Copyright � 2010 by the Genetics Society of AmericaDOI: 10.1534/genetics.110.118711

Detection of a Gravitropism Phenotype in glutamate receptor-like 3.3 Mutantsof Arabidopsis thaliana Using Machine Vision and Computation

Nathan D. Miller,*,1 Tessa L. Durham Brooks,*,1,2 Amir H. Assadi† and Edgar P. Spalding*,3

*Department of Botany and †Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Manuscript received May 10, 2010Accepted for publication July 14, 2010

ABSTRACT

Gene disruption frequently produces no phenotype in the model plant Arabidopsis thaliana, com-plicating studies of gene function. Functional redundancy between gene family members is one commonexplanation but inadequate detection methods could also be responsible. Here, newly developed meth-ods for automated capture and processing of time series of images, followed by computational analysisemploying modified linear discriminant analysis (LDA) and wavelet-based differentiation, were employedin a study of mutants lacking the Glutamate Receptor-Like 3.3 gene. Root gravitropism was selected as theprocess to study with high spatiotemporal resolution because the ligand-gated Ca21-permeable channelencoded 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 gridof seed-size and seedling-age conditions previously found to be important to gravitropism. Statistical testsof average responses detected no significant difference between populations, but LDA separated bothmutant alleles from the wild type. After projecting the data onto LDA solution vectors, glr3.3 mutantsdisplayed greater population variance than the wild type in all four conditions. In three conditions theprojection means also differed significantly between mutant and wild type. Wavelet analysis of the rawresponse curves showed that the LDA-detected phenotypes related to an early deceleration andsubsequent 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 begenerally applicable to the study of phenotypes and therefore gene function.

A major objective of research on the model plantArabidopsis thaliana is to determine functions for

each of its �25,000 genes. An extensive, sequence-indexed library of T-DNA insertion mutants has resultedin reverse genetics becoming a routine approach towardthis goal (Alonso and Ecker 2006). This approach isparticularly effective when the mutation results in anobservable phenotype that gives a clue about thedisrupted gene’s function (Kuromori et al. 2006).Unfortunately, the large majority of gene disruptionsin Arabidopsis produce no readily observable phenotype(Bouche and Bouchez 2001; Kuromori et al. 2006). Todate, functional descriptions for only �10% of theArabidopsis genes have been experimentally deter-mined. Reverse-genetic approaches in other organisms,such as Caenorhabditis elegans and Drosophila, have

yielded similar results (Fraser et al. 2000). One possibleexplanation for the infrequency of phenotypes is func-tional redundancy, especially when the gene is a memberof a large family. Or, the phenotype may be conditional,manifesting itself only in a particular environment ordevelopmental context that was not examined. Finally,the methodologies employed to search for a pheno-type may not match well with the missing gene’s func-tion or scale of contribution. Detecting the effect of amutation in only one of the organism’s �104 genesmay require a specialized technique. In this regard,high resolution measurements of growth over time holdmuch promise (Beemster and Baskin 1998; van der

Weele et al. 2003; Chavarrıa-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 20Arabidopsis genes homologous with those encodingmammalian ionotropic glutamate receptors (Lam et al.1998; Lacombe et al. 2001). Because the animal mole-cules were known almost exclusively as tetrameric ionchannels mediating synaptic transmission in the centralnervous system (Mayer and Armstrong 2004), theirpresence in plants attracted considerable attention. The

Supporting information is available online at http://www.genetics.org/cgi/content/full/genetics.110.118711/DC1.

Gene ID and Mutant stocks: AT1G42540, Salk_040458, andSalk_066009.

1These authors contributed equally to this work.2Present address: Department of Biology, Doane College, Crete, NE

68333.3Corresponding author: Department of Botany, University of Wisconsin,

430 Lincoln Dr., Madison, WI 53706. E-mail: spalding@wisc.edu

Genetics 186: 585–593 (October 2010)

first studies explored the structure and evolution of theplant gene family (Turano et al. 2001; Chiu et al. 2002).Subsequent studies employing antisense methods toreduce expression and constitutive promoters to over-express GLR family members indicated possible roles incoordinating carbon and nitrogen metabolism (Kang

and Turano 2003), abscisic acid biosynthesis andsignaling (Kang et al. 2004), Ca21 and Na1 homeostasis(Kim et al. 2001), Ca21 and fungal disease progression(Kang et al. 2006), and Ca21-mediated stomatal closure(Cho et al. 2009). Transcription of multiple familymembers in the same cell type made heteromericchannels seem probable in planta (Roy et al. 2008).While each study provides clues, a consistent theme hasnot emerged. A robust mutant phenotype could givevery useful direction to further experimentation butnone has been reported.

