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Investigating the Shape of the Shoot Apical Meristem in Bamboo Using a Superellipse Equation
采用超椭圆方程研究竹顶端分生组织的形态   

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参见作者原研究论文

本实验方案简略版
New Phytologist
Apr 2016

Abstract

The shoot apical meristem is the origin of bamboo wood. Its structure and morphology are important for maintaining the normal development of bamboo wood. However, the traditional method to describe the morphology of the shoot apical meristem in bamboo or other plants only depends on qualitative approaches. Here we present a protocol for precisely describing the morphology of bamboo shoot apical meristem, which is adapted from our recently published papers (Shi et al., 2015; Wei et al., 2017).

Keywords: Bamboo (竹), Shoot apical meristem (顶端分生组织), Superellipse (超椭圆)

Background

Shoot apical meristem is the source of above-ground tissues. For a long time, its morphology description has been lack of a quantitative method for morphological analysis. This protocol provides a method for better description of the outer contour of the shoot apical meristem of bamboo.

Materials and Reagents

  1. Completed paraffin sections with plant shoot apical meristem (Wei et al., 2017)

Equipment

  1. Leica DM2500 light microscope (Germany) (Leica Microsystems, model: Leica DM2500 )

Software

  1. Windows 7 Operation System (64 bit)
  2. Photoshop CS6 (Adobe, USA)
  3. R (ver. 3.3.0)
  4. MATLAB (ver. R2015b)
  5. Notepad++ (ver. 7.4.2)
  6. R and MATLAB scripts (see the Supplementary files)

Procedure

  1. The images of plant shoot apical meristem are first obtained under a DM2500 light microscope with 40-fold objective lens, and saved as BMP file using default parameters, usually the DPI of the image should be ≥ 72.
  2. Then the BMP file is opened by Photoshop CS6, and straightened by ‘Image Rotation’ function as shown in Figure 1.


    Figure 1. Straightening picture via ‘Image Rotation’

  3. A line which is parallel with the horizontal axis is added to connect the part just above the first leaf primordium and its corresponding part in another side using the ‘Line tool’ (Figure 2).


    Figure 2. A line just above the first leaf primordium is added

  4. The line and the picture are merged to form a merged picture using the function ‘Layer’ → ‘Merge Visible’.
  5. The merged picture containing the shoot apical meristem and the straight line is then extracted by ‘Magnetic Lasso Tool’ which is great for following the edges of an object. And they are copied to a new blank layer directly generated by ‘Control + N’ (Figure 3).


    Figure 3. Extracted shoot apical meristem

  6. To duplicate the resulting image, the new generated picture is then flipped by the command combination of ‘Image → Image Rotation → Flip canvas Vertical’ (Figure 4A) to produce a new vertical symmetric picture (Figure 4B).


    Figure 4. Producing a new vertical symmetric picture of the extracted shoot apical meristem

  7. A new blank layer with the size at least could contain two of the extracted shoot apical meristem is first generated by command ‘Control + N’. The shoot apical meristem and its newly produced vertical symmetric picture are then put together (Figure 5A), and merged using the function ‘Layer’→ ‘Merge Visible’ (Figure 5B).
    Note: Before merging the two images, move the two images to get close to each other until there is only a thin line space left between the two images (Figure 5B).


    Figure 5. A new picture consisted of the extracted apical meristem and its vertical symmetric image is formed

  8. The merged picture is then extracted by ‘Magnetic Lasso Tool’, and is copied to a new blank layer automatically generated by ‘Control + N’ to make the extracted picture be included by the smallest rectangle (white) in the image (Figure 6).


    Figure 6. The picture showed in Figure 5B is put in the smallest rectangle
    Note: The image boundary is exactly the smallest rectangle that includes the outermost boundary of the combined picture.

  9. The merged picture is then selected by ‘Magnetic Lasso Tool’ (Figure 7A), and is filled by a new solid black layer (Figure 7B) by the command combination of ‘Layer → New fill layer → Solid Color’.


    Figure 7. The image showed in Figure 6 is filled by a new solid black layer

  10. The new resulting picture is saved as a BMP file named ‘SF’ in the work directory. Here the directory is ‘I:\Biotool’.
  11. Open ‘MATLAB’, and change the initial directory to your work directory, and build a subdirectory under your work directory, ‘Scripts’ for example here (Figure 8).


