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