1

Detection of a Gravitropism Phenotype in glutamate receptor-like 3.3 Mutants of

Arabidopsis thaliana Using Machine Vision and Computation

Nathan D. Miller*#, Tessa L. Durham Brooks*1#, Amir H. Assadi§, Edgar P. Spalding*

*Department of Botany §Department of Mathematics

University of Wisconsin University of Wisconsin

Madison, WI 53706 Madison, WI 53706

Gene ID and Mutant stocks: AT1G42540, Salk_040458, and Salk_066009

1 Present address: Department of Biology

Doane College

Crete, NE 68333

#These authors contributed equally to this work.

Genetics: Published Articles Ahead of Print, published on July 20, 2010 as 10.1534/genetics.110.118711

2

Running title: Machine vision phenotype detection

Key words: Gravitropism, phenotype detection, machine vision, Arabidopsis,

glutamate receptor

Author for correspondence: Edgar P. Spalding

University o f Wisconsin

Department of Botany

430 Lincoln Drive

Madison, WI 53706

Fax: 608-262-7509

Tel: 608-265-5294

Email: spalding@wisc.edu

3

ABSTRACT

Gene disruption frequently produces no phenotype in the model plant Arabidopsis

thaliana, complicating studies of gene function. Functional redundancy between gene

family members is one common explanation but inadequate detection methods could

also be responsible. Here, newly developed methods for automated capture and

processing of times series of images, followed by computational analysis employing

modified linear discriminant analysis (LDA) and wavelet-based differentiation were

employed in a study of mutants lacking the Glutamate Receptor-Like 3.3 gene. Root

gravitropism was selected as the process to study with high spatiotemporal resolution

because the ligand-gated Ca2+-permeable channel encoded by GLR3.3 may contribute

to the ion fluxes associated with gravity signal transduction in roots. Time series of root

tip angles were collected from wild type and two different glr3.3 mutants across a grid of

seed-size and seedling-age conditions previously found to be important to gravitropism.

Statistical tests of average responses detected no significant difference between

populations, but LDA separated both mutant alleles from the wild type. After projecting

the data onto LDA solution vectors, glr3.3 mutants displayed greater population

variance than the wild type in all four conditions. In three conditions the projection

means also differed significantly between mutant and wild type. Wavelet analysis of the

raw response curves showed that the LDA-detected phenotypes related to an early

deceleration and subsequent slower-bending phase in glr3.3 mutants. These

statistically significant, heritable, computation-based phenotypes generated insight into

functions of GLR3.3 in gravitropism. The methods could be generally applicable to the

study of phenotypes and therefore gene function.

4

INTRODUCTION

A major objective of research on the model plant Arabidopsis thaliana is to determine

functions for each of its approximately 25,000 genes. An extensive, sequence-indexed

library of T-DNA insertion mutants has resulted in reverse genetics becoming a routine

approach toward this goal (Alonso and Ecker 2006). This approach is particularly

effective when the mutation results in an observable phenotype that gives a clue about

the disrupted gene’s function (Kuromori et al. 2006). Unfortunately, the large majority of

gene disruptions in Arabidopsis produce no readily observable phenotype (Bouché and

Bouchez 2001; Kuromori et al. 2006). To date, functional descriptions for only

approximately 10% of the Arabidopsis genes have been experimentally determined.

Reverse-genetic approaches in other organisms, such as C. elegans and Drosophila

have yielded similar results (Fraser et al. 2000). One possible explanation for the

infrequency of phenotypes is functional redundancy, especially when the gene is a

member of a large family. Or, the phenotype may be conditional, manifesting itself only

in a particular environment or developmental context that was not examined. Lastly, the

methodologies employed to search for a phenotype may not match well with the missing

gene’s function or scale of contribution. Detecting the effect of a mutation in only one of

the organism’s approximately 104 genes may require a specialized technique. In this

regard, high resolution measurements of growth over time hold much promise (van der

Weele et al. 2003; Beemster et al. 1998; Chavarría-Krauser 2006; Miller et al. 2007;

Reddy and Roy-Chowdhury 2009; Spalding 2009).

One of the surprises to come from the first plant genome sequencing effort was

the presence of 20 Arabidopsis genes homologous with those encoding mammalian

5

ionotropic glutamate receptors (Lam et al. 1998; Lacombe et al. 2001). Because the

animal molecules were known almost exclusively as tetrameric ion channels mediating

synaptic transmission in the central nervous system (Mayer and Armstrong 2004), their

presence in plants attracted considerable attention. The first studies explored the

structure and evolution of the plant gene family (Turano et al. 2001; Chiu et al. 2002).

Subsequent studies employing antisense methods to reduce expression and

constitutive promoters to overexpress GLR family members indicated possible roles in

coordinating carbon and nitrogen metabolism (Kang and Turano 2003), abscisic acid

biosynthesis and signaling (Kang et al. 2004), Ca2+ and Na+ homeostasis (Kim et al.

