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The authors have declared that no competing interests exist.

Conceived and designed the experiments: MH AT. Performed the experiments: BJ AS. Analyzed the data: HF AT. Contributed reagents/materials/analysis tools: HF. Wrote the paper: HF BJ AS MH AT. Initiated the research: MH. Did the bioinformatics analysis: HF. Developed TrichEratops: HF. Designed the project and supervised the work: AS MH AT. All authors read and approved the final version of the manuscript.

Trichomes are leaf hairs that are formed by single cells on the leaf surface. They are known to be involved in pathogen resistance. Their patterning is considered to emerge from a field of initially equivalent cells through the action of a gene regulatory network involving trichome fate promoting and inhibiting factors. For a quantitative analysis of single and double mutants or the phenotypic variation of patterns in different ecotypes, it is imperative to statistically evaluate the pattern reliably on a large number of leaves. Here we present a method that enables the analysis of trichome patterns at early developmental leaf stages and the automatic analysis of various spatial parameters. We focus on the most challenging young leaf stages that require the analysis in three dimensions, as the leaves are typically not flat. Our software TrichEratops reconstructs 3D surface models from 2D stacks of conventional light-microscope pictures. It allows the GUI-based annotation of different stages of trichome development, which can be analyzed with respect to their spatial distribution to capture trichome patterning events. We show that 3D modeling removes biases of simpler 2D models and that novel trichome patterning features increase the sensitivity for inter-accession comparisons.

The patterning of trichomes (leaf hair) on the surface of a leaf is a paradigm for studying gene regulation in developmental processes. The statistical analysis of trichome patterning requires automated methods for the location of trichomes on a curved leaf surface. This is particularly challenging for young, strongly bent leaves. We have developed the TrichEratops software that reconstructs 3D leaf surfaces from 2D stacks of conventional light-microscopy pictures. TrichEratops also calculates statistical patterning features, thereby greatly facilitating the whole data acquisition process. We show, using two

Leaf trichomes in

The genetic and molecular analysis of trichome development has revealed models that explain trichome development by a gene regulatory network of trichome promoting and inhibiting factors. Two probably in parallel acting mechanisms have been recognized

Several approaches have been published that enable a high-resolution 3D reconstruction of mature as well as of young leaves.

The method described here addresses an essential problem. Young

As leaves, in particular young leaves, are frequently not flat but bent the distances between trichomes cannot appropriately be measured directly by their 2D Euclidean distance on the sharpened image. The 2D Euclidean distance systematically underestimates the real, i.e. geodesic distance, of two points on a curved surface. Depending on the bending of the leaf, the difference between Euclidean and geodesic distances can be large. As leaf bending in turn varies considerably among the leaves of one

A: The 3rd true leaf is dissected from a one week old seedling. B: A stack of pictures is generated by varying the focus using a conventional light microscope. C: A height map of the leaf is created by taking for every (x,y) position the z position at which the vicinity of this point appears sharpest. Height values are color-coded, ranging from low (blue, green) to high (yellow, red). D: A sharp 2D image of the leaf is generated by taking for each (x,y) position the corresponding pixel intensity in the z-stack image specified by the height map. The position of trichomes and their stages are determined in this 2D view. E: A 3D surface model of the leaf is calculated from the picture stack by fitting an elastic map to the height map, and the trichomes are mapped onto this surface. Scale bars 100 µm.

We used the Sobel transform to assign to each (x,y) position a z-stack position for which its vicinity in the corresponding 2D image appears sharpest. The z-axis for each stack was properly scaled by acquiring a reference of known thickness positioned next to the leaves (

To identify moderate changes in trichome patterning, the different trichome developmental stages within young leaves have to be acquired (average leaf length of 320 µm for Col-0 wild type). Towards this end we define four developmental classes of trichomes. For the analysis of trichome patterning, we do not discriminate between all previously defined developmental stages

TrichEratops offers 4 different views of the leaf surface. The 2D sharpened image view (A) is used to mark trichome positions and their classes (red, purple, blue and green dots). Additionally, the leaf-centric xy-coordinate system can be set (blue axes), and the calibration marks for z-stacking can be specified (white and dark blue dot on the top half of the image). The 3D surface view (B) serves as a visual control of the reconstruction quality. The shortest paths between trichomes can be included optionally. The top control panel offers functionality for loading, saving, processing, and analysis of the image stacks.

