Visualising Differential Growth of Arabidopsis Epidermal Pavement Cells Using Thin Plate Spline Analysis

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The Plant Cell
Sep 2015



Epidermal pavement cells in Arabidopsis leaves and cotyledons develop from relatively simple shapes to form complex cells that have multiple undulations of varying sizes. Analyzing the growth of individual parts of the cell wall boundaries over time is essential to understanding how pavement cells develop their complex shapes. Thin plate spline analysis is a method for visualizing the change of size and shape of objects through warping or deformation of a regular mesh and can be applied to understand cell wall growth. This protocol describes the application of thin plate spline analysis to visualize the development of individual pavement cells over time.


Understanding the spatial pattern of growth of a cell provides insight into how plant cells form different shapes. Epidermal pavement cells of Arabidopsis thaliana cotyledons and leaves are a good model system for investigating how complex cells grow as their cell wall boundaries develop multiple undulations of different size from boundaries that were initially simple arcs (Armour et al., 2015; Fu et al., 2005). Growth of plant cells has been measured by fixing externally applied markers to cells such as algal Nitella internodes (Green et al., 1970), root cells (Shaw et al., 2000), and trichomes (Schwab et al., 2003). However measurement of cell growth from externally applied landmarks is sometimes not feasible such as when the strong fluorescence of externally applied fluorescent markers would obscure fluorescently labeled cytoskeletal elements within cells (Armour et al., 2015). Thin plate spline analysis which visualizes the changing positions of a defined number of homologous landmarks over time or between different objects has previously been used to analyze changes in the three dimensional size and shape of objects such as hominid skulls (Rosas and Bastir, 2002; Gunz et al., 2009), or the two dimensional shapes of insect wings (Börstler et al., 2014) and leaves (Polder et al., 2007). This protocol describes how to use thin plate spline analysis to visualize size and shape changes of individual cells. This technique is relatively easy to utilize on a range of cell images as it uses the input of the outline of a cell at sequential times to approximate the relative growth rate and growth direction of different areas of the cell wall.

Materials and Reagents

  1. Petri dish (35 x 10 mm) (SARSTEDT, catalog number: 82.1135.500 )
  2. 3M Micropore surgical tape 1.25 cm (3M, catalog number: 1530-0 )
  3. Wildtype Arabidopsis thaliana (Col-0) seeds
  4. Sodium hypochlorite solution (White King Premium Bleach, Woolworths, catalog number: 10006062A )
  5. Sterile distilled water
  6. Murashige and Skoog salts (Sigma-Aldrich, catalog number: M5519 )
  7. Sucrose (Sigma-Aldrich, catalog number: S8501 )
  8. OxoidTM bacteriological agar (Thermo Fisher Scientific, Thermo ScientificTM, catalog number: LP0011 )
  9. 1 µM solution of 3 kDa fluorescein conjugated dextran (Thermo Fisher Scientific, Molecular ProbesTM, catalog number: D3305 )


  1. Sterile laminar flow hood
  2. Zeiss Axiophot photomicroscope (D-7082) with filter set (BP 450-490 FT 510 BP 515-565, Carl Zeiss, catalog number: 487910 )
  3. A 20x LD Achroplan lens with a N.A. of 0.4 (Carl Zeiss, catalog number: 421350-9970-000 [current version]; 440845-0000-000 [old version])
  4. an Olympus microscope digital camera (OLYMPUS, model: DP71 )
  5. Plant growth chamber, set at 22 °C, on a 16-h-day:8-h-night cycle
  6. P10, 0.5-10 μl pipette (Eppendorf, catalog number: 4920000024 )


  1. ImageJ (available at
    1. ImageJ macros and lookup tables (
      1. 0WillRainbow.lut
      2. Add-Points-From-TPSlist-To-ROImanager_.ijm
      3. BranchInfo-to-ROI-lines-overlay_.ijm
      4. Formatted-Points-List-To-ROImanager_.ijm
      5. TPS-rel-expansion-prepare_.ijm
      6. TPS-rel-expansion-format_.ijm
    2. ImageJ plugins
      1. Stack Focuser (available at
  2. tpsDig2 (available at
  3. PAST (available at
  4. Plaintext editor (e.g., Notepad++ on Windows, TextEdit on Mac OSX or gedit on Linux)


