Image acquisition is an important step in the study of cytoskeleton organization. As visual interpretations and manual measurements of digital images are prone to errors and require a great amount of time, a freely available software package named MicroFilament Analyzer (MFA) was developed. The goal was to provide a tool that facilitates high-throughput analysis to determine the orientation of filamentous structures on digital images in a more standardized, objective and repeatable way. Here, the rationale and applicability of the program is demonstrated by analyzing the microtubule patterns in epidermal cells of control and gravi-stimulated Arabidopsis thaliana roots. Differential expansion of cells on either side of the root results in downward bending of the root tip. As cell expansion depends on the properties of the cell wall, this may imply a differential orientation of cellulose microfibrils. As cellulose deposition is orchestrated by cortical microtubules, the microtubule patterns were analyzed. The MFA program detects the filamentous structures on the image and identifies the main orientation(s) within individual cells. This revealed four distinguishable microtubule patterns in root epidermal cells. The analysis indicated that gravitropic stimulation and developmental age are both significant factors that determine microtubule orientation. Moreover, the data show that an altered microtubule pattern does not precede differential expansion. Other possible applications are also illustrated, including field emission scanning electron micrographs of cellulose microfibrils in plant cell walls and images of fluorescent actin.
Visualizing filamentous cell structures, such as the cytoskeleton or cellulose microfibrils, is performed mainly by microscopic imaging. However, to relate a certain organization to specific cellular functions and to validate long-standing hypotheses, a very accurate description of the pattern, free of biases, is required. The growing interest in computer-based modeling, part of a systems biology approach that is currently widely used to tackle biological ‘problems’ (Yuan et al., 2008; Dzhurakhalov et al., 2012), underlies the need for an unambiguous analysis and description of these filamentous structures. The currently used methods of visual interpretation and manual measurements (Sugimoto et al., 2003; Wang et al., 2007; Sainsbury et al., 2008) are prone to errors, and may be subject to bias based on the researcher who performs the measurements. Furthermore, these analyses are very laborious and time-consuming. To address these difficulties, the software package ‘MicroFilament Analyzer’ (MFA) was developed. This allows large-scale analyses to be performed in a more standardized, repeatable and much faster way. The software is designed to detect filaments on digital images and to assign one or more main orientation to them. The current interest in analysis software is supported by several other publications (Yin Kong et al., 2005; Higaki et al., 2010; Uyttewaal et al., 2012). Here, the application and usefulness of the MFA program are demonstrated by analysis of microtubule behavior during the root gravitropic response in Arabidopsis.
Earth's gravity is responsible for the natural downward growth of roots into the soil, where they take up water and nutrients. Perception of changes in plant orientation within the gravity field results in re-directed growth to regain the normal vertical position, a phenomenon that has puzzled scientists for over 200 years (Knight, 1806; Darwin and Darwin, 1880). Recently it was shown that statoliths, modified plastids in specialized columella cells of the Arabidopsis root tip, serve as a ‘tilt switch’ to initiate an asymmetric auxin redistribution between the upper and lower side of the root (Band et al., 2012). It is hypothesized that this auxin asymmetry triggers differential cell elongation at the lower and upper side of the root (Boonsirichai et al., 2002; Swarup et al., 2005; Morita, 2010). Rigid plant cell walls between neighboring cells prevent sliding of cells past one another. Therefore, differential cell expansion on opposite root sides results in the observed bending of the root.