2001), Ca2+ and fungal disease progression (Kang et al. 2006), and Ca2+-mediated

stomatal closure (Cho et al. 2009). Transcription of multiple family members in the same

cell type made heteromeric channels seem probable in planta (Roy et al. 2008). While

each study provides clues, a consistent theme has not emerged. A robust mutant

phenotype could give very useful direction to further experimentation but none has been

reported.

The Arabidopsis GLR genes are different enough from the animal

neurotransmitter-gated channels in key regions, such as the putative ion-conducting

pore and extracellular amino-terminal domains, that equivalent molecular function

cannot be assumed (Davenport 2002). But the demonstration that wild-type plants

respond to glutamate with a strong membrane depolarization and fast transient rise in

cytoplasmic Ca2+ concentration made ligand-gated channel activity for the plant GLR

molecules a viable hypothesis (Dennison and Spalding 2000). The hypothesis was

strongly supported when these ionic events were found to be blocked by mutations in

6

the GLR3.3 and GLR3.4 genes (Qi et al. 2006; Stephens et al. 2008). In spite of these

strong ionic phenotypes, growth or development defects that typically guide hypotheses

about gene function could not be found. Either such phenotypes do not exist in glr3.3

mutants, or some nonstandard methods for finding them were necessary. Here, a

highly automated process for quantifying dynamic root growth and behavior involving

image processing and mathematical analysis was employed to search for a root growth

behavior phenotype (Miller et al. 2007; Durham Brooks et al. 2010). The results

demonstrate a function for GLR3.3 in root gravitropism and provide an example of how

a single-gene phenotype can be isolated by applying appropriate technology.

MATERIALS AND METHODS

Plant material

Arabidopsis thaliana (Columbia ecotype) seeds were sieved with grading sizes of

250µm2, 280 µm2, 300 µm2, and 355 µm2. Seeds between 250 µm2 – 280 µm2 were

classified as small and those from 300 µm2 – 355 µm2 were classified as large. Sieved

seeds were surface sterilized with 70% ethanol, 2% Triton X-100 and were planted on a

1% agar medium containing 1 mm KCl, 1 mm CaCl2, 5 mm 2-[N-morpholino]-

ethanesulfonic acid and pH adjusted to 5.7 with 1,3-

bis[tris(hydroxymethyl)methylamino]propane. After stratification at 4°C for 3–7 days, the

seeds were germinated on a vertically oriented plate and grown for 2-4 days under

50 μmol m−2 s−1 white light.

Mutant genotyping

Seeds of plant lines containing T-DNA insertions in GLR3.3 (At1g42540) were obtained

from the Salk Institute (http://signal.salk.edu/cgi-bin/tdnaexpress). The lines used were

7

Salk_040458 (glr3.3-1, second exon insertion) and Salk_066009 (glr3.3-2, first intron

insertion). Homozygous individuals were genotyped using the method described

previously (Qi et al., 2006). The PCR products from amplification with the left border

primer were sequenced to verify the position of the insertion.

Imaging

Petri plates containing seedlings were mounted vertically and transverse to the optical

axis of one of seven CCD cameras (Marlin F146B, Allied Vision Technologies (AVT),

Newburyport, MA, USA, www.alliedvisiontec.com) outfitted with a close-focus zoom lens

(NT59-816; Edmund Optics, http://www.edmundoptics.com). An infrared backlight

(NT55-819, Edmund Optics) having a peak output at 880 nm, was positioned behind

each Petri plate for back illumination. Resulting images were 1392 × 1040 pixels at 8-

bit pixel depth, with a maximum resolution of approximately 5 μm per pixel. Only one

root per plate was analyzed, even if there were two or three present. An x,y,z

positioning device on the plate holder was used to pose the selected root in the center

of the frame. To initiate the experiment, the plate was rotated until the tip of the root was

horizontal as best judged by eye, i.e. within a degree or two of the camera’s horizon.

File-acquisition rate and storage of the images in tag image file format (TIFF) was

controlled by AVT software. Each camera acquired images of a seedling root every 2

min for 10 h beginning when the seedling was rotated to induce gravitropic root

bending. A total of 255 such ‘movies’ were acquired for the studies presented here. All

the components required for an imaging apparatus and a step-by-step assembly guide

may be found at http://phytomorph.wisc.edu/hardware/fixed-cameras.php.

Image analysis

8

Using the image processing methods detailed in the Supplemental Material section

(http://botany.wisc.edu/spalding/PlantJournal2007/Supplemental_Material.htm) of Miller

et al. (2007), the midline was extracted from each root image. Tip angle was calculated

by first performing principal components analysis on a 5-pixel region of the midline near

the root tip. The tip angle was the angle formed between the first principal component

and the camera’s horizon. Growth rate was calculated as the differential of the midline

length over time. Growth rates between mutant and wild type roots were not different to

a statistically significant degree and were not used in the analyses presented here.

