroscope (Olympus), or scanned on anHP6300C scanner (Hewlett Packard, Boise, ID, USA). Imagesobtained were digitized using the
software package(http://rsb.info.nih.gov/ij) and digital data were further analysedin
(SPSS Science, Birmingham, UK) using acustom-designed transform.
Theoretical background
By definition, any phenotypic alteration in primary rootshape caused by a mutation, or by an external factor, suggeststhat primary root development deviates from a model patternwhich can be described as vertical downward growth withgravitropic set-point angle (GSA) equal to 0 (Digby & Firn, 1995).
If a primary root elongates with a variable, time-dependent speed
V = V
(
τ
) and maintains GSA = 0 over thegrowth period
t
, the root tip will be located at a depth equalto root length
L
:
Eqn 1
In the root developmental mutants, and to some extent inthe wild-type (wt) plants, the direction of root growthdeviates from the vertical axis, and the speed of rootelongation in the vertical direction is equal to
V
y
, a projectionof
V
on the vertical axis (Fig. 1a–c). The real depth of the roottip penetration can be calculated as:
Eqn 2
Here we designate the dimensionless ratio between
L
y
and
L
as the vertical growth index (
VGI
), and use this parameterfor quantification of root morphology (Fig. 1):
VGI = L
y
/L
Eqn 3
If a root grows downward (GSA = 0
°
), displaying positivegravitropism, its
VGI
is equal to +1. For roots with adiagravitropic phenotype (GSA = 90
°
or 270
°
),
VGI
will be 0.In an extreme situation when a root grows upward, displayingnegative gravitropism (GSA = 180
°
),
VGI
will be equal to
−
1. In all intermediate cases,
VGI
will lie in the range between0 and cos
β
, where
β
is an angular coordinate of the root tipas shown in Fig. 1.
Geometrically
VGI
represents cos
θ
, where
θ
is an anglebetween the vector of gravity and straightened root, the tip ofwhich is located at depth
L
y
(Fig. 1d). If the root shape isclose to linear,
θ
will be similar to
β
(Fig. 1c), and in this case
β
will adequately describe the root developmental pattern.Although
VGI
characterizes the deviation of root morphologyfrom the model gravitropic phenotype, this parameter on itsown does not describe the prevailing lateral directions ofgrowth. This information can be retrieved using the horizontalgrowth index (
HGI
, Fig. 1), which is defined as:
HGI = L
x
/L
Eqn 4
where
L
x
is an abscissa of the root tip (Fig. 1c) calculated as:
Eqn 5
where
V
x
is a horizontal projection of
V
.We assign a positive sign to the anticlockwise angular
deviations of growth from the downward vertical direction.Therefore the sign of
L
x
will be positive if the root tip isdeviated to the right, and negative if the deviation is in theopposite direction.
A root growing vertically and displaying either positiveor negative gravitropism (GSA = 0
°
or 180
°
) will be character-ized by
HGI
= 0. Diagravitropic phenotypes with horizontalroot growth patterns will yield
HGI
= 1 if the root tip islocated to the right from the vertical axis (GSA = +90
°
), and
HGI
=
−
1 if roots are pointing to the left (GSA =
−
90
°
). Forall intermediate root tip locations,
HGI
will be in the rangebetween 0 and sin β.L V
t ( ) =
0� τ τd
L Vy
t
y ( ) =0
� τ τd
L Vx
t
x ( ) =0
� τ τd
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Research 643Methods
By definition dLy and dLx projections of marginal linearelongation dL at a variable time τ (Fig. 1a–c) can be found as:
dly = cos α(l ) dl = Vy dτ Eqn 6
dlx = sin α(l ) dl = Vx dτ Eqn 7
where α = α(l ) is an angle between the vector of gravity anddirection of root elongation at the point with curvilinearcoordinate l , calculated along the root as a distance from theroot base to a current point on the root contour (Fig. 1c).Because the trajectory of root tip movement is imprinted inthe root shape, l also characterizes the length of the root attime τ (Fig. 1a–c). As before, Vy and Vx in equations 6 and 7are vertical and horizontal projections of V (τ).
Introduction of equations 6 and 7 into equations 2 and 5,respectively, yields:
Eqn 8
where l is a curvilinear coordinate as in equations 6 and 7 and∫L designates a line integral along the root contour.
