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 (Ca(2+)) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca(2+) oscillations. Among these an ion channel, Doesn't Make Infections1, is preferentially localized on the inner nuclear envelope and a Ca(2+) ATPase is localized on both the inner and outer nuclear envelopes. Doesn't Make Infections1 is conserved across plants and has a weak but broad similarity to bacterial potassium channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counterbalance the charge caused by the influx of Ca(2+) into the nucleus. Ca(2+) channels and Ca(2+) pumps are needed for the release and reuptake of Ca(2+) from the internal store, which is hypothesized to be the nuclear envelope lumen and endoplasmic reticulum, but the release mechanism of Ca(2+) remains to be identified and characterized. Here, we develop a mathematical model based on these components to describe the observed symbiotic Ca(2+) oscillations. This model can recapitulate Ca(2+) oscillations, and with the inclusion of Ca(2+)-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.