Linear discriminant analysis and its optimization

To find the projection of the data best satisfying each objective function, a minmax

optimizer in the optimization toolkit of the MATLAB scientific programming language

(Mathworks, www.mathworks.com/products) was applied to the entire population of tip

angle versus time points for 300 iterations. These 300 results were filtered to find the

solution of this population producing the smallest p-values between the mutant and wild-

type. To determine if the projection resulted in significant separation, tests of

significance were performed. A two-sample t-test was used to calculate significance of

the solution to Eq. 1 optimization. During the iterative search for variance separation

(Eq. 2 and Eq. 3), an F-test determined the significance level of each result. Statistical

significance of the final result was determined with a Brown-Forsythe test.

Wavelet analysis

Wavelet analysis was performed on each individual tip angle response using the first or

second order derivative of the Gaussian distribution as the transforming function with

window sizes from 1 to 20. To determine the significance of the wavelet-transformed

9

data, t-tests were run between each mutant allele and the wild-type populations for each

scale at each condition. Regions of the response in which the mutant data differed from

the wild type were considered significant when p was less than 0.05 at any wavelet

scale in both alleles.

Fitting of wavelets to the LDA solution vector was performed as follows. The four

first order Gaussian derivatives that best correlated with the solution vector were

determined using a watershed algorithm. Then, pairwise combinations of these four

wavelets were least-squares fit to the solution vector. The pair with the best fit was

identified then summed to create the wavelet fit of the LDA solution vector.

RESULTS

A bank of seven CCD cameras each equipped with a close-focus zoom lens formed the

front end of a computer-controlled image acquisition and analysis platform that was

used in a previous study to investigate the plasticity of wild-type root gravitropism

(Durham Brooks et al. 2010). The size of the seed from which the seedling emerged

and post-germination age significantly affected response trajectory when measured with

high resolution at 2 min intervals over a 10 h period (Durham Brooks et al. 2010).

Therefore, seed size (small or large) and seedling age (2 d or 4d) created a 2 x 2

condition grid in which a gravity response phenotype was sought in two T-DNA insertion

(mutant) alleles of GLR3.3 (At1g42540). All image data acquired during this study are

available at http://phytomorph.wisc.edu/download.

Figure 1 shows the average time course of root tip angle after gravistimulation in

the wild type and two glr3.3 alleles in each of the four chosen conditions. As found in a

10

recent characterization of the wild type (Col-0 ecotype), young seedlings responded

vigorously and transiently overshot the ultimate steady-state angle regardless of seed

size or genotype (A and B). Older seedlings more steadily approached the new vertical

upon re-orientation (C and D). Both glr3.3 alleles developed tip angle slightly differently

than the wild type in conditions B, C, and D (for example, note the initial response

rates), though t-tests indicated that the differences were not significant at any of the

time points (data not shown). However, a null result based on population averages

does not rule out an effect of the glr3.3 mutation on this root growth response.

Other methods for finding evidence of differences between populations of

measurements exist. Linear discriminant analysis (LDA), first devised by Fisher (1936)

to investigate a plant taxonomy question using sepal size, is one such method. A

method similar to Fisher’s original LDA for separating two groups was implemented to

determine if two groups (glr3.3-1 and glr3.3-2) could be separated similarly from a third

(the wild type). The input data were tip angle time points (301 per trial x n trials per

condition). They were treated as a high-dimension data cloud by recasting each time

course as a single point in 301-dimensional space. The next step was to design an

objective function that specified the hypothesis to test as follows. One objective

function sought a linear projection of the data that maximally separated the two mutant

population means from the wild-type mean while minimizing the standard deviations of

each, i.e.

min�

max���, �� min�

max � |����� ���|����� � ��� , |����� ���|����� � ��� � �. �. ��� 1 (Eq 1)

where:

11

�� 1��

� ���

� is the expected value for the Jth group; i.e., wt, mut1, mut2

�

��� 1�� 1 ����

�

� ���� is the variance for the Jth group; i.e., wt, mut1, mut2

�

and

��

� is the ith trial for the Jth group

The second objective function sought a linear projection of the data that minimized the

variance of the wild-type population relative to the mutant populations, i.e.

min�

max���, �� min�

max � �������� , �������� � �. �. ��� 1 (Eq 2)

The third found a linear projection of the data that minimized the variance of the mutant

populations relative to the wild type population, i.e.

min�

max���, �� min�

max � ��������

, ��������

� �. �. ��� 1 (Eq 3)

Each of the above objective functions contains a sub function for each glr3.3 allele. A

minmax optimizer was employed to search the 301-dimensional space for a vector w

that, when the data were projected onto it, minimized the value of the overall objective

function. In the case of Eq. 1, the minimum value of the function would be achieved

when a vector had been found that maximally separated the mutant population means

from the wild type. A t-test was then performed to determine if the mutant means after

projection onto w were significantly different from the wild type but not themselves (Eq.

1); a Brown-Forsythe test was used to determine if the mutant variances were

significantly larger than the wild-type variance (Eq. 2), or if the wild-type variance was

larger than the mutant variances (Eq. 3). The solution vector w for Eq. 1 and an

12

equivalent result with explanation obtained with an LDA method similar to Fisher (1936)

without use of a minmax optimizer are shown in Figure S1.