    Figure 8. Set a work directory

  12. Put MATLAB script, ‘profile.m’ (Supplementary files) under the ‘Scripts’ directory, and carry out the “profile” on the command line as follows (Shi et al., 2015):
    profile (1, 1, 'I:\Biotool\SF.bmp', 'I:\Biotool\edge_data.csv')
    After running the script, the user can obtain a ‘.csv’ file under the directory ‘I:\Biotool\’ named ‘edge_data’ which has stored the planar coordinates of the ‘SF’ picture boundary (Figure 9A). The user can also obtain the figure based on the extracted boundary as shown in Figure 9B.


    Figure 9. ‘edge_data’ (red rectangle) which has stored the planar coordinates of the picture (A) and the figure based on the extracted boundary (B) are obtained in this step

  13. Put ‘R’ scripts which are developed by Shi et al. (2015) basing on the superellipse equation proposed by Gielis (2003), ‘fit.sf.R’ (Shi et al., 2015), ‘optim.sf.R’ (Shi et al., 2015) and ‘simu.sf.R’ (Shi et al., 2015) under the ‘Scripts’ directory (Supplementary files). And open ‘fit.sf.R’, ‘optim.sf.R’ and ‘simu.sf.R’ via Notepad++. Change the directories indicated by the red arrows to your own directory (Figure 10).


    Figure 10. Change the directories indicated by the red arrows in ‘fit.sf.R’ (A), ‘optim.sf.R’ (B) and ‘simu.sf.R’ (C) to your own directory

  14. Open ‘R’ function, and paste the following codes in the console (For more information about those codes, please see the Supplementary file, Appendix S2 of the published paper of Shi et al. (2015) (http://journal.frontiersin.org/article/10.3389/fpls.2015.00856/full):

    wd <- c("I:/Biotool/Scripts/")
    source (paste (wd, "simu.sf.R", sep=""))
    source (paste (wd, "optim.sf.R", sep=""))
    source (paste (wd, "fit.sf.R", sep=""))
    source (paste (wed, "area.sf.R", sep=""))

    data  <- read.csv ("I:/Biotool/edge_data.csv", header=F)
    x.provi <- data [,1]
    y.provi  <- data[,2]

    x0.val <- 200
    y0.val <- 200
    theta.val <- pi/4
    a.val <- 50
    k.val <- 0.95
    n.val <- 1.90
    Phi  <- seq(0, 2*pi, len=1000)
    Para <- c (x0.val, y0.val, theta.val, a.val, k.val, n.val)
    CV.val <- 0.01
    res1  <- simu.sf(phi=Phi, par=Para, CV=CV.val, fig.opt = F)
    x.simu <- res1$x
    y.simu <- res1$y

    x.width <- range(x.provi)[2] - range(x.provi)[1]
    y.width <- range(y.provi)[2] - range(y.provi)[1]
    a.ini <- max (y.width, x.width)/2
    x0.ini <- (min(x.provi) + max(x.provi))/2
    y0.ini <- (min(y.provi) + max(y.provi))/2
    theta.ini <- pi/4
    k.ini <- 0.95
    n.ini <- 1.90
    res2  <- optim.sf(x.provi, y.provi, x0.ini, y0.ini, theta.ini, a.ini, k.ini,
    n.ini, fig.opt="F", para.list="F", convergence="Chi.square")

    x0. range <- x0.ini
    y0. range <- y0.ini
    theta.range <- seq(0, pi/2, by=pi/8)
    a.range <- a.ini
    k.range <- seq(0.8, 1, by=0.1)
    n.range <- seq(1.8, 2.2, by=0.1)
    res3  <- fit.sf(x.provi, y.provi, x0=x0.range, y0=y0.range,
    theta=theta.range, a=a.range, k=k.range, n=n.range,
    para.list=F, fig.opt=F, convergence="Chi.square")
    res4  <- fit.sf(x.provi, y.provi, res3$par[1], res3$par[2],
    res3$par [3], res3$par [4], res3$par [5], res3$par [6],
    para.list=T, fig.opt=T, convergence="Chi.square")

    After the performing, it will finally generate a picture named ‘Data.fitting’ (Figure 11). The solid dark line represents the observed out contour of the two combined shoot apical meristems; the red solid line represents the predicted ring. The dark dashed line represents the direction of major axis; the blue dashed line represents the direction of x-axis. And their theta which indicates the angle value between the dark dashed line and the blue dashed line was calculated and displayed in R console (Figure 12).