Substitution of Ly and Lx in equations 3 and 4 with equation8 generates alternative definitions for VGI and HGI:
Eqn 9
Although equation 9 is less suitable for practical computation,it provides another geometrical interpretation for VGI and
HGI. In accordance with equation 9, VGI is defined as anaverage cosine of the angle α between the vector of gravity anddirection of root elongation (Fig. 1c). This definition obviouslymakes sense for VGI as a parameter describing root gravitro-pism. By analogy, HGI in equation 9 is defined as an averagesine of the angle α between the vector of gravity and directionof root elongation.
Some phenotype characterizations may require quantificationof root straightness without reference to a direction of rootgrowth. For this purpose, root straightness (S ) can be definedas a length of chord connecting the base and apex of a primaryroot (Lc) (Fig. 1c) normalized onto the length of a root (L):
S = Lc/L Eqn 10
S is related to VGI and HGI through the formula:
S = √(VGI 2 + HGI 2) Eqn 11
The angular coordinate β of the tip (Fig. 1c) can be calculatedfrom VGI and HGI with use of the formulae:
cos β = VGI /S = [VGI /√(VGI 2 + HGI 2)]sin β = HGI /S = [HGI /√(VGI 2 + HGI 2)] Eqn 12
β as a parameter characterizing root growth is far less informativethan VGI and HGI, but might be useful for some analyses.
Figure 1 illustrates how VGI and HGI are calculated forthe analysis of primary root morphology. The same analysis,however, is applicable to the lateral roots.
Fig. 1 Quantification of root geometry of Arabidopsis with use of vertical growth index (VGI) and horizontal growth index (HGI). (a) Seedling at time τ after germination. (b) Increase in root length dL after marginal time interval dτ. (c) Seedling at time t when the root shape is analysed. The length of root is L. The trajectory of the root tip movement during development is imprinted in the root contour. Marginal elongation dL at any point on the root contour can be presented by a linear segment with vertical and horizontal projections dLy and dLx, respectively. At any time τ during root development (t ≥ τ ≥ 0) corresponding to the root length l(τ), the direction of root growth deviates from vertical by an angle α. l also can be considered as a curvilinear coordinate along the root (L ≥ l ≥ 0) as measured from the root base. Ly and Lx are, respectively, ordinate and abscissa of the root tip at time t when the measurements are taken. β is an angular coordinate of root tip and Lc is a chord connecting root base and tip. (d) Geometrically, VGI represents cos θ, where θ is an angle between the vector of gravity and straightened root, the tip of which is located at depth Ly.
L l l L l ly L x L
cos sin = =� �α α( ) d ( ) d
VGIL
l l HGIL
l lL L
cos sin = =1 1� �α α( ) d ( ) d
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Research644 Methods
Results
Statistical assessment of VGI as a parameter for characterization of root morphology
It has been shown recently that in the trh1 Arabidopsis mutant,root hair development is blocked soon after initiation (Rigaset al., 2001) and roots are defective in the gravitropic response(Vicente-Agullo et al., 2004). Because the root agravitropicphenotype in this mutant is rather weak during the initialphase of development, trh1 plants are ideally suited for assess-ing the sensitivity of VGI as a parameter for characterizationof root morphology. The minute differences between the2 dag wt (WS ecotype) and trh1 plant populations shownin Fig. 2 can be detected and justified only with use ofappropriate statistical methods, which in turn require robustnumerical parameters that can describe the shape of the root.To analyse these differences, we used several different approaches.
First, we assessed the root shape using the angular deviationβ of the root tip from the vertical, as described by Fujita& Syono (1996) and Rutherford & Masson (1996). Meanvalues (M) of β in wt and trh1 were 1.67° and 0.38°, respec-tively (Table 1). Because of the high standard deviation (s) ofthis parameter (Table 1), the t-test did not reveal any differ-ence between the root shape of wt and trh1 plants. As seen inFig. 2, the 2 dag roots were slightly wavier that the wt, but didnot display anisotropy in bending. As deviations of rootgrowth to the right and to the left had equal probabilities,the positive and negative β balanced each other, yieldingmean values close to 0. As a result, the coefficient of variation(CoV = s /M ) characterizing data dispersion, was enormouslyhigh, reaching 47.36 in trh1. Although β might be useful asan indicator of an averaged root deviation from vertical, it isnot suitable for analysis of minor differences in gravitropismsuch as those shown in Fig. 2.
