Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

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

Additional file 4 of Nuclear pores enable sustained perinuclear calcium oscillations

Critical surface for propagation failure. Contains a figure that illustrates how a small diffusion constant and large uptake rate can lead to propagation failure, as explained in Methods subsection Conditions for signalling propagation on an isolated membrane. (PDF 1590 kb

Additional file 2 of Nuclear pores enable sustained perinuclear calcium oscillations

Notes on the effect of the refractory period on Ca2+ signatures. Contains a discussion and figures concerning an alternative implementation of an refractory period, and also the effects of coupling strength on the similarity between nuclear and cytosolic calcium signatures. (PDF 804 kb

Quantification of DNA Repair Rates in Chlamydomonas reinhardtii

As a mechanism for maintaining DNA integrity, a cell is unable to proceed in the cell cycle until damaged DNA has been repaired. In this experiment a population of Chlamydomonas reinhardtii, in their gametic stage, was divided into two groups and their growth rates were compared after one group was damaged with ultraviolet radiation. The number of damaged and undamaged cells were counted at specific time intervals and a statistical analysis was performed. The hypothesis is that the damaged and undamaged cells would exist as two distinct populations until, after a period of time, the damaged population repairs its DNA. At this point the damaged population would hypothetically resume a normal growth rate, becoming statistically indistinguishable from the undamaged population. Inferential statistical methods and regression techniques support the claim that between 48 and 72 hours the damaged population in fact “catches up” to the undamaged population and the two groups become nearly identical. This finding has implications for the rate at which Chlamydomonas reinhardtii are able to repair damaged DNA and re-enter the cell cycle

Additional file 1 of Nuclear pores enable sustained perinuclear calcium oscillations

CICR follows a diffusion path integrating all channels and pores. Contains a figure that illustrates how an alternative diffusion path requires the existence of pores and channels on both sides of the NE. (PDF 176 kb

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