    Figure 11. The predicted image of the picture showed in Figure 7A


    Figure 12. Parameters of the predicted image. The given parameters include the abscissa and ordinate of the pole (x0, y0) in the Cartesian system, the angle theta between the major axis and the x-axis, the major semi-axis a, the ratio k of the minor semi-axis (b) to the major semi-axis (a), the power n, the coefficient of determination (R.square), the χ2 (Chi.square) or the residual sum of squares (RSS).

Data analysis

For more information about the scripts’ function, please see the Supplementary file, data sheet 2 of the published paper of Shi et al. (2015) (http://journal.frontiersin.org/article/10.3389/fpls. 2015.00856/full). Here we also provide an example for using the protocol to compare the morphology of the shoot apical meristems (SAM) between Moso bamboo shoot and its thick wall variant at different developmental stage (Figure 13). In this example, by using the mathematical modeling, we found that the SAM morphology of the thick wall Moso bamboo shoot is flatter than the wild type Moso (Figure 13).


Figure 13. SAMs comparisons between the thick wall Moso and its corresponding wild type using the protocol presented here (Wei et al., 2017). Morphology of apical meristems of the thick wall Moso (A) and wild type Moso (B) bamboo shoots at different developmental stages (S2 to S6). Outlines of the apical meristem of the wild type Moso (C) and the thick wall variant (D) (black solid lines) and the predicted outlines using superellipse equation (red solid lines) at different developmental stages (from S-2 to S-5). Each outline was combined by two corresponding semi-outlines of the apical meristem. The dark dashed line represents the direction of major axis and the red dashed line represents the direction of x-axis. Scale bars = 50 μm.

Acknowledgments

This study was supported in part by Natural Science Foundation of China (grant Nos. 31670602 and 31301808) (to W.Q.), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The protocol was adapted from previous work (Shi et al., 2015; Wei et al., 2017). The authors declare no conflicts of interest or competing interests that may impact the design and implementation of this protocol.

References

  1. Gielis, J. (2003). A generic geometric transformation that unifies a wide range of natural and abstract shapes. Am J Bot 90(3): 333-338.
  2. Shi, P. J., Huang, J. G., Hui, C., Grissino-Mayer, H. D., Tardif, J. C., Zhai, L. H., Wang, F. S. and Li, B. L. (2015). Capturing spiral radial growth of conifers using the superellipse to model tree-ring geometric shape. Front Plant Sci 6: 856.
  3. Wei, Q., Jiao, C., Guo, L., Ding, Y., Cao, J., Feng, J., Dong, X., Mao, L., Sun, H., Yu, F., Yang, G., Shi, P., Ren, G. and Fei, Z. (2017). Exploring key cellular processes and candidate genes regulating the primary thickening growth of Moso underground shoots. New Phytol 214(1): 81-96.

简介

枝顶端分生组织是竹木的起源。 其结构和形态对于保持竹木的正常发展非常重要。 然而,传统的描述竹子或其他植物茎尖分生组织形态的方法仅仅依靠定性的方法。 在这里,我们提出了一个准确描述竹笋尖端分生组织形态的方案,该方案是根据我们最近发表的文章(Shi等人,2015; Wei等人, ,2017)。

【背景】射击根尖分生组织是地上组织的来源。 长期以来,形态描述一直缺乏形态学分析的定量方法。 该协议为更好地描述竹子茎尖分生组织的外部轮廓提供了一种方法。

关键字:竹, 顶端分生组织, 超椭圆

材料和试剂

  1. 用植物茎尖分生组织完成石蜡切片(Wei等人,2017)

设备

  1. Leica DM2500光学显微镜(德国)(Leica Microsystems,型号:Leica DM2500)

软件

  1. Windows 7操作系统(64位)
  2. Photoshop CS6(Adobe,美国)
  3. R(版本3.3.0)
  4. MATLAB(ver。R2015b)
  5. 记事本++(版本7.4.2)
  6. R和MATLAB脚本(请参阅补充文件) >

程序

  1. 首先在DM2500光学显微镜下用40倍物镜获得植物顶芽分生组织的图像,并使用默认参数作为BMP文件保存,通常图像的DPI应≥72。
  2. 然后通过Photoshop CS6打开BMP文件,并通过“图像旋转”功能进行校正,如图1所示。