Figure 2 shows the mean values of the results obtained with glr3.3 mutants and

wild type after projection onto the LDA solution vector that minimized Eq. 1 (maximal

separation of mutant and wild-type population means). Conditions B, C, and D

produced statistically significant differences, demonstrating that the gravitropic

responses of the two glr3.3 alleles in these three conditions were not the same as the

wild type. These differences may be considered a growth and development phenotype

for the glr3.3 mutant, albeit one that could not be detected by monitoring the response

of the millimeter-sized root apex without the aid of imaging equipment and computation.

A non-mathematical way to interpret these results is that the distributions of mutant and

wild-type tip angle measurements were not identical. The response of mutant roots to

gravity differed on average from that the wild type as measured morphometrically from

high-resolution image time series.

Figure 3 shows the results of searching for differences in variance (optimizing

Eq. 2) between the mutant and wild-type populations. Normal distributions that best fit

the data are shown along with the actual data points. In all four conditions, glr3.3

populations displayed significantly greater variance than the wild type. In other words,

either glr3.3 allele caused the gravitropic response to be less consistent than the wild

type. Evidence for this was highly statistically significant, while tests for the opposite

effect (Eq. 3, greater variance in the wild type) produced no significant results for three

of the four conditions (data not shown). Interestingly, the optimal solution vectors for

Eq. 1 and Eq. 2 were similarly sinusoidal in shape, though not functionally

13

interchangeable (Figure S2). This may indicate that the portions of the response that

the LDA used to separate the means were also the portions in which the mutants varied

more than the wild type. The sinusoidal shape of the solution to Eq. 1 suggested the

next step of analysis.

Figure 4A shows the solution vector (black line) obtained by optimizing Eq. 1

using data from condition C. The shape is reminiscent of a Gaussian distribution

derivative. This raised the possibility that LDA solution vectors satisfying Eq. 1

achieved their separating effects through a property related to the derivative of a

Gaussian distribution. This possibility was further explored using data obtained in

condition C. The two best fitting first-order Gaussian derivative wavelets were found by

a custom algorithm, and are co-plotted (blue dashed lines) with the LDA solution vector

obtained for condition C (Figure 4A). The sum of the two wavelets (solid blue line)

represents a wavelet fit to the solution vector. If this wavelet could separate the mutant

and wild-type population means, the Gaussian derivative components of the solution

vector were probably responsible for its effectiveness in finding a phenotype (Figure

2C). As shown In Figure 4B, the fitted Gaussian derivative wavelet separated mutant

population means from the wild type in condition C similarly to the raw LDA separation

vector, though with lesser statistical significance. This may be expected because the

Gaussian wavelets did not capture all of the features present in the LDA separation

vector. The features not captured probably contributed additionally to the separation of

mutant and wild-type tip angle responses. The fact that the projection values obtained

from the wavelet fit were approximately 3-fold higher compared to the raw LDA

separation vector values is probably due to the fact that the wavelet fit tends to lie

14

above the raw separation vector after the 2 h point, increasing the value of each

individual projected onto it relative to the raw vector. The consistency between the

results indicates that the LDA separation vector distinguished the mutant alleles from

the wild type in condition C by acting to a considerable degree as a combination of two

first order Gaussian derivatives.

Convolving a curve with the first derivative of the Gaussian distribution is

common method of obtaining the first derivative of the curve. Thus, the result in Figure

4B could be taken as evidence that the phenotypic difference uncovered by optimizing

solutions to Eq. 1 is actually a difference in the rate of tip angle change at particular

times in the response. This was more directly investigated by performing first and

second-order Gaussian derivative wavelet analysis on the raw data for conditions where

Eq. 1 optimization produced significant solutions (conditions B, C, and D). Wavelets at

scales from 1 to 20 were applied at each point in time to each individual tip angle

response. T-tests of the wavelet-transformed data were performed between each

mutant allele and the wild type to determine how well population means were separated

for each wavelet function tested. After this analysis, significant separation of mutant

population means from the wild type was achieved for condition C but not the others.

Figure 5A shows the original graph of tip angle in response to gravistimulation.

Superimposed on this time course are step functions showing where first order (red) or

second order (blue) Gaussian derivative wavelets significantly separated both mutant

allele populations from the wild type (p < 0.05). In other words, glr3.3 mutations (both

alleles) affected the first derivative, or swing rate (Durham Brooks et al. 2010) when the

red line steps up. The second derivative, or acceleration of the tip angle, differed in

15

glr3.3 mutants when the blue line steps down. Putting the two effects together shows

that tip reorientation in glr3.3 plants decelerated significantly more than the wild type

approximately 4.3 h after the onset of gravitropism, when the tip angle was passing

through approximately 40 degrees. From 4.5 h until approximately 7 h, glr3.3 plants

bent more slowly (lower swing rate, first derivative) than wild type. This period was

followed by a brief period during which the wild type decelerated, or 'braked' relative to

the mutants. At the 10-h point, tip angles were closely matched. What the preceding

analysis showed (Figure 5A) is that in condition C the time course by which the root tips

reached the same new steady-state orientation was GLR3.3-dependent.