The Arabidopsis GLR genes are different enoughfrom the animal neurotransmitter-gated channels in keyregions, such as the putative ion-conducting pore andextracellular amino-terminal domains, that equivalentmolecular function cannot be assumed (Davenport

2002). But the demonstration that wild-type plantsrespond to glutamate with a strong membrane depolar-ization and fast transient rise in cytoplasmic Ca21

concentration made ligand-gated channel activity forthe plant GLR molecules a viable hypothesis (Dennison

and Spalding 2000). The hypothesis was stronglysupported when these ionic events were found to beblocked by mutations in the GLR3.3 and GLR3.4 genes(Qi et al. 2006; Stephens et al. 2008). In spite of thesestrong ionic phenotypes, growth or development defectsthat typically guide hypotheses about gene functioncould not be found. Either such phenotypes do not existin glr3.3 mutants or some nonstandard methods forfinding them were necessary. Here, a highly automatedprocess for quantifying dynamic root growth and behav-ior involving image processing and mathematical anal-ysis was employed to search for a root growth behaviorphenotype (Miller et al. 2007; Durham Brooks et al.2010). The results demonstrate a function for GLR3.3 inroot gravitropism and provide an example of how asingle-gene phenotype can be isolated by applyingappropriate technology.

MATERIALS AND METHODS

Plant material: A. thaliana (Columbia ecotype) seeds weresieved with grading sizes of 250, 280, 300, and 355 mm2. Seedsbetween 250 and 280 mm2 were classified as small and thosefrom 300 to 355 mm2 were classified as large. Sieved seeds weresurface sterilized with 70% ethanol, 2% Triton X-100 and wereplanted on a 1% agar medium containing 1 mm KCl, 1 mm

CaCl2, and 5 mm 2-[N-morpholino]-ethanesulfonic acid, andpH was adjusted to 5.7 with 1,3-bis[tris(hydroxymethyl)me-thylamino]propane. After stratification at 4� for 3–7 days, theseeds were germinated on a vertically oriented plate andgrown for 2–4 days under 50 mmol m�2 sec�1 white light.

Mutant genotyping: Seeds of plant lines containing T-DNAinsertions in GLR3.3 (At1g42540) were obtained from theSalk Institute (http://signal.salk.edu/cgi-bin/tdnaexpress). Thelines used were Salk_040458 (glr3.3-1, second exon insertion)and Salk_066009 (glr3.3-2, first intron insertion). Homozy-gous individuals were genotyped using the method describedpreviously (Qi et al. 2006). The PCR products from amplifica-tion with the left border primer were sequenced to verify theposition of the insertion.

Imaging: Petri plates containing seedlings were mountedvertically and transverse to the optical axis of one of seven CCDcameras [Marlin F146B; Allied Vision Technologies (AVT),Newburyport, MA, www.alliedvisiontec.com] outfitted with aclose-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, waspositioned behind each petri plate for back illumination.Resulting images were 1392 3 1040 pixels at 8-bit pixel depth,with a maximum resolution of�5 mm per pixel. Only one rootper plate was analyzed, even if there were two or three present.An x, y, z positioning device on the plate holder was used topose the selected root in the center of the frame. To initiatethe experiment, the plate was rotated until the tip of the rootwas horizontal as best judged by eye, i.e., within a degree or twoof the camera’s horizon. File-acquisition rate and storage ofthe images in tag image file format (TIFF) was controlled byAVT software. Each camera acquired images of a seedling rootevery 2 min for 10 h beginning when the seedling was rotatedto induce gravitropic root bending. A total of 255 such‘‘movies’’ were acquired for the studies presented here. All thecomponents 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: Using the image processing methods de-tailed in the supplemental material section (http://botany.wisc.edu/spalding/PlantJournal2007/Supplemental_Material.htm) of Miller et al. (2007), the midline was extractedfrom each root image. Tip angle was calculated by firstperforming principal components analysis on a 5-pixel regionof the midline near the root tip. The tip angle was the angleformed between the first principal component and thecamera’s horizon. Growth rate was calculated as the differen-tial of the midline length over time. Growth rates betweenmutant and wild-type roots were not different to a statisticallysignificant degree and were not used in the analyses presentedhere.