To eliminate the difficulties associated with the alternatingsign of β, we assessed the modulus β (| β |) as a parameterdescribing root gravitropism (Table 1). Mean | β | was slightlyhigher in trh1 roots, reflecting stronger bending of the trh1
roots. Again, however, in both plant types the standarddeviation was quite high. Consequently the t-test yieldedthe probability of rejection of the null hypothesis as only 83%.Based on this test, the difference between the two phenotypeswas statistically insignificant. This conclusion demonstratesthat neither β nor | β | can be used as a morphometric parameterto describe small aberrations in root morphology.
The same data were analysed using VGI as an indicator ofthe agravitropic growth pattern. This analysis yielded VGI =0.95 and 0.89 in wt plants and trh1, respectively. The lowerVGI of the trh1 plants indicated that the averaged declinationof trh1 roots from the vertical was higher than in the wildtype. Importantly, the standard deviation of VGI was < 15% ofthe mean in both plant types (CoV, Table 1). The low disper-sion of the data clearly demonstrates that VGI characterizesthe fundamental biological processes that are less prone tostochastic variations, and are intrinsic for the given genotype.This property of VGI makes it a very sensitive tool for detectionof such minor changes in root morphology as those shownin Fig. 2. In contrast to β and | β |, VGI indicated a statisti-cally significant (P > 0.95) difference between the trh1 and wttype phenotypes at a very early developmental stage, whenqualitative comparison cannot produce a reliable conclusion.
As θ = arccos VGI has the same dimension as β, the applica-bility of these parameters for describing root morphology canbe compared directly. As expected, the magnitudes of the inte-gral averaged angular declination θ (15.2° and 25.3° for wtand trh1, respectively) were much higher than those of β and| β |. Most importantly with use of this parameter, differencesin the morphology of trh1 and wt roots were revealed une-quivocally with P = 0.998 (Table 1).
In the 4 dag plants, the difference between trh1 andwt plants was much more pronounced (Vicente-Agullo et al.,2004). However, as based on the β analysis, the probability ofrejection of the null hypothesis was only 0.75 (Table 1). Useof | β | gave better results (P = 0.981), while the dispersion ofthis parameter still was high and CoV exceeded 100% for thewt plants. VGI distribution, in contrast, was less scattered andfor both wt and trh1 the CoV value was < 30%. Comparison
Table 1 Statistical assessment of the primary root shape of trh1 and wild type (wt, WS ecotype) Arabidopsis plants using different morphometric parameters
ParameterPhenotype
2 dag seedlings 4 dag seedlings
β (°) | β | (°) VGI (rel) θ (°) β (°) | β | (°) VGI (rel) θ (°)
wt trh1 wt trh1 wt trh1 wt trh1 wt trh1 wt trh1 wt trh1 wt trh1
Mean (M) 1.67 0.38 8.2 12.4 0.95 0.89 15.2 25.3 6.69 12.8 10.7 20.6 0.91 0.68 21.8 45.3SD (s) 13.3 18.0 10.6 12.9 0.08 0.13 12.0 12.3 18.5 22.3 16.4 15.1 0.18 0.20 14.3 15.4CoV = s/M 7.96 47.36 1.29 1.04 0.95 0.15 0.78 0.49 2.77 1.74 1.53 0.73 0.20 0.29 0.66 0.34P* 0.25 0.83 0.96 0.998 0.75 0.981 0.99998 0.999999992
*Significance level of difference between wt and trh1 as assessed with use of given morphometric parameter. β, angular coordinate of the root tip; | β |, modulus of the root tip angular coordinate; VGI, vertical growth index; θ = arccos VGI.
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Research 645Methods
of wt and trh1 using VGI yielded t = 4.60, which was almosttwice as high as that obtained using | β | (t = 2.42). Given n =30, P in this case was as high as 0.99998, indicating a differencein root morphology between the trh1 and wt phenotypes. Aneven stronger indication in favour of morphological differ-ences between trh1 and wt roots was obtained using θ as amorphological parameter (P = 0.999999992).