The phenotypic differences in Figure 5A are statistically robust and consistent

between two independent mutant alleles. Nonetheless, a further test was performed

because variation due to maternal environment can be large and pervasive enough to

affect growth and development of the next generation, especially when measured with

high resolution in seedlings presumably highly dependent on their seed environment.

Therefore, mutant and wild-type seed stocks generated independently of those used in

Figure 5A were assayed in condition C by the same methods. Although the shapes of

the responses in Figure 5B differed from those in Figure 5A (further evidence that

relatively minor maternal effects can significantly affect seedling behavior) the

phenotype was rediscovered by the wavelet analysis. Both glr3.3 alleles braked and

entered a phase of slower swing rate as the tip angle passed through 40 degrees as in

Figure 5A. Again, following this slower response phase, a second-derivative difference

compensated to bring the mutant and wild-type tip angles into close agreement.

Despite substantial differences between the gravitropism time courses displayed by

16

seedlings from Generation 1 (Figure 5A) and Generation 2 (Figure 5B) roots, the

acceleration and rate phenotypes were similar in relation to when they developed in the

tip angle time course. Independent generations of two glr3.3 mutant alleles displayed

slower tip swing than wild type as the tip angle passed between 40 and 50 degrees.

DISCUSSION

Gravitropism is a developmental process integral to plant life at least since the

colonization of land. Its facets include environmental signal perception, transduction,

hormone transport, cell expansion, all effected with tight spatial and temporal control

(Blancaflor and Masson 2003; Moulia et al. 2009). Therefore, many genes may be

expected to make small contributions, especially to the modulatory or regulatory

functions. GLR3.3 may be such a gene, for the following reasons. The large, transient

membrane depolarization triggered in wild-type root cells by micromolar levels of amino

acid ligands (Dennison and Spalding 2000) is essentially eliminated by glr3.3 mutations

(Qi et al. 2006; Stephens et al. 2008), as is the large, transient spike in cytoplasmic

Ca2+ that accompanies the depolarization (Qi et al. 2006). So, at the cell-physiological

level, the loss-of-function effects are severe. This is the basis for the proposal that

GLR3.3 is a foundational subunit in multimeric GLR channels present in root and

hypocotyl cells (Stephens et al. 2008). Because genetic redundancy between other

members of the GLR family is not evident in the ionic and electrophysiological assays of

immediate GLR function, redundancy is not a strong explanation for the subtle nature of

the organ-level phenotype described here. However, it is possible that the GLRs affect

growth and development through functions not related to their ion conduction and that

17

redundancy in these unknown functions reduce the phenotypic effect of the glr3.3

mutations.

An alternative interpretation of the phenotypes discovered by this application of

machine vision and computation is that channels containing GLR3.3 subunits affect the

stability of the gravitropic response. Without GLR3.3, the response is more variable or

less restrained to develop in a canalized way (Figure 3). Perhaps other growth

responses are similarly less well regulated in glr3.3 mutants so that the proper view of

this gene’s function is as a stabilizer of growth and development. This interpretation

borrows heavily on what has been reported for Hsp90 (Queitsch et al. 2002; Sangster et

al. 2008), and the idea that fundamental mechanisms define the degree of plasticity a

response is permitted (Schlichting and Smith 2002; Schlichting 2008). The role of

plasticity determinants as points of selection and agents of evolutionary change is an

active area of research at the interface of evolution and development (Sultan 2004;

Pigliucci 2005). Another area of research at the other end of the spectrum, intrinsic

noise in gene expression resulting from the low copy numbers of the relevant molecules

per cell (Elowitz et al. 2002) offers a related perspective on how a mutation may cause

little mean phenotype but greater variance in a response. A gene could function to

reduce the intrinsic stochastic component of gene expression in a cell. Mutation of such

a function would be expected to make a cellular response such as coordinated gene

expression more variable, not much affect the mean, but nonetheless have natural

selection consequences (Çağatay et al. 2009).

If growth and development were more routinely measured with high resolution

and in multiple conditions, the frequent conclusion that a mutant has no phenotype may

18

be replaced by the finding of a defect in modulation or regulation of a process. Such

phenotypes may appear minor or unimportant when observed in the laboratory and

considered singly. However, growth and development may be better thought of as a

process that depends on hundreds or thousands of such modulatory effects that

integrate to confer the appropriate degree of response plasticity in evolutionarily

relevant scenarios.

Regardless of whether the effects described here represent the largest or the

smallest contributions to growth and development to be discovered for GLR3.3, they

add some insight into the root gravitropism mechanism. The wavelet analysis

demonstrated that GLR3.3 promoted curvature development after the tip angle reached

40 degrees. Previous research demonstrated that maximum swing rate occurs at a tip

angle of approximately 30 degrees, regardless of condition or overall response time

course (Durham Brooks et al. 2010). Following this maximum, tip angle rapidly

decelerates as part of autotropic straightening, which counteracts gravitropic signaling

so that the reoriented portion of the root begins to grow straight (Stankovic et al. 1998).