Linear discriminant analysis and its optimization: To findthe projection of the data best satisfying each objectivefunction, a minmax optimizer in the optimization toolkit ofthe MATLAB scientific programming language (Mathworks,www.mathworks.com/products) was applied to the entirepopulation of tip angle vs. time points for 300 iterations.These 300 results were filtered to find the solution of thispopulation producing the smallest P-values between themutant and wild type. To determine whether the projectionresulted in significant separation, tests of significance wereperformed. A two-sample t-test was used to calculate signifi-cance of the solution to Equation 1 optimization. During theiterative search for variance separation (Equations 2 and 3), anF-test determined the significance level of each result. Statis-tical significance of the final result was determined with aBrown–Forsythe test.

Wavelet analysis: Wavelet analysis was performed on eachindividual tip angle response using the first- or the second-order derivative of the Gaussian distribution as the trans-forming function with window sizes from 1 to 20. To determinethe significance of the wavelet-transformed data, t-tests wererun between each mutant allele and the wild-type populations

586 N. D. Miller et al.

for each scale at each condition. Regions of the response inwhich the mutant data differed from the wild type wereconsidered significant when P , 0.05 at any wavelet scale inboth alleles.

Fitting of wavelets to the linear discriminant analysis (LDA)solution vector was performed as follows. The four first-orderGaussian derivatives that best correlated with the solutionvector 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 fitwas identified and then summed to create the wavelet fit of theLDA solution vector.

RESULTS

A bank of seven CCD cameras each equipped with aclose-focus zoom lens formed the front end of acomputer-controlled image acquisition and analysisplatform that was used in a previous study to investigatethe plasticity of wild-type root gravitropism (Durham

Brooks et al. 2010). The size of the seed from which theseedling emerged and postgermination age significantlyaffected response trajectory when measured with highresolution at 2-min intervals over a 10-hr period (Durham

Brooks et al. 2010). Therefore, seed size (small or large)and seedling age (2 days or 4 days) created a 2 3 2condition grid in which a gravity response phenotypewas sought in two T-DNA insertion (mutant) alleles ofGLR3.3 (At1g42540). All image data acquired duringthis study are available at http://phytomorph.wisc.edu/download.

Figure 1 shows the average time course of root tipangle after gravistimulation in the wild type and two

glr3.3 alleles in each of the four chosen conditions. Asfound in a recent characterization of the wild type (Col-0ecotype), young seedlings responded vigorously andtransiently overshot the ultimate steady-state angle re-gardless of seed size or genotype (Figure 1, A and B).Older seedlings more steadily approached the new ver-tical upon reorientation (Figure 1, C and D). Both glr3.3alleles developed tip angle slightly differently than thewild type in conditions B, C, and D (for example, notethe initial response rates), although t-tests indicatedthat the differences were not significant at any of thetime points (data not shown). However, a null resultbased on population averages does not rule out an effectof the glr3.3 mutation on this root growth response.

Other methods for finding evidence of differencesbetween populations of measurements exist. LDA, firstdevised by Fisher (1936) to investigate a plant taxon-omy question using sepal size, is one such method. Amethod similar to Fisher’s original LDA for separatingtwo groups was implemented to determine whether twogroups (glr3.3-1 and glr3.3-2) could be separated simi-larly from a third (the wild type). The input data were tipangle time points (301 per trial 3 n trials per condition).They were treated as a high-dimension data cloud byrecasting each time course as a single point in 301-dimensional space. The next step was to design anobjective function that specified the hypothesis to test asfollows. One objective function sought a linear pro-jection of the data that maximally separated the twomutant population means from the wild-type meanwhile minimizing the standard deviations of each; i.e.,

