Abstract
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.
Background
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
Equipment
Software
Procedure
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 (http://www.bio-protocol.org/attached/file/20161017/20161017210209_7507.xls)
Notes
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).
Acknowledgments
This protocol is adapted from Armour et al., 2015. This research was supported by an Australian Postgraduate Award to WJA.
References
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