  1. Growing and imaging Arabidopsis seedlings
    1. Germinate wild-type Arabidopsis thaliana Col-0 seeds in vitro on 35 mm diameter Petri dishes
      1. Sterilize seeds in 1% sodium hypochlorite for 10 min and then rinse with sterile distilled water three times.
      2. Three seeds are then placed in a single line onto Petri dishes prepared using 1x Murashige and Skoog salts, 1% sucrose and 0.8% bacteriological agar, sealed with surgical tape, then kept at 4 °C for 24 h to stratify the seeds.
      3. Transfer Petri dishes into a plant growth room at 22 °C, on a 16-h-day:8-h-night cycle. Petri dishes should sit flat so that the roots grow downwards into the agar, rather than be positioned vertically. Monitor seeds for signs of germination.
    2. At 1 day after germination, check that a cotyledon from one of the three seeds has unfurled and, in a sterile laminar flow hood, gently place about 0.5 μl of a 1 µM 3 kDa fluorescein conjugated dextran onto the adaxial cotyledon surface using a pipette. Wait 5 min for the dextran to dry.
    3. Image epidermal pavement cells on a Zeiss Axiophot photomicroscope and collect a series of images at different focal planes to convert into 2D cell projections.
      1. Place Petri dish directly on the stage of a Zeiss Axiophot photomicroscope with the lid removed.
      2. Capture images of the epidermal pavement cells using a series of incremental focal planes with a blue fluorescent light filter and a 20x LD Achroplan objective lens. It is recommended to capture between 5-15 slices per cell at an interval spacing of 0.5-1 µm.
      3. After imaging, rinse cotyledons using a pipette and sterile distilled water then return seedlings to the plant growth room.
      4. Open the saved image series in ImageJ and create a 2D projection of the epidermal pavement cells using the Stack Focuser plugin. Save 2D projection as a TIFF.
    4. Repeat steps A2-A3 at 24 and 48 h after initial imaging.

  2. Extracting coordinates from cell outlines
    1. Using a program such as ImageJ or Adobe Photoshop, create an outline of the cell at one time point by tracing the anticlinal walls of the cell using a black pencil tool. Make sure to include a small region of walls of neighboring cells (branches). Copy this black outline onto on a new TIFF image with a white background (Figure 1A).
    2. Open a cell outline image in ImageJ ensuring it appears as a white outline on a black background and the scale is set on the image so it is calibrated. Skeletonize the outline using the Skeletonize command to produce a one pixel wide outline of the cell (Figure 1B).
    3. Perform a skeleton analysis using the command ‘Analyze Skeleton 2D/3D’ with options ‘Prune ends’ and ‘Show detailed info’ selected to calculate the individual anticlinal wall lengths between the wall junctions (Figures1B-1D). Save the ‘Branch Information’ table, invert the image that has the branches pruned to get a black outline on white background (Figure 1C) and save this image as a TIFF.

      Figure 1. A cell outline of a single Arabidopsis epidermal pavement cell. A. A tracing of the anticlinal walls of a cell. B. The skeletonized outline of the cell has branches extending away from the cell, representing the sites of walls in neighboring cells (black arrowhead) and junctions where anticlinal walls of the cell met (white arrowheads). C. After the cell has been analyzed by skeleton analysis, the branches are removed (pruned, black arrowhead) and the length along the anticlinal wall is calculated as the branch length between wall junctions (white arrowheads). D. An individual wall from the cell between the two white arrowheads in (C).

    4. Using the skeleton outline of the cell run the macro ‘BranchInfo-to-ROI-lines-overlay_.ijm’. It will prompt for the height of the image in pixels and µm and ask for the ‘Branch information’ table to be opened. This macro will put labelled overlay lines on the cell outline so that each wall can be matched to its row number in the Branch information table.
    5. Repeat steps B1-B4 for every image of the cell captured at sequential time points.
    6. In the same folder as the skeletonized outline images, create a plaintext file with the file extension ‘.tps’ that contains the following two lines for each image, where X is the specific time point that the cell was originally imaged.
      LM = 0
      IMAGE = imageNameTimeX.tif
    7. Open the ‘.tps’ file in the tpsDig2 program, outline the cell using the ‘outline object tool’ and then right click the image for more options and select ‘Save as XY coords.’. Repeat for each time point then save the resulting data of the cell outline coordinates.
    8. Open this ‘.tps’ data in a plain-text editor and save the list of X and Y coordinates as a separate file for each time point using the ‘.txt’ file format.
    9. Open a cell outline image in ImageJ and then run the macro ‘Add-Points-From-TPSlist-To-ROIManager_.ijm’. This will prompt to open up the X and Y coordinates ‘.txt’ file made in step B8. A results table of the X and Y coordinates in a format suitable for ImageJ and calibrated to the image dimensions is then created. Save the results table as a ‘.txt’ file and repeat for each time point.
    10. Modify the ‘.txt’ files for each time point in a text editor so that the first X and Y coordinates refer to the same corresponding cell wall junction across all time points. Refer to the ROI number of the points generated on the image overlay in step B9.
    11. Open the cell outline image in ImageJ and then run the macro ‘Formatted-Points-List-To-ROImanager_.ijm’. This will prompt to open up the new paired X and Y coordinates ‘.txt’ file made in step B10 and converts the X and Y coordinates into a format suitable for ImageJ, calibrated to the image dimensions. Save the list of coordinates in the ROI manager as a ‘.zip’ file.
    12. Repeat steps B9-B11 for each time point.