Figure 1.—Change in root tip angleof wild type and two glr3.3 mutants aftergravistimulation in four conditions: (A)2-day-old seedlings from small seeds,15 # n # 23; (B) 2-day-old seedlingsgerminated from large seeds, 18 # n #27; (C) 4-day-old seedlings germinatedfrom small seeds, 15 # n # 23; and(D) 4-day-old seedlings germinatedfrom large seeds, 14 # n # 22. Tip an-gle was automatically measured fromhigh-resolution time series of root im-ages bending toward gravity using cus-tom image analysis software. Error barsare standard error of the mean.

Machine Vision Phenotype Detection 587

minw

max f 1; f 2½ �

¼ minw

max�jmmut1 � mwt j

smut1 1 swt;�jmmut2 � mwt j

smut2 1 swt

� �s:t:kwk¼ 1;

ð1Þwhere

mJ ¼1

N J

Xi

wDJi

is the expected value for the J th group, i.e., wt, mut1,mut2,

s2J ¼

1

N J � 1

Xi

ðwDJ

i � mJ Þ2

is the variance for the J th group, i.e., wt, mut1, mut2, and

DJ

i

is the ith trial for the J th group.The second objective function sought a linear pro-

jection of the data that minimized the variance of thewild-type population relative to the mutant populations;i.e.,

minw

max f 1; f 2½ � ¼ minw

max�smut1

swt;�smut2

swt

� �s:t:kwk ¼ 1:

ð2ÞThe third found a linear projection of the data thatminimized the variance of the mutant populationsrelative to the wild-type population; i.e.,

minw

max f 1; f 2½ � ¼ minw

max�swt

smut1;�swt

smut2

� �s:t:kwk ¼ 1:

ð3ÞEach of the above objective functions contains a sub-function for each glr3.3 allele. A minmax optimizer wasemployed to search the 301-dimensional space for avector w that, when the data were projected onto it,minimized the value of the overall objective function. Inthe case of Equation 1, the minimum value of thefunction would be achieved when a vector was foundthat maximally separated the mutant population meansfrom the wild type. A t-test was then performed todetermine whether the mutant means after projectiononto w were significantly different from the wild type butnot themselves (Equation 1); a Brown–Forsythe test wasused to determine whether the mutant variances weresignificantly larger than the wild-type variance (Equa-tion 2) or whether the wild-type variance was larger thanthe mutant variances (Equation 3). The solution vectorw for Equation 1 and an equivalent result with explana-tion obtained with an LDA method similar to Fisher

(1936) without use of a minmax optimizer are shown insupporting information, Figure S1.

Figure 2 shows the mean values of the results obtainedwith glr3.3 mutants and wild type after projection onto

the LDA solution vector that minimized Equation 1(maximal separation of mutant and wild-type popula-tion means). Conditions B, C, and D produced statisti-cally significant differences, demonstrating that thegravitropic responses of the two glr3.3 alleles in thesethree conditions were not the same as the wild type.These differences may be considered a growth anddevelopment phenotype for the glr3.3 mutant, albeitone that could not be detected by monitoring theresponse of the millimeter-sized root apex without theaid of imaging equipment and computation. A non-mathematical way to interpret these results is that thedistributions of mutant and wild-type tip angle measure-ments were not identical. The response of mutant rootsto gravity differed on average from that of the wild typeas measured morphometrically from high-resolutionimage time series.

Figure 2.—Time-course data of root tip angle for each in-dividual was plotted in a higher-dimensional space, allowingfor each individual to be represented as one point in 301 di-mensions. Linear discriminant analysis was used to find a vec-tor such that when the individuals were projected onto it, itmaximally separated the mutant means from the wild type.Population means are shown after projection of individualgravitropic responses onto the linear solution of Equation 1optimization. (A) Two-day-old seedlings germinated fromsmall seeds. (B) Two-day-old seedlings germinated fromlarge seeds. (C) Four-day-old seedlings germinated from smallseeds. (D) Four-day-old seedlings germinated from largeseeds. Asterisks indicate significant differences in populationmeans as determined by a two-sample t-test. **P , 0.01,***P , 0.001.