Under normal growth conditions, the anisotropic longitudinal expansion of root epidermal cells is the outcome of vacuole-generated turgor pressure and stress relaxation inside the cell wall (Cosgrove, 2005). The load-bearing structures in the cell wall are the hemicellulose-tethered cellulose microfibrils, which are synthesized at the plasma membrane by cellulose synthase (CESA) complexes (Kimura et al., 1999; Guerriero et al., 2010). These chains of β(1→4)-linked d-glucose units have a high mechanical strength that prevents stretching along their long axis. Therefore, the orientation of cellulose microfibrils determines the direction of cell growth. Loosening of the tethers between parallel ordered cellulose microfibrils facilitates expansion of cells along the root axis (Cosgrove, 2005). Several cell wall-modifying proteins such as expansins (Cosgrove, 2000) and xyloglucan endotransglucosylase/hydrolases (XTHs) (Nishitani and Vissenberg, 2007; Van Sandt et al., 2007) are involved in wall relaxation. Cortical microtubules have been shown to influence the deposition of cellulose microfibrils into the cell wall. They mark the insertion position of the CESA complexes into the plasma membrane (Crowell et al., 2009; Gutierrez et al., 2009), and serve as tracks (Paredez et al., 2006) whereby the POM-POM2/CELLULOSE SYNTHASE INTERACTING1 protein (POM-POM2/CSI1) acts as a linking protein, guiding the CESAs along the microtubule arrays (Li et al., 2012; Bringmann et al., 2012). This implies an organizational pattern of newly formed cellulose microfibrils that mirrors that of cortical microtubules.
Therefore, the microtubule patterns of cells located in the bending zone of the Arabidopsis root were studied at intervals of 30 min during the first 2 h of induced gravitropism. The MFA analysis showed a clear effect of gravitropic stimulation on microtubule organization, and, moreover, a differential pattern in cells located at opposite sides of the curvature.
Results and Discussion
This section provides a comprehensive description of the custom-made image-processing tool MicroFilament Analyzer (MFA), designed using Matlab R2010a (Mathworks, www.mathworks.nl). The software program is written in basic Matlab code, and is compiled to a Microsoft (www.microsoft.com) Windows standalone executable. By installing Matlab Component Runtime 7.13 (MCR), the compiled program is able to run without the full Matlab software environment. The MCR freeware, some test files, a manual and the actual MicroFilament Analyzer program are freely available for research and educational purposes at http://www.ua.ac.be/bimef/MFA. It runs a user-friendly interface and comprises several features:
Aligning and scaling features
‘Magic wand’ selection tools
Build-in gamma correction
Area and perimeter calculation
A dedicated filament detection unit
Post-analysis and display capabilities
A main orientation detection function
Save and export features
Explanation of the buttons are displayed in the status box of the interface, guiding the user through the operating procedure.
The following stepwise sequence illustrates the rationale of use of the analysis tool.
Loading of the image data
The input consists of two related pictures (Figure 1a). The first is an optical section taken at the equatorial plane of the cells, showing all cell boundaries. The second image, referred to as a z-stack image below, is the maximum projection of a set of successive optical sections through the tissue of interest. If no section image is available, a copy of the z-stack image may be used instead. The program is able to handle color jpg, bmp or tif image formats, with no restrictions in pixel size.
Alignment of the images
The structures in the optical section image should perfectly match those in the z-stack image, which is not always the case, for example due to possible shortcomings in the microscope operating software and/or procedures. To this end, the optical section image may be uniformly re-sized in this part of the program, either semi-automatically or manually. The images are displayed on top of each other in different colors and with transparency to assist in possible overlay correction (Figure 1b).
To match the images semi-automatically, it is sufficient to sequentially mark two pairs of corresponding image features in both pictures. In the manual case, left-right and up-down repositioning of the z-stack image with respect to the optical section is possible by using the arrowheads on the panel (Figure S1a). More arrowheads for manual up- or down-scaling the optical section are also available. Re-scaling of a digital image requires bicubic interpolation. In order to ensure that the z-stack image resolution is uncompromised for filament detection, the optical section image is the one that is scaled, rather than the z-stack image. All these manipulations allow the user to achieve a near-perfect alignment of both images.
Once finished, the program saves a re-scaled version of the optical section image, and a version of the repositioned and cropped z-stack image.
Identification of the individual cells
To obtain information for each cell, the exact coordinates of all individual cell boundaries are required (Figure 1c). A ‘magic wand’ tool is available to select a particular cell in the optical section image, simply by clicking with the computer mouse in the inner cell area. The program will recognize the internal cell boundary contour automatically. This tool uses a normalized intensity threshold value that is adjustable by the user (Figure S1b). All continuous gray-scale pixel values below this changeable threshold value are considered to be part of the inner cell area. In the case of complex cell geometries or blurry image quality, the program provides the option to manually add and subtract regions by manually drawing cell boundaries on the optical section image.