The results presented in Table 1 prove that VGI and therelated parameter θ appropriately describe morphologicaldifferences between root phenotypes. They are characterizedby a relatively low noise-to-signal ratio and are extremelysensitive to minute changes in root morphology.
Because of the improved sensitivity, VGI performed betterthan | β | as a morphometric parameter characterizing root
Fig. 2 Root shape of Arabidopsis seedlings at 2 days after germination (dag). (a) Wild type (wt, WS ecotype) plants; (b) trh1 mutants. Every row of images represents an independent experiment in which wt and trh1 plants were grown on a vertical phytagel surface in a single plate. Images show the plants as observed through phytagel. Scale bar, 10 mm.
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Research646 Methods
shape. There was, however, some correlation between thesetwo parameters (Fig. 3). Interestingly, the correlation washigher in 2 dag than in 4 dag plants (r2 = 0.80 vs 0.70, respec-tively). These differences are caused by the lower curvature ofthe 2 dag roots. These roots can therefore be better approxi-mated with linear segments, thus β is more similar to θ, whichin turn is derived from VGI. This observation pinpoints ashortfall of | β | as a morphometric parameter. In essence,| β | characterizes the sum of angular deviations of the growthvector from vertical (α, Fig. 1) during root development. Ifthese deviations occur in both directions, for example in wavyor crescent-shaped patterns, the use of | β | will result inoverestimation of the strength of gravitropic behaviour. Thishappens because clockwise and anticlockwise angular devia-tions compensate each other, yielding | β | similar to thatobtained in wt plants. Because of this intrinsic problem | β |works satisfactorily only for the description of root shapewhich is close to linear. For these roots | β | ≈ θ = arccos VGI(Fig. 1).
VGI as a morphometric parameter is free from this defectbecause it characterizes the average cosine of the angulardeviation α (equation 9). The cosine of α is equal to 1 only if aroot grows downward (α = 0). For any other growth directions,cos α < 1, therefore any deviation from the vertical at anytime during root growth causes a reduction in VGI in a cumu-lative fashion. These advantages of using VGI for the quanti-tative description of root geometry are illustrated in Fig. 3c,which shows images of four trh1 and one wt seedling. Theangular deviation | β | of the tip is similar in all plants, and isin the range 16° to 20° (Fig. 3b) despite the fact that growthpatterns of these roots are obviously very different. Theobserved differences in root shape of these four seedlings aresatisfactorily reflected by VGI ranging between 0.21 and 93.
Application of VGI and HGI to the study of root morphology dynamics
The most important advantage of the parametric presentationof root morphology is the possibility of considering the shapeas any other quantitative trait and using it for the study ofquantitative trait loci (QTL), dose–response kinetics or anyother genetic and physiological analyses.
Here we used VGI to study the dynamics of the root devel-opmental pattern in different mutants with defects in rootgravitropic behaviour. For this purpose we analysed Arabidopsismutants trh1 (Rigas et al., 2001; Vicente-Agullo et al., 2004),aux1-7 (Swarup et al., 2001), pin2/eir1-1 (Müller et al., 1998)and axr2 (Nagpal et al., 2000). AUX1 and PIN2 encode puta-tive transporters that facilitate, respectively, the influx andefflux of auxin (Müller et al., 1998; Swarup et al., 2001). Thepotassium transporter TRH1 is also required for auxin trans-port in Arabidopsis roots (Vicente-Agullo et al., 2004), whileAXR2 encodes a member of the Aux/IAA protein family andis involved in auxin signalling (Nagpal et al., 2000).
Fig. 3 Vertical growth index (VGI) quantifies root shape more accurately than the modulus of the root tip angular coordinate | β |. (a) Correlation between VGI and | β | in Arabidopsis seedlings at 2 days after germination (dag). (b) Correlation between VGI and | β | in 4 dag seedlings. Closed circles, wild type (wt, WS ecotype); open circles, trh1. Dot-labelled symbols indicate roots with similar | β | but different VGI (i–iv, trh1; v, wt). (c) Images of seedlings, morphometric parameters of which are represented by dot-labelled symbols in (b). Straight lines indicate the angular coordinate β of the root tip. Despite having similar β, these roots display different strengths of agravitropic phenotype, which are accurately reflected by VGI. Images show plants as observed through the phytagel. Scale bar, 5 mm.