The glr3.3 phenotype is detected soon after this event, indicating that this gene may act

to counter or buffer against the straightening response.

Some ionic and electrophysiological events have been observed to follow gravity

stimulation (Lee et al. 1983; Scott and Allen 1999; Plieth and Trewavas 2002; Massa et

al. 2003). Of them, only the rapid change in cytoplasmic pH in the gravity sensing cells

of the apex has been causally linked to the ensuing growth/curvature response (Fasano

et al. 2001; Hou et al. 2004). Possibly, GLR3.3 and other family members generate

ionic events in response to gravity that relate more to response modulation as

19

established here than creation of the differential growth responsible for tip bending. The

present results may prove helpful in directing cell physiology studies to the time and

place when gravity-induced ionic phenomena related to response modulation and

dependent on GLR3.3 may be found.

The method described here will be most valuable when used to generate

quantitative descriptions of large numbers of mutants that can be mapped onto each

other over the course of a developmental process such as gravitropism. Machine

learning methods could be used to classify the LDA results of different mutants to find

functional relationships between genes even if visible phenotypes are not present or

draw the attention in a different direction. A similar approach has been used in C.

elegans to classify locomotive behavior of a subset of mutants involved in nervous

system function (Geng et al. 2003). If widely adopted in Arabidopsis research, the

approach used here would result in a much larger fraction of today’s mutant populations

being useful to the process of discovering gene function.

20

FIGURE LEGENDS

Figure 1. Change in root tip angle of wild type and two glr3.3 mutants after

gravistimulation in four conditions: (A) Two-day-old seedlings from small seeds, 15 ≤ n

≤ 23 (B) Two-day-old seedlings germinated from large seeds, 18 ≤ n ≤ 27 (C) Four-day-

old seedlings germinated from small seeds, 15 ≤ n ≤ 23, and (D) Four-day-old seedlings

germinated from large seeds, 14 ≤ n ≤ 22. Tip angle was automatically measured from

high-resolution time series of root images bending toward gravity using custom image

analysis software. Error bars are standard error of the mean.

Figure 2. Time course data of root tip angle for each individual was plotted in a higher-

dimensional space, allowing for each individual to be represented as one point in 301-

dimensions. Linear discriminant analysis was used to find a vector such that when the

individuals were projected onto it, it maximally separated the mutant means from the

wild type. Population means are shown after projection of individual gravitropic

responses onto the linear solution of Eq 1 optimization. (A) Two-day-old seedlings

germinated from small seeds. (B) Two-day-old seedlings germinated from large seeds,

(C) Four-day-old seedlings germinated from small seeds, and (D) Four-day-old

seedlings germinated from large seeds. Asterisks indicate significant differences in

population means as determined by a two-sample t test. **, p < 0.01; ***, p < 0.001.

Figure 3. Population variances after projection of individual gravitropic responses onto

the linear solution of Eq. 2 optimization. Shown is the normal distribution that best fits

the projection data and below each normal fit are the points corresponding to each

individual within the population. (A) Two-day-old seedlings germinated from small

seeds, (B) Two-day-old seedlings germinated from large seeds, (C) Four-day-old

21

seedlings germinated from small seeds, and (D) Four-day-old seedlings germinated

from large seeds. Pound symbols indicate significant differences in population variance

between mutant and wild-type as determined by a Brown-Forsythe test. ##, p < 0.01;

###, p < 0.001.

Figure 4. Describing a mean-separating LDA solution vector as a composition of first-

order Gaussian derivative wavelets. (A) An LDA solution vector for Eq 1 optimization in

condition C is shown in black. The two first-order Gaussian wavelets that best fit the

solution vector are shown with dashed blue lines. Summing these two wavelets gives

the solid blue line, which represents a wavelet fit of the LDA solution vector. (B) The

individual responses from condition C were projected onto the LDA solution vector (left

three bars) or onto the wavelet fit (solid blue line from panel A). A two-sample t test

determined that the wavelet fit significantly separated the population means. * p <0.05;

** p < 0.01; *** p < 0.001

Figure 5: Derivative analysis of two independent generations of glr3.3 alleles

responding to gravistimulation in condition C (four-day-old roots from small seeds).

Shown are the average tip angle responses to gravistimulation for wild type (black) and

the mutant alleles (orange and light orange). Error bars show the standard error of the

mean. (A) Generation 1 of mutant and wild-type seed stocks. (B) Generation 2 of

mutant and wild-type seed stocks. n ≥ 8 for all populations. Regions of the time

courses in which first-order Gaussian derivative wavelets significantly separated the

mutant populations from the wild type are indicated by an upward deflections in the red

line (p < 0.05 as determined by a two-sample t test). Downward deflections of the blue

line indicate portions of the time courses in which second-order Gaussian wavelets

22

significantly separated the mutant populations from the wild type (p < 0.05 as

determined by a two-sample t test).

