Buffering capacity explains signal variation in symbiotic calcium oscillations

Legumes form symbioses with rhizobial bacteria and arbuscular mycorrhizal fungi that aid plant nutrition. A critical component in the establishment of these symbioses is nuclear-localized calcium (Ca2+) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca2+ oscillations. Among these an ion channel, DMI1, is preferentially localized on the inner nuclear envelope and a Ca2+ ATPase is localized on both the inner and outer nuclear envelopes. DMI1 is conserved across plants and has a weak but broad similarity to bacterial potassium (K+) channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counter balance the charge caused by the influx of Ca2+ into the nucleus. Ca2+ channels and Ca2+ pumps are needed for the release and re-uptake of Ca2+ from the internal store, which is hypothesised to be the nuclear envelope lumen and ER, but the release mechanism of Ca2+ remains to be identified and characterised. Here we develop a mathematical model based on these components to describe the observed symbiotic Ca2+ oscillations. This model can recapitulate Ca2+ oscillations, and with the inclusion of Ca2+-binding proteins it offers a simple explanation for several previously unexplained phenomena. These include long periods of frequency variation, changes in spike shape, and the initiation and termination of oscillations. The model also predicts that an increase in buffering capacity in the nucleoplasm would cause a period of rapid oscillations. This phenomenon was observed experimentally by adding more of the inducing signal.