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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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Time series Nod1 given as an example of a raw Nod Factor induced Ca2+ spiking trace and after detrending using a moving average (blue) and Empirical Mode Decomposition (red).The Y axis is a fluorescence ratio between Ca2+ sensitive and Ca2+ insensitive dyes. The X axis is time in seconds.
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pone-0006637-g001: Time series Nod1 given as an example of a raw Nod Factor induced Ca2+ spiking trace and after detrending using a moving average (blue) and Empirical Mode Decomposition (red).The Y axis is a fluorescence ratio between Ca2+ sensitive and Ca2+ insensitive dyes. The X axis is time in seconds.

Mentions: The establishment of the legume/rhizobial symbiosis involves a molecular communication between the plant and the bacteria, with bacterially-derived Nod (nodulation) factor acting as a central signal to the plant. Perception of Nod factor by legumes activates most of the developmental processes associated with the formation of a nodule. The Nod factor signal transduction pathway of legumes has been well characterized and involves calcium oscillations, termed calcium spiking. An example of calcium spiking is given in Figure 1. Receptor-like kinases are involved in the perception of Nod factor and this leads to induction of calcium spiking via cation channels, that appear to regulate potassium movement and components of the nuclear-pore complex [1]. This signal transduction pathway has also been shown to function in the establishment of a second symbiotic interaction: the mycorrhizal symbiosis. This interaction involves the colonization of the plant root by mycorrhizal fungi that aid the plant in the uptake of nutrients from the soil. Mycorrhizal fungi have been shown to activate calcium oscillations, but with a different structure to Nod factor induced calcium spiking [2]. This suggests that the symbiosis signaling pathway can be differentially activated by both rhizobia and mycorrhizal fungi.


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)

Time series Nod1 given as an example of a raw Nod Factor induced Ca2+ spiking trace and after detrending using a moving average (blue) and Empirical Mode Decomposition (red).The Y axis is a fluorescence ratio between Ca2+ sensitive and Ca2+ insensitive dyes. The X axis is time in seconds.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0006637-g001: Time series Nod1 given as an example of a raw Nod Factor induced Ca2+ spiking trace and after detrending using a moving average (blue) and Empirical Mode Decomposition (red).The Y axis is a fluorescence ratio between Ca2+ sensitive and Ca2+ insensitive dyes. The X axis is time in seconds.
Mentions: The establishment of the legume/rhizobial symbiosis involves a molecular communication between the plant and the bacteria, with bacterially-derived Nod (nodulation) factor acting as a central signal to the plant. Perception of Nod factor by legumes activates most of the developmental processes associated with the formation of a nodule. The Nod factor signal transduction pathway of legumes has been well characterized and involves calcium oscillations, termed calcium spiking. An example of calcium spiking is given in Figure 1. Receptor-like kinases are involved in the perception of Nod factor and this leads to induction of calcium spiking via cation channels, that appear to regulate potassium movement and components of the nuclear-pore complex [1]. This signal transduction pathway has also been shown to function in the establishment of a second symbiotic interaction: the mycorrhizal symbiosis. This interaction involves the colonization of the plant root by mycorrhizal fungi that aid the plant in the uptake of nutrients from the soil. Mycorrhizal fungi have been shown to activate calcium oscillations, but with a different structure to Nod factor induced calcium spiking [2]. This suggests that the symbiosis signaling pathway can be differentially activated by both rhizobia and mycorrhizal fungi.

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