23

REFERENCES

Alonso, J. M., and J. R. Ecker, 2006 Moving forward in reverse: genetic technologies to

enable genome-wide phenomic screens in Arabidopsis. Nat. Rev. Genet. 7: 524-

536.

Beemster, G. T. S., and T. I. Baskin, 1998 Analysis of Cell Division and Elongation

Underlying the Developmental Acceleration of Root Growth in Arabidopsis thaliana

Plant Physiol. 116: 1515-1526

Blancaflor, E. B., and P. H. Masson, 2003 Plant gravitropism. Unraveling the ups and

downs of a complex process. Plant Physiol. 133: 1677-1690.

Bouché, N., and D. Bouchez, 2001 Arabidopsis gene knockout: phenotypes wanted.

Curr. Opin. Plant Biol. 4: 111-117.

Çağatay, T., Turcotte, M., Elowitz, M. B., Garcia-Ojalvo, J., and G. M. Süel, 2009

Architecture-dependent noise discriminates functionally analogous differentiation

circuits. Cell 139: 512-522.

Chavarría-Krauser, A., 2006 Quantification of curvature production in cylindrical organs,

such as roots and hypocotyls. New Phytol. 171: 633-641.

Chiu, J. C., E. D. Brenner, R. DeSalle, M. N. Nitabach, T. C. Holmes, et al., 2002

Phylogenetic and expression analysis of the glutamate-receptor-like gene family in

Arabidopsis thaliana. Mol. Biol. and Evol. 19: 1066-1082.

Cho, D., S. A. Kim, Y. Murata, S. Lee, S. K. Jae, et al., 2009 Deregulated expression of

the plant glutamate receptor homolog AtGLR3.1 impairs long-term Ca-

programmed stomatal closure. Plant J. 58: 437-449.

Davenport, R., 2002 Glutamate receptors in plants. Ann. of Bot. 90: 549-557.

24

Dennison K. L., and E. P. Spalding, 2000 Glutamate-gated calcium fluxes in

Arabidopsis. Plant Physiol. 124: 1511-1514.

Durham Brooks, T. L., N. D. Miller, and E. P. Spalding, 2010 Plasticity of Arabidopsis

root gravitropism throughout a multi-dimensional condition space quantified by

automated image analysis. Plant Physiol. 152: 206-216.

Elowitz, M. B., A. J. Levine, E. D. Siggia, and P. S. Swain, 2002 Stochastic gene

expression in a single cell. Science 16: 1183-1186.

Fasano, J. M., S. J. Swanson, E. B. Blancaflor, P. E. Dowd, T. H. Kao, and S. Gilroy,

2001 Changes in root cap pH are required for the gravity response of the

Arabidopsis root. Plant Cell 13: 907-922.

Fisher, R. A., 1936 The use of multiple measurements in taxonomic problems. Annals of

Eugenics 7: 179-188.

Fraser, A. G., R. S. Kamath, P. Zipperlen, M. Martinez-Campos, M. Sohrmann, et al.,

2000 Functional genomic analysis of C. elegans chromosome I by systematic RNA

interference. Nature 408: 325-330.

Geng, W., P. Cosman, J. H. Baek, C. C. Berry, and W. R. Schafer, 2003 Quantitative

classification and natural clustering of Caenorhabditis elegans behavioral

phenotypes. Genetics 165: 1117-1126.

Hou, G., V. L. Kramer, Y-S. Wang, R. Chen, G. Perbal, et al., 2004 The promotion of

gravitropism in Arabidopsis roots upon actin disruption is coupled with the

extended alkalinization of the columella cytoplasm and a persistent lateral auxin

gradient. Plant J. 39: 113-125.

25

Kang, J., and F. J. Turano, 2003 The putative glutamate receptor 1.1 (AtGLR1.1)

functions as a regulator of carbon and nitrogen metabolism in Arabidopsis thaliana.

Proc. Nat. Aca. Sci. USA 100: 6872-6877.

Kang, J., S. Mehta, and F. J. Turano, 2004 The putative glutamate receptor 1.1

(AtGLR1.1) in Arabidopsis thaliana regulates abscisic acid biosynthesis and

signaling to control development and water loss. Plant Cell Physiol. 45: 1380-

1389.

Kang, S., H. B. Kim, H. Lee, J. Y. Choi, S. Heu, et al., 2006 Overexpression in

Arabidopsis of a plasma membrane-targeting glutamate receptor from small radish

increases glutamate-mediated Ca2+ influx and delays fungal infection. Mol. Cells

21: 418-427.

Kim, S. A., J. M. Kwak, S. K. Jae, M. H. Wang, and H. G. Nam, 2001 Overexpression of

the AtGluR2 gene encoding an Arabidopsis homolog of mammalian glutamate

receptors impairs calcium utilization and sensitivity to ionic stress in transgenic

plants. Plant Cell Physiol. 42: 74-84.

Kuromori, T., T. Wada, A. Kamiya, M. Yuguchi, T. Yokouchi, et al., 2006 A trial of

phenome analysis using 4000 Ds-insertional mutants in gene-coding regions of

Arabidopsis. Plant J. 47: 640-651.