588 N. D. Miller et al.

Figure 3 shows the results of searching for differencesin variance (optimizing Equation 2) between the mutantand wild-type populations. Normal distributions thatbest fit the data are shown along with the actual datapoints. In all four conditions, glr3.3 populations dis-played significantly greater variance than the wild type.In other words, either glr3.3 allele caused the gravitropicresponse to be less consistent than the wild type.Evidence for this was highly statistically significant, whiletests for the opposite effect (Equation 3, greater vari-ance in the wild type) produced no significant results forthree of the four conditions (data not shown). In-terestingly, the optimal solution vectors for Equations1 and 2 were similarly sinusoidal in shape, though notfunctionally interchangeable (Figure S2). This mayindicate that the portions of the response that theLDA used to separate the means were also the portionsin which the mutants varied more than the wild type.The sinusoidal shape of the solution to Equation 1suggested the next step of analysis.

Figure 4A shows the solution vector (black line)obtained by optimizing Equation 1 using data fromcondition C. The shape is reminiscent of a Gaussiandistribution derivative. This raised the possibility thatLDA solution vectors satisfying Equation 1 achievedtheir separating effects through a property related to thederivative of a Gaussian distribution. This possibility wasfurther explored using data obtained in condition C.The two best fitting first-order Gaussian derivative wave-

lets were found by a custom algorithm and are coplotted(blue dashed lines) with the LDA solution vectorobtained for condition C (Figure 4A). The sum of thetwo wavelets (solid blue line) represents a wavelet fit tothe solution vector. If this wavelet could separate themutant and wild-type population means, the Gaussianderivative components of the solution vector wereprobably responsible for its effectiveness in finding aphenotype (Figure 2C). As shown in Figure 4B, thefitted Gaussian derivative wavelet separated mutantpopulation means from the wild type in condition Csimilarly to the raw LDA separation vector, though withless statistical significance. This may be expectedbecause the Gaussian wavelets did not capture all ofthe features present in the LDA separation vector. Thefeatures not captured probably contributed addition-ally to the separation of mutant and wild-type tip angleresponses. The fact that the projection values obtainedfrom the wavelet fit were approximately threefoldhigher compared to the raw LDA separation vectorvalues is probably due to the fact that the wavelet fittends to lie above the raw separation vector after the2-hr point, increasing the value of each individualprojected onto it relative to the raw vector. The consis-tency between the results indicates that the LDAseparation vector distinguished the mutant alleles fromthe wild type in condition C by acting to a considerabledegree as a combination of two first-order Gaussianderivatives.

Figure 3.—Population variances af-ter projection of individual gravitropicresponses onto the linear solution ofEquation 2 optimization. Shown is thenormal distribution that best fits theprojection data and below each normalfit are the points corresponding to eachindividual within the population. (A)Two-day-old seedlings germinated fromsmall seeds. (B) Two-day-old seedlingsgerminated from large seeds. (C) Four-day-old seedlings germinated fromsmall seeds. (D) Four-day-old seedlingsgerminated from large seeds. Poundsymbols indicate significant differencesin population variance between mut-ant and wild type as determinedby a Brown–Forsythe test. ##P , 0.01,###P , 0.001.

