Exploring the diversity of epidermal pavement cell shapes R´ozaVill}oV}of´ely Department of Plant Sciences University of Cambridge | Trinity College This dissertation is submitted for the degree of Doctor of Philosophy September 2017 Corrections submitted August 2018 2 Abstract Pavement cells in the leaf epidermis can exhibit a wide variety of shapes. Undulations in the anticlinal cell wall are a particularly interesting feature present in many model species: for example, Arabidopsis thaliana, tobacco and maize; but absent in others, like Brachypodium distachyon. Epider- mal cell patterning is qualitatively similar between individuals of the same species but different species can have wildly different shapes and there is no comprehensive data set available for epidermal cell shapes. Moreover, the cell shape changes during development this has only been quantitatively studied in Arabidopsis. This work presents and analyses three sets of cell shape data. The first part examines the morphogenesis of the curiously shaped pavement cells of maize leaves these cells are highly elongated and form deep undulations in the anticlinal wall as they mature. The second part analyses the cell shapes of more than 200 species and concludes that strong undulations like those observed in Arabidopsis and maize are quite extreme: 95% of the species examined develop more shallow undulations or none at all. This part also investigates the extent to which cell shape features correlate with leaf shape features and the phylogenetic distance. The third part studies more subtle variances in the patterning of the cotyledons of different Arabidopsis thaliana ecotypes. Analysing cell shapes also poses an interesting mathematical challenge: quantifying two- dimensional shapes is a nontrivial mathematical problem as it requires representing the information defined by the coordinates of the outline by only a few quantities. Throughout this project, different metrics have been used alongside principal component analysis to reduce the num- ber of variables. These metrics include traditional morphometric variables, elliptic Fourier descriptors and various other state-of-the-art methods for shape characterisation. 3 4 Declaration This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the Preface and specified in the text. It is not substantially the same as any that I have submitted, or, is being concurrently submitted for a degree or diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. I further state that no substantial part of my dissertation has already been submitted, or, is being concurrently submitted for any such degree, diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. It does not exceed the prescribed word limit for the relevant Degree Committee. 5 6 Contents 1 Introduction 13 1.1 Living on the edge . 14 1.2 Getting in shape . 15 1.3 Theories . 16 1.4 Constraints . 18 1.5 The biochemistry of lobe growth . 20 1.6 Discussion . 23 1.7 Conclusions . 23 2 Quantifying shape 25 2.1 Background . 25 2.2 Parametric representation . 26 2.3 Biological significance: using landmarks . 27 2.4 Geometric morphometrics . 28 2.5 Series decompositions: one size fits all . 32 2.6 Principal Component Analysis (PCA) . 34 2.7 Capturing shape and structure . 35 2.8 Potential sources of error . 35 2.9 Discussion . 36 2.9.1 Comparing geometric descriptors . 37 2.9.2 Testing elliptic Fourier descriptors . 40 2.10 Conclusions . 40 3 Morphogenesis in maize 43 3.1 Motivation . 43 3.2 Aims . 45 3.3 Experimental methods . 46 3.3.1 Plant material . 46 3.3.2 Imaging . 46 3.3.3 Segmentation . 47 3.4 First glance . 48 3.5 Quantitative analysis: proof of principle . 50 3.6 Along and across leaves . 53 7 8 CONTENTS 3.6.1 Methods . 53 3.6.2 Elongation . 54 3.6.3 Undulation depth . 55 3.6.4 Absolute size . 55 3.6.5 Shape change in time . 55 3.7 Fourier analysis . 60 3.8 Discussion . 63 3.9 Conclusion . 65 4 Variety in vascular plants 67 4.1 Motivation . 67 4.2 Aims . 68 4.3 Contributions . 68 4.4 Experimental methods . 69 4.4.1 Plant material . 69 4.4.2 Sample preparation . 69 4.4.3 Staining and imaging . 70 4.4.4 Segmentation . 70 4.4.5 Leaf shape . 