  3. Generating thin plate splines
    1. Using the cell outline image and the ROI ‘.zip’ file in ImageJ record the ROI number that corresponds to each wall junction at each time point.
    2. To conduct a thin plate spline analysis, an equal number of homologous landmarks are needed at each time point. The number of homologous landmarks for an anticlinal wall segment over all time points was calculated by dividing the wall length at the initial time by 0.5 µm as follows:
      d = w/0.5 µm
      d is the desired number of loci (homologous landmarks) in an anticlinal wall segment rounded to the nearest integer,
      w is the length of each wall segment.
    3. The position of these homologous landmarks is calculated using the slope-intercept formula: f(a) = m x a + (p - [m x d])
      m = (p - 1)/(d - 1)
      f(a) is the selected loci from the list of xy coordinate pairs that describe the cell outline on each day,
      p is the number of xy coordinate pairs in a section of wall,
      m is the gradient of the slope.
    4. An editable example Excel file can be used to organize the data and get the final list of output coordinates as described in steps C2 and C3 (see Data analysis). It consists of a spreadsheet with 6 tabs; an input tab called intervalRaw, a tab with the output x and y coordinates for each time point called intervalSelection and four data tabs labelled t1, t2, t3 and t4 that contain a complete list of x and y coordinate pairs at each time point with the same layout as the file generated in step B10. The input tab can be modified to suit a different number of walls by copying the formula for additional rows. Additional time periods can be added with an example of the layout provided for time point t4 which is left blank for this purpose. For the output tab the cell references of the gradient (m) and constant (b) needs to match with the selected wall and time period. This can be achieved in the formulas of columns B through E by increasing the value of both cell references by 1 the row after the last loci of each wall (row highlighted in red). The formulas in columns B through E in the output tab may need to be modified depending on the number of loci in each wall.
    5. The selected coordinates should be arranged into labelled columns as follows and saved in a text editor as a ‘.txt’ file for each time period:
      no, x , yIJ, yTPS
      1 , 823 , 286, 853
      2 , 824, 287 , 852
      3 … … …
    6. Check all coordinates have been selected correctly for equal spacing by opening a cell outline image in ImageJ, run the macro ‘Formatted-Points-From-TPSlist-To-ROIManager_.ijm’ and open the ‘.txt’ file created for the same time point. This will show all the points in the ‘.txt’ file in the ROI manager as an overlay on an image.

      Figure 2. A .tps file open in Notepad++ text editor program showing an example data set with four homologous landmarks at three time periods. This example data set shows how .tps files are arranged as a list beginning with the number of homologous landmarks (LM), followed by the x and y values of those coordinates, the image name (IMAGE) and the number of the time period (ID). Data for additional time periods are entered in this same sequence directly below.

    7. Combine the data for each time point into a new ‘.tps’ file using a text editor with the following lines for each time period (Figure 2):
      LM = number of homologous landmarks
      x1 = x coordinate 1  y1 = y coordinate 1 (in TPS format)
      x2 = x coordinate 2  y2 = y coordinate 2 (in TPS format)
      …   …
      IMAGE = imageNameTimeX.tif
      ID = number of the time period
    8. With this ‘.tps’ file for all time points make new tps files for time n + 1 and n + 2, n + 2 and n + 3, etc.
    9. Open a ‘.tps’ file in PAST, select all data cells and then conduct a Procrustes transformation with options to use 2D, rotate to major axis and keep size (only translate and rotate). Perform a ‘Thin plate splines and warps 2D’ and save bitmap (BMP) images of the thin plate splines for time n versus n + 1, time n + 1 versus n + 2, etc. These should be saved as two different formats; output the images in (1) grayscale format by selecting expansion factors and deselecting color map and (2) plain thin plate spline format with expansion factors deselected.

