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Nonlinear time series analysis of nodulation factor induced calcium oscillations: evidence for deterministic chaos?

Hazledine S, Sun J, Wysham D, Downie JA, Oldroyd GE, Morris RJ - PLoS ONE (2009)

Bottom Line: The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen.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 desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.

View Article: PubMed Central - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.

ABSTRACT
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.

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Flowchart of the tests run to gather evidence for chaos.A summary of results on the left of the figure are after processing with a moving average. The summary of results on the right are after detrending with Empirical Mode Decomposition (EMD).
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pone-0006637-g003: Flowchart of the tests run to gather evidence for chaos.A summary of results on the left of the figure are after processing with a moving average. The summary of results on the right are after detrending with Empirical Mode Decomposition (EMD).

Mentions: We analysed the Ca2+ oscillations (Supporting Information Experimental Data S1) by following the procedure illustrated in the flowchart of Figure 3. The full time series are used and not just interspike times. The time series of Ca2+ concentration were first detrended using two different techniques, Empirical Mode Decomposition (EMD) and a moving average (Figures S1, S2, S3, S4, S5, S6, S7, S8, S9). Using EMD does not distort the shape of the Ca2+ spikes and does not remove low frequency components of the experimental signal. However, because the low frequency components of the signal may not be significant, as an alternative to EMD we also detrended the data using a moving average.


Nonlinear time series analysis of nodulation factor induced calcium oscillations: evidence for deterministic chaos?

Hazledine S, Sun J, Wysham D, Downie JA, Oldroyd GE, Morris RJ - PLoS ONE (2009)

Flowchart of the tests run to gather evidence for chaos.A summary of results on the left of the figure are after processing with a moving average. The summary of results on the right are after detrending with Empirical Mode Decomposition (EMD).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2722092&req=5

pone-0006637-g003: Flowchart of the tests run to gather evidence for chaos.A summary of results on the left of the figure are after processing with a moving average. The summary of results on the right are after detrending with Empirical Mode Decomposition (EMD).
Mentions: We analysed the Ca2+ oscillations (Supporting Information Experimental Data S1) by following the procedure illustrated in the flowchart of Figure 3. The full time series are used and not just interspike times. The time series of Ca2+ concentration were first detrended using two different techniques, Empirical Mode Decomposition (EMD) and a moving average (Figures S1, S2, S3, S4, S5, S6, S7, S8, S9). Using EMD does not distort the shape of the Ca2+ spikes and does not remove low frequency components of the experimental signal. However, because the low frequency components of the signal may not be significant, as an alternative to EMD we also detrended the data using a moving average.

Bottom Line: The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen.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 desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.

View Article: PubMed Central - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.

ABSTRACT
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.

Show MeSH