71 4.4.6 Shape analysis . 71 4.5 Cell shapes . 72 4.5.1 Fourier descriptors . 72 4.5.2 Geometric descriptors . 74 4.6 Phylogenetic correlations . 86 4.7 Leaf shape . 89 4.7.1 Geometric descriptors of leaves . 89 4.7.2 Correlation of leaf shape and cell shapes . 89 4.8 Abaxial and adaxial sides . 93 4.9 Discussion . 94 4.10 Conclusions . 95 5 The tales of thaliana 97 5.1 Motivation . 97 5.2 Aims . 99 5.3 Experimental methods . 100 5.3.1 Plant material . 100 5.3.2 Staining and imaging . 100 5.3.3 Segmentation . 101 5.3.4 Shape analysis . 101 5.4 Cell shapes by individual descriptors . 101 5.5 Correlation with geographic parameters . 107 5.6 Combining geometric descriptors . 108 5.7 Discussion . 114 5.8 Conclusions . 115 CONTENTS 9 6 Discussion 117 6.1 Sampling . 117 6.2 Sample preparation and imaging . 118 6.3 3D shapes . 119 6.4 Segmentation . 119 6.5 Quantitative methods . 119 6.6 Shape and strength . 122 6.7 Shape reproducibility . 123 6.8 Underlying mechanical properties . 124 7 Conclusions and outlook 127 8 Acknowledgements 131 A Elastic properties of composites 145 B Cell shape data for the maize experiment 149 C Cell shape data for vascular plants 161 D Cell shape data from Arabidopsis lines 183 D.1 Cell outlines . 183 D.2 Cell descriptors . 183 10 CONTENTS List of Figures 1.1 Some examples of cell shapes . 13 1.2 Different modes of growth . 16 1.3 The pathways leading to lobe formation in pavement cells . 21 1.4 Stress-induced reinforcement . 22 2.1 Examples of fitting parametric functions to represent shapes found in nature . 27 2.2 Morphometrics using landmarks . 28 2.3 Testing geometric descriptors . 39 2.4 Testing Fourier descriptors . 40 3.1 Complex cell shapes in maize leaf epidermis . 43 3.2 The development of maize leaves . 44 3.3 Variation of maize cell shapes with age . 49 3.4 Diversity of cell shapes in maize . 50 3.5 Aspect ratio, circularity, ellipticity of maize cells . 51 3.6 Preliminary analysis results | maize . 52 3.7 Parametrising the maize cell . 54 3.10 Cell shape reconstruction from the first n Fourier coefficients 60 3.11 Contributions of the first four principal components . 61 3.12 Maize data as captured by Fourier PCA . 62 3.13 Confocal images of maize cells . 63 4.1 Fourier reconstructions using the first n harmonics . 79 4.2 Contributions of the first four principal components . 80 4.3 Individual Fourier analyses of two species . 81 4.4 Fourier shape analysis . 82 4.5 Geometric descriptors . 83 4.6 Solidity against aspect ratio by orders . 84 4.7 Solidity against aspect ratio by orders . 85 4.8 Phylogenetic analyses of leaf and cell shape descriptors . 88 4.9 Leaf descriptors . 90 4.10 Correlations between cell shape and leaf shape measures . 91 4.11 Comparing abaxial and adaxial undulations . 94 11 12 LIST OF FIGURES 5.1 Geographic data of the MAGIC parent lines . 98 5.2 Geometric descriptors of MAGIC parent and mutant lines . 103 5.3 PCA on geometric descriptors . 110 5.4 Correlations between area and circularity . 111 5.5 Fractals and cell shapes . 114 6.1 Cumulative contributions of the first 15 harmonics for the set of example cell shapes used in the analysis in Chapter 2. 120 6.2 Comparing the contribution of geometric descriptors for maize and Arabidopsis .......................... 121 6.3 Elastic modulus of the maize cell wall at different indentation forces . 123 7.1 A comparison of simulated cell patterns to real data . 129 Chapter 1 Introduction Pavement cells come in a fascinating variety of shapes. Some, like Arabidop- sis thaliana, are mesmerisingly complex: lobes nonchalantly branching off other lobes, like pieces in a chaotic miniature puzzle game. Neverendingly long maize cells, though neatly ordered parallel to the leaf, hold onto each other with little lobes like teeth on a zipper. Irises have most certainly run out of imagination after painting their flowers: their leaves are paved with long, rectangular cells, like a brick wall. Pretty orchids are oddly boring on the cell level: their leaves are covered in little irregular polygons. Figure 1.1 { Some examples of cell shapes The hidden diversity of epidermal cells raises.