  4. Generating thin plate spline images that show the relative expansion rate
    1. Using the fold-growth scale on the grayscale thin plate spline images generated in step C9 record the maximum and minimum fold expansion values for each time interval that are presented as an overlay on the thin plate spline images (Figure 3A).
    2. Determine the maximum relative expansion rate using the formula ln(maximum fold expansion)/number of hours between time n + 1 and n. This should be the maximum relative expansion across all days. As this will set the highest value of expansion represented on the relative expansion scale it can be adjusted to be the nearest round number above that necessary for the dataset.
    3. Open the grayscale thin plate spline images at each time interval in ImageJ. Using the point tool place a point in the center of every grid square and add each ROI to the ROI Manager. Save this list of ROI points for each time point as a separate ‘.zip’ file.
    4. Run the macro ‘TPS-rel-expansion-prepare_.ijm’. This macro will ask for a grayscale thin plate spline image made by PAST and the corresponding ROI ‘.zip’ file made in the previous step. This will automatically extract the grayscale value and XY coordinate for each point and then save this information as ‘xyGrayscaleValues-NAME.txt’. Repeat for each time point.
    5. Run the macro ‘TPS-rel-expansion-format_.ijm’. It will prompt for the ‘xyGrayscaleValues-NAME.txt’ text file, the blank thin plate spline image for coloring and the ROI ‘.zip’ file made in step D3. In addition, the following values need to be put in to the dialog box: (1) The maximum expansion (fold growth) across all time periods, (2) minimum expansion (fold growth) across all time periods, and (3) maximum log ratio expansion (this will be what the final scale will be in so if you have multiple cells make sure this value is large enough to cover all use cases, see step D2). This will generate a color PNG image of the relative expansion rate for the thin plate spline appended with the label ‘-output’ (Figure 3B). Repeat for each time point.

      Figure 3. Thin plate splines of the growth of a single Arabidopsis epidermal pavement cell from time n to time n + 1. A. The thin plate spline made by PAST is a grayscale fold-growth measurement. B. After processing to extract the grayscale values and recoloring the grid squares, the relative expansion rates of the thin plate spline of a cell over time can be determined.

Data analysis

Thin plate spline analysis is used to visualize changes in the size and shape of objects. Comparing the thin plate spline of a cell from day to day reveals areas where the relative growth rate is higher as indicated by warmer colors and directions of growth are indicated by changes in the shape of the mesh. This protocol uses the outline of a cell over time to make an approximation of the growth of different regions of the cell wall. This allows different regions of growth rates to be identified rather than generating absolute values of expansion suitable for further statistical analysis.
A spreadsheet with representative data that shows how to sort the data outlined in steps C2-C4 is given in the file Intervals-calculation.xls (


This method is designed for visualizing the changes in growth of single cells but it can be adapted to different spatial scales. Growing conditions, such as the concentration or variety of nutrients used, or light intensities might vary between experiments. Altering the percentage of bacteriological agar used could affect the root growth of the seedlings. The agar needs to be soft enough for the roots to penetrate through it but firm enough that the roots are firmly embedded and can provide a firm anchor for the growth of seedlings. Macro running times will depend on the size of the images and data. For a single cell such as in Figure 3B the running time of the macros is typically 2-15 sec on an Intel Core i5 processor with the slowest macro being TPS-rel-expansion_format.ijm at 15 sec. Additional text files of the raw values of the expansion rate and the RGB values of the each individual grid of the thin plate spline are automatically saved in the same folder as the output images of step D5 (ExpansionValues-NAME.txt and xyColourValuesNAME.txt).


This protocol is adapted from Armour et al., 2015. This research was supported by an Australian Postgraduate Award to WJA.