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Research 647Methods
During the first 2 dag, the growth of trh1 plants wasmarginally but statistically significantly, different from wt plants(Fig. 4a,b; Table 1). During the following 2 d the VGI of wtplants decreased only slightly in contrast to trh1 mutants,in which the VGI dropped significantly from 0.9 to ≈ 0.7(Fig. 4a,b). Representative images of wt and trh1 plantscorresponding to different phases of root development aredemonstrated in Fig. 4a.
As shown in Fig. 4a, roots of both WS and trh1 seedlingshave a tendency to deviate to the right from vertical. Becauseof the way we photographed the plants, in this paper direc-tions of deviation from vertical are given as viewed throughthe agar. The right-hand deviation we observed correspondsto a left-hand deviation if viewed from above the agar surface.This direction of deviation was previously reported for Lerand WS ecotypes (Ferrari et al., 2000; Furutani et al., 2000)and is probably genetically encoded, as it was independent ofthe orientation of the plate with seedlings in the growth cab-inet (not shown). The preferential direction of root deviationfrom vertical is probably related to the chirality of thecytoskeleton molecules (Thitamadee et al., 2002), and thistrait is important for the study of cognate mutants (Ferrariet al., 2000; Thitamadee et al., 2002). Information on thedirection of slanting or bending, however, cannot be derivedfrom the analysis of VGI. To quantify the horizontal compo-nent of root growth and detect a preferential direction oflateral deviation from vertical, we used another parameter,HGI (see Methods).
Although during the first 2 dag VGI of wt and trh1 rootswas different, we did not detect a significant difference in HGIof these plants (Fig. 4b). This observation supports the ideathat VGI and HGI are independent morphometric parame-ters and describe different developmental processes. Both VGIand HGI analysis are required for a complete descriptionof root morphology. In the 2 dag trh1 plants, VGI was lowerthan in the wt (Table 1; Fig. 4b) because root growth in themutant deviated more strongly from the model patterncharacterized by GSA = 0 (Digby & Firn, 1995). However, atthis initial stage of plant development, roots did not bend inany particular preferential direction (Fig. 2). Such a bendingpattern yields HGI close to 0 and appears to be similar in wtand trh1 roots (Figs 2, 4b). HGI of both plant types increasedthrough 2–4 dag, indicating that a reduction in VGI observedat this developmental stage is associated with root bending/slanting to the right. This effect, however, was more pronouncedin the trh1 mutant.
Up to 6 dag there was no difference in root length betweenwt and trh1 plants, while afterward the wt roots grew morequickly than the mutant (Fig. 4c). Despite the similar rate ofgrowth in trh1 and wt roots, VGI dynamics in these plantswas completely different. This observation confirms the lackof correlation between the root length and VGI, and thus theapplicability of this parameter for comparing the shapes ofroots of different sizes and ages.
Fig. 4 Root gravitropism is dependent on age of Arabidopsis seedling. (a) Representative images of wild type (wt, WS ecotype, i–iii) and trh1 (iv–vi) seedlings at 2 (i, iv); 3 (ii, v); and 6 (iii, vi) days after germination (dag). Vertical growth index (VGI) for each root is indicated by a number next to the image. Scale bar, 5 mm. Images show plants as observed through phytagel. (b) Time-dependence of VGI and horizontal growth index (HGI) in wild type (wt, closed symbols) and trh1 (open symbols) roots. Circles, VGI; squares, HGI; (i–vi) label experimental points, representative images for which are shown in (a). VGI of trh1 plants declines sharply at 2–4 dag. HGI of both wt and trh1 plants is always positive in seedlings older than 3 dag, indicating that in both plants growth direction deviates to the right from the vertical. Each experimental point is mean ± SE, n = 30 plants. (c) Root length in wt plants (closed circles) and trh1 plants (open circles). Data are interpolated with fifth order polynomials (closed lines).
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Research648 Methods
In comparison to WS, roots of Columbia (Col-0) plantsdeviated less from the vertical (Figs 4b, 5a), but also slantedpreferentially to the right. The right-hand side slanting, however,was much less pronounced than in WS, and consequentlyHGI was statistically different from 0 for the short period oftime at 2.5–3.5 dag only (Fig. 5b).