All identified cells are numbered successively, and an image containing the indicated cell boundaries in different colors is automatically saved, allowing subsequent back-tracing of the location of the cells. There is no theoretical limit to the number of cells that may be selected. Furthermore, the program saves a spreadsheet file (*.xls, compatible with Microsoft Excel and OpenOffice) with several automatically calculated parameters of all cells, including the inner cell area, cell circumference and the geometrical center of each cell. To obtain the cell area, the actual number of pixels in the selected cell is counted, the cell circumference or perimeter is computed by calculating and adding the distance between each adjoining pair of pixels around the border of the cell area, and the geometrical center of a cell is found by calculating the center of mass of the cell area.
Pre-processing of the images
Before detecting the filaments, the z-stack image may be optimized by manually altering the image contrast using an adjustable value for the gamma correction (Figure S1c).
Detection analysis of the filaments
The filaments that are present in a z-stack image are detected by an approach that we call a ‘virtual rotating polarizer’. In optics, a wire grid polarizer converts light of random wave polarizations/orientations into light of a single well-defined wave polarization by blocking all other light. A similar idea is used for the z-stack analysis. A virtual line grid is placed in a horizontal start position over the image, and the filaments that lie on top of these grid lines and thus have the same orientation as the lines are identified. Next, the grid is slightly rotated and the analysis is repeated for this new angle (Figure 1d). If necessary, the initial horizontal orientation of the line grid may be altered by adjusting the ‘offset’ value, which changes the 0° position of the polarizer in a clockwise direction. For every angle, the image is sub-divided in adjacent parallel polarization lines. The angle interval that is analyzed ranges from 0° to 180° in stepwise increments chosen by the user (Figure S1d). An analysis from 180° to 360° delivers the same result, as the filaments on the image have a direction but not a sense. The smallest meaningful and detectable increment in angle step size is 3°, as filaments are detected on a pixel-based matrix that has limited angular resolution. By performing the analysis per 1° angle, for example, the same filament will be detected three times over, generating a misleading output because of multiple occurrences of the same filament.
For every line, the connectivity of every pixel is successively studied by comparing their neighboring gray-scale values on an orthogonal cross-section through the filament/line. The diameter indicates the width of the neighborhood comparison. A pixel is considered to be part of a filament if the difference between its gray-scale value and the mean gray-scale value of its sideways neighbors falls above a user-set intensity difference threshold (Figure S1d). If above the threshold, the pixel is part of the filament. If below the threshold, the filament is ended, and the search for a new filament commences along the polarization line.
For every filament, a condition has to be met before it is accepted as a true filament in the final analysis, i.e. it has to exceed a user-set minimal length requirement (Figure S1d) for successively recognized pixels along a line. The program gives a relative weight to all detected filaments according their length: longer filaments have higher relative weight, given by their lengths divided by the minimal length. The color of the filaments in the z-stack image, and thus the markers used in the biological sample, is of no direct importance, as the program focuses on the angular structure of the filaments within a gray-scale representation of the z-stack. Numeric data are generated for all recognized filaments, relating to their start, end and center coordinates, their length, the angle of their orientation, and to which cell they belong. A visual representation of the detected filaments in the z-stack is saved, and the numeric data are exported to an automatically generated spreadsheet (*.xls).
Post-processing of the data
Once the number of filaments and their orientation within each cell are known, the obtained data may be displayed per cell in a graph to provide insight into the results. Three display options are available (Figure 2a and Figure S1e). The first display plots the weighted number of filaments per angle on a linear graph. The second method displays the data as polar coordinates. The radius at an angle corresponds to the weighted number of filaments for that angle. The human brain is extremely well-suited and quick to recognize visual patterns, such as the dominant orientation of the filaments in a cell, especially when the data are presented on a circular/polar plot. Finally, the data may also be shown as an integrated linear plot of the cumulative sum of the weighted number of filaments per angle per cell.