  1. Armour, W. J., Barton, D. A., Law, A. M. and Overall, R. L. (2015). Differential growth in periclinal and anticlinal walls during lobe formation in Arabidopsis cotyledon pavement cells. Plant Cell 27(9): 2484-2500.
  2. Börstler, J., Lühken, R., Rudolf, M., Steinke, S., Melaun, C., Becker, S., Garms, R. and Krüger, A. (2014). The use of morphometric wing characters to discriminate female Culex pipiens and Culex torrentium. J Vector Ecol 39(1): 204-212.
  3. Fu, Y., Gu, Y., Zheng, Z., Wasteneys, G. and Yang, Z. (2005). Arabidopsis interdigitating cell growth requires two antagonistic pathways with opposing action on cell morphogenesis. Cell 120(5): 687-700.
  4. Green, P. B., Erickson, R. O. and Richmond, P. A. (1970). On the physical basis of cell morphogenesis. Ann NY Acad Sci 175(1): 712-731.
  5. Gunz, P., Mitteroecker, P., Neubauer, S., Weber, G. W. and Bookstein, F. L. (2009). Principles for the virtual reconstruction of hominin crania. J Hum Evol 57(1): 48-62.
  6. Polder, G., van der Heijden, G. W. A. M., Jalink, H. and Snel, J. F. H. (2007). Correcting and matching time sequence images of plant leaves using penalized likelihood warping and robust point matching. Comput electron agr 55(1): 1-15.
  7. Rosas, A. and Bastir, M. (2002). Thin-plate spline analysis of allometry and sexual dimorphism in the human craniofacial complex. Am J Phys Anthropol 117(3): 236-245.
  8. Schwab, B., Mathur, J., Saedler, R., Schwarz, H., Frey, B., Scheidegger, C. and Hulskamp, M. (2003). Regulation of cell expansion by the DISTORTED genes in Arabidopsis thaliana: actin controls the spatial organization of microtubules. Mol Genet Genomics 269(3): 350-360.
  9. Shaw, S. L., Dumais, J. and Long, S. R. (2000). Cell surface expansion in polarly growing root hairs of Medicago truncatula. Plant Physiol 124(3): 959-970.



[背景] 了解细胞生长的空间模式提供了洞察植物细胞如何形成不同的形状。拟南芥子叶和叶的表皮铺路细胞是用于研究复杂细胞如何生长的良好模型系统,因为它们的细胞壁边界从最初为简单弧的边界开始形成不同大小的多个起伏(Armor et al。,2015; Fu et al。,2005)。通过将外部施加的标记物固定到细胞例如藻类氮细胞节间(Green等人,1970),根细胞(Shaw等人, ,2000)和毛状体(Schwab等人,2003)。然而,从外部施加的界标测量细胞生长有时是不可行的,例如当外部施加的荧光标记物的强荧光会遮蔽细胞内荧光标记的细胞骨架元件时(Armor等人,2015)。显示定义数量的同源界标随时间或在不同物体之间的变化位置的薄板样条分析先前已用于分析诸如人类头骨的物体的三维大小和形状的变化(Rosas和Bastir,2002; Gunz ,2014)和叶子(Polder et al ,2009),或昆虫翅膀的二维形状(Börstler等人, 。,2007)。该协议描述如何使用薄板样条分析来显示单个细胞的大小和形状变化。该技术相对容易在一系列细胞图像上利用,因为其在连续时间使用细胞轮廓的输入来近似细胞壁的不同区域的相对生长速率和生长方向。


  1. 培养皿(35×10mm)(SARSTEDT,目录号:82.1135.500)
  2. 3M微孔手术带1.25cm(3M,目录号:1530-0)
  3. 野生型拟南芥(Col-0)种子
  4. 次氯酸钠溶液(White King Premium Bleach,Woolworths,目录号:10006062A)
  5. 无菌蒸馏水
  6. Murashige和Skoog盐(Sigma-Aldrich,目录号:M5519)
  7. 蔗糖(Sigma-Aldrich,目录号:S8501)
  8. Oxoid TM细菌琼脂(Thermo Fisher Scientific,Thermo Scientific TM ,目录号:LP0011)
  9. 1μM的3kDa荧光素缀合的葡聚糖溶液(Thermo Fisher Scientific,Molecular Probes TM ,目录号:D3305)


  1. 无菌层流罩
  2. 具有滤光器组(BP 450-490 FT 510 BP 515-565,Carl Zeiss,目录号:487910)的Zeiss Axiophot光学显微镜(D-7082)
  3. 具有N.A.为0.4(Carl Zeiss,目录号:421350-9970-000 [当前版本]; 440845-0000-000 [旧版本])的20x LD Achroplan透镜
  4. Olympus显微镜数字照相机(OLYMPUS,型号:DP71)
  5. 植物生长室,设置在22°C,在16小时:8小时周期
  6. P10,0.5-10μl移液管(Eppendorf,目录号:4920000024)