    图1.通过“图像旋转”矫直图片

  3. 添加一条与水平轴平行的线,使用“线条工具”(图2)添加第一个叶原基上方的部分与另一侧的相应部分。


    图2.刚刚在第一片叶原基上方的一条线被添加

  4. 使用“图层”→“合并可视”功能合并线条和图片以形成合并的图片。
  5. 然后用“磁性套索工具”提取含有茎尖分生组织和直线的合并图片,该工具非常适合跟踪物体的边缘。并将它们复制到由“Control + N”(图3)直接生成的新空白图层。


    图3.提取的茎尖分生组织

  6. 为了复制结果图像,新生成的图像被“图像→图像旋转→翻转画布垂直”(图4A)的命令组合翻转以产生新的垂直对称图像(图4B)。


    图4.生成一个新的垂直对称图片的提取芽尖端分生组织

  7. 一个新的空白层至少可以包含两个提取的芽顶端分生组织首先由命令“Control + N”生成。然后将茎尖分生组织及其新产生的垂直对称图片放在一起(图5A),并使用函数“层”→“合并可见”合并(图5B)。
    注意:在合并两幅图像之前,移动两幅图像以使两幅图像彼此靠近,直到两幅图像之间只剩下细线空间(图5B)。


    图5.由提取的顶端分生组织及其垂直对称图像组成的新图像

  8. 合并后的图片通过“磁性套索工具”提取出来,并复制到由'Control + N'自动生成的新的空白图层中,使提取的图像被图像中最小的矩形(白色)所包含(图6) 。


    图6.图5B中显示的图片放在最小的矩形中
    注意:图像边界恰好是包含组合图片的最外边界的最小矩形。

  9. 然后由“磁性套索工具”(图7A)选择合并的图像,并通过“层→新填充层→纯色”的命令组合来填充新的实心黑层(图7B)。


    图7.图6中显示的图像由一个新的纯黑色图层填充
  10. 新的结果图像保存为工作目录中名为“SF”的BMP文件。这里的目录是'我:\ Biotool'。
  11. 打开“MATLAB”,并将初始目录更改为工作目录,并在工作目录下创建一个子目录,例如“脚本”(图8)。


    图8.设置工作目录

  12. 把MATLAB脚本'profile.m'(补充文件)在“脚本”目录下,按如下方式在命令行上执行“配置文件”(Shi等,2015):
    (1,1,'I:\ Biotool \ SF.bmp','I:\ Biotool \ edge_data.csv')
    在运行该脚本之后,用户可以在存储“SF”图片边界(图9A)的平面坐标的名为“edge_data”的目录“I:\ Biotool”下获得“.csv”文件。用户也可以根据提取的边界获得图形,如图9B所示。


    在此步骤中获得已经存储了图片(A)的平面坐标和基于提取的边界(B)的图形的“边缘数据”(红色矩形)

  13. 把Shi等人开发的'R'脚本(2015)根据Gielis(2003)提出的超椭圆方程,'fit.sf.R'(Shi等人,2015),'optim.sf.R'(在“脚本”目录(补充文件)。并通过Notepad ++打开“fit.sf.R”,“optim.sf.R”和“simu.sf.R”。将红色箭头指示的目录更改为您自己的目录(图10)。


    图10.将“fit.sf.R”(A),“optim.sf.R”(B)和“simu.sf.R”(C)中的红色箭头指示的目录更改为您自己的目录目录

  14. 打开“R”功能,并将下面的代码粘贴到控制台中(有关这些代码的更多信息,请参见Shi等人发表的论文的附录S2(2015)( http://journal.frontiersin.org/article/10.3389/fpls.2015.00856/full):

    wd <- c("I:/Biotool/Scripts/")
    source (paste (wd, "simu.sf.R", sep=""))
    source (paste (wd, "optim.sf.R", sep=""))
    source (paste (wd, "fit.sf.R", sep=""))
    source (paste (wed, "area.sf.R", sep=""))

    data  <- read.csv ("I:/Biotool/edge_data.csv", header=F)
    x.provi <- data [,1]
    y.provi  <- data[,2]

    x0.val <- 200
    y0.val <- 200
    theta.val <- pi/4
    a.val <- 50
    k.val <- 0.95
    n.val <- 1.90
    Phi  <- seq(0, 2*pi, len=1000)
    Para <- c (x0.val, y0.val, theta.val, a.val, k.val, n.val)
    CV.val <- 0.01
    res1  <- simu.sf(phi=Phi, par=Para, CV=CV.val, fig.opt = F)
    x.simu <- res1$x
    y.simu <- res1$y