In contrast to trh1, in aux1 we observed a strong agravitropicphenotype (VGI = 0.58 ± 0.10) on the first dag. But as in trh1,after 2 dag VGI started to decrease further towards a newsteady-state level in the range of 0.4, which was approachedat 5.5 dag. Up to 4 dag, HGI of the aux1 plant was negative,indicating left-hand deviation of the growth vector, whilein older seedlings there was no preferential direction of rootbending and consequently HGI was close to 0 (Fig. 5b).
VGI dynamics in pin2 (Fig. 5c) was qualitatively similarto those observed in trh1 and aux1 (Fig. 4b). In these plants,steady-state VGI during the first few dag was followed by asharp transition to a new, lower stable level. Similarly to aux1,an agravitropic phenotype of pin2 roots was stronger than thatof trh1, and was characterized by lower VGI throughoutseedling development. Transition between higher and lowersteady-state VGI in pin2 occurred later than in trh1 and aux1.As well as in trh1, in pin2 roots negative HGI was not detectedat any stage of development (Fig. 5d).
Root-growth patterns in axr2 were different from thoseobserved in auxin-transport mutants. On the first dag, VGI ofaxr2 roots was close to 0 because the direction of vertical
projection of root growth was almost random. HGI, however,was positive (0.33 ± 0.14), indicating a prevailing orientationof emerging roots to the right (Fig. 5c,d). During the next dayof growth, VGI gradually increased to ≈ 0.2. No significantchanges in VGI were observed at 2–4 dag, while after 4 dagthe gravitropic behaviour of axr2 roots recovered further,and at 7 dag VGI approached ≈ 0.4, similarly to aux1 andpin2. Analysis of HGI shows that the preferential direction ofgrowth is continuously changing in axr2 roots during the firstfew days of development from the right-hand one (HGI = 0.33± 0.14) at 1 dag to left-bending (HGI = −0.26 ± 0.08) at4 dag. After 4 dag, HGI was becoming less negative andapproached 0 at 7 dag, indicating a lack of preferential direc-tion of root bending.
Application of VGI analysis for studying mechanical obstacle-avoidance reaction
In natural conditions in soil, roots grow in a mechanicallyheterogeneous environment. To explore this environmentefficiently, roots must develop some means of sensing amechanical obstacle, and a strategy for optimizing growthtrajectories. In a real environment the direction of root growthis a compromise between several tropisms. The major stimulithat predetermine the direction of root growth are gravityand mechanical impedance of the substrate. The effect ofmechanical obstacles on root-growth pattern can be emulated
Fig. 5 Dynamics of root vertical growth index (VGI, a,c) and horizontal growth index (HGI, b,d) in wt (Col-0, a,b) and agravitropic Arabidopsis mutants with defects in auxin influx (aux1, a,b), efflux (pin2, c,d) or auxin signalling (axr2, c,d). Each experimental point is mean ± SE, n = 30 plants.
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by tilting agar plates containing growing plants (Okada& Shimura, 1990; Mullen et al., 1998). When the platesare inclined at 45°, wt Arabidopsis roots demonstrate a wavypattern of growth. This response, however, is impaired inwav6-52 (allelic to pin2/agr1-1) and wav5-33 (allelic to aux1)mutants (Okada & Shimura, 1990).
Here we studied the effect of plate inclination on rootgrowth patterns in wt (WS ecotype) and trh1 plants. Tiltingthe plate at an angle < 30° practically did not affect the devel-opmental pattern in either wt or trh1 roots (Fig. 6a). At theseangles, both root types maintained the same VGI as in verticalplates. A wider angle between the plate and the vertical planetriggered the declination of root growth from the linear pattern
in the wt, and caused a further increase in curvature of thetrh1 roots, with the net result seen as a sharp decrease in VGI(Fig. 6a,b). Interestingly, the threshold tilt angle was similar inboth plant types.
Plate tilting at 40° triggered wavy growth in wt roots(Fig. 6b), as has been demonstrated earlier (Okada & Shimura,1990; Mullen et al., 2000). Starker deviation from lineargrowth under this experimental condition resulted in lowerVGI (Fig. 6a). The response to plate tilting was exaggerated intrh1 seedlings, where a coiling pattern often superimposedwavy growth (Fig. 6b), yielding a VGI much lower than thoseobserved in wt plants (Fig. 6a).