  1. ImageJ(位于
    1. ImageJ宏和查找表(
      1. 0WillRainbow.lut
      2. Add-Points-From-TPSlist-To-ROImanager_.ijm
      3. BranchInfo-to-ROI-lines-overlay_.ijm
      4. Formatted-Points-List-To-ROImanager_.ijm
      5. TPS-rel-expansion-prepare_.ijm
      6. TPS-rel-expansion-format_.ijm
    2. ImageJ插件
      1. Stack Focuser(可在 http://imagej.nih .gov/ij/plugins/stack-focuser.html
  2. tpsDig2(可在
  3. PAST(可在
  4. 纯文本编辑器(例如,Windows上的记事本++,Mac OSX上的TextEdit或Linux上的gedit)


  1. 生长和成像拟南芥幼苗
    1. 在35mm直径的培养皿上在体外发芽野生型拟南芥 Col-0种子
      1. 在1%次氯酸钠中消毒种子10分钟,然后用无菌蒸馏水冲洗三次。
      2. 然后将三个种子放在一条线上,放置在使用1×Murashige和Skoog盐,1%蔗糖和0.8%细菌琼脂制备的培养皿上,用手术胶带密封,然后在4℃保持24小时以分层种子。 />
      3. 将培养皿转移到22℃的植物生长室中,16小时 - 日:8小时 - 周期。培养皿应该平放,使根部向下生长到琼脂中,而不是垂直放置。监测种子的发芽迹象
    2. 在发芽后1天,检查来自三个种子之一的子叶已经展开,并且在无菌层流罩中,使用移液管将约0.5μl的1μM3kDa荧光素缀合的葡聚糖轻轻地放置在近轴子叶表面上。等待5分钟使葡聚糖干燥。
    3. 图像表皮路面细胞在蔡司Axiophot显微镜上,并收集一系列图像在不同的焦平面转换成2D细胞投影。
      1. 将培养皿直接放在蔡司Axiophot显微镜的镜台上,取下盖子
      2. 使用具有蓝色荧光滤光片和20x LD Achroplan物镜的一系列增量焦平面捕获表皮铺路细胞的图像。建议每个细胞捕获5-15个切片,间隔为0.5-1μm。
      3. 成像后,使用移液管和无菌蒸馏水冲洗子叶然后返回幼苗到植物生长室。
      4. 在ImageJ中打开保存的图像系列,并使用Stack Focuser插件创建表皮路面细胞的2D投影。将2D投影保存为TIFF。
    4. 在初始成像后24和48小时重复步骤A2-A3
  2. 从单元格大纲中提取坐标
    1. 使用诸如ImageJ或Adobe Photoshop之类的程序,通过使用黑色铅笔工具跟踪细胞的背侧壁来在一个时间点创建细胞的轮廓。确保包括邻近单元格(分支)的一小块墙壁区域。将此黑色轮廓复制到具有白色背景的新TIFF图像上(图1A)。
    2. 在ImageJ中打开单元格轮廓图像,确保它在黑色背景上显示为白色轮廓,刻度设置在图像上,以便进行校准。使用Skeletonize命令对轮廓进行骨架化,以产生单元格的一个像素宽的轮廓(图1B)。
    3. 使用命令"分析骨骼2D/3D"执行骨架分析,选择"修剪结束"和"显示详细信息"来计算壁结之间的单独的背斜壁长度(图1B-1D)。保存"分支信息"表,将已剪枝的图像反转以在白色背景上获得黑色轮廓(图1C),并将此图像另存为TIFF。

      图1.单个 Arabid 表皮路面细胞的细胞轮廓。 A.细胞的背斜壁的跟踪。 B.细胞的镂空轮廓具有从细胞延伸的分支,代表相邻细胞(黑色箭头)中的壁的位点和细胞的防侧壁遇见的连接(白色箭头)。 C.通过骨架分析对细胞进行分析后,去除枝条(修剪,黑色箭头),沿着背斜壁的长度计算为壁连接处(白色箭头)之间的分枝长度。 D.(C)中两个白色箭头之间的单元格中的单个墙。