Lacombe, B., D. Becker, R. Hedrich, R. DeSalle, M. Hollmann, et al., 2001 The identity

of plant glutamate receptors. Science 292: 1486-1487.

Lam, H. M., J. Chiu, M. H. Hsieh, L. Meisel, I. C. Oliveira, et al., 1998 Glutamate-

receptor genes in plants. Nature 396: 125-126.

26

Lee, J. S., T. J. Mulkey, and M. L. Evans, 1983 Gravity-induced polar transport of

calcium across root tips of maize. Plant Physiol. 73: 874-876.

Massa, G. D., J. M. Fasano, and S. Gilroy, 2003 Ionic signaling in plant gravity and

touch responses. Gravit. Space Biol. Bull. 16: 71-82.

Mayer, M. L., and N. Armstrong, 2004 Structure and function of glutamate receptor ion

channels. Annu. Rev. Physiol. 66: 161-181.

Miller, N. D., B. M. Parks, and E. P. Spalding, 2007 Computer-vision analysis of

seedling responses to light and gravity. Plant J. 52: 374-381.

Moulia B., and M. Fournier, 2009 The power and control of gravitropic movement in

plants: a biomechanical and systems biology view. J. Exp. Bot. 60: 461-486.

Pigliucci, M., 2005 Evolution of phenotypic plasticity: where are we going now? Trends

Ecol. Evol. 20: 481-486.

Plieth, C., and A. J. Trewavas, 2002 Reorientation of seedlings in the Earth's

gravitational field induces cytosolic calcium transients. Plant Physiol. 129: 786-

796.

Qi, Z., N. R. Stephens, and E. P. Spalding, 2006 Calcium entry mediated by GLR3.3, an

Arabidopsis glutamate receptor with a broad agonist profile. Plant Physiol. 142:

963-971.

Queitsch, C., T. A. Sangster, and S. Lindquist, 2002 Hsp90 as a capacitor of phenotypic

variation. Nature 417: 618-624.

Reddy, G.V., and A. Roy-Chowdhury, 2009 Live-imaging and image processing of

shoot apical meristems of Arabidopsis thaliana pp. 305-316 in Plant Systems

27

Biology, edited by D. A. Belostotsky. (vol 553 in the series Methods in Molecular

Biology), Humana Press, New York

Roy, S. J., M. Gilliham, B. Berger, P. A. Essah, C. Cheffings, et al. 2008 Investigating

glutamate receptor-like gene co-expression in Arabidopsis thaliana. Plant Cell

Environ. 31: 861-871.

Sangster, T. A., N. Salathia, S. Undurraga, R. Milo, K. Schellenberg, et al., 2008 HSP90

affects the expression of genetic variation and developmental stability in

quantitative traits. Proc. Natl. Acad. Sci. USA 105: 2963-2968.

Schlichting, C. D., 2008 Hidden reaction norms, cryptic genetic variation, and

evolvability. Ann. N.Y. Acad. Sci. 1133: 187-203.

Schlichting, C. D., and H. Smith, 2002 Phenotypic plasticity: linking molecular

mechanisms with evolutionary outcomes. Evol. Ecol. 16: 189-211.

Scott, A. C., and N. S. Allen, 1999 Changes in cytosolic pH within Arabidopsis root

columella cells play a key role in the early signaling pathway for root gravitropism.

Plant Physiol. 121: 1291-1298

Spalding, E. P., 2009 Computer vision as a tool to study plant development, pp. 317-

326 in Plant Systems Biology, edited by D. A. Belostotsky. (vol 553 in the series

Methods in Molecular Biology), Humana Press, New York.

Stankovic, B., D. Volkmann, and F. D. Sack, 1998 Autotropism, automorphogenesis,

and gravity. Physiol. Plant. 102: 328-335.

Stephens, N. R., Z. Qi, and E. P. Spalding, 2008 Glutamate receptor subtypes

evidenced by differences in desensitization and dependence on the GLR3.3 and

GLR3.4 genes. Plant Physiol. 146: 529-538.

28

Sultan, S. E., 2004 Promising directions in plant phenotypic plasticity. Perspect. Plant

Ecol. Evol. Syst. 6: 227-233.

Turano, F.J., G. R. Panta, M. W. Allard, and P. van Berkum, 2001 The putative

glutamate receptors from plants are related to two superfamilies of animal

neurotransmitter receptors via distinct evolutionary mechanisms. Mol. Biol. Evol.

18: 1417-1420.

van der Weele, C. M., H. S. Jiang, K. K. Palaniappan, V. B. Ivanov, K. Palaniappan, et

al., 2003 A new algorithm for computational image analysis of deformable motion

at high spatial and temporal resolution applied to root growth. Roughly uniform

elongation in the meristem and also, after an abrupt acceleration, in the elongation

zone. Plant Physiol. 132: 1138-1148.

ACKNOWLEDGMENTS

This work was supported by NSF grant DBI-0621702 and DOE grant DE-FG02-

04ER15527 to EPS, and an NSF graduate fellowship to TLDB.