In both plant types plate tilting weakly affected HGI,except at 10° inclination when the HGI of trh1 plants wassharply reduced. Lack of HGI response to 40° plate tiltingcontrasts with a sharp reduction in VGI, and reflects the factthat these experimental conditions trigger wavy or coilingroot growth rather than bending or slanting in a preferentialdirection.
By tilting the plate, we forced roots to grow agravitropi-cally. Results shown in Fig. 5 indicate that tilting to an angleof > 30° is perceived by roots as a stark declination from thevertical and triggers root bending in the plane of the agar–airinterface. The purpose of this response is probably to avoida mechanical obstacle and restore the gravitropic growthpattern. Because the threshold tilt angle for an induction ofthis response is similar in wt and trh1 plants, the mutationprobably does not affect the perception of gravity, but rathercauses defects in a responsive mechanism, such as differentialcell elongation.
Discussion
VGI and HGI are parameters quantifying deviation of theroot developmental pattern from model downward verticalgrowth. In contrast to the angular coordinate of the root tipused previously for quantification of agravitropic behaviour(Fujita & Syono, 1996), these parameters account for cumul-ative effects of all angular deviations during root growth(Fig. 3). Because of this feature VGI, particularly, as parametercharacterizing root gravitropic behaviour, is extremely sensitiveand enables characterization of weak agravitropic phenotypes(Fig. 2; Table 1).
Using VGI and HGI to analyse the dynamics of root-growthpatterns, we found that gravitropic behaviour is dependent onthe age of seedlings and the background genotype (Table 1;Figs 4, 5). Roots of both wt ecotypes WS and Col-0 were char-acterized by VGI in the range 0.9–1 (Figs 4, 5). The WS rootswere slightly less gravitropic, particularly at 2–4 dag (Fig. 4).In both ecotypes, roots tended to deviate to the right from thevertical, as indicated by positive HGI. This tendency, how-ever, was much less pronounced in the Col-0 ecotype, and wasstatistically significant (95% confidence) at 2.5–3.5 dag only.The left–right asymmetry in root development was previously
Fig. 6 Root bending in the plane of the phytagel–air interface is dependent on tilting of plates with Arabidopsis seedlings. (a) Vertical growth index (VGI, circles) and horizontal growth index (HGI, squares) as a function of tilt angle (closed symbols, wt; open symbols, trh1). Tilting over 30° causes a reduction in VGI in both wt and trh1 roots. Each point is mean ± SE, n = 20 plants. (b) Representative images of wt and trh1 plants grown at the tilt angle 45°. Scale bar, 5 mm.
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observed in WS and Ler ecotypes (Rutherford & Masson,1996; Ferrari et al., 2000; Furutani et al., 2000; Thitamadeeet al., 2002). The deviation from vertical, however, was notdetectable in 10-d-old Col-0 when quantified by measurementsof the tip angular coordinate (Rutherford & Masson, 1996).The right-slanting root phenotype has been shown to correlatewith a left-handed rotation of the root about its axis (Rutherford& Masson, 1996). At the molecular level, this phenotype isprobably associated with microtubule orientation in epidermalcells (Furutani et al., 2000; Thitamadee et al., 2002).
Some similarity in the dynamics of gravitropic behaviourwas found between trh1, aux1 and pin2 mutants. These lineswere characterized by higher VGI during the first few days ofdevelopment, followed by fast transition to new, lower steady-state VGI. The agravitropic growth in trh1 and pin2 mutantsfeatured positive HGI, which is characteristic for right-hand-side root bending. Interestingly, both trh1 and pin2phenotypes are caused by defects in auxin efflux transport(Luschnig et al., 1998; Müller et al., 1998; Vicente-Agulloet al., 2004). Therefore we suggest that the common patternof VGI dynamics in trh1 and pin2 reflects the similarity ofauxin physiology defects in these mutants. However, agravit-ropism in pin2 roots was stronger than in trh1, and transitionto lower steady-state VGI occurred 1.5–2 d later than in trh1and aux1. In contrast to trh1 and pin2, roots of the aux1mutant with a defect in auxin influx displayed negative HGI,indicative of left bending.