    4. 使用单元格的骨架轮廓运行宏"BranchInfo-to-ROI-lines-overlay_.ijm"。它将提示图像的高度(以像素和μm为单位),并要求打开"分支信息"表。此宏将在单元格轮廓上放置带标签的重叠线,以便每个墙可以与分行信息表中的行号匹配。
    5. 对在连续时间点捕获的细胞的每个图像重复步骤B1-B4。
    6. 在与镂空轮廓图像相同的文件夹中,创建一个文件扩展名为".tps"的纯文本文件,每个图像包含以下两行,其中X是单元格最初成像的特定时间点。
      LM = 0
      IMAGE = imageNameTimeX.tif
    7. 打开tpsDig2程序中的'.tps'文件,使用'outline对象工具'勾勒出单元格,然后右键单击该图像以获得更多选项,并选择'另存为XY坐标'。对每个时间点重复,然后保存单元格轮廓坐标的结果数据。
    8. 在纯文本编辑器中打开此'.tps'数据,并使用'.txt'文件格式将X和Y坐标列表保存为每个时间点的单独文件。
    9. 在ImageJ中打开单元格轮廓图像,然后运行宏'Add-Points-From-TPSlist-To-ROIManager_.ijm'。这将提示打开在步骤B8中做出的X和Y坐标'.txt'文件。然后创建适合ImageJ并且被校准到图像尺寸的格式的X和Y坐标的结果表。将结果表保存为".txt"文件,并对每个时间点重复。
    10. 修改文本编辑器中每个时间点的'.txt'文件,以便第一个X和Y坐标指所有时间点上相同的相应单元格墙结点。请参阅步骤B9中在图像叠加层上生成的点的ROI数。
    11. 在ImageJ中打开单元格轮廓图像,然后运行宏"Formatted-Points-List-To-ROImanager_.ijm"。这将提示打开在步骤B10中做出的新的配对的X和Y坐标'.txt'文件,并将X和Y坐标转换为适合于ImageJ的格式,该格式被校准为图像尺寸。将ROI管理器中的坐标列表另存为'.zip'文件。
    12. 对每个时间点重复步骤B9-B11。

  3. 生成薄板花键
    1. 在ImageJ中使用单元格轮廓图像和ROI'.zip'文件记录每个时间点对应于每个墙交叉点的ROI数。
    2. 为了进行薄板样条分析,在每个时间点需要相等数量的同源地标。通过将初始时间的壁长度除以0.5μm来计算在所有时间点上的背斜壁段的同源界标的数目如下:
      d = w /0.5μm
    3. 使用斜率截距公式计算这些同源地标的位置:f(a)= m×a +(p - [m×d])
      m =(p-1)/(d-1)
    4. 可编辑的示例Excel文件可用于组织数据并获得输出坐标的最终列表,如步骤C2和C3中所述(请参阅数据分析)。它包含一个包含6个标签的电子表格;称为intervalRaw的输入标签,具有称为intervalSelection的每个时间点的输出x和y坐标的标签以及标记为t1,t2,t3和t4的四个数据标签,其包含在每个时间点的x和y坐标对的完整列表,与在步骤B10中生成的文件相同的布局。可以通过复制其他行的公式来修改输入选项卡以适合不同数量的墙。可以添加附加时间段,其中为时间点t4提供的布局的示例为时间点t4留空。对于输出选项卡,梯度(m)和常数(b)的单元格引用需要与所选的墙和时间段匹配。这可以在列B到E的公式中通过将每个壁的最后轨迹(红色突出显示的行)之后的行增加1的两个单元格引用的值来实现。可能需要根据每个墙中的轨迹数修改输出标签中列B到E中的公式。
    5. 所选坐标应按如下方式排列成标签列,并在文本编辑器中作为每个时间段的".txt"文件保存:
      3 ... ... ...
    6. 通过在ImageJ中打开单元格轮廓图像,检查所有坐标已正确选择为等间距,运行宏格式化点 - 从 - TPSlist-To-ROIManager_.ijm'并打开同时创建的'.txt'文件点。这将在ROI管理器中将'.txt'文件中的所有点显示为图像上的叠加层

      图2.在Notepad ++文本编辑器程序中打开的.tps文件,显示了在三个时间段具有四个同源地标的示例数据集。此示例数据集显示如何将.tps文件排列为以同源地标(LM)的数目,随后是那些坐标的x和y值,图像名称(IMAGE)和时间段(ID)的数目。附加时间段的数据以直接下面的相同顺序输入。