Furthermore, the program contains a feature to automatically determine a number of dominant direction(s) of the filaments within each cell. However, a linear (or polar) graph of the number of filaments per angle in a certain cell may appear very noisy and spiked (because of limited or strongly varying numbers of filaments at a particular angle) (Figure 2a). Therefore, smoothing of the graph is first required to permit detection of general trends of dominant filament orientations. The necessary smoothing of the data is performed using a moving-average algorithm (Kenney and Keeping, 1962; Whittaker and Robinson, 1967; http://mathworld.wolfram.com/MovingAverage.html), a type of finite impulse response filter that is used to analyze a set of data points by creating a series of averages of various subsets of the full dataset. Given a linear series of data points (numbers) and a user-defined window size, which selects a subset of points, the moving average may be obtained by first taking the average of the first subset. The fixed window size is then shifted or moved one data point forward, creating a new subset of numbers, which is then again averaged, and so on. The window size (in degrees, in our case) may be varied in the program (Figure S1e). This is followed by a peak-search algorithm. Without smoothing, the peak-search algorithm detects spikes and outliers as dominant orientations. The peak-search algorithm locates the main local maxima in the smoothed linear data. It compares each number to its neighboring values. If an element of data is larger than both of its neighbors, the element is considered a local peak and thus a dominant orientation. Moreover, the number of dominant orientations that the program is allowed to identify in a cell is user-dependent (Figure S1e). In this case, the algorithm selects only the highest local maxima peaks that exceed a user-set percentage (Figure S1e) that a peak should surpass the average weighted number of detected filaments per angle, i.e. the threshold value (Figure 2a, yellow line). Furthermore, the program takes into account a user-defined value for the minimal separation (in degrees) that must occur between the main detected dominant orientations (Figure S1e).
The output of this analysis is summarized and added to the previously mentioned spreadsheet file, which includes the measured cell parameters, the number of filaments per angle per cell, and also its dominant filament angle(s) (Figure 2b).
Validation of the software
To compare use of the software program with manual measurements, an image of microtubules in the shoot apical meristem was analyzed (Figure 3a) (Hamant et al., 2008). The initial analysis of the image took 1 h (O. Hamant, personal communication, INRA and Université de Lyon, CNRS, ENS, Laboratoire de Reproduction et Développement des Plantes). For the MFA program, the most intense activity is selection of cells. Because no section image was available, selection was performed manually, and it took approximately 4 min to select 50 cells (Figure 3b). Subsequently, the detection procedure took approximately 10 min, during which no researcher input is required, and the detection module may be run several times using different settings to obtain optimal results (Figure 3c). The generated outcome was reported in the spreadsheet file, which shows the original experimental results (Hamant et al., 2008). These preferential microtubule orientations are indicated on Figure 3(d). Moreover, this demonstrates the analysis speed of the program.
Use of MFA to quantify microtubule organization in epidermal cells of Arabidopsis roots during a gravitropic response
Bending of roots is a typical response upon gravitropic stimulation. As shown in Figure 4(a), there is a statistically significant increase in the degree of bending over time (simple linear regression, P <0.001) with a mean angle of 43° after 2 h of induced gravitropism. As gravitropic bending is hypothesized to result from differential cell expansion, differences in cellular behavior may be expected in the transitional region between the meristematic and expansion zones within the root where bending initiates (Wolverton et al., 2002). The main focus is on the epidermal cells, where the most significant growth effects are expected. The bending degree is determined in relation to the distance from the extreme root tip. For clarity, this distance is divided into four zones, each 100 μm long and ranging from 200–600 μm from the root tip. From Figure 4(b), it is clear that bending is maximal in the zone closest to the root tip (zone 1: 200–299 μm from the root tip), and gradually decreases further up, with statistical significance (general mixed models, |t|>2). This effect is more pronounced with prolonged duration of gravi-stimulation (general mixed models, |t|>2). To examine cell length, an additional factor taken into account is the cell's location. A distinction is made between cells present in the upper or lower flank of the bending zone. Similarly positioned cells in control roots (grown along the gravitropic axis) are grouped together because both sides are indistinguishable and represent the control group. In close proximity to the root tip (zone 1: 200–299 μm from the root tip), there is no statistically significant difference in cell length, regardless of treatment. However, as the distance from the tip and cell length increases, there is a discrepancy between the three locations sampled. Cells present in the lower flank remain smaller than cells in the upper flank, with statistical significance (Figure 5), whereas control cells show intermediate cell lengths (general mixed models, |t|>2). Hence, our data confirm the previously reported differential cell expansion in the bending zone of curved roots (Mullen et al., 1991; Wolverton et al., 2002). This effect on cell expansion may be attributed to the asymmetrical auxin redistribution, with higher concentrations in the lower flank of the root and lower concentrations in the upper flank (Swarup et al., 2005; Band et al., 2012).
