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 time 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.
A major objective of research on the model plant Arabidopsis thaliana is to determine functions for each of its ∼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 ∼10% of the Arabidopsis genes have been experimentally determined. Reverse-genetic approaches in other organisms, such as Caenorhabditis 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. Finally, 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 ∼104 genes may require a specialized technique. In this regard, high resolution measurements of growth over time hold much promise (Beemster and Baskin 1998; van der Weele et al. 2003; 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 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 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
A. thaliana (Columbia ecotype) seeds were sieved with grading sizes of 250, 280, 300, and 355 μm2. Seeds between 250 and 280 μm2 were classified as small and those from 300 to 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, and 5 mm 2-[N-morpholino]-ethanesulfonic acid, and pH was adjusted to 5.7 with 1,3-bis[tris(hydroxymethyl)methylamino]propane. After stratification at 4° for 3–7 days, the seeds were germinated on a vertically oriented plate and grown for 2–4 days under 50 μmol m−2 sec−1 white light.
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 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.
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, 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 ∼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.
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 vs. 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 whether 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 Equation 1 optimization. During the iterative search for variance separation (Equations 2 and 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 was performed on each individual tip angle response using the first- or the 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 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 < 0.05 at any wavelet scale in both alleles.
Fitting of wavelets to the linear discriminant analysis (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 and then summed to create the wavelet fit of the LDA solution vector.
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 postgermination age significantly affected response trajectory when measured with high resolution 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 × 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 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 (Figure 1, A and B). Older seedlings more steadily approached the new vertical upon reorientation (Figure 1, 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), although 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. 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 whether 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 × 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.,(1)whereis the expected value for the Jth group, i.e., wt, mut1, mut2,is the variance for the Jth group, i.e., wt, mut1, mut2, andis 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.,(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.,(3)
Each of the above objective functions contains a subfunction 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 Equation 1, the minimum value of the function would be achieved when a vector was found that maximally separated the mutant population means from the wild type. A t-test was then performed to determine whether the mutant means after projection onto w were significantly different from the wild type but not themselves (Equation 1); a Brown–Forsythe test was used to determine whether the mutant variances were significantly larger than the wild-type variance (Equation 2) or whether the wild-type variance was larger than the mutant variances (Equation 3). The solution vector w for Equation 1 and an equivalent result with explanation obtained with an LDA method similar to Fisher (1936) without use of a minmax optimizer are shown in supporting information, 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 Equation 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 nonmathematical 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 of the wild type as measured morphometrically from high-resolution image time series.
Figure 3 shows the results of searching for differences in variance (optimizing Equation 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 (Equation 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 Equations 1 and 2 were similarly sinusoidal in shape, though not functionally 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 Equation 1 suggested the next step of analysis.
Figure 4A shows the solution vector (black line) obtained by optimizing Equation 1 using data from condition C. The shape is reminiscent of a Gaussian distribution derivative. This raised the possibility that LDA solution vectors satisfying Equation 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 coplotted (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 less 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 threefold higher compared to the raw LDA separation vector values is probably due to the fact that the wavelet fit tends to lie above the raw separation vector after the 2-hr 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 Equation 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 Equation 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 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 ∼4.3 hr after the onset of gravitropism, when the tip angle was passing through ∼40°. From 4.5 hr until ∼7 hr, 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-hr 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° 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 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°.
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, and cell expansion, all effected with tight spatial and temporal control (Blancaflor and Masson 2003; Moulia and Fournier 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 redundancy in these unknown functions reduces 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 the 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 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°. Previous research demonstrated that maximum swing rate occurs at a tip angle of ∼30°, 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 established here than to 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.
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.
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, and Salk_066009.
↵1 These authors contributed equally to this work.
↵2 Present address: Department of Biology, Doane College, Crete, NE 68333.
Communicating editor: B. Bartel
- Received May 10, 2010.
- Accepted July 14, 2010.
- Copyright © 2010 by the Genetics Society of America