In order to account for variation in leaf size and to obtain a unified leaf representation, we defined an orthogonal coordinate system on each leaf. The origin of the coordinate system is placed in the middle of the petiole at the leaf lamina's base. The y-axis and its scaling are determined manually by a unit vector pointing from the origin towards the top of the leaf, such that it separates the leaf into two equal halves. This implicitly defines the direction and scaling of the baseline x-axis (

A: The meta leaf is generated by transforming all trichomes of all leaves of a given genotype to a common coordinate system (yellow axes) as illustrated by two sample leaves. The origin of each leaf is defined manually, and the unit vector in longitudinal axis direction is defined by the center of mass of the leaf. The basal axis is perpendicular to the longitudinal axis. The meta leaf shows the distribution of different trichome classes across the leaf, where red (respectively magenta, blue, green) dots indicate initiation (respectively two branch-, three branch-, and mature trichomes). B: The trichome localization along the longitudinal leaf axis is visualized. The vertical axis shows the proportion of different trichome classes at a given distance from the origin. C: The distribution of trichome classes on the meta leaf surface is shown in a 3D histogram. Trichome numbers at each position are shown as bars. The colors for the trichome classes are chosen as in A. Scale bars 100 µm.

To evaluate the accuracy obtained by measuring the geodesic instead of the euclidean distances we compared the Col-0 wild type line with

By combining the 2D trichome position information with the elastic map representation of a leaf, we can assign to each trichome a point on the 3D leaf surface (

A: 3D reconstruction of an

Similarly, the leaf area calculations derived from 2D and 3D reconstructions can differ substantially (

When comparing wild type and

To facilitate the comparison of the trichome pattern between different lines we developed several methods to quantify different aspects of the spatial distribution of trichome classes and studied the differences between wild type and

In a first step, we compared the relative proportions of trichome classes along the basal-distal axis. We found similar proportions in wild type and the

Left panel: Example of a Col-0 leaf, middle panel: Example of a

The meta leaf minimizes the influence of the leaf shape and areas by normalizing it to a unit shape. This is particularly important, because the wild type has a bigger leaf index (i.e., minor axis (leaf width) divided by major axis (leaf length)) than the

The previous finding that trichome density (defined as the number of trichomes per leaf area) in

There were no obvious differences in the regional distribution of trichome densities between wild type and

Although the final trichome pattern is generated by two events, the initiation in young leaves and the separation by epidermal cell divisions and expansion, most of the genetic analysis is based on the pattern seen in mature leaves. The analysis of trichome initiation is complicated by the fact that young leaves are typically not flat. One possibility is the reconstruction of propidium iodide stained Confocal Scanning Laser Microscopy images

How relevant is it to calculate the geodesic rather than the Euclidean distances? When calculating the differences for individual leaves we found a 10%–20% difference between the two types of measurements (

For an evaluation of our analysis tools we chose the comparison of wild type with the trichome density mutant

In a first step, the whole leaf area and the leaf index are determined to detect gross variations in leaf shape that in turn may influence the trichome patterns. The second step is the creation of the meta leaf and the analysis of the trichome distribution along the longitudinal axis on a normalized leaf surface area. The distinction between different trichome developmental stages enables the detailed analysis of different aspects: 1) the relative size of the trichome initiation zone, the differentiation zone and the mature trichome zone. 2) the relative overlap of the three zones. As shown in

The third step is the analysis of global and local trichome density. The global trichome density is a coarse measure, as it simply relates the number of trichomes to the leaf area. The Voronoi area is a local measure of trichome density; it measures the area around trichomes that is free of other trichomes. All peripheral trichomes are not considered and therefore border effects are excluded. Therefore the Voronoi area analysis is likely to be more suitable to capture subtle changes in the trichome initiation caused by interactions between the trichomes. The difference between the two methods is demonstrated in

In summary, we provide a new semi-automated tool enabling the fast acquisition of image stacks, the 3D construction and analysis of relevant aspects of trichome patterning. This tool will enable a more detailed quantitative analysis of

For all experiments, the ^{−2} s^{−1}/8 h darkness; 21°C).