    7. 使用文本编辑器将每个时间点的数据合并为一个新的'.tps'文件,每个时间段使用以下行(图2):
      LM =同源地标数量
      x 1 = x坐标1  y <1> = y坐标1(以TPS格式)
      x 2 = x coordinate 2  y <2> = y坐标2(以TPS格式)
      ...    ...
      IMAGE = imageNameTimeX.tif
      ID =时间段数
    8. 使用所有时间点的'.tps'文件为时间n + 1和n + 2,n + 2和n + 3,等创建新的tps文件。
    9. 在PAST中打开'.tps'文件,选择所有数据单元格,然后使用选项执行Procrustes转换,使用2D,旋转到主轴并保持大小(仅平移和旋转)。对于时间n对n + 1,时间n + 1对n + 2,等等执行薄板样条和"薄板样条和翘曲2D"并保存薄板样条的位图(BMP)图像。这些应保存为两种不同的格式;通过选择展开因子和取消选择颜色映射来输出(1)灰度格式的图像,以及(2)取消选择展开因子的平滑薄板样条格式。
  4. 生成显示相对膨胀率
    1. 使用在步骤C9中生成的灰度薄板样条图像上的折叠生长尺度记录在薄板样条图像上呈现为覆盖图的每个时间间隔的最大和最小折叠膨胀值(图3A)。
    2. 使用公式ln(最大折叠展开)/时间n + 1和n之间的小时数确定最大相对膨胀率。这应该是所有天的最大相对扩展。因为这将设置在相对扩展标度上表示的最大扩展值,可以将其调整为数据集所需的最接近的循环数。
    3. 在ImageJ中的每个时间间隔打开灰度薄板样条图像。使用点工具在每个网格正方形的中心放置一个点,并将每个ROI添加到ROI管理器。将每个时间点的ROI点列表保存为单独的".zip"文件。
    4. 运行宏"TPS-rel-expansion-prepare_.ijm"。该宏将要求由PAST产生的灰度薄板样条图像和在上一步骤中产生的相应ROI".zip"文件。这将自动提取每个点的灰度值和XY坐标,然后将此信息保存为"xyGrayscaleValues-NAME.txt"。对每个时间点重复此操作。
    5. 运行宏'TPS-rel-expansion-format_.ijm'。它将提示"xyGrayscaleValues-NAME.txt"文本文件,用于着色的空白薄板样条图像和在步骤D3中做出的ROI'.zip'文件。此外,需要在对话框中输入以下值:(1)所有时间段的最大扩展(倍增长),(2)所有时间段的最小扩展(倍增长),以及(3)最大对数比扩展(这将是最终比例将是什么,所以如果你有多个单元格,请确保这个值足够大,以覆盖所有的用例,请参阅步骤D2)。这将生成附加有标签'-output'的薄板样条的相对膨胀率的彩色PNG图像(图3B)。对每个时间点重复。

      图3.从时间n到时间n + 1的单个拟南芥表皮铺面细胞的生长的薄板样条。 A.由PAST制成的薄板样条是一个灰度倍增生长测量。 B.在处理提取灰度值并重新整理网格之后,可以确定细胞的薄板样条随时间的相对膨胀率。


薄板样条分析用于可视化对象的大小和形状的变化。通过比较细胞的薄板样条,可以看出由较暖的颜色和生长方向所指示的相对生长速率较高的区域通过网格形状的变化来表示。该协议使用细胞的轮廓随时间推移对细胞壁的不同区域的生长进行近似。这允许识别生长速率的不同区域,而不是生成适于进一步统计分析的绝对膨胀值 具有代表性数据的电子表格显示了如何对步骤C2-C4中概述的数据进行排序,这些数据在文件Intervals-calculation.xls(


这种方法被设计用于可视化单细胞生长的变化,但它可以适应不同的空间尺度。生长条件,例如所用营养物的浓度或种类,或光强度可能在实验之间变化。改变使用的细菌琼脂的百分比可以影响幼苗的根生长。琼脂需要足够软,以使根穿透它,但是坚固到足以牢固地嵌入根并且可以为幼苗的生长提供牢固的锚。宏运行时间将取决于图像和数据的大小。对于诸如图3B中的单个单元,宏在15秒时在Intel Core i5处理器上的运行时间通常为2-15秒,最慢的宏是TPS-rel-expansion_format.ijm。薄板样条的每个单独网格的展开率和RGB值的原始值的附加文本文件被自动保存在与步骤D5(ExpansionValues-NAME.txt和xyColourValuesNAME.txt)的输出图像相同的文件夹中, 。




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引用:Armour, W. J., Barton, D. A. and Overall, R. L. (2016). Visualising Differential Growth of Arabidopsis Epidermal Pavement Cells Using Thin Plate Spline Analysis. Bio-protocol 6(22): e2022. DOI: 10.21769/BioProtoc.2022.