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Patterns of Symbiotic Calcium Oscillations Patterns of symbiotic calcium oscillations A thesis submitted to the University of East Anglia for the degree of Doctor of Philosophy Anna Emma Ulrika Granqvist John Innes Centre Norwich, September 2012 c This copy of the thesis has been supplied on condition that anyone who consults ! it is understood to recognise that its copyright rests with the author and that use of any information derived there from must be in accordance with current UK Copyright Law. In addition, any quotation or extract must include full attribution. To my family, with love Abstract Nuclear-localised calcium (Ca2+) oscillations have been shown to be necessary for the establishment of both arbuscular mycorrhizal and rhizobial symbioses. This thesis focuses on the analysis of the nature of this Ca2+ signature and an investigation into how this signature might have changed during the evolution of arbuscular mycorrhizal and root nodule symbioses. The work combines mathe- matical and experimental biology. A method for detecting frequencies using Bayesian inference, Bayesian Spec- trum Analysis, has been tested and further developed for use in the analysis of Ca2+ oscillations. A mathematical model of the oscillatory system has been inves- tigated with bifurcation analysis, focusing on how Ca2+-binding proteins might account for the experimentally observed variation in the signal. Data were collected for Ca2+ spiking induced by the diffusible signal molecules from the arbuscular mycorrhizal and rhizobial symbioses. No significant differ- ences were found between the patterns of Ca2+ oscillations. This study was extended to a group of phylogenetically diverse plants in order to investigate whether there is evidence for changes in the patterns of Ca2+ oscillations during the evolution of the signalling pathway from the more ancient arbuscular symbio- sis to the more recent root nodule symbiosis. Although some variation in Ca2+ patterns was found, this did not show a consistent correlation with phylogenetic relationships. Taken together, the present study suggests possible sources of the observed variability of Ca2+ patterns. It also indicates that the system of Ca2+ oscillations is a highly conserved part of the symbiotic signalling pathway. iii Contents Abstract iii List of Figures vii List of Tables ix List of Abbreviations x Publications xii 1 General introduction 1 1.1 Motivation . 1 1.1.1 Nitrogen . 1 1.1.2 Phosphorous . 2 1.2 Plant-microbe root symbioses . 3 1.2.1 Arbuscular mycorrhiza . 3 1.2.2 Root nodule symbioses . 4 1.3 Initial symbiotic events . 6 1.3.1 Signal exchange in the soil . 6 1.3.2 The common SYM pathway . 8 1.4 The role of calcium signalling . 12 1.4.1 Calcium oscillations in animal cells . 13 1.4.2 Calcium oscillations in plant stomatal guard cells . 13 1.4.3 Calcium oscillations in the SYM pathway . 14 1.4.4 Calcium oscillations in defence pathways . 16 1.5 Establishment of endosymbiosis . 16 1.5.1 Mycorrhizal infection . 17 1.5.2 Rhizobial infection . 18 1.6 Hormone influences . 21 1.7 Cross-talk with defence responses . 24 1.8 Project objectives and thesis structure . 25 2 Methods and materials 26 2.1 Experimental methods . 26 2.1.1 Plant growth . 26 iv 2.1.2 Crude isolation of Nod factors . 28 2.1.3 Root hair deformation assay . 28 2.1.4 Calcium imaging . 29 2.2 Experimental material . 32 2.3 Computational methods . 34 2.3.1 Fourier Analysis . 34 2.3.2 Bayesian Spectrum Analysis . 34 2.3.3 Modelling calcium oscillations . 38 3 Employing Bayesian Spectrum Analysis to detect periodicity 39 3.1 Introduction . 39 3.1.1 Fourier Analysis . 40 3.1.2 Bayesian Spectrum Analysis . 41 3.1.3 Model comparison . 45 3.2 Results . 49 3.2.1 Simulated test cases . 