Machine Vision Phenotype Detection 589

Convolving a curve with the first derivative of theGaussian distribution is common method of obtainingthe first derivative of the curve. Thus, the result in Figure4B could be taken as evidence that the phenotypicdifference uncovered by optimizing solutions to Equa-tion 1 is actually a difference in the rate of tip anglechange at particular times in the response. This wasmore directly investigated by performing first- andsecond-order Gaussian derivative wavelet analysis onthe raw data for conditions where Equation 1 optimiza-tion produced significant solutions (conditions B, C,and D). Wavelets at scales from 1 to 20 were applied ateach point in time to each individual tip angle response.T-tests of the wavelet-transformed data were performedbetween each mutant allele and the wild type to de-termine how well population means were separated foreach wavelet function tested. After this analysis, signif-icant separation of mutant population means from thewild type was achieved for condition C but not theothers. Figure 5A shows the original graph of tip angle inresponse to gravistimulation. Superimposed on thistime course are step functions showing where first-order(red) or second-order (blue) Gaussian derivative wave-lets significantly separated both mutant allele popula-tions from the wild type (P , 0.05). In other words, glr3.3mutations (both alleles) affected the first derivative, orswing rate (Durham Brooks et al. 2010), when the redline steps up. The second derivative, or acceleration ofthe tip angle, differed in glr3.3 mutants when the blueline steps down. Putting the two effects together showsthat tip reorientation in glr3.3 plants deceleratedsignificantly more than the wild type �4.3 hr afterthe onset of gravitropism, when the tip angle waspassing through �40�. From 4.5 hr until �7 hr, glr3.3plants bent more slowly (lower swing rate, first de-rivative) than wild type. This period was followed by abrief period during which the wild type decelerated or‘‘braked’’ relative to the mutants. At the 10-hr point, tipangles were closely matched. What the precedinganalysis showed (Figure 5A) is that in condition Cthe time course by which the root tips reached the

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

The phenotypic differences in Figure 5A are statisti-cally robust and consistent between two independentmutant alleles. Nonetheless, a further test was per-formed because variation due to maternal environmentcan be large and pervasive enough to affect growth anddevelopment of the next generation, especially whenmeasured with high resolution in seedlings presumablyhighly dependent on their seed environment. There-fore, mutant and wild-type seed stocks generated in-dependently of those used in Figure 5A were assayed incondition C by the same methods. Although the shapesof the responses in Figure 5B differed from those inFigure 5A (further evidence that relatively minor ma-ternal effects can significantly affect seedling behavior),the phenotype was rediscovered by the wavelet analysis.Both glr3.3 alleles braked and entered a phase of slowerswing rate as the tip angle passed through 40� as inFigure 5A. Again, following this slower response phase, asecond-derivative difference compensated to bring themutant and wild-type tip angles into close agreement.Despite substantial differences between the gravitrop-ism time courses displayed by seedlings from generation1 (Figure 5A) and generation 2 (Figure 5B) roots, theacceleration and rate phenotypes were similar in re-lation to when they developed in the tip angle timecourse. Independent generations of two glr3.3 mutantalleles displayed slower tip swing than wild type as the tipangle passed between 40� and 50�.

DISCUSSION

Gravitropism is a developmental process integral toplant life at least since the colonization of land. Its facetsinclude environmental signal perception, transduction,hormone transport, and cell expansion, all effected withtight spatial and temporal control (Blancaflor andMasson 2003; Moulia and Fournier 2009). Therefore,many genes may be expected to make small contribu-tions, especially to the modulatory or regulatory func-

Figure 4.—Description of a mean-separating LDA solution vector as acomposition of first-order Gaussian de-rivative wavelets. (A) An LDA solutionvector for Equation 1 optimization incondition C is shown in black. Thetwo first-order Gaussian wavelets thatbest fit the solution vector are shownwith dashed blue lines. Summing thesetwo wavelets gives the solid blue line,which represents a wavelet fit of theLDA solution vector. (B) The individualresponses from condition C were pro-jected onto the LDA solution vector(left three bars) or onto the wavelet

fit (solid blue line from 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.

590 N. D. Miller et al.

tions. GLR3.3 may be such a gene, for the followingreasons. The large, transient membrane depolarizationtriggered in wild-type root cells by micromolar levels ofamino acid ligands (Dennison and Spalding 2000) isessentially eliminated by glr3.3 mutations (Qi et al. 2006;Stephens et al. 2008), as is the large, transient spike incytoplasmic Ca21 that accompanies the depolarization(Qi et al. 2006). So, at the cell-physiological level, theloss-of-function effects are severe. This is the basis for theproposal that GLR3.3 is a foundational subunit inmultimeric GLR channels present in root and hypocotylcells (Stephens et al. 2008). Because genetic redun-dancy between other members of the GLR family is notevident in the ionic and electrophysiological assays ofimmediate GLR function, redundancy is not a strongexplanation for the subtle nature of the organ-levelphenotype described here. However, it is possible thatthe GLRs affect growth and development throughfunctions not related to their ion conduction and thatredundancy in these unknown functions reduces thephenotypic effect of the glr3.3 mutations.

