Understanding how the cell uses a limited set of proteins to transduce very different signals into specific cellular responses is a central goal of cell biology and signal transduction disciplines. Although multifunctionality in signal transduction is widespread, the mechanisms that allow differential modes of signaling in multifunctional signaling pathways are not well defined. In legume plants, a common symbiosis signaling pathway composed of at least seven proteins mediates infection by both mycorrhizal fungi and rhizobial bacteria. Here we show that the symbiosis signaling pathway in legumes differentially transduces both bacterial and fungal signals (inputs) to generate alternative calcium responses (outputs). We show that these differential calcium responses are dependent on the same proteins, DMI1 and DMI2, for their activation, indicating an inherent flexibility in this signaling pathway. By using Lyapunov and other mathematical analyses, we discovered that both bacterial-induced and fungalinduced calcium responses are chaotic in nature. Chaotic systems require minimal energy to produce a wide spectrum of outputs in response to marginally different inputs. The flexibility provided by chaotic systems is consistent with the need to transduce two different signals, one from rhizobial bacteria and one from mycorrhizal fungi, by using common components of a single signaling pathway.chaos ͉ mycorrhization ͉ nodulation

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.

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.