The third true leaf was dissected from one week old seedlings. Dissected leaves were transferred to a slide previously covered by 1% agar to avoid desiccation. To allow comparison between leaves we selected leaves with a maximum of 6 matures trichomes. Manual stacks of the leaves were acquired with a Leica DM5000B microscope equipped with a LEICA DFC 360 FX camera using a 10× objective. While the experimenter manually focuses along the z-axis by turning the focus of the light microscope, the Leica LAS AF software automatically generates a series of pictures ( = z-stack) by acquiring one picture per 104 ms . Start and end point were the last and first unsharp layers. 50–70 pictures were taken per leaf. To scale the Z axis the “dissector Z-axis mechanical method” was used with a piece of a cover slide (#1, art Nr H878, ROTH, Karlsruhe) positioned next to the leaf as described before (Xavier-Vidal, 2010). The thickness of the cover slide was determined using a scaling slide, PYER SGI LIMITED (1mm/0,01 mm DIV, Kent, UK), to set the exact ratio pixel/mm. For this the piece of a cover slide was placed vertically in agar to allow a precise measurement of its thickness (see

In order to get a 3D map of Z positions from the stack, the sharpest value for every pixel needed to be found. For this purpose we used the fact that clear edges indicate sharp pixel. Edges in the Images were detected by the Sobel transform

This approach was inspired by the Stack Focuser plugin for ImageJ by Michael Umorin. The z positions can be used to generate a sharpened 2D image from the image stack, by choosing for each (x,y) position the pixel intensity of the image at the corresponding z stack position (see

Elastic maps are a tool to approximate non-linear principal manifolds

Let S bet the coordinates

This grid defines a connected unordered graph

Every data point

The overall energy of the elastic map

The overall energy of the elastic map

The leaf was identified by Otsu thresholding

Some leaves were difficult to segment as they were in spatial proximity to the cover slides. For these leaves we implemented a manual segmentation in our software that enables to draw a line around the leaf and to take the area in the convex hull of this line as leaf area.

All analysis steps were implemented in a software called TrichEratops (

From the z-stack, 3D surface and area are calculated and geodesic distance can be derived for the trichomes.

The software can handle 3D images as well as 2D images (for older leaves). All the analysis steps were implemented in Matlab. The TrichEratops software is available under the GPL3.0 license at

2D Euclidean distance is the simple vector length between two points. For the 3D Euclidean distance, the z coordinate was determined by the elastic map. For the geodesic distance the shortest path on the 3D mesh was calculated by the Fast Marching algorithm

Relative abundance (in %) of trichome classes (red: initiation, magenta: 2-branch trichomes, blue: 3-branch trichomes, green: mature trichomes) for wildtype (left) and the

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Microscopic pictures used to scale the z-axis. A: A scaling slide PYER SGI LIMITED (1 mm/0.01 mm DIV, Kent, UK) used to scale the 2D distance of the microscope. From that the ratio pixel per µm was determined. Each graduation equals 10 µm. B: A piece of a cover slide used for the z-axis scaling was placed vertically into agar. The line shows how the thickness of the cover slide was precisely measured. Subsequently, this piece of a cover slide was placed flat next to an acquired leaf and served as a reference for the z-axis.

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A: Relative increase (in %) of geodesic distances between two trichomes over the corresponding 3D Euclidean distances, summarized as separate boxplots for each leaf. Wildtype leafs are marked in green, leafs of

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Comparison of 2D leaf area and 3D leaf area. Each line corresponds to one leaf (green: wild type, blue:

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Meta leaf construction and analysis of spatial distribution of trichome classes for the

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Comparison of leaf area, leaf length and leaf index for Col-0 and

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Comparison between TrichEratops and other existing methods. Despite of all other methods TrichEratops combines light microscopy (without long sample preparation) and 3D reconstruction of the leaf surface. Furthermore it calculates patterning features similar to existing methods (voronoi area, metaleaf, coordinates).

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Trichome counts for both genotypes and counts of finite Voronoi cells. Finite Voronoi cells are Voronoi regions that are bounded and whose edge points lie on the leaf surface.

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Wilcoxon test for difference in trichome density between Col-0 and

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Wilcoxon test for difference in 2D Voronoi Area between Col-0 and

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Wilcoxon test for difference in 3D Voronoi Area between Col-0 and

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Wilcoxon test for difference in geodesic distance to nearest neighbor between Col-0 and

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Supplementary References.

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