The major factors controlling cell growth are the mechanical properties of the cell wall, which are partly dependent on the orientation of the cellulose microfibrils. Therefore, the differential growth observed during bending may be attributed to varying microtubule patterns, which orchestrate an altered cellulose microfibril deposition (Blancaflor and Hasenstein, 1993; Bao et al., 2001; Himmelspach and Nick, 2001). However, other reports suggest that there is no involvement of microtubules in the control of differential cell expansion (Blancaflor and Hasenstein, 1995; Hasenstein et al., 1999; Bichet et al., 2001). In this paper, we have addressed this issue by monitoring microtubule organization during the graviresponse of Arabidopsis roots using MFA.
In the first step, a projection of a z-stack and a mid-plane image are uploaded into the program to verify the overlap between them. Next, the cells of interest are defined as shown in Figure 6. For each location, the outermost cell line is sampled. If necessary, minimal editing of the image may be performed by adjusting the contrast of the z-stack image. Altering the signal to noise ratio may either reduce false detection of background noise, or improve the recognition of filaments with a rather low signal (Figure 7). To minimize image modification, the original settings are mainly preserved and only corrected if really necessary. Over-exposed zones may also lead to false results. An option to reduce detection errors in this case is to exclude these regions from the analysis by manually selecting the surrounding area in step 3 (selecting cells).
Then the module is run according to several adjustable parameters. Standard settings should initially be chosen to generalize the process. However, settings that accomplish perfect detection in more mature cells may give poor results in the young meristematic zone. Because of the large heterogeneity between the sampled cells, it is possible to opt for optimal detection in every distinct case.
The outcome after detection is a set of filaments for each individual cell. These data are further processed to obtain the main orientation(s) of microtubules within each cell. Peaks that exceed more than 75% of the threshold value are considered as a dominant orientation, and two main orientations should be separated by a minimum of 20°. To analyze all images the same way, the output is corrected for positioning of the root on the image. The reference point is a horizontal orientation, and deviations from this standard are taken into account by adjusting the offset value. To handle the data more easily, all cells are classified into four categories according to the number and angle(s) of the detected main orientation(s). These groups are related to a specific pattern of microtubule organization. A first distinguishable pattern is a transverse (trans) orientation (80–100°) relative to the long axis of the cell and consequently the root. Note that a longitudinal orientation (170–10°) was not observed in this specific analysis and is therefore not included in the description of the data. The intermediate values, from (10–80°) and (100–170°), are called oblique. Combinations of two main angles are grouped together in the category ‘others’. When there are three or more main orientations present, it is named a random orientation. These four patterns of microtubule organization are shown in Figure 8, together with the MFA detection output image and the polar plot with the peak detection analysis. The number of detected filaments or microtubules per cell varies; for example, the number of detected filaments in Figure 8 varies from 75 (Figure 8a, small cell) to 689 (Figure 8c, larger cell), with a mean of 272 filaments per cell.
Even though digitalization is essential for high-throughput analysis, there is a small drawback. As microtubule organization is categorized according to a few unambiguous standards, this simplification may neglect some special cases, for example as shown in Figure 9. Both cells are assigned a random organization, but a subjective eye would make a distinction between an unordered structure (Figure 9a,b) and a more organized structure (Figure 9c,d). However, the frequency of observing a pattern such as that in the cell in Figure 9(c) is <2%, and thus the consequences of possible mis-classification of these rare cases are minimal for the eventual conclusion of this study. If desirable, this issue could be overcome by sub-dividing the cells into specific regions, e.g. the bottom, middle and top part of the cell, by manual selection in step 3.