Root development in the axr2 mutant, impaired in auxinsignalling, was different from auxin-transport mutants. Thedirection of growth in emerging roots was nearly random,but with some prevailing growth to the right-hand side, asindicated by positive HGI (Fig. 5c,d). In contrast to mutantswith a defect in auxin transport, in axr2 gravitropic behaviourwas improved in older seedlings and, similarly to pin2 andaux1, they were characterized by VGI in the range of 0.4 at 7 dag.The direction of root growth was also continuously changingin axr2, from strong right bending at 1 dag to left bending at4 dag, while no preferential direction of root angular devia-tion was observed in 7 dag plants. Again, this behaviour wasdifferent from auxin-transport mutants (Fig. 5b,d), in whichroots were preferentially bent either to the right (trh1 andpin2) or to the left (aux1).
Because VGI quantifies the fundamental attributes of rootgeometry, it enables a direct comparison of gravitropic behav-iour in different mutants and ecotypes, independently ofparticular root shape. In 3 dag plants, for instance, the strengthof gravitropic behaviour followed the sequence Col-0 (0.96 ±0.00) > WS (0.92 ± 0.02) > trh1 (0.82 ± 0.02) > pin2 (0.68 ±0.04) = aux1 (0.55 ± 0.09) > axr2 (0.21 ± 0.07). The differ-ences between agravitropic mutants were less obvious in 7 dagseedlings, for which the above sequence was transformed intothe following: Col-0 (0.95 ± 0.00) = WS (0.94 ± 0.01) >trh1 (0.69 ± 0.03) > pin2 (0.44 ± 0.04) = aux1 (0.45 ± 0.08)= axr2 (0.43 ± 0.05).
The alterations in mutant gravitropic behaviour (Figs 4, 5)are probably caused by age-dependent activation of genes andinduction of physiological processes that either complementthe mutant phenotype, as in axr2, or strengthen it, as in trh1,pin2 and aux1. We suggest that reduced gravitropism in trans-port mutants at 3–7 dag is caused by the restricted availabilityof shoot-derived auxin, which is normally delivered to roots atthis stage of development in wt plants (Bhalerao et al., 2002).The sharp increase in IAA content in roots at 3–7 dag(Bhalerao et al., 2002) may be also partially responsible for thesecond phase of gravitropism recovery, observed after 3 dagin the axr2 mutants, assuming that they are not impaired inauxin translocation. An alternative hypothesis is required toexplain VGI increase with age of axr2 seedlings during the first3 dag, when no increases in IAA content were observed inArabidopsis wt plants (Bhalerao et al., 2002).
Studying the growth of trh1 roots on tilted plates, we foundthat this challenge triggers additional deviation from thevertical, particularly when the tilt angle is > 30° (Fig. 6). Again,in these conditions, roots bent preferentially to the right.Interestingly, the threshold tilt angle was practically the samefor trh1 and wt roots. The latter observation suggests that trh1mutants do not have a defect in the perception of gravity.Severe reduction in VGI, however, clearly indicates that thetrh1 mutation affects the downstream gravity-responsivemechanism, probably differential cell elongation.
The exaggerated response to a 40° plate inclination in trh1roots was often associated with root coiling (Fig. 6b). A similarphenomenon was observed previously in aux1 (wav5-53 ) mutants(Okada & Shimura, 1990). wav5-53, however, were lacking thewavy growth pattern, which we did observe in the trh1 mutant(Fig. 6b). Similarly, wavy root growth on tilted plates was notdetected in pin2 (wav6-52 ) mutants (Okada & Shimura, 1990),although both trh1 and pin2 are impaired in auxin efflux (Chenet al., 1998; Müller et al., 1998; Vicente-Agullo et al., 2004).
In conclusion, experimental data shown here demonstratethat VGI and HGI are robust and sensitive quantitativedescriptors of root phenotypes and of developmental responsesto external factors. Statistical analysis using these parametersallows us to reveal the prevailing growth pattern in a plantpopulation, which otherwise may remain masked by sponta-neous root-growth deviations in individual plants.
Acknowledgements
The authors are grateful to K. Palme for providing pin2/eir1-1 seeds. This research was supported by grants to A.G. andL.D. from the Biotechnology and Biological Sciences ResearchCouncil (UK).
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