49 3.2.2 Calcium spiking . 56 3.2.3 Clock genes . 61 3.3 Discussion . 62 4 Bifurcation analysis of a calcium spiking model reveals sources of pattern variation 64 4.1 Introduction . 64 4.1.1 Components needed for the symbiotic calcium oscillations . 66 4.2 Description of the calcium model . 68 4.2.1 Model components and equations . 69 4.2.2 Model parameters . 73 4.3 Results . 75 4.3.1 The influence of calcium buffers on spiking patterns . 76 4.3.2 Other sources of variation . 81 4.4 Discussion . 82 5 Comparing patterns of calcium oscillations in Medicago truncatula 84 5.1 Introduction . 84 5.1.1 Rhizobial LCOs . 84 5.1.2 Mycorrhizal LCOs . 85 5.1.3 LCOs, COs and calcium spiking . 85 5.1.4 The model legume Medicago truncatula . 86 5.2 Results . 86 5.2.1 Interspike intervals . 87 5.2.2 Spike structures . 89 v 5.2.3 Periodicity . 91 5.3 Discussion . 92 6 Defining the patterns of symbiotic calcium oscillations in diverse species in the nitrogen-fixing clade 96 6.1 Introduction . 96 6.1.1 The legume family and symbiosis . 97 6.1.2 The Parasponia case . 98 6.1.3 Actinorhizal symbioses . 98 6.2 Results . 99 6.2.1 Choice of plant species to study . 99 6.2.2 Induction of spiking with LCOs . 101 6.2.3 Calcium oscillations in distantly related legumes . 102 6.2.4 Calcium oscillations in the non-legume genera Parasponia and Trema . 105 6.2.5 Data analysis of species-specific spiking . 107 6.3 Discussion . 111 7 General discussion 113 7.1 Patterns of symbiotic calcium oscillations . 113 7.2 Similarities and differences in calcium signatures . 114 7.3 The role of calcium-binding proteins . 115 7.4 Evolution of the common SYM pathway . 117 7.5 Prospects for biotechnology involving the common SYM pathway . 118 Appendices 120 .A Mathematical background . 120 .A.1 Interpretations of probability theory . 120 .A.2 Dynamical systems theory . 120 .A.3 Linear algebra . 121 .A.4 Power series and polynomials . 123 .B Supplementary figures and tables . 125 Bibliography 132 vi List of Figures 1.1 Evolution of root symbioses . 5 1.2 The SYM pathway . 9 1.3 Ca2+ spiking in the model legume Medicago truncatula . 15 1.4 Infection of the plant root by arbuscular mycorrhiza . 17 1.5 Different modes of rhizobial infection in symbiosis . 19 1.6 The Nod factor signalling pathway in different cell layers . 21 2.1 FRET with the Ca2+ indicator cameleon YC2.1 . 29 2.2 The signal from the Ca2+ reporter Cameleon YC2.1 . 30 2.3 Flowchart of the automated model development procedure for Bayesian Spectrum Analysis . 36 3.1 An example of Fourier theory . 41 3.2 Joint probability . 42 3.3 Time series with a background trend . 50 3.4 Short time series . 51 3.5 Effects of noise on precision in FFT and BSA . 52 3.6 Higher harmonics . 53 3.7 Multiple close frequencies with noise . 54 3.8 Change of frequency . 55 3.9 Near-periodic oscillations . 56 3.10 BSA and Ca2+ spiking ........................... 59 3.11 Local BSA and Ca2+ spiking........................ 60 3.12 BSA and circadian genes . 62 4.1 Initial signalling events in the SYM pathway . 65 4.2 Phase space diagram of the Ca2+ spiking model . 70 4.3 The Ca2+ spiking model . 71 4.4 Simulated Ca2+ spiking with the model including buffers . 73 4.5 Simulations of different spike shapes . 74 4.6 Examples of variability in Ca2+ spiking . 75 4.7 Unstable and stable steady states . 76 4.8 Bifurcation analysis of buffer parameters . 77 4.9 Bifurcation analysis of buffer parameters for Oregon Green . 77 4.10 Two-parameter bifurcation diagrams of buffer parameters . 79 vii 4.11 Two-parameter bifurcation diagrams of buffer parameters . 79 4.12 The effect of buffer concentrations on Ca2+ spiking period . 80 4.13 Increasing buffer levels can inhibit Ca2+ oscillations..
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