An alternative interpretation of the phenotypes dis-covered by this application of machine vision andcomputation is that channels containing GLR3.3 sub-units affect the stability of the gravitropic response.Without GLR3.3, the response is more variable or lessrestrained to develop in a canalized way (Figure 3).Perhaps other growth responses are similarly less wellregulated in glr3.3 mutants so that the proper view of thisgene’s function is as a stabilizer of growth and de-velopment. This interpretation borrows heavily on whathas been reported for Hsp90 (Queitsch et al. 2002;Sangster et al. 2008), and the idea that fundamentalmechanisms define the degree of plasticity the response ispermitted (Schlichting and Smith 2002; Schlichting

2008). The role of plasticity determinants as points ofselection and agents of evolutionary change is an activearea of research at the interface of evolution anddevelopment (Sultan 2004; Pigliucci 2005). Anotherarea of research at the other end of the spectrum, intrin-

sic noise in gene expression resulting from the low copynumbers of the relevant molecules per cell (Elowitz

et al. 2002), offers a related perspective on how a mu-tation may cause little mean phenotype but greater var-iance in a response. A gene could function to reduce theintrinsic stochastic component of gene expression in acell. Mutation of such a function would be expected tomake a cellular response such as coordinated gene ex-pression more variable, not much affect the mean, butnonetheless have natural selection consequences(CxaGatay et al. 2009).

If growth and development were more routinelymeasured with high resolution and in multiple condi-tions, the frequent conclusion that a mutant has nophenotype may be replaced by the finding of a defect inmodulation or regulation of a process. Such phenotypesmay appear minor or unimportant when observed in thelaboratory and considered singly. However, growth anddevelopment may be better thought of as a process thatdepends on hundreds or thousands of such modulatoryeffects that integrate to confer the appropriate degree ofresponse plasticity in evolutionarily relevant scenarios.

Regardless of whether the effects described hererepresent the largest or the smallest contributions togrowth and development to be discovered for GLR3.3,they add some insight into the root gravitropism mech-anism. The wavelet analysis demonstrated that GLR3.3promoted curvature development after the tip anglereached 40�. Previous research demonstrated that max-imum swing rate occurs at a tip angle of�30�, regardlessof condition or overall response time course (Durham

Brooks et al. 2010). Following this maximum, tip anglerapidly decelerates as part of autotropic straightening,which counteracts gravitropic signaling so that thereoriented portion of the root begins to grow straight(Stankovic et al. 1998). The glr3.3 phenotype is detectedsoon after this event, indicating that this gene may act tocounter or buffer against the straightening response.

Some ionic and electrophysiological events have beenobserved to follow gravity stimulation (Lee et al. 1983;

Figure 5.—Derivative analysis of twoindependent generations of glr3.3 al-leles responding to gravistimulation incondition C (4-day-old roots from smallseeds). Shown are the average tip angleresponses to gravistimulation for wildtype (black) and the mutant alleles (or-ange and light orange). Error bars showthe standard error of the mean. (A)Generation 1 of mutant and wild-typeseed stocks. (B) Generation 2 of mutantand wild-type seed stocks. n $ 8 for allpopulations. Regions of the timecourses in which first-order Gaussianderivative wavelets significantly sepa-

rated the mutant populations from the wild type are indicated by an upward deflection in the red line (P , 0.05 as determinedby a two-sample t-test). Downward deflections of the blue line indicate portions of the time courses in which second-order Gauss-ian wavelets significantly separated the mutant populations from the wild type (P , 0.05 as determined by a two-sample t-test).

Machine Vision Phenotype Detection 591

Scott and Allen 1999; Plieth and Trewavas 2002;Massa et al. 2003). Of them, only the rapid change incytoplasmic pH in the gravity-sensing cells of the apex hasbeen causally linked to the ensuing growth/curvatureresponse (Fasano et al. 2001; Hou et al. 2004). Possibly,GLR3.3 and other family members generate ionic eventsin response to gravity that relate more to responsemodulation as established here than to creation of thedifferential growth responsible for tip bending. Thepresent results may prove helpful in directing cellphysiology studies to the time and place when gravity-induced ionic phenomena related to response modula-tion and dependent on GLR3.3 may be found.

