title: Nonlinear time series analysis of nodulation factor induced calcium oscillations: evidence for deterministic chaos?
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.
authors.affiliation: Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.
authors.forename: Saul
authors.initials: S
authors.lastname: Hazledine
authors.forename: Jongho
authors.initials: J
authors.lastname: Sun
authors.forename: Derin
authors.initials: D
authors.lastname: Wysham
authors.forename: J Allan
authors.initials: JA
authors.lastname: Downie
authors.forename: Giles E D
authors.initials: GE
authors.lastname: Oldroyd
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Morris
mesh_terms: D002118:Calcium / Q000378:metabolism*; D007887:Fabaceae / Q000502:physiology*; D018517:Plant Roots / Q000502:physiology; D013269:Stochastic Processes; D013559:Symbiosis
chemical_list: D002118:Calcium
references.citation: Proc Natl Acad Sci U S A. 2004 Feb 3;101(5):1392-6
references.pmid: 14734814
references.citation: Eur J Biochem. 2002 Mar;269(5):1333-55
references.pmid: 11874447
references.citation: Biophys J. 2008 Mar 15;94(6):2404-11
references.pmid: 18065468
references.citation: Nat Rev Mol Cell Biol. 2004 Jul;5(7):566-76
references.pmid: 15232574
references.citation: FEBS Lett. 1993 May 10;322(2):197-200
references.pmid: 8482391
references.citation: Biophys J. 2006 Apr 1;90(7):2628-40
references.pmid: 16399841
references.citation: Nature. 1997 Oct 2;389(6650):492-5
references.pmid: 9333237
references.citation: Phys Rev Lett. 1992 Jan 27;68(4):427-430
references.pmid: 10045894
references.citation: Biophys J. 2003 Jan;84(1):42-56
references.pmid: 12524264
references.citation: Biophys J. 2005 Sep;89(3):1603-11
references.pmid: 15994893
references.citation: Biochem J. 1991 Apr 1;275 ( Pt 1):277-80
references.pmid: 1850241
references.citation: Curr Opin Plant Biol. 2006 Aug;9(4):351-7
references.pmid: 16713329
references.citation: Biophys Chem. 2001 Mar 15;90(1):17-30
references.pmid: 11321672
references.citation: Biophys Chem. 2008 Jan;132(1):33-8
references.pmid: 17964062
references.citation: Phys Rev Lett. 1994 Sep 26;73(13):1781-1784
references.pmid: 10056885
references.citation: Biophys Chem. 1997 May 21;66(1):25-41
references.pmid: 17029867
references.citation: Biochem J. 1990 Jul 15;269(2):499-502
references.pmid: 2386488
references.citation: Mol Biol Evol. 2004 Oct;21(10):1855-70
references.pmid: 15215322
references.citation: Biophys Chem. 2003 Jun 1;104(2):509-22
references.pmid: 12878318
references.citation: Chaos. 1999 Jun;9(2):413-435
references.pmid: 12779839
references.citation: Biophys J. 2000 Sep;79(3):1188-95
references.pmid: 10968983
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Apr;47(4):2401-2404
references.pmid: 9960271
references.citation: Proc Natl Acad Sci U S A. 2007 Sep 18;104(38):14889-94
references.pmid: 17846430
references.citation: Plant J. 2006 Jun;46(6):961-70
references.pmid: 16805730
references.citation: Phys Rev Lett. 1990 Mar 12;64(11):1196-1199
references.pmid: 10041332
references.citation: Phys Rev Lett. 1996 Jul 22;77(4):635-638
references.pmid: 10062864
references.citation: Proc Natl Acad Sci U S A. 2001 Jun 19;98(13):7107-12
references.pmid: 11416195
references.citation: Mol Plant Microbe Interact. 2002 Dec;15(12):1245-52
references.pmid: 12481997
references.citation: Proc Natl Acad Sci U S A. 2008 Jul 15;105(28):9823-8
references.pmid: 18606999