| Summary: | Calcium (Ca2+) plays an integral role in a vast array of signalling pathways within both animals and plants. The study of these pathways has proven to be a fruitful avenue of research for experimental biologists and mathematical modellers. While the signalling processes have been well studied in animals, the same cannot be said of plants. This work takes a mathematical look at two important Ca2+ signalling pathways in plants, with a focus on how these signals are generated. Nuclear Ca2+ oscillations in legumes occur at a key step in the development of symbioses. The oscillations occur both inside the nucleus and in the perinuclear cytoplasm, and are temporally coordinated. We present and develop a model for simulating diffusion on the surface of the nucleus and relate the properties of this signalling to behaviour in the bulk. We show that diffusion of Ca2+ through the nuclear pore complexes provides a possible mechanism for this coordination and that this mechanism is robust to differences in Ca2+ diffusion rates in the two compartments or to different numbers of Ca2+ channels. Ca2+ has also been seen to propagate a wave travelling systemically through the root in response to salt stress. This wave is essential to the transcription of stress response genes in the leaves. We examine a range of di�erent models for propagation of the wave, demonstrating that a combined reactive oxygen species (ROS) and Ca2+ wave cooperatively propagate the signal. The presence of this accompanying ROS wave was confirmed in experiments by our collaborators. The present study highlights two very different Ca2+ signals and demonstrates the value of mathematical modelling for interpreting, understanding and furthering experimental investigations.
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