    x.width <- range(x.provi)[2] - range(x.provi)[1]
    y.width <- range(y.provi)[2] - range(y.provi)[1]
    a.ini <- max (y.width, x.width)/2
    x0.ini <- (min(x.provi) + max(x.provi))/2
    y0.ini <- (min(y.provi) + max(y.provi))/2
    theta.ini <- pi/4
    k.ini <- 0.95
    n.ini <- 1.90
    res2  <- optim.sf(x.provi, y.provi, x0.ini, y0.ini, theta.ini, a.ini, k.ini,
    n.ini, fig.opt="F", para.list="F", convergence="Chi.square")

    x0. range <- x0.ini
    y0. range <- y0.ini
    theta.range <- seq(0, pi/2, by=pi/8)
    a.range <- a.ini
    k.range <- seq(0.8, 1, by=0.1)
    n.range <- seq(1.8, 2.2, by=0.1)
    res3  <- fit.sf(x.provi, y.provi, x0=x0.range, y0=y0.range,
    theta=theta.range, a=a.range, k=k.range, n=n.range,
    para.list=F, fig.opt=F, convergence="Chi.square")
    res4  <- fit.sf(x.provi, y.provi, res3$par[1], res3$par[2],
    res3$par [3], res3$par [4], res3$par [5], res3$par [6],
    para.list=T, fig.opt=T, convergence="Chi.square")

    执行完成后,最终会生成一张名为“Data.fitting”的图片(图11)。黑色实线表示观察到的两个组合的茎尖分生组织的外轮廓;红色的实线表示预测的环。黑色虚线表示长轴的方向;蓝色的虚线表示x轴的方向。计算显示黑色虚线和蓝色虚线之间角度值的theta值并显示在R控制台中(图12)。


    图11.图7A所示的预测图像


    图12.预测图像的参数给定的参数包括笛卡尔系统中极点(x0,y0)的横坐标和纵坐标,长轴与x轴之间的角度θ,主半轴a,次半轴b与主半轴a的比值k,功率n,确定系数(R.square),χ2(方块)或剩余的平方和(RSS)。

数据分析

有关脚本功能的更多信息,请参见Shi等人发表的文章(2015)( http://journal.frontiersin.org/article/10.3389/fpls。2015.00856 / full )。在这里我们也提供了一个使用协议的例子来比较不同发育阶段(图13)毛竹笋和厚壁变种之间茎尖分生组织(SAM)的形态。在这个例子中,通过使用数学模型,我们发现厚壁毛竹笋的SAM形态比野生型毛竹(图13)平坦。


图13.使用此处提供的协议,厚壁Moso及其相应的野生型之间的SAM比较(Wei等人,2017)。在不同的发育阶段(S2到S6),厚壁毛(A)和野生型毛(B)竹笋尖端分生组织的形态。在不同发育阶段(从S-2到S-2),野生型Moso(C)和厚壁变异体(D)(黑色实线)的顶端分生组织轮廓和使用超椭圆方程(红色实线) 5)。每个轮廓由两个相应的根尖分生组织的半轮廓组合而成。黑色的虚线表示主轴的方向,红色的虚线表示x轴的方向。比例尺= 50微米。

致谢

本研究由中国自然科学基金(批准号:31670602,31301808)(江苏省高等学校重点学科项目资助项目)资助。该协议是根据以前的工作改编的(Shi等人,2015; Wei等人,2017)。作者声明不存在可能影响本协议设计和实施的利益冲突或利益冲突。

参考

  1. Gielis,J。(2003)。 统一各种自然和抽象形状的通用几何变换 Am J Bot 90(3):333-338。
  2. Shi,P.J.,Huang,J.G.,Hui,C.,Grissino-Mayer,H.D.,Tardif,J.C.,Zhai,L.H.,Wang,F.S.and Li,B.L。(2015)。 使用超椭圆形来塑造针叶树几何形状的针叶树螺旋径向生长
    前植物科学 6:856
  3. 本文作者相关文章魏炜乔娇C.郭,丁丁Y.曹J. J.冯J.董东X.毛,L.孙禹禹F. F。 Yang,G.,Shi,P.,Ren,G。和Fei,Z.(2017)。 探索关键细胞过程和调控Moso地下芽主要增厚生长的候选基因
    新Phytol 214(1):81-96。
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引用:Wei, Q. and Shi, P. (2017). Investigating the Shape of the Shoot Apical Meristem in Bamboo Using a Superellipse Equation. Bio-protocol 7(23): e2644. DOI: 10.21769/BioProtoc.2644.
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