The frequency distributions of microtubule organization are tested for differences according to the location within the root and time of treatment (Figure 10). This analysis shows that microtubule patterns are related to the growth stage of the cells (i.e. cell length or distance from the root tip). Regardless of treatment or location, the most abundant organizational pattern in the first zone is a random orientation (ordinal logistic regression, P <0.01). This is consistent with the initially unordered pattern of newly formed microtubules in the post-mitotic stage (Hasezawa et al., 2000; Baluska et al., 2001; Wasteneys, 2002). As the distance from the root tip and the cell length increases, the distribution of patterns varies between the conditions. Cells in the subsequent zones of vertically grown roots show a prominent transverse orientation in 60% of the cells on average. This corresponds with their ability to expand strongly in the longitudinal direction. However, gravi-stimulated roots progressively lose this mainly transverse microtubule organization. The proportion of transversally orientated microtubules gradually decreases in favor of an oblique and combined organization (ordinal logistic regression, P <0.05). This shift is first noticeable after 30 min of gravitropic stimulation in the early expansion zone, from 300–399 μm (zone 2). Longer periods of gravi-stimulation extend this trend to the following zones. An oblique orientation is rarely present in control roots, but appears more frequently upon gravi-stimulation as the favorable orientation or in a combined composition. This pattern may facilitate curved growth rather than strict longitudinal expansion, a feature also seen in gravi-stimulated maize coleoptiles (Himmelspach et al., 1999).
Moreover, there is a statistically significant difference in microtubule organization between upper-located and lower-located cells (ordinal logistic regression, P <0.05). The shift in frequency distributions is more pronounced in the lower part, where cells retain a random or combined orientation. The higher frequency of ordering of microtubules in a unique oblique or transverse pattern in the upper zone may indicate that they are more prone to elongation than the lower cells. As a result, these upper-located elongating cells provide a stronger pushing force to the cells located closer to the tip than the cells at the bottom do. As a result of the different pushing force, the upper part grows more than the lower part and initiates the bend.
The first noticeable difference in microtubule organization is observed in cells in the upper part of the root in the second zone after 30 min of gravi-stimulation. However, at this time point, the cell length in the subsequent zone (zone 3: 400–499 μm) already differs from the control situation (Figure 5), implying that the altered microtubule patterns do not precede bending but rather are a consequence of altered growth of the root. This confirms previous reports by Blancaflor and Hasenstein (1995), Hasenstein et al. (1999) and Bichet et al. (2001). The trigger that drives the observed altered microtubule organization may be gravitropic signaling or mechanical stimuli (Ikushima and Shimmen, 2005). As well as microtubules, other factors such as differential loosening or cross-linking of the cell wall, and/or modifications in the growth-driving turgor pressure, may orchestrate the differential elongation. Altered expansin distributions have indeed been described in bending maize roots (Zhang and Hasenstein, 2000), and increased cross-linking activity was demonstrated in cells with a decreasing elongation rate (De Cnodder et al., 2005).
In conclusion, the MFA software has been shown to be successful in detecting modifications in microtubule patterns. Moreover, the applicability of MFA is not limited to microtubule images; the program may be used to analyze any filamentous structure in any digital image, such as actin (Figure 11a). As well as confocal microscopy images of the cytoskeleton, digital images of cellulose microfibrils acquired by field emission scanning electron micrography were also analyzed (Figure 11b). These images show merely the shade effect of the cellulose fibrils instead of the fibrils per se. Nevertheless, the program is able to detect these structures, and a comparable pattern is generated as shown on the output file with the detected filaments (Figure 11b, far right). The program is compatible with various image formats, and recognizes filaments irrespective of the marker used (green, red or yellow color). To provide an integral software package, several tools are available that may be applied with considerable flexibility (e.g. alignment possibilities and cell selection features). The program assigns one or more strict main orientation(s) rather than an averaged angle as for the tool described by Uyttewaal et al. (2012). For analysis of individual cells, calculation of parameters such as cell area and perimeter is also possible.