The method described here will be most valuable whenused to generate quantitative descriptions of largenumbers of mutants that can be mapped onto eachother over the course of a developmental process such asgravitropism. Machine learning methods could be usedto classify the LDA results of different mutants to findfunctional relationships between genes even if visiblephenotypes are not present or draw the attention in adifferent direction. A similar approach has been used inC. elegans to classify locomotive behavior of a subset ofmutants involved in nervous system function (Geng et al.2003). If widely adopted in Arabidopsis research, theapproach used here would result in a much largerfraction of today’s mutant populations being useful tothe process of discovering gene function.

This work was supported by National Science Foundation (NSF)grant DBI-0621702 and Department of Energy grant DE-FG02-04ER15527 to E.P.S. and by an NSF graduate fellowship to T.L.D.B.

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Communicating editor: B. Bartel

Machine Vision Phenotype Detection 593

GENETICSSupporting Information

http://www.genetics.org/cgi/content/full/genetics.110.118711/DC1

Detection of a Gravitropism Phenotype in glutamate receptor-like 3.3Mutants of Arabidopsis thaliana Using Machine Vision and Computation

Nathan D. Miller, Tessa L. Durham Brooks, Amir H. Assadi and Edgar P. Spalding

Copyright � 2010 by the Genetics Society of AmericaDOI: 10.1534/genetics.110.118711

N. D. Miller et al. 2 SI

FIGURE S1.—Solution vectors by two different methods. The solution vector that minimizes Eq. 1 when applied to

the data obtained in condition C is shown in black. A highly similar result obtained by an alternative method similar to

that described by Fisher (1936) is shown in orange. The alternative method treats an entire time course as a linear

combination of tip angle measurements (TA) at each time point multiplied by a unitless coefficient . A given trial of

301 time points can thus be represented by a single number X,

X = 1 *TA (1 ) + 2 *TA (2 )+… + 3 0 1 *TA (301)

An equivalent statement is that X is the dot product of the and TA vectors, X = • TA. The design of the experiments performed here allowed each genotype sampled with n trials to be characterized by a population of n X values. In

Fisher’s discriminant analysis and the version used to create the above orange line, the set of values that maximizes

the difference between the mutant and wild type distributions of X values were found. The square of the student's t-

statistic was the function Fisher and we used to determine the distance between the X distributions being discriminated.

When the derivative of this function with respect to is 0, the distance between the distributions is maximum. A least

squares method was used to find the set of values, the vector , that nullified the derivative of the squared t-test

function. The resulting is the set of values that best separates the mutant from the wild type (orange line above). Fisher (1936) sought a linear combination of sepal length and width measurements that best separated the species Iris

setosa from Iris versicolor. Our application required finding a linear combination of tip angle measurements that best

separated two groups from each other (wild type and glr 3.3) with the added constraint that the resulting did not

separate the two glr3.3 alleles from each other. This added constraint, separating A from B/C instead of A from B, was

the reason we chose the minimax optimizer over the Fisher LDA method as the primary approach described in the text.

But Fisher's original solution described here produced the equivalent result (orange line in the above figure) when the

data from the two mutant alleles were pooled and a mutant (A) from wild type (B) discrimination was performed. The resulting solution vector did not separate the two mutant alleles from each other when they were subjected to an A from

B discrimination (data not shown). Before the discrimination procedures, PCA was used to reduce the dimensionality of

the data from 301 down to the 6 dimensions that contained 99% of the variance. The result was projected back into

301 dimensions before plotting in the figure.

N. D. Miller et al. 3 SI

FIGURE S2.—Solution vectors for separating mutant variances or means from wild type. The vector of weighting

coefficients that separated the mutant and wild-type means (black line) was similar in shape to that which found the

mutant variances to be larger than the wild type (purple line). However, they were not functionally interchangeable.

The mean-splitting vector could not achieve the variance separation of Eq. 2, nor could the variance splitting vector

achieve the mean separation of Eq. 1.