The intended aim is to provide a user-friendly tool that standardizes the processing of images consisting of filamentous structures in a faster and unbiased way. For plant biologists, these include actin, microtubules and cellulose microfibrils. However, not all possibilities are explored and integrated in the current version of the program. There will be continuous maintenance and support of the software program, with regular upgrades. Details of bugs, suggestions and requests to extend its abilities are therefore welcomed (email@example.com).
Plant growth and microscopy
Microtubules were visualized in Arabidopsis thaliana Col-0 using the transgenic line MAP4–GFP (Marc et al., 1998). Seeds were surface-sterilized and sown on vertical 125 × 125 mm Petri plates as detailed previously (French et al., 2009). Each plate contained 60 ml half-strength Murashige and Skoog medium (Sigma, www.sigmaaldrich.com) solidified using 1% w/v agar. After 2 days at 4°C, plates were transferred to controlled environment chambers at 23°C under continuous light with a photon flux density of 150 μmol m−2 sec−1. Five-day-old seedlings were gravi-stimulated by turning the plates 90°. At 30, 60, 90 and 120 min after gravi-stimulation, images of GFP-tagged microtubules were taken for 7–10 randomly sampled roots using an inverted SP5 spectral detection confocal microscope (Leica, www.leica.com). A stack of successive images was taken from the upper side of the root to the mid-plane. These stacks were processed using the freely available program Fiji (http://fiji.sc/Fiji; Abramoff et al., 2004). Optical sections were selected to create a projection image (z-stack) showing the cortical microtubule pattern in the cells of interest. In addition, a mid-plane section was selected to identify cell boundaries. The z-stack images were further analyzed using the MFA software. Root and cell parameters, such as the degree of curvature, cell length and the distance from the root tip, were measured using Fiji. The degree of curvature was determined as the deviation of the root tip from the straight, non-responding part of the root. The same method was used to measure the curvature of individual cells. In total, 561 cells were analyzed from 47 roots.
Statistical tests were performed using the R package version 2.13.2 (http://www.R-project.org/; R Development Core Team, 2011). The duration of gravitropic stimulation was tested for its effect on root bending using simple linear regression. Cell analyses regarding the degree of curvature and cell length were performed using general mixed models. The distance from the extreme root tip and the time of induced gravitropism (treatment) were included as continuous and categorical factors, respectively. Individual roots were considered as a random factor, nested within treatment. Moreover, the distance was dependent upon the factor ‘root’. The data for cell length were logarithmically transformed to obtain a linear model. In addition, cell location was taken into account as a continuous parameter for this analysis. Therefore, each location was given a certain value, corresponding to 0.5 and 1.5 for the lower-located and upper-located cells in the curved zone, respectively. The control cells had an intermediate value of 1 (Van Dongen et al., 1999). The categorical response variable, microtubule organization, had four levels, ordered in a sequence of random (three main orientations), ‘others’ (two main orientations), oblique and transverse. The frequency distributions were tested using ordinal logistic regression, with treatment, distance and location as continuous parameters. The three locations were ranked in the following order: lower-located (0.5), upper-located (1) and control (1.5) cells (Van Dongen et al., 1999). The graphs presented were also designed using R version 2.13.2.
The authors would like to thank O. Hamant (INRA and Université de Lyon, CNRS, ENS, Laboratoire de Reproduction et Développement des Plantes) for providing the images of the shoot apical meristem, and the Inter-university Attraction Poles Programme/Belgian State/Belgian Science Policy (IUAP VI/33), the Fonds voor Wetenschappelijk Onderzoek (FWO-Flanders Research Foundation) and the University of Antwerp for funding. Moreover, the UK Biotechnology and Biological Sciences Research Council and the UK Engineering and Physical Sciences Research Council are acknowledged for funding to the Centre for Plant Integrative Biology.